- -- - REACTING LABORATOR Y FINAL REPORT ON NASA GRANT NGR 19-00 1-01 6 EVALUATION OF THE ENERGY TRANSFER IN THE CHAR ZONE DURING ABLATION Part I: Theoretical and Experimental Results for Heat Shield Surface Temperatures up to 3000°F by Ralph W. Pike, Associate Professor Principal Investigator Gary C. April, Research Associate Eduardo G. del Valle, Research Associate Department of Chemical Engineering May I , 1969 I LOUIS IANA STATE UNIVERSITY 1 - -- - - - - - - - - - https://ntrs.nasa.gov/search.jsp?R=19700005775 2020-03-23T20:55:43+00:00Z PREFACE This i s P a r t I of two p a r t s of a f i n a l r e p o r t on NASA Grant NGR 19-001-016, Evaluat ion of the Energy Transfer i n t h e Char Zone during Ablat ion. This p a r t desc r ibes the t h e o r e t i c a l and experimental r e s u l t s obtained f o r the energy absorbed by the nonequilibrium, equi l ibr ium and frozen flow of pyro lys is gases i n t he char zone f o r h e a t s h i e l d su r f ace temperatures up t o 3000°F. In P a r t I1 of t h i s f i n a l r e p o r t r e sea rch r e s u l t s w i l l be presented f o r the a n a l y s i s of the energy absorbed i n the char zone and the decomposition zone. dur ing a b l a t i o n f o r hea t s h i e l d su r f ace temperatures up t o 6000°F. Also the o the r t op ic s s p e c i f i e d i n the research proposals w i l l be included i n t h i s r e p o r t . P a r t I1 w i l l be completed by J u l y 1, 1969. This r e p o r t , P a r t I, a l s o serves a s t h e Ph.D. d i s s e r t a - t i o n of Gary C . Apr i l . P a r t I1 w i l l a l s o serve a s t he Ph,D. d i s s e r t a t i o n of Eduardo G . d e l Val le . ENERGY TRANSFER IN THE CHAR ZONE OF A CHARRING ABLATOR A Dissertation Submitted to the Graduate Faculty of the Louisiana State University and Agricultural and Mechanical College in partial fulfillment of the requirements for the degree of Doctor of Philosophy The Department of Chemical Engineering Gary Charles April B, S., Louisiana State University, 1962 M.S., Louisiana State University, 1968 May, 1969 To Lynne for her Love, Patience and Understanding ACKNOWLEDGMENTS This r e sea rch was performed under the d i r e c t i o n of D r , Ralph W. P ike . His encouragement and guidance is g r a t e f u l l y acknowledged, Appreciat ion i s a l s o expressed t o the National Aeronautics and Space Adminis t ra t ion ' s Langley Research Center which sponsored the r e sea rch and, e s p e c i a l l y , t o Robert T. Swann, Grant Monitor, whose i n t e r e s t and consu l t a t i on gave an added sense of achievement t o t he r e sea rch . The au thor would a l s o l i k e t o acknowledge t h e E. I. DuPont DeNemours Company f o r making poss ib l e , through an educa t iona l leave of absence, t he oppor tuni ty t o r e t u r n t o t h e u n i v e r s i t y f o r an advanced degree; the Charles E. Coates Memorial Fund of the L.S.U. Foundation f o r funds t o pay a po r t ion of t h e typing cos t of t he d i s s e r t a t i o n , and, the L.S.U. Computer Research Center f o r the use of t h e i r f a c i l i t i e s during the course of the s tudy . Spec ia l thanks a r e a l s o given t o Eduardo d e l Va l l e , co-worker during the r e sea rch , John Balhoff , a very consciencious and adept iii Chemical Engineering s tudent who a s s i s t ed wi th much of the experimental program, Marty Love who typed the manuscript , and many f r i e n d s who con t r ibu ted t o t he succes s fu l completion of t h i s r e sea rch . TABLE OF CONTENTS ACKNOWLEDGMENT LIST OF TABLES LIST OF FIGURES ABSTRACT CHAPTER I INTRODUCTION A. The Nature of Aerodynamic Heat ing During P l ane t a ry Reentry B . Abla t ive Thermal P ro t ec t i on of P l ane t a ry Reentry Vehicles C . Energy Transfer i n t h e Char Zone of a Charring Ablator 11. STATUS OF PREVIOUS RESEARCH ON FLOW I N THE CHAR ZONE A. Trans ien t Models f o r t h e Analyses of Thermal P ro t ec t i on Systems B . Analysis of t h e Char Zone of a Charring Ablator C . Summary of Previous Research on Flow i n t h e Char Zone I 11. DEVELOPMENT OF THE MATHEMATICAL ANALYSIS FOR REACTING FLOW I N THE CHAR ZONE OF A CHARRING ABLATOR A. I n t roduc t ion B . Statement of t h e Problem C . R e s t r i c t i o n s t o t h e General Equations of Change f o r Flow i n t h e Char Zone PAGE iii i x x i x xxv i i D. Der iva t ion of t h e Equations of Change f o r Flow i n t h e Char Zone E. Boundary Condit ions f o r t h e Flow of Py ro lys i s Products Through t h e Char Zone F. Appl ica t ion of t h e Transport Equation t o Frozen, Equi l ibr ium and Non-Equilibrium Flow i n t h e Char PAGE 106 G. Numerical So lu t ion of t h e Equations of Change 143 H . Numerical So lu t ion of t h e Heat Flux and 154 Momentum Equations I. Summary of t h e Theore t i ca l Development of t h e Equaticns of Change f o r Flow i n t h e Char Zone I V . CHAR ZONE THERMAL ENVIRONMENT SIMULATOR 164 A. I n t roduc t ion 164 B . Char Holder 166 C. Radiant Heat ing System 169 D. Py ro lys i s Gas Feed and Sampling System 174 E. Ana ly t i ca l and Measuring Equipment 180 F. Radioact ive Tracer Analyses 188 V. OPERATING PROCEDURES FOR THE CHAR ZONE THERMAL 19 9 ENVIR8WIE;EST SIMULATOR A. Pre-Sta r tup Phase 199 B . S t a r t u p Phase 200 C. Experimental Phase 201 D o Shutdown Phase 202 E. Ana ly t i ca l Phase 203 PAGE V I . RESULTS OF THE NON-EQUILIBRIUM ANALYSIS OF 215 PYROLYSIS GAS FLOW I N THE CHAR ZONE A. In t roduct ion 215 B . Non-Equilibrium Flow of Pyrolys is Gases i n t h e 216 Char Zone C. Experimental Simulation of t h e Flow of React- 233 ing Pyrolys is Products i n t h e Char Zone D. Comparison of t h e Non-Equilibrium Flow Results with t h e Resul t s of t h e Frozen and Equilibrium Flow Analyses E. Parametric Study of t h e Flow of Pyrolys is 261 Gases i n t h e Char Zone F. Calcula t ion of t h e Reacting Gas Heat Capacity 264 G . Flow of Pyrolys is Products Through Porous 265 Graphite H. Radioactive Tracer S tudies Using Porous 276 Graphite I. Carbon Deposition Studies by Radioactive 282 Tracer Methods J. C a t a l y t i c Reactions of t h e Pyro lys i s Products 286 i n t h e Char Zone K. Summary of t h e C a t a l y t i c S tudies t o Increase 307 Reactions i n t h e Char Zone L. Oxidative Degradation of Low Density 313 Nylon-Phenolic Resin Chars i n an A i r Stream a t Elevated Temperatures V I I . CONCLUSIONS AND RECOMMENDATIONS 331 APPENDIX A. INTEGRITY OF THE CALCULATIONS I N THE TEMPRE 343 SYSTEM APPENDIX B. ITERATIVE AND NON-ITERATIVE TEMPRE SYSTEM 37 2 v i i A P P E N D I X C . P H Y S I C A L AND THERMODYNAMIC PROPERTIES A P P E N D I X D. SUMMARY O F EXPERIMENTAL AND ANALYTICAL RESULTS A P P E N D I X E . I N T E G R I T Y O F THE ANALYTICAL METHODS A P P E N D I X F. ISOTHERMAL FLOW A N A L Y S I S A P P E N D I X G . METHODS FOR E S T T M T I N G P Y R O L Y S I S PRODUCT COMPOSITIONS A P P E N D I X H, M I M I C SOLUTIONS O F THE FROZEN FLOW, VARIABLE P R O P E R T I E S ENERGY EQUATION NOMENCLATURE V I T A P A G E 46 2 47 1 v i i i LIST OF TABLES Table No. Page No. CHAPTER I 1.- 1 I n i t i a l Reentry Veloc i ty and Kine t i c Energy f o r Space Vehicles a t Various A l t i t u d e s Above t h e Earth 1 - 2 L i s t of M a t e r i a l s Tested f o r Heat P ro t ec t i on of Reentry Vehicles CHAPTER I1 2-1 Summary of Experimental Resu l t s f o r t h e Flow of A i r , CO , H20, and Methyl Methacrylate ~ h r o u ~ 8 Porous Mat r ices 2-2 Comparison of t h e Temperature D i f f e r - ence Between t h e Gas and Sol id Phases f o r t h e Flow of Methane Gas Through Porous Mat r ices Having a Thickness of 0.025 t o 0.033 Feet and a Po ros i t y of 0.5 CHAPTER 111 3-1 Summary of t h e Important Equations Related t o t h e Flow of Py ro lys i s Products i n t h e Char Zone 3-2 General Equations f o r t h e So lu t ion of t h e Equi l ibr ium Composition of Gas-Condensed Mixture by t h e Free Energy Minimization Technique 3-3 Py ro lys i s Products Resul t ing from t h e 137 Thermal Decomposition of a Nylon- Phenol ic Resin Composite Excluding t h e High Molecular Weight Species Table No. 3-4 Pyro lys i s Products Resul t ing f r ~ m t h e Thermal Decomposition of Nylon- Phenol ic Resin Composites Inc lud ing t h e High Molecular Weight Species Fourth Order Runge-Kutta Formulae f o r Solving t h e D i f f e r e n t i a l Energy Equation f o r Flow of Py ro lys i s Gases Through t h e Char Zone Comparison o f Various Runge-Kutta Increment S i z e s f o r t h e Frozen Flow Var iab le P r o p e r t i e s Model Comparison o f Various Simpson's Rule Increment S i ze s f o r t h e Frozen Flow, Var iab le P r o p e r t i e s Model CHAPTER I V I d e n t i f i c a t i o n and P r o p e r t i e s of t h e Char and Graphi te Specimens Tested i n t h e Char Zone Thermal Environment Simulator Page No. 138 Heat ing Lamp Requirements and Descr ip t ion 173 f o r Maintaining t h e Char Front Tempe- r a t u r e a t a S p e c i f i c Value Simulated Py ro lys i s Gas Mixtures Used 177 i n Experiments on t h e Char Zone Thermal Environment Simulator Standard Deviat ion of t h e Gas Chro- matographic Analyses CHAPTER V I Py ro lys i s Product Composition Resul t ing 218 from t h e Thermal Degradation of Nylon- Phenolic Resin Composites Excluding High Molecular Weight Species Table No. 6-2 Pyrolysis Products Resulting from the Thermal Degradation of Nylon-Phenolic Resins Including the Identified High Molecular Weight Species Composition of the Simulated Pyrolysis Products as Compared with the Analyses of Sykes for the Thermal Degradation of Low Density Nylon-Phenolic Resins Comparison of the Experimental Heat of Pyrolysis with Calculated Values Based on Heats of Formation of the Reported Pyrolysis Gas Components Page No. 2 19 Simulated Pyrolysis Gas Mixtures Used 224 in Experiments on the Char Zone Thermal Environment Simulator Important Reactions and Associated Kinetic Data for the Pyrolysis Product Species in the Char Zone Between 500 - 3000°F Comparison of Calculated and Experimental 235 Exit Gas Compositions from the Char Zone Thermal Environment Simulator for Mass Flux R tes Between 0.00133 2 and 0.108 lb/ft -sec and Front Surface Temperatures Between 1680° and 2300°F Pyrolysis Gas Flow Through Low Density Nylon-Phenolic Resin Chars. Frozen Flow Behav'or at Mass Flux Rates Below 0.01 2 lb/f% -sec Flow of Pyrolysis Gases Through Low Density Nylon-Phenolic Resin Chars. Effect of Decreasing the Mass Flow Rate at a Temperature of 1690°F Flow of Pyrolysis Gases Through Low Density Nylon-Phenolic Resin Chars. Effect of Increasing the Front Surface Temperature at a Mass Flux Rate of 2 0.002 lblft -sec Table No. 6-11 Flow of Pyrolysis Gases Through Low Density Nylon-Phenolic Resin Chars, Effect of Changing the Front Surface Temperature2at a Mass Flux Rate of 0.001 lblft -sec and Varying Pyrolysis Gas Compositions Page No. 243 Flow of Pyrolysis Gases Through Nylon- 244 Phenolic Resin Chars. Effect of Changing the Mass Flux for a Front Surface Temperature of 2035OF and Varying Pyrolysis Gas Compositions Results of the Analyses of Frozen, Equilibrium and Non-Equilibr ium Flow of Pyrolysis Gas Products Through a One-Quarter Inch Thick Low Density Nylon-Phenolic Resin Ablative Heat Shield Char at 1500°F Results of the Analyses of Frozen, Equilibrium and Non-Equilibrium Flow of Pyrolysis Gas Products Through a One-Quarter Inch Thick Low Density Nylon-Phenolic Resin Ablative Heat Shield Char at 2000°F Results of the Analyses of Frozen, Equilibrium and Non-Equilibrium Flow of Pyrolysis Gas Products Through a One-Quarter Inch Thick Low Density Nylon-Phenolic Resin Ablative Heat Shield Char at 2500°F Results of the Analyses of Frozen, Equilibrium and Non-Equilibrium Flow of Pyrolysis Gas Products Through a One-Quarter Inch Thick Low Density Nylon-Phenolic Resin Ablative Heat Shield Char at 3000°F Comparison of the Surface Heat Flux Values for Each Flow Model and Two Pyrolysis Gas Compositions at a Front Surface Temperature of 2500°F Table No. 6-18 Flow o f Py ro lys i s Gases Through Graphi te . E f f ec t of Changing Mass Flux Rates a t a Front Sur face Temperature of 1950°F Flow of Py ro lys i s Gases Through Graphi te . E f f ec t of Changing t h e Front Surface T e m p e r a t ~ r e ~ a t Mass Flux Rate of 0.0032 l b / f t - s ec Flow of Py ro lys i s Gases Through Porous Graphi te . E f f ec t of Having Graphi te "Fines" i n t h e Pore Spaces Page No, 269 Flow of Py ro lys i s Gases Through Porous Graphi te . Exi t Gas Compositions Resul t ing From Experiments i n Which t h e "Fines" were Cleared From t h e Pore Spaces by Passing Helium Through t h e Specimens Flow of Py ro lys i s Gases Through Graphi te and Chars. Comparison of Resul t s Re la t i ve A c t i v i t i e s of Halogens and Organic Hal ide C a t a l y s t s Flow of Pyrolysis Gases Through Graphi te . Resu l t s of Bromine Catalyzed Experiments Comparison of t h e Exi t Gas Compositions f o r Bromine Catalyzed and Non-Catalysts Experiments Flow o f Py ro lys i s Gases Through Graphi te . Resu l t s of Molybdenum- Tungsten Catalyzed Experiments Comparison o f t h e Exi t Gas Compositions f o r Molybdenum- Tungsten Catalyzed and Non- C a t a l y s t s Experiments x i i i Table No. 6-28 Flow of Pyrolysis Gases Through Graphite. Results of Platinum Catalyzed Experiments Comparison of the Calculated and Measured Maximum Conversion for Air Oxidation of Nylon- Phenolic Resin Chars APPENDIX A Comparison of Various Runge-Kutta Increment Sizes for the Frozen Flow Constant Physical Properties Model Comparison of Various Runge-Kutta Increment Sizes for the Frozen Flow Variable Physical Properties Model Page No, 312 Analytical Solution of the Energy 35 2 Equation (3-29) for Constant Physical Properties Comparison of the Analytical Solution 35 3 of the Frozen Flow, Constant Physical Properties Model with the Runge-Kutta Solution for Two Increment Sizes Comparison of the Runge-Kutta Solution 355 for the Frozen Flow, Variable Physical Properties with Two Solutions Obtained Using MIMIC (Analog-Digital Simulator) Comparison of the Equilibrium Composition 363 of Ammonia and Unsymmetrical Dimethyl Hydrazine (UDNK) - Red Fuming Nitric Acid (RFNA) Propellent at 10 atm. Pressure Comparison of Various Runge-Kutta 365 Increment Sizes for the Non-Equilibrium Flow Model Comparison of Various Simpson1s Rule 369 Increment Sizes for the Frozen Flow, Variable Physical Properties Model Table No. Page No. APPENDIX C Empirical Constants for Calculating the 463 Heat Capacity of Elements to 1000°K Empirical Constants for Calculating the Heat Capacity of Elements Above 1000°K Empirical Constants for Calculating the 465 Heat Capacity and Free Energy of Compounds to 1000°K Empirical Constants for Calculating 466 the Heat Capacity and Free Energy of Compounds Above 1000°K Lennard-Jones Potentials and Enthalpy of Formation of Compounds Values of the Collision Integral Used to Calculate the Pure Component Viscosity and Thermal Conductivity APPENDIX I) Summary of Test Data for Simulated Pyrolysis Gas Flow Through Porous Chars and Graphite in the Char Zone Thermal Environment Simulator Flow of Simulated Pyrolysis Products Through Low Density Nylon-Phenol Resin Chars, Comparison of the Experimental Exit Gas Composition (Mole Percent) with the Frozen, Equilibrium and Non-Equilibrium Flow Models Flow of Simulated Pyrolysis Products 486 Through Graphite Specimens. Comparison of the Exit Gas Composition (Mole Percent) with the Frozen,Equilibrium and Non- Equilibrium Flow Models Table No. D-4 Flow of Simulated Pyro lys is Products Through Graphite Specimens i n t h e Presence of Heterogeneous Ca ta lys t s Coated on the Specimen Surface D-5 Flow of Simulated Pyro lys is Products Through Graphite Specimens i n t he Presence of Homogeneous Ca ta lys t s Contained i n t h e I n l e t Stream Page No. 492 D- 6 A i r Oxidat ion o f ~ y l o n - P h e n o l i c Resin Char 497 Specimens Between 1485'F. and 2047'F. D- 7 Summary of Radioact ive Tracer Analyses 498 of t he Various Ex i t Product Streams Leaving t h e Char Zone Thermal Environment Simulator (Experiment XXVIII) D-8 Summary of Radioact ive Tracer Analyses of t he Various Ex i t Product Streams Leaving t h e Char Zone Thermal Environment Simulator (Experiment XXIX) D- 9 Summary of Radioact ive Tracer Analyses of t he Various Ex i t Product Streams Leaving t h e Char Zone Thermal Environment Simulator (Experiment XXX) D- 10 Summary of t h e Radioact ive Tracer Analyses 501 of t he Various Ex i t Product Streams Leaving t h e Char Zone Thermal Environment Simulator (Experiment xXXI) D - 1 1 Summary of Radioact ive Tracer Analyses of the Exi t Product Streams From the Char Zone Thermal Environment Simulator (Experiment XXXII) APPENDIX E E- 1 Measured Compositions of the Gas Species i n t h e Feed Stream t o the Char Zone Thermal Environment Simulator E- 2 Ca lcu la t ion of t he Variances f o r Each of the Gas Species Lis ted i n Table E-1 Table No. Page No. E- 3 Calcula t ion of t he Net Variances, Standard Deviat ion of Each Species and the Overa l l Standard Deviat ion E-4 Measured Compositions of Repl ica te Ex i t Gas Samples from the Char Zone Thermal Environment Simulator E- 5 Calcu la t ion of the Net Variance, Standard 5 10 Deviat ion f o r Each Group of Samples and the Overa l l Standard Deviat ion E- 6 Variances and Standard Deviat ion f o r 5 11 the Analysis of Phenol i n Water E- 7 Measured Rad ioac t iv i ty of Gas Species 513 i n t h e Ef f luen t Stream of the Gas Chromatographic System E- 8 Determination of t he Standard Deviat ion 5 14 of Radioact ive Gas Samples of t he Eff luent Stream from t h e Gas Chromatograph APPENDIX F F- 1 Conversion of Pyro lys is Reactions i n 531 Mole Percent f o r a Mass Flux of 8 .01 lb / f t2 - sec , Char Thickness = 0.25 inches, Po ros i ty = 0 .8 F- 2 Conversion of Hydrogen, Oxygen and 533 Hydrogen-Oxygen Reactions i n Mole Percent f o r a Mass Flux of 0 .01 l b / f t 2 - s e c F-3 Conversion of Nitrogen and Ammonia 534 Reactions i n Mole Percent f o r a Mass Flux of 0 .01 l b / f t 2 - s e c F-4 Conversion of Carbon, Hydrogen and 536 Oxygen React ions i n Mole Percent f o r a Mass Flux of 0 .01 l b / f t 2 - s e c x v i i Table No. Page No. APPENDIX G Heats o f Formation and Heat C a p a c i t i e s 5 4 1 of Var ious P y r o l y s i s P roduc t s Heat o f Formation o f Nylon-66 From 542 t h e Exper imental Heat o f Combustion Data Heat o f Formation o f Phenol ic R e s i n from t h e Exper imental Heat of Combustion Data 543 Bond Energ ies Between Atoms i n t h e 549 CHON System Various Spec ies I d e n t i f i e d a s P y r o l y s i s 55 1 Gas Produc t s by Gas Chromatographic and /or Mass Spec t rograph ic A n a l y s i s o f Thermally Degraded Nylon-Phenolic R e s i n Composites Comparison o f t h e Exper imental Heat o f P y r o l y s i s w i t h C a l c u l a t e d Values Based on Heats o f Formation o f t h e Reported P y r o l y s i s G a s Components Comparison o f t h e Exper imental Heat o f P y r o l y s i s w i t h C a l c u l a t e d Values Based on t h e Heats o f Formation o f Reported P y r o l y s i s P roduc t s Comparison o f t h e Exper imental Heat o f P y r o l y s i s w i t h C a l c u l a t e d Values Based on Heats o f Formation o f t h e Reported Pyro lys is Gas Components Most R e p r e s e n t a t i v e Composition o f t h e P y r o l y s i s P roduc t s Evolved During t h e Thermal Degradat ion o f Nylon-Phenolic Res ins APPENDIX H H- 1 Comparison o f t h e Runge-Kutta S o l u t i o n f o r Frozen Flow V a r i a b l e P h y s i c a l P r o p e r t i e s w i t h Two S o l u t i o n s Obtained Using MIMIC ( A n a l o g - ~ i g i t a l S i m u l a t o r ) x v i i i LIST OF FIGURES Figure No. CHAPTER I 1-1 Slender Body Flow Field 1-2 Blunt Body Flow Field 1-3 Schematic Diagram of the Various Zones Developed During Reentry of a Capsule Protected by an Ablative Heat Shield CHAPTER 13: 2-1 Comparison of Calculated and Measured Temperature Distributions, Porosity = 0.259 2-2 Comparison of Calculated and Measured Temperature Distributions, Porosity = 0.395 2-3 Comparison of Calculated and Measured Temperature Distributions, Porosity - 0.477 2 -4 Temperature Distributions for Air and Helium Flows Through Nickel Foametal 2-5 Temperature Distributions for NH Flow 3 Through a Porous Matrix as a Function of the Reaction Constant and Surface Emissivity 2-6 Temperature Distributions for NH3 Flow Through a Porous Matrix as a Function of the Reaction Constant and Surface Emissivity 2-7 Temperature Distributions for Air Flow Through a Porous Matrix 2-8 Temperature Distributions for CO low Through a Porous Matrix 2 2-9 Temperature Distributions for Methyl Methacrylate Flow Through a Porous Matrix Page No. Figure No. Page No. 2-10 Equations for the Fluid and Matfix Temperatures for Flow Through Porous Media 2-11 Frozen, Transition and Equilibrium Regions 69 for the Thermal Decomposition of Methane to Carbon and Hydrogen in a Porous Carbon Matrix 2-12 Frozen, Transition and Equilibrium Regions 7 0 for the Thermal Decomposition of Methane to Carbon and Hydrogen in a Porous Carbon Matrix 2-13 Experimental and Calculated Values of the 78 Mobility for Methane-Helium Flow Through Porous Media 2-14 Experimental Values of the Mobility for 7 9 Acetylene-Helium Flow Through Porous Media 2-15 Experimental Values of the Mobility for 8 1 Water-Helium Flow Through Porous Media 2-16 Experimental Values of the Mobility for 82 Methane-Hydrogen-Helium Flow Through Porous Media 2-17 Experimental. Values of the Mobility for 83 Acetylene-Hydrogen-Helium Flow Through Porous Media 2-18 Experimental Values of the Mobility for 8 4 the Flow of Various Gas Mixtures Through Porous Media CHAPTER I11 3-1 Schematic Diagram of the Char Zone 100 3-2 Thickness of the Char and Virgin Plastic 102 as a Function of Time Figure No. Page No, 3 -3 Equilibrium Composition of t h e Simulated 129 Pyro lys is Products i n Equilibrium with Sol id Carbon 3 -4 Isothermal Conversion of Methane t o 135 Hydrogen and Ethane Between 500 and 3000°F CHAPTER I V 4-1 Schematic Diagram of t h e Char Zone Thermal 165 Environment Simulator 4-2 Sec t iona l Diagram of t h e Char Holder and 167 Associated P a r t s 4-3 Various Steps i n t h e Molding Procedure 170 f o r Low Density Nylon-Phenolic Resin Chars and Graphi te 4 -4 In f r a red Quartz Heating Lamps 172 4-5 E l e c t r i c a l C i r c u i t Diagrams of t h e Radiant 175 Heating System 4-6 Sec t iona l Diagram of t h e Radiant Heating 17 6 System 4-7 Photograph of t h e Char Zone Thermal Environment Simulator 4-8 Photograph of t h e Gas Chromatographic 183 System 4-9 Typical Gas Chromatographic Scan f o r Activated Charcoal Column 4-10 Typical Gas Chromatographic Sean f o r Porapak S Column 4-11 Photograph of t h e Liquid S c i n t i l l a t i o n 190 Spectrometer 4-12 P l o t of t h e Percent Radioac t iv i ty of Each 192 Species i n a Typical Exi t Gas Sample from t h e Char Zone Thermal Environment Simulator Figure No. Page No. 4-13 Schematic Diagram of t h e Muffler Furnace 193 System Used t o Combust t h e Char Specimens from t h e Char Zone Thermal Environment Simulator t o Water and Carbon Dioxide f o r Radioac t iv i ty Analysis 4-14 Plo t of t h e Percent Radioac t iv i ty vs . t h e Dimensionless Char Distance I l l u s t r a t i n g t h e Location of Carbon Deposit ion CHAPTER V 5-1 Equipment Used t o C a l i b r a t e t h e Gas Chromatographic System 5-2 Typical Ca l ib ra t ion Curve f o r Methane on t h e Poropac S Column CHAPTER V I 6-1 Temperature P r o f i l e f o r t h e Frozen, Equilibrium and Non-Equilibrium Flow of Pyrolys is Gases Through t h e Char Zone of a Nylon-Phenolic Resin Ablator 6-2 Temperature P r o f i l e f o r t h e Frozen, Equilibrium and Non-Equilibrium Flow of Pyrolys is Gases Through t h e Char Zone of a Nylon-Phenolic Resin Ablator 6-3 Temperature P r o f i l e f o r t h e Frozen, Equilibrium, and Non-Equilibrium Flow of Pyrolys is Gases Through t h e Char Zone of a Nylon-Phenolic Resin Ablator 6 -4 Temperature P r o f i l e f o r t h e Frozen, Equilibrium, and Non-Equilibrium Flow of Pyrolys is Gases Through t h e Char Zone of a Nylon-Phenolic Resin Ablator x x i i Figure No. Page No. 6-5 Temperature P r o f i l e , Pressure Drop and 25 7 Surface Heat Flux f o r t h e Flow of Py ro lys i s Gases Through a One-Quarter Inch Thick Nylon-Phenolic Char 6-6 Aerodynamic Heating vs . t h e Mass Flux of 262 Pyro lys i s Gases i n t h e Char Zone of a Charring Abla t ive Heat Shield (Low Density Nylon-Phenolic Resin Composite) 6-7 P lo t of t h e Reacting Gas Beat Capacity f o r Frozen, Equilibrium and Non- Equil.ibrium Flow of Pyro lys is Gases Through t h e Char Zone 6-8 Typical Methane-Hydrogen Concentrat ion P r o f i l e i n t h e Exi t Gas Stream from t h e Char Zone Thermal Environment Simulator f o r t h e Inc lus ion of Graphi te "Fines" i n t h e Pore Spaces 6-9 Typical Methane-Hydrogen Concentrat ion 278 P r o f i l e s i n t h e Exi t Gas Stream from t h e Char Zone Thermal Environment Simulator a f t e r Clear ing t h e Pore Spaces of Graphi te "Fines" with Helium o r Nitrogen Plow 6-10 Radioact ive and Gas Chromatographic P r o f i l e s 280 of t h e Exit Product Specfes f o r Methane and Phenol Degradation 6-11 Carbon Deposition P r o f i l e f o r t h e Thermal 283 Degradation of Phenol, a Major Component i n t h e Pyro lys i s Gas Stream 6-12 Carbon Deposition P r o f i l e f o r t h e Thermal 284 Degrada tbn of Methane, a Major Component i n t h e Pyro lys i s Gas Stream 6-13 Carbon Deposition P r o f i l e f o r t h e Thermal 298 Decomposition of Phenol, a Major Component i n t h e Pyro lys is Gas Stream Figure No; Page No. 6-14 Carbon Deposition P r o f i l e f o r t he Thermal 299 Degradation of Phenol Catalyzed by Bromine i n a Concentrat ion of 4% (by weight) 6-15 Carbon Deposition P r o f i l e f o r t h e Thermal 301 Degradation of Methane, a Major Component i n t h e Pyro lys is Gas Stream 6-16 Carbon Deposition P r o f i l e f o r t h e Thermal 302 Degradation of Methane Catalyzed by Bromine i n a Concentrat ion of 4% (by weight) 6-17 Carbon Deposition P r o f i l e f o r t h e Thermal 308 Degradation of Methane, a Major Component i n t h e Pyro lys is Gas Stream 6 Carbon Deposition P r o f i l e f o r t h e Thermal 309 Degradation of Methane Catalyzed with a Molybdenum-Tungsten Co-Catalyst Coating on t h e Graphi te 6-19 Carbon Deposition P r o f i l e f o r t h e Thermal 310 Degradation of Phenol, a Major Component i n t h e Pyro lys is Gas Stream 6-20 Carbon Deposition P r o f i l e f o r t h e Thermal 311 Degradation of Phenol Catalyzed with a Molybdenum-Tungsten Go-Catalyst Coating on t h e Graphi te 6-21 A i r Oxidation of Nylon-Phenolic Resin Chars 3 15 Between 1485°F and 2047°F 6-22 Ph,otograph of t h e Char Front Surface 317 Af ter Eleven Minutes Exposure t o A i r 2 Plowing a t a Mass Flux of 0.035 l b / f t -sec and a Temperature of 2047°F 6-23 Conversion of Oxygen f o r t h e Flow of A i r 3 19 Through a Lou Density Nylon-Phenolzc Re i n Char a t a Mass Flux of 0.035 l b / 9 f t -sec and a Temperature of 1485°F Figure No. Page No. APPENDIX A Block Flow Diagram oE the TEMPRE System 345 Comparison of Calculated Physical Property 357 Values with Experimental Values in the Literature Char Thermal Conductivity Data and the 361 Associated Least Squares Curve APPENDIX B TEMPRE System for Calculating the Energy 373 Transfer in the Char Zone of a Charring Ablator APPENDIX C Cornell-Katz Plot for a Low Density Nylon-Phenolic Resin Char Char Thermal Conductivity as a Function of Temperature APPENDIX F Conversion of Pure Ethylene and Pure Acetylene at Isothermal Conditions (500°F - 3000°F) Schematic Diagram of the Char Layer APPENDIX G Mechanism of Phenolic Nova1.a~ Degradation 548 to Char xxv PROGRAM LISTINGS L i s t i n g No. APPENDIX B B- 1 I t e r a t i v e TEMPRE (Main) Program B-2 N o n - I t e r a t i v e TEMPRE (Main) Program B-3 TEMPRE Subprograms B-4 I n p u t Format B-5 Output Format APPENDIX F F- l Computer Program f o r C a l c u l a t i n g t h e Conversion o f a Reac t ion a t I s o t h e r m a l Condi t ions Page No. APPENDIX H H- 1 M I M I C Program f o r So lv ing t h e D i f f e r e n t i a l 5 63 Energy Equat ion (H-1) H- 2 M I M I C Program f o r So lv ing t h e D i f f e r e n t i a l 565 Energy Equat ion (H-22) The energy t r a n s f e r a s soc i a t ed wi th the r e a c t i n g flow of py ro lys i s products through the char l aye r of a low dens i ty nylon- phenolic r e s i n cha r r ing a b l a t o r was s tud ied experimental ly and t h e o r e t i c a l l y . It was found t h a t a non-equilibrium flow model, employing f i n i t e r e a c t i o n r a t e d a t a f o r t he important r e a c t i o n s among the py ro lys i s products , was necessary t o accu ra t e ly desc r ibe t h e energy t r a n s p o r t w i th in the cha r , The important r e a c t i o n s and k i n e t i c d a t a f o r a temperature range of 500' t o 3000°F, with experimental s imula t ion t o 2300°F, were determined and incorporated i n t o the mathematical model, c a l l e d the TEMPRE System, This model, i n conjunct ion wi th experimental r e s u l t s obtained i n a Char Zone Thermal Environment Simulator , were used t o c l e a r l y show the shortcomings of the l i m i t i n g cases of f rozen and equi l ibr ium flow i n p r e d i c t i n g the t r u e behavior w i th in t h e char l a y e r . A comparison of the experimental d a t a obtained using low d e n s i t y , nylon-phenolic r e s i n chars was made wi th the r e s u l t s obtained us ing g raph i t e a s a simulated char . The non-equilibrium flow model a c c u r a t e l y predic ted energy t r anspor t i n the g raph i t e medium us ing the same important r e a c t i o n s and k i n e t i c d a t a developed f o r flow through cha r s , This conclusion was needed t o j u s t i f y the use of g raph i t e f o r t he measurement of carbon depos i t i on from methane and phenol, and, i n the c a t a l y s t eva lua t ion s t u d i e s . Carbon depos i t i on and decomposition product d i s t r i b u t i o n s were determined f o r methane and phenol using carbon-14 t r a c e r s . The product d i s t r i b u t i o n s were h e l p f u l i n providing a d d i t i o n a l evidence t h a t t he chemical r e a c t i o n s included i n t he model were c o r r e c t . The i d e n t i f i e d products of methane and phenol thermal decomposition were carbon monoxide, carbon d ioxide , methane, e thylene , ace ty lene and phenol, Carbon depos i t i on measurements w i t h i n the char l aye r were used t o l o c a t e the temperature where chemical r e a c t i o n s among the py ro lys i s products became s i g n i f i - c a n t . I n genera l , depos i t i on was g r e a t e s t near t he f r o n t su r f ace where the temperature va r i ed between 1800 - 2300°F. The above r e s u l t s were a l s o used i n t he c a t a l y s t eva lua t ion s t u d i e s . The in t roduc t ion of a c a t a l y s t i n t o t he py ro lys i s product stream (homogeneous) o r a s a coa t ing on the g raph i t e (heterogeneous) was made i n o rde r t o a c c e l e r a t e r e a c t i o n r a t e s and have them occur a t lower temperatures . This r e s u l t e d i n a higher energy absorp t ion by the py ro lys i s products . Bromine (homogeneous) had an e x c e l l e n t a c t i v i t y f o r t h i s by lowering the temperature a t which r e a c t i o n s s t a r t from about 1900°F t o about 1500°F. This e f f e c t was a l s o measured by comparing the experimental e x i t gas compositions wi th the compositions c a l - cu l a t ed by the non-equilibrium flow model using convent ional xxv i i i non-ca t a ly t i c , k i n e t i c da t a . The r e l a t i v e d i f f e r ence i n t hese va lues was a good measure of the e x t e n t of chemical r e a c t i o n r e s u l t i n g from the a d d i t i o n of t he c a t a l y s t i n t o the system. Molybdenum and tungsten c o - c a t a l y s t s (heterogeneous) had e s s e n t i a l l y no e f f e c t i n a c c e l e r a t i n g chemical r eac t ions wi th in the cha r . The s l i g h t l y d i f f e r e n t carbon depos i t ion p r o f i l e s obtained were not w i th in experimental accuracy t o conclus ive ly i n d i c a t e a b e n e f i c i a l i nc rease i n the r a t e of chemical r e a c t i o n s . Platinum c a t a l y s t was a l s o t e s t e d but it showed no a c t i v i t y f o r a c c e l e r a t i n g the chemical r e a c t i o n s . It i s known t h a t platinum i s poisoned by carbon monoxide, and t h i s i s p re sen t i n the py ro lys i s products . In a d d i t i o n t o t he above, t he a i r ox ida t ion of nylon- phenol ic r e s i n chars was s tud ied t o determine the r a t e of ox ida t ion of t he char wi th d i s t a n c e from the f r o n t su r f ace . The maximum r a t e was obtained wi th a i r flowing from the heated f r o n t su r f ace through the char and leaving the r e a r su r f ace . There was no flow of py ro lys i s products , With a f r o n t s u r f a c e temperature of 2047°F and an a i r mass f l u x of 2 0.035 l b / f t s e c an 81% conversion of oxygen was obta ined , The gas l eav ing the back su r f ace contained 4.0% 0 This 2 " i nd ica t ed t h a t ox ida t ion was tak ing p l ace a t a l l depths w i t h i n t h e cha r , and t h i s was confirmed wi th a non-equilibrium flow c a l c u l a t i o n . 1, INTRODUCTION - The Nature of Aerodynamic Heating During Plane tary Reentry - One of the most s e r i o u s problems encountered when space v e h i c l e s r e e n t e r a p l ane t a ry atmosphere i s aerodynamic hea t ing . ~ y p i c a l r e e n t r y v e l o c i t i e s f o r va r ious Ear th o r b i t a l missions a r e l i s t e d i n Table 1-1, Before a manned spacec ra f t can land s a f e l y , t hese speeds must be reduced t o convent ional a i r c r a f t speeds. This can be accomplished by applying a r eve r se t h r u s t o r by t ak ing advantage of t he f r i c t i o n a l r e s i s t a n c e of t he atmosphere, Since the r e t u r n v e l o c i t y i s of t he same magnitude a s the launch v e l o c i t y , t h e r eve r se t h r u s t method r equ i r e s the same quan t i t y of f u e l f o r t he r e e n t r y phase. This doubles t he f u e l requirement f o r t he mission and makes the added weight t o the system p r o h i b i t i v e . Hence, i t i s more e f f i c i e n t t o use the aerodynamic braking method t o reduce the v e h i c l e speed t o a s a f e l e v e l (1 ,2 ,3 ) . A high speed o r b i t i n g v e h i c l e possesses a l a r g e amount of 1 2 k i n e t i c energy (K.E. = - mV ) , In aerodynamic braking , t h i s energy 2 is converted t o h e a t a s the body descends through the r e s i s t i n g atmosphere. In Table 1-1 the k i n e t i c energy (per u n i t weight) possessed by a v e h i c l e a t va r ious o r b i t a l a l t i t u d e s above the Ear th is a l s o l i s t e d , For example, a 5000 pound v e h i c l e having an Al ti tu de s Ab ov e th e Ea rt h (1 ,Z ) Or bi ta l Al ti tu de Ki ne ti c En er gy Na ut ic al M il es Ci rc um lu na r Ve nu s o r M a r s i n i t i a l r e e n t r y v e l o c i t y of 26,000 f e e t per second must convert 67,500,000 BTU of k i n e t i c energy t o hea t . Consider a v e h i c l e t h a t i s cons t ruc ted of s t r u c t u r a l s t e e l having a s p e c i f i c h e a t of 0.117 BTU per pound per degree Fahrenhei t . I f a temperature increase of 1150°F i s a t t a i n e d , the maximum amount of h e a t t h a t i s absorbed is 675,000 BTU, o r one percent of t h e t o t a l hea t generated. It i s ev ident from t h i s example t h a t on ly a small f r a c t i o n of t he thermal energy can be permit ted t o reach the v e h i c l e without causing d e s t r u c t i v e e f f e c t s . The remaining l a rge f r a c t i o n (99 pe rcen t ) must be t r a n s f e r r e d t o t he surrounding atmosphere by the proper s e l e c t i o n of t he veh ic l e shape and ma te r i a l s of cons t ruc t ion (1 ,3) . There a r e two genera l c l a s s i f i c a t i o n s a f body configura- t i o n used i n b a l l i s t i c r e e n t r y design (3 ,4 ,5 ,6) : t h e s l ende r body and b lun t body conf igura t ions . The s l ende r body shape causes a minimum aerodynamic drag cond i t i on wi th only s l i g h t d i s turbance of t h e a i r flow. A t y p i c a l low drag , high speed shape i s shown i n Figure 1-1 wi th the a s soc i a t ed flow f i e l d t h a t r e s u l t s . This shape produces a weak, a t tached shock wave wi th a l a rge percentage of t he hea t generated being absorbed by the body. The use of s lender body conf igura t ions is b e s t s u i t e d t o b a l l i s t i c m i s s i l e and supersonic flow app l i ca t ions where low h e a t i n g loads a r e experienced f o r s h o r t per iods of time . Since r e e n t r y of space veh ic l e s r equ i r e s a maximum amount of energy t r a n s f e r t o the atmosphere, the b lun t o r high drag conf igura t ion is more appl icable . In Figure 1-2 the t y p i c a l flow f i e l d c h a r a c t e r i s t i c s f o r the b lun t body is shown. An extremely s t rong, detached shock wave extends we l l beyond the body. A major por t ion of the energy is absorbed by the a i r flowing between the shock wave and veh ic l e su r face and is c a r r i e d away i n the wake behind the c r a f t . The shock l aye r becomes progress ive ly h o t t e r during the course of r een t ry causing d i s s o c i a t i o n and ion iza t ion of the a i r . This r e s u l t s i n hea t t r a n s f e r by conduction, convection and r a d i a t i o n t o the su r face of the vehic le . Although t h e hea t absorbed is a small por t ion of the hea t generated, the r e l a t i v e amount is s u f f i c i e n t t o produce su r face temperatures i n excess of 6000°F. Therefore, a thermal p ro tec t ion system must be employed t o p r o t e c t the veh ic l e from these high temperatures and hea t f luxes . One poss ib le s o l u t i o n is t o provide enough s t r u c t u r a l mass *.* - t o s a f e l y absorb the hea t ( 3 , 7 ) . However, s i n c e most metals a r e poor hea t s i n k s , t h i s method would r e s u l t i n extreme weight p e n a l t i e s . Transpi ra t ion cooling is a second method (8). This tech- nique p r o t e c t s the veh ic l e by i n j e c t i n g a f l u i d through open- ings a t t he body surface i n t o the boundary l aye r . The in j ec ted f l u i d blocks hea t t r a n s f e r i n t o the ma te r i a l and maintains a s a f e temperature a t the space cabin wal l . This method Attached Shock - F i g u r e 1-1. S l e n d e r Body Flow F i e l d F i g u r e 1 -2 , B lun t Body Flow F i e l d l ikewise r e q u i r e s a d d i t i o n a l v e i g h t such a s equipment t o pump and r e g u l a t e the flow of coolan t ; and a s a r e s u l t , i t is p r o h i b i t i v e i n manned r een t ry a p p l i c a t i o n s . Other methods of hea t p r o t e c t i o n e x i s t ( i . e . convect ive, f i lm and r a d i a t i o n cool ing) but the most succes s fu l technique has been a b l a t i v e cool ing ( 7 , 9 ) , Abla t ive Thermal P ro t ec t ion of Plane tary Reentry Vehicles Abla t ive cool ing i s s i m i l a r t o hea t s i n k and t r a n s p i r a t i o n cool ing i n method, but it i s d r a s t i c a l l y d i f f e r e n t i n t he mechanisms used t o achieve the d e s i r e d r e s u l t s . Ablat ion s a c r i f i c e s s t r u c t u r a l s t a b i l i t y t o preserve thermal r e s i s t i - v i t y by me l t ing , vapor iz ing and/or subliming r e l a t i v e l y t h i n l a y e r s of t he m a t e r i a l a t the su r f ace . Although absorp t ion of h e a t by phase change is the d i s t i n g u i s h i n g f e a t u r e of t he process , energy d i s s i p a t i o n by r a d i a t i o n , conduction, convect ion, t r a n s p i r a t i o n and chemical r e a c t i o n is l ikewise achieved (7 , lO) . I d e a l l y , an a b l a t i v e ma te r i a l must possess a low thermal conduc t iv i ty , h igh h e a t capac i ty and l a r g e hea t of degradat ion t o e f f e c t i v e l y r e s t r i c t the extreme temperatures t o the su r f ace of the v e h i c l e . Success has been achieved employing compositions of nylon, phenol ic r e s i n , s i l i c o n elastomers and o the r s . A p a r t i a l l i s t of t he many d i f f e r e n t m a t e r i a l s t e s t e d f o r use a s a b l a t i v e h e a t s h i e l d s i s presented i n Table 1-2 (5 ,9 ,14 ) , There a r e two kinds of a b l a t i v e p r o t e c t i o n systems. One is? non-charr ing, and the o the r is cha r r ing . A non-charring a b l a t o r i s one i n which the m a t e r i a l vapor izes i n t o gases and e n t e r s the boundary l aye r counter t o t he hea t flow. This counter flow of mass e f f e c t i v e l y blocks h e a t t r a n s f e r i n t o the ma te r i a l and p r o t e c t s t he veh ic l e . Teflon (po ly t e t r a f luo roe thy lene ) i s one such non-charr ing compound which undergoes cha in shor ten ing s t e p s t o form small polymer u n i t s t h a t even tua l ly vapor ize . Extensive r e sea rch wi th Teflon and o t h e r non-charring a b l a t i v e m a t e r i a l s have been repor ted over a wide range of a p p l i c a t i o n s (11,l.z) The cha r r ing a b l a t o r , on the otherhand, has proven t o be one of the most succes s fu l hea t s h i e l d s f o r r een t ry h e a t pro- t e c t i o n , Being a combination of p l a s t i c s t h a t decompose t o a char of porous carbon and low molecular weight gases , i t p r o t e c t s t he v e h i c l e by conduction, convect ion, p l a s t i c decomposition, t r a n s p i r a t i o n , endothermic chemical r eac t ions of t he py ro lys i s gases , r e r a d i a t i o n from the char su r f ace , and th ickening of the boundary l aye r . The cha r r ing a b l a t o r is convenient ly d iv ided i n t o t h r e e sepa ra t e zones which include the p l a s t i c decomposition zone, the char zone o r l a y e r , and the boundary l a y e r a s shown i n Figure 1-3. I n t he decomposition zone the v i r g i n p l a s t i c degrades t o char and low molecular weight gases . These gases flow through the char zone and undergo chemical r e a c t i o n s such a s cracking, f r e e r a d i c a l formation and ion iza t ion . A very la rge quan t i t y - shear force a t the char surface - r a d i a t i v e heat t r ans fe r t o the char surface - r e r a d i a t i v e heat t r a n s f e r from the char surface W - mass f lux of pyrolysis gases leaving char surface - convective heat t r ans fe r to the char surface Figure 1-3, Schematic Diagram of the Various Zones Developed During Reentry of a Capsule Protected by an Ablative Heat Shield. of h e a t is absorbed by these predominantly endothermic r e a c t i o n s a s the gas temperature increases from the decomposition zone t o t he char su r f ace . These hot gases a r e then in j ec t ed i n t o the boundary l a y e r wi th a d d i t i o n a l absorp t ion of h e a t due t o expansion and f u r t h e r chemical r eac t ions (13,14,15). Energy Transfer i n the Char Zone of a Charring Ablator ------ Each of t he above reg ions has been the s u b j e c t of a s i z e a b l e r e sea rch e f f o r t , and var ious types of mathematical models t o desc r ibe the cha r r ing a b l a t o r process have been developed. Previous work on these reg ions is d iscussed i n the susequent s e c t i o n on the S t a t e of the A r t . I n t h i s d i s s e r t a t i o n an e f f o r t i s made t o ob ta in a b e t t e r d e s c r i p t i o n of the phenomena t ak ing p l ace i n the char zone. An accura te d e s c r i p t i o n is needed of t h e energy t r a n s f e r i n the char l aye r and the spec ies compositions and f luxes en t e r ing the boundary l aye r . A t p resent these v a r i a b l e s a r e evaluated by cons ider ing the flow t o be e i t h e r f rozen (no r e a c t i o n ) o r i n chemical equi l ibr ium. For frozen flow the lower l i m i t on the energy t r a n s f e r is computed s i n c e the energy absorbed by the py ro lys i s products is j u s t t h e change i n s e n s i b l e hea t a s these gases flow through t h e porous char . This is the s imples t case t o eva lua t e mathemati- c a l l y , and the c l a s s i c a l t r a n s p i r a t i o n cool ing s o l u t i o n t o t h e energy equat ion is app l i cab le (16). For equi l ibr ium flow i n the char zone the upper l i m i t on t he energy t r a n s f e r i s obtained s i n c e chemical r e a c t i o n r a t e s a r e i n f i n i t e l y f a s t , and the composition of the py ro lys i s products only vary wi th the temperature a s p red ic t ed by the r - modynamic equi l ibr ium. This approximation g ives t he maximum amount of h e a t t h a t can be absorbed s i n c e the r e a c t i o n s occurr ing a r e predominantly endothermic. The mathematical d e s c r i p t i o n of t h i s case i s more d e t a i l e d than f o r f rozen flow s i n c e an a d d i t i o n a l term f o r hea t absorp t ion by chemical reac- t i o n must be included i n the energy equat ion. Many inves t iga - t o r s f e e l t h i s model would more accu ra t e ly desc r ibe the a c t u a l behavior i n t he char zone s i n c e the r e a c t i o n r a t e s should be very f a s t a t t he high temperatures encountered. For a more accu ra t e d e s c r i p t i o n of the r e a c t i n g flow i n the char zone the k i n e t i c s of the chemical r e a c t i o n s must be included i n so lv ing the energy equat ion. The s o l u t i o n is more complex than the l i m i t i n g cases because compositions of the py ro lys i s products must be ca l cu la t ed from the r e a c t i o n r a t e express ions which a r e d i f f e r e n t i a l equat ions , Of a l l the poss ib l e r e a c t i o n s t h a t could occur i n t he char zone wi th in the temperature range encountered, the ones t h a t a c t u a l l y occur must be s e l e c t e d and included i n the a n a l y s i s . I n a d d i t i o n , experiments must be conducted t o a s su re t he t h e o r e t i c a l model accu ra t e ly p r e d i c t s t he energy t r a n s f e r i n the char zone. This can be accomplished by flowing a mixture of compounds t y p i c a l of the a c t u a l py ro lys i s gases through chars formed i n a r c - j e t h e a t e r s . The cha r s can be r a d i a n t l y heated t o s imula te t h e su r f ace hea t ing during r een t ry . Gases en t e r ing and leaving the char zone can be analyzed t o determine t h e ex t en t of t h e r e a c t i o n s t ak ing p l ace i n t h e char . Thus t h e accuracy of t h e mathematical computations can be assessed . Furthermore, t h e r e s u l t s of t h e a n a l y s i s , r e f e r r e d t o a s t h e non-equilibrium model, can be compared wi th t h e l i m i t i n g cases . I n t h i s way t h e l i m i t a t i o n s incur red by assuming equi- l ib r ium o r frozen flow a r e evaluated. A d e t a i l e d i n v e s t i g a t i o n i n t o t h e types of r e a c t i o n s occurr ing , t h e amount of carbon depos i t i on t ak ing p l ace i n t h e char l a y e r , and ways t o make t h e a b l a t i o n of char forming ma te r i a l s more e f f i c i e n t i s determined. REFERENCES 1. Ely, Lawrence D o , Return from Space, Charles C. Thomas, Pub l i she r , S p r i n g f i e l d , I l l i n o i s , 6-9 (1966). 2. S e i f e r t , Howard S. , and Kenneth Brown, B a l l i s t i c Mis s i l e and Space Vehicle Systems, John Wiley and Sons, Inc . , - New York, 448-9 (1961), 3 . Ordway, F red r i ck I . , James P. Gardner, and Mi tche l l R . Sharpe, Jr . , Basic Ast ronaut ics , Prent ice-Hal l , Inc. , Englewood C l i f f s , New Je r sey , 346-9 (1962). 4. Duncan, Robert C . , Dynamics of Atmospheric Entry, McGraw- H i l l Book Co., Inc . , New York, 117-9 (1962). 5. Mar t in , John J . , Atmospheric Reentry, Prent ice-Hal l , Inc . , Englewood C l i f f s , New Je r sey , 83-6 (1966). 6. Wingrove, Rodney C , , "F l igh t Dynamics of P lane tary Entry," Recent Developments - i n Space F l i g h t Mechanics, - 9 , 225 (1966). 7 . Steverding, Bernard, and Vernon A. N iebe r l e in , "Ablation f o r Heat sh i e ld ing , " Chemical Engineering, - 72 (15) , 163 (Ju ly 19, 1965). 8. Kel ley, J , B . , and M . R . L'Ecuyer, "Transpi ra t ion Cooling - I t s Theory and Appl ica t ion ," Report No. TM-66-5, J e t Propul- s i o n Center, Purdue Univers i ty , Contract NsG 592, N66-30856 (June 1966). 9. Abraham, Lewis H. , S t r u c t u r a l Design of Miss i l e s - and Space- c r a f t , McGraw-Hill Book Co., I n c , , New York, 247-65 (1962). 10. Fein, M. M . , S. J. Tunkel and M . S. Cohen, "New Developments i n Ablat ive Cooling," - CEP Symposium Se r i e s , 60 (52) , 99 (1964), 11. Matt ing, Fred W. and Dean R. Chapman, "Analysis of Surface Ablat ion of Noncharring Mate r i a l s wi th Descr ip t ion of Associated Computing Program," NASA TN D-3758 (December 1966). 12, Kuehn, Donald M. and Daryl J. Monson, "Attached and Separated Boundary Layers on Highly Cooled, Ablat ing and Nonablating Models a t M = 13.8," NASA TN D-4041 (June 1967). 13. Diaconis , N. S., W. R . Warren, Jr. and T. E , Shaw, "The Hypervelocity Heat P ro t ec t ion Problem," Propulsion - and Reentry, XVIth. I n t e r n a t i o n a l As t ronaut ica l Congress, Athens (1965). 14. Schmidt, Donald L. , Engineering Design f o r P l a s t i c s , Chapter 13, Reinhold Publishing Co., Inc . , New York (1962). 15. Freedman, S. I., ~evelopments in Heat Transfer, Chapter 5, M. I. T. Press, Cambridge, Massachusetts (1962). 16. Bird, R , B., W. E. Stewart, and E. N. Lightfoot, Transport Phenomena, John Wiley & Sons, Inc., New York, 328-30 (1960). II, STATUS OF PREVIOUS RESEARCH ON FLOW I N THE CHAR ZONE - - ------ Research and development of a b l a t i v e h e a t s h i e l d s f o r space v e h i c l e s can be placed i n t o two broad ca t agor i e s . The f i r s t involves d e t a i l e d i n v e s t i g a t i o n of var ious i s o l a t e d processes w i t h i n the a b l a t i o n mechanism. These s t u d i e s i nc lude the flow of py ro lys i s gases through porous media (1 ,2 ,3 ,4 ,5 ,6 ,7 ,8 ,9 ,10 ) , p l a s t i c decomposition chemistry (11,12,13,14), boundary l aye r i n t e r a c t i o n wi th the char su r f ace (15,16), and many o t h e r s (17,18,19,20,21) . The second category covers the a n a l y s i s of t he t r a n s i e n t response dur ing r e e n t r y of the combined h e a t and mass t r a n s f e r mechanisms occurr ing between t h e . h e a t s h i e l d and the flow f i e l d (15,16,23). Research i n both a reas is e s s e n t i a l i n the development of e f f e c t i v e thermal p r o t e c t i o n systems. The former category improves the accuracy of the t r a n s i e n t response c a l c u l a t i o n s , whi le the l a t t e r allows f o r more e f f i c i e n t and economic design of the a b l a t i v e h e a t s h i e l d s . This research desc r ibes the t r anspor t phenomena r e s u l t i n g from the flow o f py ro lys i s gas products through the char zone of a cha r r ing a b l a t o r . In p a r t i c u l a r , the py ro lys i s products a r e those formed by the thermal degradat ion of nylon-phenolic r e s i n composites. The n a t u r e and ex ten t of chemical r e a c t i o n between t h e p y r o l y s i s p roduc t s and t h e c h a r zone, a long w i t h t h e energy absorbed by t h e f low i n t h i s zone, a r e o f major i n t e r e s t . Likewise , knowledge o f t h e e x t e n t o f carbon d e p o s i t i o n r e s u l t i n g from t h e v a r i o u s hydrocarbon c r a c k i n g r e a c t i o n s t h a t t a k e p l a c e is impor tan t i n deve lop ing a r e a l i s t i c model t o p r e d i c t a b l a t o r performance, The f o l l o w i n g s e c t i o n s w i l l d i s c u s s some of t h e t y p i c a l t r a n s i e n t r e s p o n s e a n a l y s e s b r i e f l y , and r e l a t e d work t o f low i n t h e c h a r zone i n d e t a i l , I n p a r t i c u l a r , t h e t r a n s i e n t a n a l y s i s o f K r a t s c h , E. fie ( 2 1 ) , Kenda l l , - e t . - a l . (15) and Swann, z. &. (16) w i l l be reviewed w i t h emphasis on t h e a n a l y s i s o f t h e c h a r zone. Subsequen t ly , a d e t a i l e d rev iew of work p e r t i n e n t t o f low i n porous media w i t h and w i t h o u t chemical r e a c t i o n s i s p r e s e n t e d , These i n c l u d e t h e s t u d i e s o f Koh and d e l Casa l ( 1 , 2 , 3 ) f o r t r a n s p i r a t i o n c o o l i n g , of C la rk (4) f o r h igh t empera tu re e x p e r i m e n t a l s t u d i e s u s i n g methane f low through porous carbon and g r a p h i t e , and o f Weger, g. s. (5 ,6 ) f o r carbon d e p o s i t i o n s t u d i e s r e s u l t i n g from thermal c r a c k i n g o f hydrocarbon g a s e s a s t h e y p a s s through h e a t e d c h a r specimens. T r a n s i e n t Models f o r t h e Analyses o f Thermal P r o t e c t i o n Systems - The need f o r a c c u r a t e t r a n s i e n t a n a l y s e s o f thermal p r o t e c t i o n systems o f space v e h i c l e s is r e q u i r e d t o i n s u r e t h e s a f e r e t u r n o f t h e s p a c e c r a f t and i t s occupan ts , The i n t e r a c t i o n o f t h e shock h e a t e d gas and t h e a b l a t i v e h e a t s h i e l d i s ex t remely complex, There is no s i n g l e ground t e s t f a c i l i t y where experiments can s imula te the r e e n t r y of a space veh ic l e . Wind tunnel t e s t s a r e used t o s tudy flow f i e l d c h a r a c t e r i s t i c s , whi le r a d i a n t , induc- t i o n and r e s i s t a n c e hea t ing f a c i l i t i e s a r e used t o s imula te the thermal environment encountered during a b l a t i o n . Therefore, an accu ra t e mathematical model is e s s e n t i a l t o e f f e c t i v e l y p r e d i c t the behavior of these thermal p r o t e c t i o n systems during r een t ry . Almost a l l of t he major aerospace f i rms and governmental o rgan iza t ions i n t e r e s t e d i n r e e n t r y have modeled the t r a n s i e n t response of a b l a t i v e hea t s h i e l d s , It is impossible t o d i scuss a l l of t hese var ious t r a n s i e n t ana lyses ; however, a b r i e f h i s - t o r y and a few t y p i c a l models, namely those of Kratsch, - e t . - a l . (21) , Kendall , - e t , - a l , (15) and Swann, go 2. (16) w i l l be d iscussed . The weaknesses i n these ana lyses w i l l be pointed o u t , and i t w i l l be shown how t h i s work w i l l permit an improve- ment t o p re sen t t r a n s i e n t models. One of the e a r l i e s t t h e o r e t i c a l s t u d i e s of the a b l a t i o n of a char forming p l a s t i c by Sca la (17) "attempted t o d e f i n e the key physicochemical a spec t s of t he problem and included a d i scuss ion of the importance and func t ion of the char l a y e r during the a b l a t i o n process" (18) , In a l a t e r s tudy wi th Gi lbe r t (18), they recognized the e x i s tance "of a complex mixture of low and h igh molecular weight gaseous spec i e s t h a t i n t e r a c t chemically w i th the char and the gases i n the boundary l aye r near the sur face" ( l 8 ) , Although the complexity of chemical r e a c t i o n s wi th in the char zone was d iscussed , the model of Sca l a and G i l b e r t (18) was f o r a gas mixture conta in ing carbon monoxide, methane, hydrogen and ammonia which remained f rozen a s i t t r ansp i r ed through t h e cha r . S imi l a r ly , t h e models of B a r r i a u l t and Yos (19) and Meyers and Harmon (20) considered t h e flow t o be f rozen i n t h e char zone. The a n a l y s i s of Kratsch g. &, (21) was a one dimensional, t r a n s i e n t a n a l y s i s t h a t coupled t h e energy and mass t r a n s f e r i n char-forming a b l a t i v e hea t s h i e l d s . Depolymerization k i n e t i c s of t h e a b l a t i v e p l a s t i c was handled by an Arrhenius-type expression based on thermogravimetric a n a l y s i s d a t a . Chemical e r ros ion of t h e carbonaceous medium by r e a c t i o n s occuring wi th in and a t t h e s u r f a c e of t h e char were included, The receding su r f ace boundary cond i t i on and aero-convect ive and gas - r ad ia t ion hea t ing boundary cond i t i on were spec i f i ed input func t ions t o t h e computer c a l c u l a t i o n s . The in-depth a n a l y s i s of t h e char l a y e r considered t h e py ro lys i s gas products t o be i n thermodynamic equi l ibr ium a s they passed through t h e zone. Only gas phase r e a c t i o n s were included, This r e s u l t e d i n an ove rp red ic t ion of t h e carbon i n t h e condensed phase a s observed i n experimental char analyses and was a t t r i b u t e d t o a s h i f t i n gas phase con t ro l l ed r e a c t i o n s t o gas-so l id phase con t ro l l ed r e a c t i o n s wi th in t h e char . No provi- s ions t o inc lude such chemical i n t e r a c t i o n s of t h e py ro lys i s gases with t h e s o l i d carbon was made; however, an empir ica l adjustment based on experimental d a t a was incorporated t o c o r r e c t f o r t h e ove rp red i c t i on of s o l i d carbon. This work was t h e f i r s t a t tempt t o desc r ibe a r a t h e r complex system wi th a model t h a t was no t r e s t r i c t e d by t h e over- s i m p l i f i c a t i o n o f f rozen f low, cons tan t phys ica l p r o p e r t i e s , o r omit ted h e a t abso rp t ion terms. The a n a l y s i s o f Kendal l , s. &. (15) coupled a laminar , equi l ib r ium boundary l a y e r s o l u t i o n wi th a one dimensional, t r a n s i e n t response of t h e a b l a t i v e composite. The boundary l a y e r s o l u t i o n was r e l a t e d t o t h e shock l a y e r by spec i fy ing edge boundary cond i t i ons . S imi l a r ly , t h e boundary l a y e r s o l u t i o n was r e l a t e d t o t h e t r a n s i e n t response of t h e a b l a t i v e composite by su r f ace cond i t i ons . Four op t ions were a v a i l a b l e t o couple t h e a b l a t i n g su r f ace wi th t h e boundary l a y e r . These included spec i fy ing ( a ) wal l en tha lpy , (b) py ro lys i s gas spec i e s mass f l u x e s , ( c ) wa l l component mass f l u x wi th su r f ace equi l ib r ium o r (d) coupled mass and energy balance a t t h e wal l a s provided by a t r a n s i e n t cha r r ing conduction s o l u t i o n . The one dimensional , in-depth a n a l y s i s considered t h e v i r g i n p l a s t i c t o pyro lyse t o char and gaseous products and assumed thermal equi l ib r ium and zero r e s idence t i m e of t h e py ro lys i s products w i t h i n t h e char l a y e r . Char depos i t i on and/or dep l e t i on was no t considered i n t h e a n a l y s i s . A modified form of Darcyss law was used t o c a l c u l a t e t h e p re s su re d i s t r i b u t i o n a f t e r a t enpe ra tu re p r o f i l e had been e s t a b l i s h e d . The a n a l y s i s of Swann, s. &. (16) 57as a one-dimensional, numerical a n a l y s i s of t he t r a n s i e n t response of an a b l a t i v e com- p o s i t e . The thermal p ro t ec t ion system could con ta in a s many a s t h r e e l a y e r s of d i f f e r e n t m a t e r i a l s and the f i r s t two could have moving boundaries. The m a t e r i a l response was coupled t o the flow f i e l d by an energy balance a t t he char su r f ace where the convect ive hea t ing r a t e was computed us ing e i t h e r a l i n e a r o r a quadra t ic approximation t o the blocking e f f e c t i v e - ness f o r a laminar boundary l a y e r . The cold-wall convect ive hea t ing r a t e and the r a d i a n t hea t ing r a t e inc ident on the su r f ace were s p e c i f i e d func t ions of t ime. These va lues appeared a s inputs t o t h e computer s o l u t i o n . The su r f ace was removed by vapor i za t ion a t t he subl imation temperature and by d i f f u s i o n c o n t r o l l e d chemical r eac t ions of oxygen a t the su r f ace . The energy equat ion appl ied t o t he char zone which was used by Swann, g. &. (16) can be pu t i n t he fol lowing form: where W i s the mass f l ux of p y r o l y s i s products a t x and W i s 0 t he mass f l u x of the py ro lys i s products en t e r ing the char zone, The term i n bracke ts i s r e f e r r e d t o a s an e f f e c t i v e r e a c t i n g gas h e a t capac i ty which i s computed cons ider ing the flow t o be f r o z e n ( r H .R = 0) o r i n thermodynamic equi l ibr ium ( ~ H . R . $ 0 ) . J j J J The r e s u l t s of t h i s research w i l l permit t h e c a l c u l a t i o n of t h e non-equilibrium r e a c t i n g gas hea t capac i ty , i . e . t h e term i n bracke ts of equat ion (2-1) . The computation of t h e energy absorbed by chemical r e a c t i o n s f o r non-equilibrium flow w i l l be discussed i n t h e next chapter . This w i l l permit t he c a l c u l a t i o n of t h e non-equilibridm r e a c t i n g gas h e a t capac i ty t o be used with a simultaneous s o l u t i o n of t h e t r a n s i e n t energy equat ion (2-1) . With t h e s e r e s u l t s t h e t r a n s i e n t response of a cha r r ing a b l a t o r can be predic ted f o r non-equilibrium flow i n t h e char zone. Analysis of t h e Char Zone of a Charring Ablator The a n a l y s i s of t h e char zone of a cha r r ing a b l a t o r i s i n essence a s tudy of flow through porous media accompanied by chemical r e a c t i o n s i n t h e f l u i d and between t h e f l u i d and t h e medium. The porous medium i s carbon, and t h e f l u i d i s t h e py ro lys i s products r e s u l t i n g from thermal degradat ion of t h e a b l a t i v e composite. Although t h e r e has been ex tens ive work by t h e petroleum indus t ry on flow through porous media f o r improving well pe r fo r - mance (22) , t h e r e has been l i t t l e work desc r ib ing t h e complex, non-equilibrium flow encountered i n t h e char zone during a b l a t i o n . However, t h e r e has been a s i g n i f i c a n t amount of research i n t h e aerospace f i e l d on t r a n s p i r a t i o n cool ing . To desc r ibe flow i n t h e char zone t h e r e have been two types of ana lyses . The f i r s t involves flow of f l u i d s having cons t an t phys ica l p r o p e r t i e s wi th t h e gas and s o l i d phases a t d i f f e r e n t temperatures ( thermal non-equi l ibr ium). The second involves flow i n porous media wi th v a r i a b l e phys ica l p r o p e r t i e s but wi th thermal -equi l ibr ium between t h e s o l i d and gas . The s t u d i e s of Koh and d e l Casal (1 ,2 ,3 ) were most d i r e c t l y r e l a t e d t o t h i s work and i l l u s t r a t e both ana lyses . I n p a r t i c u l a r , t h e f i r s t paper presented a n a l y t i c a l s o l u t i o n s t o t h e one- dimensional energy equa t ion f o r (a ) cons t an t phys ica l p r o p e r t i e s wi th thermal non-equilibrium and (b) v a r i a b l e phys ica l p r o p e r t i e s with thermal equi l ib r ium between phases . .The second s tudy was f o r chemical non-equilibrium f low through porous mat r ices wi th thermal equi l ib r ium. The t h i r d paper gave a summary of an experimental s tudy used t o v e r i f y t h e models proposed i n t h e a n a l y t i c a l s t u d i e s . Clark (4) extended t h e t r a n s p i r a t i o n cool ing a n a l y s i s of Koh and d e l Casal (2) t o s imulated a b l a t i v e cha r s . I n t h i s s tudy methane-helium mixtures were passed through r e s i s t a n c e hea ted porous carbon and g r a p h i t e specimens i n a temperature range from 2000" t o 3500°F. Weger, s. a. (4 ,5) used a chemical non-equilibrium a n a l y s i s of gas flow through cha r s and carbon specimens t o s tudy t h e e x t e n t of carbon depos i t i on r e s u l t i n g from hydrocarbon c racking r e a c t i o n s . The e f f e c t of carbon d e n s i f i c a t i o n on t h e cha r and flow p r o p e r t i e s were analysed. An induc t ion furnace was used t o achieve uniformly high temperatures ac ros s the char specimens. T ransp i r a t ion Cooling Studies by Koh and d e l Casal : The works of Koh and d e l Casal (1 ,2 ,3) summarized the approach taken i n both types of t r a n s p i r a t i o n ana lyses descr ibed above. In t h e i r f i r s t paper a n a l y t i c a l s o l u t i o n s t o the one dimensional energy equat ion were presented . These included the s p e c i a l cases of (a) cons tan t p r o p e r t i e s wi th thermal non-equilibrium between the gas and s o l i d phases, and (b) v a r i a b l e p rope r t i e s wi th thermal equi l ibr ium between the two phases. The equat ions used by t h e authors f o r a non-react ing ( f rozen) , t r a n s p i r a t i o n cool ing a n a l y s i s were (1 ) : Equation (2-2) i s an o v e r a l l energy balance f o r a f l u i d flowing i n the porous mat r ix and equates the energy t r a n s f e r by mat r ix conduction a t the p o i n t x t o the change i n f l u i d en tha lpy between an i n i t i a l temperature, Tfi ' and the temperature a t po in t x, f Equation (2-3) is an energy balance f o r t he coolant phase and equates t he energy t r a n s f e r from the coolant by convection t o t he energy t r a n s f e r from the coolant t o t he s o l i d phase. The energy t r a n s f e r by gas conduction was omitted from the equat ion a s i n s i g n i f i c a n t wi th r e spec t t o t he gas convect ion. Equations (2-2) and ( 2 - 3 ) were used t o couple t he coolant and s o l i d phases of t he system f o r t he thermal non-equilibrium cond i t i on . The pressure d i s t r i b u t i o n w i t h i n the mat r ix was determined us ing ~ a r c y ' s Law a s given below which neg lec t s i n e r t i a l e f f e c t s . The one-dimensional, s t eady s t a t e con t inu i ty equat ion was used and i s : W = pv = cons tan t (2-5) The equat ion of s t a t e f o r t h e coolant phase was the fol lowing: The boundary condi t ions used t o so lve these equat ions were the p re s su re and mat r ix temperature a t t he r e a r (x=O) and f r o n t (x=L) su r f aces of the mat r ix . The r e s u l t s f o r t he a n a l y s i s were presented f o r two cases . The f i r s t considered t h e h e a t t r a n s f e r c o e f f i c i e n t and the phys ica l and thermodynamic p r o p e r t i e s a s cons t an t s , whi le the second was a v a r i a b l e p r o p e r t i e s s o l u t i o n . I n t he s o l u t i o n f o r t he f i r s t case , t he equat ions were non- dimensionalized and an a n a l y t i c a l s o l u t i o n was obtained. Theapproach used by t h e au thors fol lows. Rewri t ing equat ions (2-2) and (2-3) i n dimensionless form gave: and where The boundary cond i t ions i n dimens ion le s s form were: D i f f e r e n t i a t i o n of equation (2-9) wi th r e spec t t o and sub- s t i t u t i n g the expressions f o r % and d% /d i n t o equat ion (2-10) f f 'fl gave a second order d i f f e r e n t i a l equat ion i n terms of 0 : m The gene ra l s o l u t i o n of t h i s equat ion was: where and Using t h e dimensionless boundary condi t ions t o eva lua t e C and C 1 2 i n equat ion (2-19) r e s u l t e d i n t he fol lowing dimensionless temperature d i s t r i b u t i o n s f o r the mat r ix (0 ) and coolant m (0,) a s func t ions of t h e dimensionless mat r ix th ickness (I): Resul t s of t he above a n a l y s i s were presented i n t h e form of graphs and w i l l be discussed fol lowing t h e review of t he va r iab l e p r o p e r t i e s ana lys i s . The v a r i a b l e p r o p e r t i e s a n a l y s i s of Koh and d e l Casal (1) was made f o r t h e ca se of thermal equi l ibr ium between the coolant and s o l i d phases. A reduct ion i n t he complexity of t he previous a n a l y s i s r e s u l t e d which p e r m i t t e d p h y s i c a l p r o p e r t y d a t a i n t h e form o f polynomial e x p r e s s i o n s t o be i n c o r p o r a t e d i n t o t h e e q u a t i o n s o b t a i n e d f o r t h e t h e r m a l e q u i l i b r i u m a n a l y s i s . A summary of t h e approach used by t h e a u t h o r s f o l l o w s . Once a g a i n t h e energy e q u a t i o n (2-2) was r e w r i t t e n i n d i m e n s i o n l e s s form a s : where : The the rmal c o n d u c t i v i t y and h e a t c a p a c i t y of t h e c o o l a n t were c a l c u l a t e d by t h e u s u a l polynomials where a and b were c o e f f i - c i e n t s i n t h e e x p r e s s i o n s : S u b s t i t u t i o n o f e q u a t i o n s ( 2 - 2 8 ) and ( 2 - 2 9 ) i n t o e q u a t i o n ( 2 - 2 4 ) fo l lowed by i n t e g r a t i o n gave: The t r ans fo rmed boundary c o n d i t i o n d e s c r i b e d by e q u a t i o n ( 2 - 7) was used t o o b t a i n ( 2 - 3 0 ) , and t h i s is : The i n l e t and o u t l e t s u r f a c e t e m p e r a t u r e s were r e l a t e d t o B u s i n g t h e second t ransformed boundary c o n d i t i o n ( 2 - 8 ) which was: The r e s u l t i n g e q u a t i o n , a p p l y i n g t h e s e boundary c o n d i t i o n s , was: The s o l u t i o n o f Darcy ' s Equa t ion f o r c o o l a n t f low was l i k e - w i s e g i v e n i n d imens ion less form a s : where the v i s c o s i t y was -evaluated us ing a polynomial express ion . The cons tan t and v a r i a b l e p r o p e r t i e s models of Koh and d e l Casal (1) were compared wi th the experimental da t a of TurnacEiff (23) i n which one h a l f inch diameter spheres were used a s t he flow medium. The f l u i d s s tud ied were a i r and he 1 ium . Resu l t s of the comparison of the cons tan t p r o p e r t i e s , thermal non-equilibrium s o l u t i o n (equat ions 2-19 and 2-23) wi th the experimental d a t a were presented a s dimensionless p l o t s of temperature (matrix and f l u i d ) a s a func t ion of mat r ix thickness f o r va lues of mat r ix po ros i ty between 0.259 and 0.477 and f l u i d Reynolds number between 62 and 862, The phys i ca l p r o p e r t i e s of the f l u i d were evaluated a t a mean temperature of 110°F a t t h e back and f r o n t su r f aces . These p l o t s a r e reproduced i n Figures 2-1, 2-2 and 2-3. A s can be seen a very good agreement between the a n a l y t i c a l and expe r i - mental r e s u l t s was obtained. ?1 Figure 2-1. Comparison of Ca lcu la ted and Measured Temperature D i s t r i b u t i o n s , Po ros i t y = 0.259. M a t r i x Coolant 0 .0 0 .2 0 .4 0 .6 0 .8 1 . 0 F igure 2-2. Comparison of c a l c u l a t e d and Measured Temperature D i s t r i b u t i o n s , P o r o s i t y = 0,395. M a t r i x Coolant -- F i g u r e 2-3. Comparison o f C a l c u l a t e d and Measured Temperature D i s t r i b u t i o n s , P o r o s i t y = 0,477. Three important conclusions were drawn from t h e cons tan t p r o p e r t i e s , thermal non-equi l ibr ium a n a l y s i s . F i r s t , a decrease i n the Reynolds number a t f i xed p o r o s i t y va lues decreased the d i f f e r e n c e between the mat r ix and f l u i d temperatures . The Reynolds number can be decreased by decreas- ing t h e f l u i d v e l o c i t y , o r , by decreas ing the pore diameter of t he mat r ix . I n e i t h e r case the mass f l u x of coolan t t o the mat r ix is reduced causing longer holdup of t he f l u i d phase w i t h i n the mat r ix . This a d d i t i o n a l holdup time favors thermal equi l ibr ium between the s o l i d and f l u i d phases. Secondly, a decrease i n the Reynolds number a t f i xed p o r o s i t y va lues increased the d i f f e r e n c e between the f l u i d r e s e r v o i r tempera- t u r e ( t he temperature of t he f l u i d p r i o r t o e n t r y i n t o the mat r ix a t the back s u r f a c e ) and the mat r ix back su r f ace temperature f o r a cons t an t f r o n t su r f ace temperature. This i s caused by reducing t h e n e t capac i ty of the f l u i d t o absorb h e a t t r a n s f e r r e d t o t h e back su r f ace from the heated f r o n t s u r f a c e . Thi rd ly , the r e s u l t s of Turnac l i f f can be ex t r apo la t ed t o t r a n s p i r a t i o n cool ing , where a mat r ix pore diameter i s used t h a t i s s e v e r a l o rde r s of magnitude smal le r ( f o r the same va lues of f l u i d v e l o c i t y ) than t h a t used by Turnac l i f f (23) . This showed t h a t thermal equi l ibr ium between t h e s o l i d and f l u i d was a reasonable approximat ion f o r t r a n s p i r a t ion cool ing. For t he v a r i a b l e p r o p e r t i e s , thermal equi l ibr ium s o l u t i o n (equat ion 2-33), Koh and d e l Casal analysed a i r and helium flow through Nickel Foametal mat r ices having po ros i ty values between 0.42 and 0.735. The i n l e t temperature of the coolant was 540°R and the mat r ix f r o n t su r f ace temperature was 2700°R. The r e s u l t s , presented aga in a s a dimensionless p l o t of tempe- r a t u r e a s a func t ion of mat r ix th ickness , a r e reproduced i n Figure 2-4. Also shown were temperature p r o f i l e s f o r the cons t an t p r o p e r t i e s s o l u t i o n . A c l o s e approximation t o t h e v a r i a b l e p r o p e r t i e s s o l u t i o n was obtained a t a mat r ix po ros i ty va lue of 0.42, However, a s t he p o r o s i t y was increased ( t o 0.53 and 0.735), depar ture of the cons t an t p rope r t i e s temperature d i s t r i b u t i o n s from those of t he v a r i a b l e p r o p e r t i e s a n a l y s i s was observed. This ind ica ted t h e importance of a v a r i a b l e phys i ca l p r o p e r t i e s a n a l y s i s i n any r e a l i s t i c model of flow through media having moderate t o h igh (>0.50) poros i ty . In t h e above ana lyses , s impl i fy ing assumptions were made t o o b t a i n a n a l y t i c a l so lu t ions . Important modes of energy absorp- t i o n , such a s f l u i d conduction and chemical r e a c t i o n , were omit ted from the models, This g r e a t l y r e s t r i c t e d the a p p l i - c a t i o n of t he models t o a small c l a s s of problems ( i . e . , flow of an i n e r t coolan t through a porous medium i n t r a n s p i r a t i o n cool ing) . In order t o extend t h e i r ana lyses t o a broader a r ea of a p p l i c a t i o n , Koh and d e l Casal i n a second paper (2) proposed d i s s o c i a t i o n of t he coolant w i t h i n the porous matr ix. F i g u r e 2-4. Temperature D i s t r i b u t i o n s f o r A i r and Helium Flows Through Nicke l Foametal , The d i s s o c i a t i o n of coolan t t o var ious products was represented by the genera l chemical r e a c t i o n below. The energy absorbed by chemical d i s s o c i a t i o n of the coolant w i t h i n the mat r ix was incorporated i n t o the thermal equi l ibr ium, energy balance equat ion (2-2) a s : In equat ion (2-37), t he term on the r i g h t hand s i d e represented the l o c a l en tha lpy f lux r e s u l t i n g from the d i s s o c i a t i o n of the coolant t o S spec i e s . The summation i n equat ion (2-37) was i made over S spec i e s t o include a d d i t i o n a l spec ies (S t o n i+l S ) t h a t e n t e r i n t o the mat r ix from the f l u i d ad jacent to the n f r o n t su r f ace by counter d i f f u s i o n . The l o c a l en tha lpy f l u x was equated t o the energy absorbed by ma t r ix conduction t o complete t h e energy balance. Once aga in energy absorp t ion by coo lan t conduction was omit ted from the a n a l y s i s . I n o rde r t o eva lua t e the l o c a l en tha lpy f l u x needed i n t h e energy equat ion (2-37), t he fol lowing equat ions were solved simultaneousPy wi th the energy equat ion; t he c o n t i - n u i t y equat ion (2-5) and the momentum equat ion ( 2 -4 ) . In a d d i t i o n the r a t e equat ion (2-38), which s p e c i f i e d the r a t e of d i s s o c i a t i o n of t he coo lan t , and the spec i e s c o n t i n u i t y equat ion (2-39), were used, The change i n the molar concent ra t ion of s p e c i e s iwas equated t o the r a t e of chemical d i s s o c i a t i o n of t h e coolant by a d i f f e r e n t i a l m a t e r i a l balance and is : Rewri t ing equation (2-39) f o r the s p e c i f i c r e a c t i o n (2-36) excluding the spec i e s (SiS1 t o S ) introduced i n t o the mat r ix n by d i f f u s i o n from the boundary l a y e r gave: where the f i r s t term on the r i g h t hand s i d e of t he equat ion represented t h e mole f l u x of spec i e i a t the r e s e r v o i r , and the second term was the increase of mole f l u x of i due t o the d i s s o c i a t i o n of "o" spec i e s . S u b s t i t u t i n g f o r W i n t o t he i energy equat ion (2-37) gave: Rearranging equat ion (2-42), w i th s u b s t i t u t i o n f o r h by i t s 'F i de f in ing equat ion (h = i f f C dT + hq) , and, normalizing P i 1 Tf the parameters T and x using equat ions (2-12) and (2-15), gave the fol lowing dimensionless , f i r s t o rde r , d i f f e r e n t i a l equat ion: where B. was def ined i n equat ion (2-14), Mi was the r a t i o of the molecular weights of s p e c i e s i t o t he molecular weight of 0 the r e s e r v o i r f l u i d , and h . was the s tandard hea t of formation 1 of s p e c i e s i. The s u b s c r i p t co r e f e r r e d t o condi t ions a t the r e s e r v o i r . To f a c i l i t a t e t h e s o l u t i o n of equat ion (2-43), the parameter R was defined a s a dimensionless mole f l u x of 0 spec i e s "0" us ing equat ions (2-39) and (2-40). A d e t a i l e d d e r i v a t i o n was presented i n t he o r i g i n a l work (2) by the au thors . The r e s u l t s of t h a t d e r i v a t i o n a r e presented below a s equat ions ( 2 - 4 4 ) and ( 2 - 4 5 ) : and These a r e two, f i r s t o rde r , d i f f e r e n t i a l equat ions f o r t he s o l u t i o n of R and w, t he mole f r a c t i o n of s p e c i e s " ~ ~ ~ . The 0 boundary condi t ions f o r t he above equat ions were the i n i t i a l mole f l u x of spec i e s ~ ~ o " i n t h e r e se rvo i r , and the f i n a l concent ra t ion of s p e c i e s " o " a t t he f r o n t su r f ace , The va lue of wL was s p e c i f i e d by an a n a l y s i s of the boundary l aye r flow. Also, s i n c e the r e a c t i o n r a t e parameters, F and K , were func t ions of temperature, the above equat ions ( 2 - 4 4 ) and ( 2 - 4 5 ) were solved s imultaneously wi th t h e energy equat ion ( 2 - 3 7 ) . The p re s su re d i s t r i b u t i o n was ca l cu la t ed from the momentum equat ion (2-4) us ing the gas equat ion of s t a t e given by equat ion (2-6). The r e s u l t i n g equat ion f o r t he pressure drop a t any po in t w i t h i n the mat r ix was: where JI was the ma t r ix permeabi l i ty , R was the un ive r sa l gas cons t an t and p,, the v i s c o s i t y . The s o l u t i o n of equat ions (2-43), (2-44), (2-45), and (2-48) f o r the d i s s o c i a t i o n of a i r and ammonia w i t h i n the porous ma t r i ce s was obtained. The r e s u l t s were presented a s p l o t s of t he dimensionless temperature a s a func t ion of mat r ix th ickness f o r var ious values of t he d i s s o c i a t i o n con- s t a n t , K. These s o l u t i o n s a r e reproduced i n Figures 2-5 and 2-6, The r e s u l t s showed the e f f e c t of the ex t en t of d i s soc i a - t i o n on the va lue of the coolant temperature and energy absorbed w i t h i n the ma t r ix , For h ighly endothermic, d i s so - c i a t i o n r e a c t i o n s w i t h i n the mat r ix , the l o c a l temperature was decreased due t o the increased energy absorp t ion by che- mical r e a c t i o n . This e f f e c t was i l l u s t r a t e d i n Figures 2-5 and 2-6 by the curves which f e l l below the K=O (no chemical r e a c t i o n ) curve. As noted, i n some cases , the non-equi l i - brium analyses (K#O) produced r e s u l t s which ind ica t ed increased Figure 2-5. Temperature Distributions for NH3 Plow Through a Porous Matrix as a Function of the Reaction Constant and Surface Emissivity, F i g u r e 2-6. Temperature D i s t r i b u t i o n s for NH Flow Through a Porous M a t r i x a s a Func t ion of t % e React ion Constant and S u r f a c e E m i s s i v i t y , temperature w i t h i n the mat r ix . This r e s u l t e d from t h e n e t decrease i n t he mass f l u x parameter, B, of equat ion (2-43) which was caused by the d i s s o c i a t i o n of the coo lan t . The dua l e f f e c t of t he r a t e of d i s s o c i a t i o n of t he coolant on the mass and energy t r a n s f e r w i t h i n the mat r ix r e s u l t e d i n the i n t e r s e c t i o n of t he var ious curves i n F igures 2-5 and 2-6. The important conclusion drawn from t h i s non-equilibrium flow a n a l y s i s was t h a t endothermic chemical ( d i s s o c i a t i o n ) r e a c t i o n s w i t h i n the mat r ix reduced the t o t a l quan t i t y of coolant requi red t o maintain the su r f ace temperature a t a s p e c i f i e d va lue . The f i r s t and second papers by Koh and d e l Casal (1 ,2) neglec ted the e f f e c t of gas conduction on t h e energy t r a n s f e r a s soc i a t ed wi th flow through porous mat r ices f o r t r a n s p i r a - t i o n cool ing , This was a v a l i d assumption f o r high mass 2 f l u x va lues ( -0 .1 I b . / f t - see) o r f o r r e l a t i v e l y small temperature g rad ien t s ac ros s the mat r ix (300GoR). However, a t e i t h e r low flow r a t e s and/or high temperature g r a d i e n t s , a s encountered i n t r a n s p i r a t i o n and a b l a t i v e cool ing app l i ca - t i o n s , t he e f f e c t of coolan t conduction must be considered. In o rde r t o develop a more genera l ized t r a n s p i r a t i o n flow model Koh and d e l Casal (3) included coolant conduction i n t he non-equi l ibr ium, cons tan t p r o p e r t i e s model d i scussed previous ly ( I ) , Also, an experimental s tudy was conducted t o t e s t t h e r e l i a b i l i t y of t h i s a n a l y t i c a l model f o r p r e d i c t - ing the temperature g rad ien t and energy abso rp t ion w i t h i n the porous mat r ix . Before the comparison i s made, however, a b r i e f d i scuss ion of t he development of t h e governing equat ions of change and the a n a l y t i c a l s o l u t i o n s w i l l be made. Once aga in the c o n t i n u i t y (2-5) , momentum (2-4) and equat ion of s t a t e (2-6) considered i n Koh and d e l Casa l ' s f i r s t paper (1) was used i n t h i s a n a l y s i s , However, when energy absorp t ion by coolant conduction was considered, t h e energy equat ion (2-2) r e l a t i n g the h e a t t r a n s f e r by conduction from each phase and the inc rease i n t he f l u i d enthalpy from the r e s e r v o i r temperature (T ) t o a l o c a l temperature (T ) f i f was modif fed a s fol lows: Likewise, t h e energy balance r e l a t i n g the energy absorp t ion by ma t r ix conduction t o t h e convect ive h e a t t r a n s f e r from the mat r ix t o t h e f l u i d a t any c ros s - sec t ion w i t h i n the mat r ix w a s : For cons t an t p r o p e r t i e s , equat ion (2-50) reduced to : Rearranging equations (2-49) and (2-51) after normaliza- tion using the definitions of the dimensionless parameters in equations (2-ll), (2-12), (2-13), (2-14), and (2-15), gave: and where C is the ratio of the fluid to matrix thermal conduct- ivity: In order to solve the above equations for the dimensionless temperature distributions, and ef, three boundary condi- em t ions were required. These included, in normalized form, the back surface temperature of the matrix (x=O), em = e a t v = O m 0 the f r o n t s u r f a c e temperature of the mat r ix , e m = l a t r ) = 1 and, a l o c a l energy balance on the f l u i d phase a t t h e back su r f ace (x=O) r e l a t i n g the n e t i nc rease i n f l u i d enthalpy t o the h e a t t r a n s f e r by f l u i d conduction. I n dimensionless form t h i s was: Combining equat ions (2-52) and (2-53) gave a t h i r d order d i f f e r e n t i a l equat ion i n : m 3 2 e m - = B e m -- AB dem A B ~ - (C + AB) -+ - c 'm = 0 d v (2-58) d713 dl2 A genera l s o l u t i o n t o (2-58) w a s : where rl, r2 ' and r were the r o o t s of t he fol lowing a u x i l i a r y 3 equat ion : S u b s t i t u t i o n of ern a f t e r d i f f e r e n t i a t i o n i n t o equat ion (2-52) r e s u l t e d i n a s o l u t i o n f o r t h e f l u i d temperature d i s t r i b u t i o n , g f , a s a func t ion of 7 . where and For t h e s p e c i a l c a se of thermal equi l ib r ium between the f l u i d and m a t r i x (T = = T ) , t h e temperature d i s t r i b u t i o n was: Tf m Also a d e t a i l e d development f o r flow of coo lan t s through porous ma t r i ce s w i t h i n t e r n a l h e a t genera t ion was presen ted . This t o p i c w i l l be d iscussed i n a subsequent s e c t i o n which desc r ibes the r e sea rch of Clark (4) i n the a r ea of a b l a t i v e cool ing . In a d d i t i o n t o t h e a n a l y t i c a l development of t he modified coolant conduction model, equat ion (2-61), Koh and d e l Casal presented experimental r e s u l t s t o t e s t t he f e a s i b i l i t y of the model under t y p i c a l t r a n s p i r a t i o n cool ing condi t ions . These a r e summarized i n Table 2-1. The f l u i d s s tud ied were water , a i r , carbon dioxide and methyl methacrylate . Metal mat r ices cons t ruc ted of tungsten, poroloy, s t a i n l e s s s t e e l and n i c k e l were used. Po ros i ty va lues va r i ed from 0.20 t o 0.75 f o r t hese media. A r a d i a n t h e a t source was used t o hea t the f r o n t su r f ace of t he mat r ix t o temperatures between 1820°F t o 3200°F. Twenty-five in f r a red qua r t z lamps, s taggered i n two rows p a r a l l e l t o t he f r o n t s u r f a c e of the mat r ix , were used. The coolant flow passed through the mat r ix from t h e back t o t he f r o n t sur face . The e x i t flow r a t e was measured w i t h a p i t o t tube. It i s of i n t e r e s t t o i n d i c a t e the s i m i l a r i t y i n design of the apparatus of Koh and d e l Casal , e t . g. (3) wi th the - apparatus used i n t h i s s tudy. Each was cons t ruc ted without knowledge of the o t h e r , y e t many of the major f e a t u r e s ( i . e . , qua r t z hea t ing lamps, specimen ho lde r , e t c . ) were s i m i l a r , Ta bl e 2- 1. Su mm ar y o f Ex pe ri me nt al R es ul ts f or t he F lo w o f Ai r, C0 2, H 20 , a n d Me th yl Me th ac ry la te Th ro ug h Po ro us M at ri ce s. (1 ,7 4 - 5. O) xl O Un sa ti sf ac to ry D at a (0 .8 - 3. 8) xl O (0 .0 7 - 4. 3) xl O * Ga s: Pr es su re D ro p pe r Un it M as s Fl ux = Li qu id : Pr es su re D ro p pe r Un it M as s Fl ux = The experimental r e s u l t s obtained wi th the r a d i a n t hea t ing apparatus by Koh and d e l Casal were compared t o t he r e s u l t s p red ic t ed by the cons tan t proper ty , thermal equi l ibr ium s o l u t i o n inc luding energy absorp t ion by coolant conduction (equat ion 2-66). These comparisons were reproduced from the o r i g i n a l paper and a r e presented a s p l o t s of dimensionless temperature a s a func t ion of mat r ix th ickness i n F igures 2-7, 2-8, and 2-9 , A s seen , very good agreement was obtained f o r a l l coolan t spec i e s (water, a i r , cqrbon dioxide and methyl methacrylate) a t mat r ix d i s t ances l e s s than 0.5. However, i n Figures 2-7 and 2-8, t he r e s u l t s f o r a i r and carbon dioxide a t mat r ix d i s t a n c e va lues g r e a t e r than 0.5, d i f f e r e d from the p red ic t ed d i s t r i b u t i o n s a s shown. This was caused, i n p a r t , by the experimental e r r o r ; and, probably i n p a r t t o t he approximate s o l u t i o n obtained by cons ider ing the phys ica l p r o p e r t i e s cons t an t , It is reasonable t o expect a b e t t e r agreement near the back su r f ace of t he ma t r ix where the coolant p r o p e r t i e s a r e not g r e a t l y inf luenced by the moderate temperature encountered (500°R - 1000°R). However, a s t he coolant approaches the f r o n t su r f ace where temperatures i nc rease r a p i d l y from 700°R t o 2200°R, t he change i n phys ica l p r o p e r t i e s could c e r t a i n l y cause a poor c o r r e l a t i o n wi th the observed r e s u l t s . Once aga in , the importance of a v a r i a b l e p r o p e r t i e s a n a l y s i s when temperature g rad ien t s g r e a t e r than ?1 F i g u r e 2-8. Temperature D i s t r i b u t i o n s f o r C02 Flow Through a Porous M a t r i x . F i g u r e 2-9. Temperature D i s t r i b u t i o n s f o r Methyl M e t h a c r y l a t e Flow Through a Porous M a t r i x . 1000°R a r e encountered i s i l l u s t r a t e d f o r the accu ra t e pred ic- t i o n of the a c t u a l behavior . No experimental r e s u l t s were presented f o r the chemical non-equilibrium a n a l y s i s (2) of flow through porous ma t r i ce s . However, carbon depos i t i on was noted dur ing the methyl methacrylate experiments r e s u l t i n g i n s e r i o u s plugging problems w i t h i n the mat r ix . The carbon depos i t was a t t r i b u t e d t o the thermal cracking of var ious hydrocarbons obtained a s products from the depolymerization r e a c t i o n s of the methyl methacry la te , The m a t e r i a l i n t he t h r e e papers by Koh and d e l Casal (1 ,2 ,3) i s summarized a s fol lows. F i r s t , t h e simultaneous s o l u t i o n s of the c o n t i n u i t y equat ion (2-5) and the momen- tum equat ion (2-4) w i th var ious forms of t he energy equat ion were presented. The equat ions were f o r the flow of coolan t through a one-dimensional porous mat r ix wi th : (1) cons tan t phys i ca l p r o p e r t i e s and thermal non- equi l ibr ium between the coolant and s o l i d phases, (2) v a r i a b l e phys i ca l p r o p e r t i e s and thermal e q u i l i - brium between the coolant and the porous mat r ix , (3) v a r i a b l e phys i ca l p r o p e r t i e s w i th thermal e q u i l i - brium be tween the phases accompanied by d i s soc i a - t i o n of the coolant w i t h i n the mat r ix , (4) cons t an t p r o p e r t i e s w i t h thermal non-equilibrium between the coolant and mat r ix and energy t r a n s f e r by s o l i d and mat r ix conduction, and, (5) cons t an t p r o p e r t i e s , thermal equi l ibr ium flow wi th energy absorp t ion by coolant and s o l i d conduction. In ca ses (1) and ( 5 ) experimental r e s u l t s by Turnac l i f f (23) and Koh and d e l Casal (3 ) , r e s p e c t i v e l y , were used t o e s t a b l i s h t h e accuracy of the s o l u t i o n s obtained; and, i n gene ra l , t he models pred ic ted the observed r e s u l t s w i th in experimental e r r o r . However, f o r the remaining cases , no experimental da t a were presented t o e s t a b l i s h the accuracy of t h e a n a l y t i c a l r e s u l t s . The con t r ibu t ions by the au thors de f in ing the e f f e c t s of gas conduction, chemical r e a c t i o n s and i n t e r n a l hea t genera t ion on the f l u i d flow and h e a t t r a n s f e r cha rac t e r - i s t i c s i n high temperature porous mat r ices f o r t r a n s p i r a t i o n cool ing were indeed s i g n i f i c a n t . Qui te n a t u r a l l y t he r e s u l t s of Koh and d e l Casal (1 ,2 ,3) f o r t r a n s p i r a t i o n cool ing can be extended t o a b l a t i o n cool ing f o r p ro t ec t ion of space v e h i c l e s . The a b l a t i v e cool ing problem i s more complex due t o : (1) t h e multicomponent na tu re of t he py ro lys i s gas phase , (2) the chemical r eac t ions of t hese gases wi th the carbonaceous l aye r formed during a b l a t i o n , and, (3) the extremely l a rge temperature g rad ien t s e x i s t i n g between the back and f r o n t su r f aces of the char which r e q u i r e a v a r i a b l e phys ica l p r o p e r t i e s s o l u t i o n t o the equat ions of change. However, t he bas i c method of desc r ib ing the energy and mass t r a n s f e r f o r flow of f l u i d s through porous media wi th chemical r e a c t i o n i s the same. In t h e next two sec t ions t h e research of Clark (4) and Weger, - e t . 2. (5 ,6) w i l l be presented. They descr ibed the phenomena occurr ing i n the char zone of a char forming a b l a t o r . Clark (4) presented an a n a l y t i c a l model f o r flow of methane and helium-methane mixtures through carbon and g raph i t e mat r ices . The importance of thermal equi l ibr ium between the gas and mat r ix was determined and the l o c a t i o n and temperature w i t h i n the porous specimens where methane underwent thermal decomposition t o carbon and hydrogen was measured. Weger, g. a. (5 ,6) formulated a k i n e t i c model f o r p r e d i c t i n g the phys i ca l proper ty changes of the carbon l aye r r e s u l t i n g from carbon depos i t i on . In p a r t i c u l a r , the e f f e c t of carbon d e n s i f i c a t i o n on char po ros i ty , and permeabi l i ty , was d iscussed . Weger, - e t . e. (6) a l s o pos tu l a t ed the r e a c t i o n s t h a t con t r ibu ted t o carbon depos i t i on and those t h a t r e s u l t e d i n carbon dep le t ion . The r e s u l t s were supported by an experimental program i n which methane, aceylene, hydrogen, carbon monoxide and water were passed through carbon and g raph i t e specimens ind iv idua l ly and i n mixtures . Ablat ive Cooling Study by Clark: The r e sea rch of Clark (4) extended, i n p a r t , the work of Koh and d e l Casal (3) t o desc r ibe a b l a t i v e cool ing. Like Koh and d e l Casal ( I ) , Clark s tud ied the thermal non-equilibrium between a porous mat r ix and the gas flowing through the medium. More impor- t a n t l y , however, Clark inves t iga t ed the thermal decomposition of methane a s it passed through the carbon and g raph i t e specimens and pinpointed the l o c a t i o n and temperature where the decomposition occurred. The a n a l y s i s by Clark was f o r one-dimensional, methane and helium-methane mixtures flowing through porous carbon and g r a p h i t e specimens. A h e a t genera t ion term was included i n t h e energy equat ion t o desc r ibe the experimental r e s u l t s obtained us ing a r e s i s t a n c e heated appara tus . The energy balance over t he s o l i d phase was: where s o l i d conduction and h e a t genera t ion terms were equated t o t he convect ive h e a t t r a n s f e r from the s o l i d t o the gas phase The energy balance r e l a t i n g the energy absorbed by gas convect ion t o the convect ive h e a t t r a n s f e r from t h e gas t o t h e s o l i d phase was: The c o n t i n u i t y (2-5) and momentum equat ions ( 2 - 4 ) were i n the form previous ly d iscussed , Heat conduction by t h e gas phase was considered small compared wi th gas convect ion and was omit ted. Heat absorp t ion by chemical r e a c t i o n was, l ikewise , de l e t ed from the energy equat ion. The fol lowing summarizes t he development of Clark t o o b t a i n a s o l u t i o n t o t he above equat ions . Combining equat ions ( 2 - 6 7 ) and ( 2 - 6 8 ) followed by i n t e g r a t i o n r e s u l t e d i n equat ion ( 2 - 6 9 ) : dT m S u b s t i t u t i o n f o r -obtained by d i f f e r e n t i a t i n g equat ion dx ( 2 - 6 8 ) and rear ranging gave a second o rde r , non-homoge- neous, l i n e a r , d i f f e r e n t i a l equat ion i n T f : The characteristic solution of equation (2-70) was given as: where and The particular solution of equation (2-70) was: k q"' m T = q"'++ kmC3 P W: (wCp) 2 + - h P The general solution was the sum of equations (2-71) and (2-74) : kq"' k c q r r + ~ m Tf = A Exp[yx] + B Exp[2500°R), energy absorp t ion by gas conduct ion becomes important. Both of these condi t ions a r e ev iden t i n a b l a t i o n cool ing a p p l i c a t i o n s . Therefore, any r e a l i s t i c model should include gas h e a t conduction i n the derived energy equat ion. Energy absorp t ion by chemical r e a c t i o n i s a l s o important and w i l l be d iscussed i n the fol lowing s e c t i o n . Chemical &-Equilibrium - Flow: Koh and d e l Casal (2 ) , Clark (4) and Weger, s. - a l . (5 ,6) recognized the importance of chemical r e a c t i o n s of t he flowing gas phase w i t h i n the porous medium. Koh and d e l Casal (2) and Clark (4) considered chemical r eac t ions an important mode of energy absorp t ion , whi le Weger, g. &. (5 ,6) used them t o exp la in changes i n phys ica l p r o p e r t i e s of the porous specimens by depos i t i on o r dep le t ion of carbon. The i d e n t i f i c a t i o n of a non-equilibrium o r t r a n s i t i o n reg ion f o r methane gas flow i n carbon (or g raph i t e ) specimens was made by Clark (4) . This t r a n s i t i o n reg ion occurred between 2500-3200°R which is we l l w i t h i n the range of temperatures experienced dur ing a b l a t i o n (1500-5000°R). It is very l i k e l y t h a t t he more complex py ro lys i s products obtained dur ing r e e n t r y would undergo s i m i l a r t r a n s i t i o n s from a frozen, through non-equilibrium t o equi l ibr ium flow over a wide range of temperatures . Therefore a non-equilibrium flow a n a l y s i s i s r equ i r ed t o accu ra t e ly p r e d i c t t h e energy absorp t ion w i t h i n the char l aye r . This f a c t was l ikewise repor ted by Weger, s. - a l . ( 6 ) who i d e n t i f i e d a v a r i e t y of r e a c t i o n s among the gases thought t o be a p a r t of t he py ro lys i s gas stream. The ex i s t ence of a chemical non-equilibrium r e a c t i o n f o r methane was proven by experimental measurement of carbon depos i t i on wi th in the porous specimens. Accurate Descr ip t ion -- of the Pyro lys is Products: In order t o s imula te t h e flow of gases r e s u l t i n g from the thermal decom- p o s i t i o n of a nylon-phenolic r e s i n composite, an accu ra t e d e s c r i p t i o n of t he var ious components must be ava i l ab l e . In a l l of t h e previous research t o d a t e , s imp l i f i ed gases (helium, methane, e t c . ) o r gas mixtures (methane, carbon monoxide, carbon d ioxide , hydrogen, e t c . ) were used. While t hese c o n s t i t u t e a p o r t i o n of t he decomposition products expected, they do no t r ep re sen t t h e e n t i r e py ro lys i s product composition. Concurrent wi th t h i s r e sea rch is work being done by Nelson (11) and Sykes (12) a t N,A.S.A.'s Langley Research Center t o i d e n t i f y t h e products of py ro lys i s . These and o t h e r r e s u l t s have been used c o n t i n u a l l y through t h i s s tudy t o achieve a n accu ra t e d e s c r i p t i o n of t h e py ro lys i s product s t ream e n t e r i n g the back su r f ace . A d i scuss ion of t he methods of s e l e c t i n g the spec i e s composition i n t h e py ro lys i s gas e n t e r i n g the char zone is presented i n Appendix G . Proper Chemical React ions - and Associated React ion Kine t i c Data: - Also e s s e n t i a l t o a c o r r e c t p r e d i c t i o n of t h e energy t r a n s f e r i n a char l a y e r is the s e l e c t i o n of t h e proper chemical r e a c t i o n s f o r desc r ib ing the non-equilibrium flow of t h e gases . A continuous searoh and screening technique has been used dur ing t h i s s tudy t o update t h e r e a c t i o n s included i n t h e model. Each r e a c t i o n chosen f o r t he model must be based on t h e py ro lys i s products i n i t i a l l y p re sen t and those gases leav ing t h e char a t t h e f r o n t su r f ace . The temperature g rad ien t ac ros s t h e char is a l s o an important parameter. More d i f f i c u l t than f ind ing s p e c i f i c chemical r e a c t i o n s is t h e t a s k of l o c a t i n g accu ra t e k i n e t i c d a t a f o r those r e a c t i o n s considered. This problem covers t h e range of no t f i n d i n g any d a t a t o f i nd ing s e v e r a l sources of d a t a which a r e c o n t r a d i c t o r y i n na tu re . In each case , a d i f f i c u l t s o l u t i o n t o t h e problem r e s u l t s , Much of t he technique used t o s c reen t h i s d a t a is presented i n Chapter 111. The above summary of previous r e sea rch has i l l u s t r a t e d some of t he important cons ide ra t ions t h a t must be included i n any r e a l i s t i c moael used f o r p r e d i c t i n g t h e energy t r a n s f e r i n t h e char zcne of a cha r r ing a b l a t o r . These r e s u l t s , a long w i t h o t h e r fundamental knowledge regard ing the a b l a t i v e coo l ing process , form a b a s i s on which an accu ra t e mathe- m a t i c a l model can be formulated. This is t h e primary o b j e c t i v e of t h i s research . I n t he fol lowing chap te r s , t he e q u a t i ~ n s of change w i l l be deve:loped s u b j e c t t o t h e r e s t r i c t i o n s def ined by the previous r e sea rch discussed i n t h i s chap te r . SoLutions of t hese equat ions f o r f rozen , chemical e q u i l i b r iurn, and chemical non-equi l ibr ium flow w i l l be obtained us ing numerical methods of computation. F i n a l l y , these ana ly t ica : r e s u l t s w i l l be compared wi th each o the r and wi th experimental d a t a LO d e t e r - mine t h e r e l i a b i l i t y of the formulated f1c.w model. REFERENCES 1. Koh, J. C . Y. and E. P. d e l Casal , "Heat and Mass Flow Through Porous Matr ices f o r T ransp i r a t ion Cooling," Paper 16, Proceedings of the 1965 Heat Transfer and Flu id Mechanics I n s t i t u t e , S tanford Univers i ty Press , Los Angeles, C a l i f o r n i a , 263-81 (June 21-23, 1965). 2. Koh, J. C. Y. and E . P. d e l Casal , "Heat and Mass Transfer wi th Chemical React ions f o r F lu id Flow Through a Porous Matrix i n Re-Entry Thermal P ro t ec t ion , " A . I . A . A . Fourth Aerospace Sciences Meeting, Los Angeles, C a l i f o r n i a (June 27-29, 1966). 3 . Koh, J. C. Y . , E . P:del Casal , R. W. Evans, and V. Deriugin, "Fluid Flow and Heat Transfer i n High- Temperature Porous Matr ices f o r Transpi ra t ion Cooling," Technical Report AFFDL-TR-66-70, The Boeing Company, 207 pages (May 1966). 4. Clark , Ronald K., "Flow of Hydrocarbon Gases i n Porous Media a t Elevated Temperatures," M.S. Thesis , Univers i ty of V i rg in i a , 108 pages (August 1968). 5. Weger, E r i c , J e r e Brew and Roger Schwind, "An I n v e s t i g a t i o n of Carbon Deposi t ion i n Chars," Report BSD-TR-66-385, Washington Univers i ty , S t . Louis, Missouri , 84 pages (1966). 6. Weger, E r i c , J e r e Brew and Ronald S e r v a i s , "An I n v e s t i g a - t i o n o f Carbon Depos i t ion i n Chars - 11," Report SAMSO- TR-68-123, Washington U n i v e r s i t y , S t . Louis , M i s s o u r i , 96 pages ( January 1968). 7. A p r i l , G . C . , R. W. P ike and E. G. d e l V a l l e , "So lu t ion o f t h e Frozen Flow Energy Equat ion," NASA-CR-77026 ( J u l y 1966). 8. A p r i l , G. C . , R. W . P ike and E. G. d e l V a l l e , "Transpor t Phenomena i n t h e Char Zone During A b l a t i o n . I: E v a l u a t i o n o f t h e Energy T r a n s f e r f o r Frozen and E q u i l i b r i u m Flow," Paper 13d, 63rd N a t i o n a l Meeting o f t h e A.I.Ch.E., S a l t Lake C i t y , Utah (May 1967). 9 . d e l V a l l e , E. G . , R, W. P ike and G. C . A p r i l , "Transpor t Phenomena i n t h e Char Zone During Abla t ion . 11: E q u i l i b r i u m Composition of Degradat ion Produc t s o f * Ablation, '"aper 13e, 63rd N a t i o n a l Meeting o f t h e A.I.Ch.E., S a l t Lake C i t y , Utah (May 1967) . 10. A p r i l , G. C . , R . W. Pike and E. G. d e l V a l l e , "Non- E q u i l i b r i u m Flow and t h e K i n e t i c s o f Chemical Reac t ions i n t h e Char Zone , I ' Symposium on A b l a t i v e P l a s t i c s , 155 th N a t i o n a l A.C.S. Meet ing, San F r a n c i s c o , C a l i f o r - n i a ( A p r i l 1968) . 11. Nelson, James B., "Determination of Kinetic Parameters of Six Ablation Polymers by Thermogravime tric Analysis, " NASA TN D-3919 (April 1967). 12. Sykes, George F.,Jr.,"Decomposition Characteristics of a Char-Forming Phenolic Polymer Used for Ablative Composites , I' NASA TN D-3810 (February 1967). 13. Ladacki, Michael, Janet V. Hamilton and Samuel N. Cohz, "Heat of Pyrolysis of Resin in Silica-Phenolic Ablator," AIAA -Journal, - 4 (lo), 1798 (October 1966). 14. Freidman, Henry L., "Pyrolysis of Plastics in a High Vacuum Arc Image Furnace -11," Journal - of Applied Polymer Science, - 9, 1005-18 (1965). 15. Kendall, Robert M., Eugene P. Bartlett, and Ronald A. Rindal, "A Multi-component Boundary Layer Chemically Coupled to an Ablating Surface," - AIAA Journal, - 5 (6), 1063 (June 1967). 16. Swann, Robert T., Claud M. Pittman and James C , Smith, "One D imens iona 1 Numer ica 1 Ana lys is of the Trans ient Response of Thermal Protection Systems," NASA TN D-2976 (September 1965). 17. S c a l a , S . M . , "A S tudy of Hypersonic A b l a t i o n , " General E l e c t r i c Co., M i s s i l e and Space Vehic le Department, Repor t R59SD438 (September 1959) . 18. S c a l a , S. M. and L. M. G i l b e r t , "Thermal Degradat ion o f a Char-Forming P l a s t i c During Hypersonic F l i g h t , " ARS - J o u r n a l , - 32 ( 6 ) , 917-24 (June 1962) . 19. B a r r i a u l t , R . J. and J. Yos, "Analysis o f t h e A b l a t i o n o f P l a s t i c Heat S h i e l d s t h a t Form a Charred S u r f a c e Layer," J o u r n a l , - 30 ( 9 ) , 823-9 (September 1960) . 20. Myers, H. and D. B. Harmon, Jr., "Energy T r a n s f e r Pro- c e s s e s i n Decomposing Polymeric Systems," Douglas A i r - c r a f t Co., M i s s i l e and Space Systems D i v i s i o n , Repor t 1020 (September 1960) . 21. K r a t s c h , K. M . , L. F. Hearne and H. R. McChesney, "Thermal Performance o f Heat S h i e l d Composites During P l a n e t a r y E n t r y , " AIAA-NASA N a t i o n a l Meet ing, P a l o A l t o , C a l i f o r n i a , 3 (September 30-October 1, 1963) . 22. Green, D. W. and R e H. Per ry , "Heat T r a n s f e r With a Flowing F l u i d Through Porous Media," - Heat T r a n s f e r , ed . by J. W. Wesfwater, Gas Chemical Engineer ing Symposium S e r ias, 57 ( 3 2 ) (1961) . 23. Turnacliff, R. D., Experimental Study of Local Convective Heat Transfer Pressure Drop for Laminar and Turbulent - Flow of Air Within 5 Uniformly --- Packed Bed of Spheres, Ph.D. Dissertation, University of -- Minnesota (1957). 111. DEVELOPMENT OF THE MATHEMATICAL ANALYSIS FOR REACTING FLOW I N THE CHAR ZONE OF A CHARRING ABLATOR In t roduct ion The momentum, energy and mass t r a n s f e r a s soc i a t ed wi th the flow of t he py ro lys i s products through the char l a y e r of a char-forming a b l a t i v e p l a s t i c i s considered. The py ro lys i s products , formed by the thermal degradat ion of the p l a s t i c hea t s h i e l d , e n t e r t he char l aye r a t the decomposition tem- pe ra tu re of the p l a s t i c , The products experience a temperature increase a s they flow through the char and undergo thermal c racking t o lower molecular weight spec ies which r e a c t wi th each o t h e r and wi th the carbonaceous char l a y e r . These predominantly endothermic r eac t ions a r e important modes of energy absorp t ion and must be included i n any r e a l i s t i c ana lys i s of the eqergy t r a n s f e r i n the char l a y e r , One of t h e main ob jec t ives of t h i s research i s t o develop an accu ra t e and r e a l i s t i c mathematical model t h a t desc r ibes the t r a n s p o r t phenomena i n t he char zone, The d e s c r i p t i o n of the momentum, energy and mass t r a n s f e r w i th in the char w i l l be obtained by reducing the genera l equat ions of change (cont inuni ty , momentum and energy) t o forms app l i cab le t o non-equilibrium flow i n the char . The r e s u l t i n g equat ions w i l l a l s o be s imp l i f i ed f o r the cases of f rozen and equi l ibr ium flow. Las t ly , t y p i c a l boundary condi t ions w i l l be s p e c i f i e d , followed by a d i scuss ion of the numerical s o l u t i o n of the equat ions . Statement of t he Problem The mathematical model desc r ib ing the t r anspor t phenomena tak ing p lace when py ro lys i s products pass through the char zone of a cha r r ing a b l a t o r has t he form of a one dimensional and s teady flow, A schematic diagram showing the py ro lys i s gas flowing through the porous char l aye r i s depic ted in Figure 3-1. As ind ica t ed , t he py ro lys i s products e n t e r the char a t t h e decomposition temperature, To ' and e x i t a t a higher f r o n t s u r f a c e temperature, TL. Changes i n the mass f l u x of t he va r ious spec ies w i th in the char occur as a r e s u l t of chemical r eac t ions a t f i n i t e r e a c t i o n r a t e s , R . A j pressure drop (P - P ) ac ros s the char is a l s o experienced. 0 L The p a r t i c u l a r r e s t r i c t i o n s and assumptions made i n the formulat ion of the model w i l l be presented and j u s t i f i e d i n t h e fol lowing paragraphs, The use of these r e s t r i c t i o n s t o s imp l i fy the genera l equat ions of change w i l l fol low. The s o l u t i o n of the r e s u l t i n g equat ions f o r f rozen , e q u i l i - brium and non-equilibrium flow w i t h i n the char zone w i l l complete t h e chap te r . Figure 3-1. Schematic Diagram of t h e Char Zone. R e s t r i c t i o n s t o the General Equations of Change f o r Flow i n the Char Zone --- To so lve any r e a l i s t i c problem, c e r t a i n s impl i fy ing assumptions and/or r e s t r i c t i o n s must be appl ied which reduce the complexity of the genera l equat ions of change. In the fol lowing s e c t i o n s , the var ious r e s t r i c t i o n s which apply t o t h i s p a r t i c u l a r problem a r e presented and j u s t i f i e d . One Dimensional, Steady Flow of Pyro lys is Products i n the - Char Zone: The flow of py ro lys i s gases w i t h i n the char zone -- i s a s teady s t a t e process s i n c e the char th ickness is cons tan t with r e s p e c t t o time a f t e r an i n i t i a l s h o r t , t r a n s i e n t per iod . During t h i s s h o r t per iod the char l aye r b u i l d s up due t o unequal r a t e s of a b l a t i o n and su r f ace removal. The d a t a of Pe ters and Wadlin (1) i n Figure 3-2 f o r a 50:50 weight r a t i o nylon-phenolic r e s i n a b l a t i v e composite formed i n a subsonic e l e c t r i c a i r a r c j e t shows t h i s g raph ica l ly . Also the res idence time of a p a r t i c l e of py ro lys i s gas f l u i d i s very s h o r t compared t o the r a t e of change of the char su r f aces . I n a d d i t i o n t o the above, t he r ad ius of curva ture of r een te r ing capsules ( eg . , Mercury, Gemini and Apollo s p a c e c r a f t ) , i s small i n comparison wi th the char th ickness such t h a t flow i s one dimensional and normal t o t he f r o n t su r f ace . This r e s t r i c t i o n does no t apply a t t h e edge where flow i n the r a d i a l d i r e c t i o n becomes s i g n i f i c a n t . However, t h i s reg ion is small i n comparison wi th the s t agna t ion reg ion where the maximum hea t ing occurs . Therefore t he edge reg ion can be neglected without s e r i o u s e t r o r . I d e a l Py ro lys i s Gas Mixtures: The py ro lys i s gases a r e - assumed t o behave a s an i d e a l gas mixture w i t h i n the char l a y e r . This i s reasonable when cons ider ing the high temperatures (1500 - 5000°F) and low p res su res (5 1 atm.) encountered during r e e n t r y , Gas and Char Physical Proper t ies : Because of the la rge --- temperature g rad ien t ac ros s the cha r , gas phys ica l p rope r t i e s (hea t capac i ty , thermal conduct iv i ty and v i s c o s i t y ) a r e considered v a r i a b l e w i th temperature. Var i a t ions wi th temperature i n t he char p r o p e r t i e s a r e no t accounted f o r based l a r g e l y on the absence of experimental d a t a f o r low d e n s i t y nylon-phenolic r e s i n chars . Weger, e t . a l . (2) repor ted v a r i a t i o n s i n the permeabi l i ty of low poros i ty (0.2 - 0.35) char specimens when s i g n i f i c a n t amounts of carbon depos i t i on and/or dep le t ion occured a t high temperatures (3000 - 4000°F) . However, f o r the temperature range considered i n t h i s r e sea rch (1500 - 3000°F), carbon depos i t i on and/or dep le t ion was smal l , and thus the permeabi l i ty could be considered cons t an t . S imi l a r ly , t he char p o r o s i t y was consid- ered uniform and equal t o 0.8 f o r low d e n s i t y nylon-phenolic r e s i n cha r s (3) and 0 .5 f o r g raph i t e (4) . The v a r i a t i o n of t he char thermal conduct iv i ty w i th temperature was accounted f o r by f i t t i n g empir ica l curves t o d a t a repor ted by the Southern Research I n s t i t u t e (5) and the J e t Propulsion Laboratory (6) of the C a l i f o r n i a I n s t i t u t e '. of Technology. These d a t a a r e presented i n Appendix C . Thermal Equclibrium Between the Pyrolys i s Products and the Char: The temperatures of t he py ro lys i s products and the char - a t any s e c t i o n normal t o the flow were assumed equal , There i s a d i f f e r e n c e between the gas and the char , bu t i t is gene ra l ly small . This i s supported by d a t a presented by Koh and d e l Casal ( 7 ) i n which a maximum temperature d i f f e r e n c e of 300°F was determined f o r the flow of a i r and helium through packed beds of spheres . The maximum temperature of t he mat r ix was 2700°F and the range of ~ e y n o l d ' s Numbers and p o r o s i t i e s were 62-862 and 0,2-0.35, r e s p e c t i v e l y , Clark (4) a l s o inves t iga t ed thermal equi l ibr ium f o r methane and methane-helium flow through porous g raph i t e . This work had very l a r g e temperature g rad ien t s (1600 - 2700°F) between the phases a t the i n l e t s u r f a c e , and showed a r ap id approach t o thermal equi l ibr ium wi th in the porous g raph i t e . For example, a d i f f e r e n c e of 3200°R a t the back su r f ace was reduced t o 600°R h a l f way through the char and t o 300°R a t the th ree -qua r t e r s po in t . Momentum Transfer i n t he Char Zone: The modified form of ~ a r c y ' s Law was used t o model the momentum t r a n s f e r w i th in the char zone. This was based on the research of Weger, e t . a l , ( 2 ) . It was shown i n t h i s work t h a t the modified form, inc luding an i n e r t i a l term, gave a more accu ra t e p r e d i c t i o n of the experimental d a t a f o r mass f l u x va lues of the order of 2 0 ,05 l b / f t - sec . PV Work and Viscous Diss ipa t ion : The p re s su re drop across --- a one-quarter inch t h i c k , low dens i ty , nylon-phenolic r e s i n L char was exper imenta l ly measured t o be approximately 15 l b / f t 2 f o r a p y r o l y s i s gas mass f l u x of 0.05 l b / f t -sec. and a f r o n t su r f ace temperature of 2000°F. The PV work con t r ibu t ion t o 3 the energy t r a n s p o r t i s 1 . 2 B T U / £ ~ -sec . The convect ive energy term i n the energy equat ion eva lua ted a t the back su r f ace where the temperature g rad ien t i s s m a l l e s t , (about 3 4 0 , 0 0 0 ° ~ / f t ) i s 1000 B T U / ~ ~ -sec f o r an average gas hea t capac i ty of 0.5 B T U / ~ ~ " F . From t h i s comparison energy d i s s i p a t i o n by PV work can be omit ted from the a n a l y s i s without e r r o r . Furthermore, s i n c e t h e v e l o c i t y (-5 f t / s e c ) and the v i s c o s i t y (,0,05cp) of t he gas mixture a r e s m a l l , energy generated by viscous d i s s i p a t i o n i s omit ted from the energy equat ion , D i f fus iona l Transport : Energy o r mass t r a n s p o r t by d i f f u s i o n i s neg l ig fb ly small i n comparison wi th the bulk f l u i d t r a n s p o r t , The average res idence time of a gas p a r t i c l e i n a one-quarter inch t h i c k char l aye r is 0 .01 seconds f o r a 2 mass f l u x va lue of 0.05 l b / f t - s ec . Work Against Gravi ty: For ho r i zon ta l flow of py ro lys i s - gases through the porous char , work aga ins t g r a v i t y i s zero , The a p p l i c a t i o n of t he above r e s t r i c t i o n s t o t he genera l equat ions of change f o r flow of p y r o l y s i s gases w i th in the char zone of a cha r r ing a b l a t o r i s d i scussed i n the next s e c t i o n of t h i s chap te r . Der iva t ion of the Equations of Change f o r Flow i n the Char Zone Species Continui ty Equation: With r e f e rence t o Figure 3-1, the c o n t i n u i t y equat ion f o r spec i e s i of a gas mixture flowing through a porous medium i s (8) : - where p i i s the concent ra t ion , j i , the mass f l u x , Ri , the - r a t e of product ion by chemical r e a c t i o n of spec ies i and v i s t he v e l o c i t y of t he py ro lys i s products w i t h i n the pores . For t he one-dimensional, s teady flow of py ro lys i s gases through the char zone, neglec t ing mass t r a n s p o r t by d i f f u s i o n , equat ion (3-1) reduces to: Summing the spec ies con t inu i ty equat ions over a l l t he gas spec i e s i n t he mixture gives t he o v e r a l l c o n t i n u i t y equa t ion : which assumes no mass l o s s o r increase due t o formation o r dep le t ion of t he s o l i d phase. I n t e g r a t i o n between the back su r f ace , z = 0 , and any p o i n t , z , w i t h i n the char r e s u l t s i n equat ion (3-4): This equat ion , de f in ing the gas mass f l u x a s t he product of t h e gas d e n s i t y and v e l o c i t y , i s equiva len t t o the s tatement t h a t the gas mass f l u x is cons tan t through the char ; W = pv = cons tan t P (3-5) where W is the mass f l u x based on the c ros s s e c t i o n a l a r e a of P 2 voids i n t h e char ( u n i t s of l b . / f t voids-sec). The mass f l u x based on t h e t o t a l a r e a is given by t h e fol lowing equat ion: where W has the u n i t s l b / f t 2 -set, t o t a l In t h e above formulat ion the change i n py ro lys i s gas mass f l u x i s considered small r e s u l t i n g from depos i t i on and/or dep le t ion by chemical r e a c t i o n s . In the event t he re is a s i g n i f i c a n t change i n the py ro lys i s gas mass f l u x due t o chemical r e a c t i o n s the app ropr i a t e form of the spec i e s con t i - n u i t y equat ions must be incorporated i n t o the a n a l y s i s a s w i l l be d iscussed subsequent ly. Momentum gquat ion: The momentum equat ion f o r flow through porous media was formulated by H. P. G . Darcy i n 1856 ( 7 ) . Darcy observed during experiments wi th a one-dimensional packed bed t h a t gas v e l o c i t y a t any po in t i n the bed was d i r e c t l y p ropor t iona l and i n the same d i r e c t i o n a s the p re s su re g rad ien t a t t h a t p o i n t . I n vec to r no ta t ion , inc luding the e f f e c t of body fo rces when cons ider ing a v e r t i c a l flow d i r e c t i o n , Darcy's Law i s : ; = -(:) (vp - Pi) Applying t h i s equat ion t o a one-dimensional, ho r i zon ta l flow through a porous char l aye r and so lv ing f o r the pressure g rad ien t g ives : This equat ion i s v a l i d a t low gas v e l o c i t i e s w i t h i n the porous medium. However, a t high gas v e l o c i t i e s the add i t i on of a term t o account f o r i n e r t i a l e f f e c t s i s included. This a d d i t i o n a l term leads t o a modified form of Darcy's law. Mult iplying both s i d e s of equat ion (3-9) by the gas d e n s i t y , p , followed by s u b s t i t u t i o n of the i d e a l gas equat ion of s t a t e (p = *) on the l e f t hand s i d e of t he equat ion r e s u l t s i n equat ion (3-10) : S u b s t i t u t i o n f o r t he mass f l u x , W, wi th rearrangement gives: - PdP = (F) [(;)(W) + @(w)'] W I n t e g r a t i o n of equat ion (3-11) between the f r o n t su r f ace pressure (P = P a t z = L) , and any poin t w i th in the char l a y e r , L (P a t z ) , r e s u l t s i n an i n t e g r a l equat ion f o r the pressure d i s tr ibu t ion over t he cha r , In t h i s equat ion a l l parameters t h a t vary wi th temperature (hence, cha r d i s t ance ) a r e l e f t under the i n t e g r a l s igns . These v a r i a t i o n s a r e ca l cu la t ed by polynomials i n temperature and from t h e simultaneous s o l u t i o n coupled from t h e energy 2 equat ion s i n c e the pressure changes a r e small ( 15 l b f / f t ) 2 compared t o the t o t a l p ressure (, 2000 l b f / f t ). Energy Equation: The form of the genera l energy equat ion f o r a gas mixture conta in ing K spec i e s i s (8): The above equat ion i s appl ied t o one dimensional, s teady flow of gases i n the char zone, Neglecting energy by viscous d i s s i p a t i o n , work aga ins t g r a v i t y and energy t r a n s f e r by d i f f u s i o n , the r e s u l t i s : Furthermore, f o r an i d e a l gas (-) = 1, and neg lec t ing the a lnT p,x, work by pressure f o r c e s ac ros s a h igh po ros i ty char , equat ion (3-14) s i m p l i f i e s t o : where q i s given by F o u r i e r ' s Law of h e a t conduction: z S u b s t i t u t i o n f o r t he mass glux, W, from equat ion (3-6) and m u l t i p l i c a t i o n of each s i d e by the po ros i ty , q , t o o b t a i n the gas phase c o n t r i b u t i o n t o t he t o t a l energy t r a n s f e r i n t he char zone gives: S imi l a r ly , f o r the s o l i d porous medium, neg lec t ing h e a t t r a n s f e r by convect ion, t he genera l energy equat ion reduces t o t he fol lowing form f o r one dimensional hea t conduction wi th chemical r e a c t ion. d d T ( 1 - E) (kc z) - ( 1 - p) HcRc = 0 The a d d i t i o n of equat ions (3-17) and (3-18) g ives t he equat ion f o r the t o t a l energy t r a n s f e r i n the char: where k r ep re sen t s an e f f e c t i v e thermal conduc t iv i ty def ined a s : e K+1 K and Z = Z HiRi + ( 1 - c) HcRc i=l i= 1 r e p r e s e n t s t he energy absorp t ion by chemical r e a c t i o n s based on the t o t a l volume of char . The s o l u t i o n of equat ion (3-19) w i l l g ive the temperature d i s t r i b u t i o n i n the char l aye r . In a d d i t i o n t o t he equat ions o f change j u s t developed, one a d d i t i o n a l equat ion is considered. This is the equat ion f o r the n e t h e a t absorp t ion wi th in the char zone. Heat Flux Equation: The h e a t f l u x equat ion determines the -- n e t h e a t t r a n s f e r w i t h i n the char l a y e r of a cha r r ing a b l a t o r . It i s def ined a s t h e d i f f e r e n c e i n the h e a t f l u x va lue a t the back and f r o n t su r f aces of t h e cha r . d T Solving f o r (k -) from the energy equat ion (3-19) by i n t e g r a t i o n e dz between the f r o n t and back su r f ace temperatures g ives t he equat ion needed t o eva lua t e t he n e t hea t f l u x w i t h i n the char . In equat ion (3-23), t he f i r s t term rep resen t s h e a t absorbed by s e n s i b l e enthalpy change and the second term accounts f o r h e a t absorp t ion by chemical r eac t ion . In summary, t he important d i f f e r e n t i a l equat ions f o r desc r ib ing the flow of py ro lys i s products i n the char l aye r a r e shown i n Table 3-1. The next s ec t ions w i l l d i s cuss these equat ions i n terms of t he va r ious models used t o desc r ibe the flow w i t h i n the char ( i . e . , f rozen, equi l ibr ium, and non-equi l ibr ium f low). Typical boundary condi t ions w i l l be d iscussed f o r the s o l u t i o n of t he equat ions . The development of t he numerical s o l u t i o n techniques w i l l complete t he theo- r e t i c a l d i scuss ion . ~ o u n d a r y Conditions f o r the Flow of Pyro lys is Products Through the Char Zone --- There a r e two important s e t s of boundary condi t ions t h a t can be s p e c i f i e d t o o b t a i n s o l u t i o n s t o t he equat ions of change, The f i r s t s e t s p e c i f i e s t h e pressure and temperature a t the f r o n t su r f ace , and, t h e temperature and py ro lys i s gas composition e n t e r i n g the back su r f ace of t he char , These a r e shown i n s ta tements ( 3 - 2 4 ) and ( 3 - 2 5 ) . and These condi t ions f o r mass f l u x , W, as, a parameter make the s o l u t i o n of the energy equat ion a two po in t boundary va lue problem. This r e q u i r e s an i t e r a t i v e so lu t ion . Because PV work was n e g l i g i b l e i n t he energy equat ion , the momentum equat ion (modified ~ a r c y ' s law) can be used t o compute the pressure d i s t r i b u t i o n a f t e r a s o l u t i o n of t he energy equat ion is obtained us ing an average pressure i n t h e char . The h e a t f l u x a t the char f r o n t su r f ace is a l s o c a l c u l a t e d us ing equat ion (3-23). The computer program used f o r t hese s o l u t i o n s is c a l l e d the I t e r a t i v e TEMPRE System (IT) and is discussed i n Appendix A , The second s e t of boundary condi t ions s p e c i f i e s the temperature, i n i t i a l py ro lys i s gas composition and the sum of the h e a t of py ro lys i s and the hea t conducted i n the v i r g i n p l a s t i c a t the back su r f ace of t he cha r , q~ For mass f l u x , W, and q a s parameters, t he s o l u t i o n of the P energy equat ion a s an i n i t i a l va lue problem can be obtained. This does not r e q u i r e an i t e r a t i v e s o l u t i o n a s d id the f i r s t ca se , To be u s e f u l , however, a parametr ic s tudy of the mass f l u x and q is needed over the range of va lues expected dur ing P r een t ry . In order t o c a l c u l a t e t he pressure d i s t r i b u t i o n wi th in the cha r , the f r o n t su r f ace pressure is aga in s p e c i f i e d . The h e a t f l u x and p re s su re d i s t r i b u t i o n c a l c u l a t i o n s a r e the same a s those made i n t he I t e r a t i v e TEMPRE System. The computer program f o r t h i s method of s o l u t i o n is c a l l e d the Non-I terat ive TEMPRE Sys tem (NIT) . Both systems a r e d iscussed i n d e t a i l i n Appendices A and B where a complete block flow diagram and program l i s t i n g a r e presne ted , The p a r t i c u l a r a p p l i c a t i o n of t he equat ions of change and the above boundary condi t ions t o frozen, equi l ibr ium and non-equilibrium flow of py ro lys i s gases w i t h i n the char l aye r w i l l be developed i n the next s e c t i o n . Appl ica t ion of t he Transport Equations to Frozen, Equilibrium and Non-Equjlibrium Flow i n the Char -- A s mentioned i n t he In t roduct ion , t he re a r e two l i m i t i n g cases c u r r e n t l y used t o s imp l i fy the a n a l y s i s of t he flow of py ro lys i s gases through the char zone, These-are t o consider the flow t o be e i t h e r f rozen o r i n thermodynamic equi l ibr ium. This r e sea rch dea l s wi th the development of a t h i r d model, one f o r non-equilibrium flow, which w i l l p r e d i c t more accu ra t e ly the a c t u a l behavior w i th in the char l a y e r . In t h i s s e c t i o n the equat ions of c o n t i n u i t y , momentum, energy and su r f ace hea t t r a n s f e r w i l l be appl ied t o develop each of the th ree flow models. I n a subsequent chap te r , t he s o l u t i o n s of t he p a r t i c u l a r equat ions f o r each model w i l l be compared wi th each o t h e r and wi th experimental d a t a , I n t h i s way the accuracy of the a n a l y s i s f o r non-equilibrium flow i n the char zone can be evaluated and the ex t en t t o which the two l i m i t i n g cases p r e d i c t t he behavior can be determined, Frozen Flow: The frozen flow model is an i d e a l i z a t i o n i n which the py ro lys i s products en t e r ing t h e char zone do not change i n composition a s they pass through the medium. There- f o r e , any b e n e f i t from the energy absorbed by the predominently endothermic chemical r e a c t i o n s which occur between the gases and char is no t ob ta ined , It s p e c i f i e s a lower l i m i t on the amount of energy absorbed i n t he char zone. Of the three cases i t i s t he s imples t because the chemical r e a c t i o n terms i n t he energy and h e a t f l ux equat ions a r e zero: Applying t h i s t o t h e equat ions of change developed previous ly r e s u l t s i n t he following s i m p l i f i c a t i o n s f o r f rozen flow i n the char l a y e r , Cont inui ty Equation W = W c = cons t an t P Momentum Equation Heat Flux Equation Energy Equation The numerical s o l u t i o n of t hese equat ions w i l l be discussed i n a l a t e r s e c t i o n . Typical r e s u l t s f o r cons tan t and v a r i a b l e phys i ca l p r o p e r t i e s a r e presented i n Appendix A . Equilibrium Flow: The equi l ibr ium flow i n the char zone gives an upper l i m i t on the amount of h e a t t h a t can be absorbed w i t h i n the char zone. The reason i s t h a t t h e r e a c t i o n s occuring w i t h i n the char a r e predominately endothermic. The s e t of equat ions used t o desc r ibe flow f o r t h i s case i s the same a s t h e equat ions developed previously: con t inu i ty (3-6) , momentum (3-12), energy (3-19), and h e a t f l ux (3-23). The d i s t i n g u i s h i n g f e a t u r e l i e s i n t h e method used t o c a l c u l a t e the energy absorp t ion by chemical r e a c t i o n s : Rewriting the s p e c i e s c o n t i n u i t y equat ion, (3-2) , i n terms of t he mole f l u x of spec i e s i gives: K+1 Therefore, i n o rde r t o eva lua te the term, H ~ R ~ , t he mass i= 1 f l u x , W , and the mass f r a c t i o n , x of the spec i e s i n t he gas i' and s o l i d phases must be known as a func t ion of temperature. The spec ies composition and molal r a t i o of gases t o carbon a r e a func t ion of temperature, p ressure and elemental compo- s i t i o n of the v i r g i n p l a s t i c and can be c a l c u l a t e d by one of the many approaches i n the l i t e r a t u r e ( 1 0 , l l ) . I n t h i s s tudy, t he f r e e energy minimization technique was used. The fol lowing s e c t i o n o u t l i n e s t h e important po in t s of t h i s method, Equil ibr ium Compositions b~ Free Energy Minimization: When s e v e r a l r e a c t i o n s occur between a number of s p e c i e s , the composition r e s u l t i n g a t equi l ibr ium depends on the simul- taneous equi l ibr ium f o r a l l s epa ra t e r e a c t i o n s . The c r i t e r i a f o r t h i s equi l ibr ium i n a chemically r e a c t i n g system a t cons tan t temperature and p re s su re i s t h a t t he f r e e energy change i s zero o r t h a t the t o t a l f r e e energy of the mixture i s a minimum, The f r e e energy change f o r a r e a c t i o n is considered a d r i v i n g fo rce which makes t h e r e a c t i o n approach equi l ibr ium. It i s a l s o a measure of the depar ture of the r e a c t i n g system from an equi l ibr ium s t a t e . Consider a mixture conta in ing q chemical spec ies (K gaseous spec i e s and K + 1 t o q condensed spec i e s ) formed from m chemical elements. The f r e e energy func t ion a t cons tan t temperature and pressure of spec i e s i (assuming i d e a l behavior) can be expressed a s : n f i, gas = n i ( F ~ ~ ~ ~ ) i + l n P + l n ( y & ) n ; 1 i i s K (3-31) K - w h e r e n = E n , and n i s t he moles of spec ies i p resen t and is t h e t o t a l i moles p re sen t i n the r e a c t i n g mixture. Assuming the a c t i v i t y c o e f f i c i e n t of the pure condensed spec i e s i s one, the f r e e energy expressions f o r these become: 'i, condensed The t o t a l f r e e energy of the mixture i s obtained by summing (3-31) and (3-33) and i s : F(n) = i , condensed i=K+1 The mixture conta ins f ixed amounts of each of the m e lements , b ' and the f r e e energy equat ion is constrained j ' by mass conserva t ion equat ions of the form: The a r ep re sen t s the formula number g iv ing the amount of i j gram atoms of the j element i n s p e c i e s i . For example, f o r CH4, a i i s one f o r carbon, and four f o r hydrogen. j A t a given temperature and p re s su re i t is necessary t o determine the amount of each chemical spec i e s p re sen t n i' t h a t minimizes t he f r e e energy (3-34). This i s sub jec t t o the s p e c i f i c a t i o n of t he t o t a l amount, b of each element. j ' Following the method of White, e t . a l . (12) t he usual Lagrangian m u l t i p l i e r procedure of equat ing the p a r t i a l d e r i v a t i v e s w i th r e s p e c t t o the n ' s of t he augmented func t ion t o zero and i so lv ing gives a complicated s e t of equat ions wi th the amount of each s p e c i e s , n expressed i m p l i c i t l y , To o b t a i n a s impler , i' but an i t e r a t i v e s o l u t i o n , a quadra t i c approximation t o the f r e e energy func t ion is formed by a Tay lo r ' s s e r i e s expansion - - about a po in t y (y1,y2, . . .yK) , and a neighboring po in t n (nl ,n2,^.on ) . This is: K To minimize Q(<) s u b j e c t t o t h e mass b a l a n c e c o n s t r a i n t s , t h e augmented f u n c t i o n employing Lagrange m u l t i p l i e r s , n i s formed. j ' At t h i s p o i n t t h e u s u a l p rocedure would be t o s e t p a r t i a l d e r i v a t i v e s o f G(:) w i t h r e s p e c t t o t h e independent v a r i a b l e s (n1,n2, ..., n ) and t h e Lagrangian m u l t i p l i e r s o s . , ~ m ) 4 e q u a l t o z e r o and s o l v e s i m u l t a n e o u s l y t h e r e s u l t i n g s e t o f m + q e q u a t i o n s f o r t h e minimum of t h e c o n s t r a i n e d q u a d r a t i c approx imat ion . Then t h e procedure would be r e p e a t e d employing a convergence c r i t e r i a t o approach t h e p o i n t of minimum f r e e energy . However, i t i s more conven ien t t o use a d i f f e r e n t p rocedure which r e q u i r e s t h a t o n l y m + 1 + s e q u a t i o n s (where s is t h e t o t a l number of s o l i d o r condensed phases p r e s e n t ) b e s o l v e d s imul taneous ly r a t h e r t h a n m + K + s e q u a t i o n s , S ince a q u a d r a t i c approximat ion i s used, t h e l i n e a r e q u a t i o n s r e s u l t i n g from t a k i n g t h e p a r t i a l d e r i v a t i v e s w i t h r e s p e c t t o t h e n ' S can be so lved d i r e c t l y . Equat ing t h e p a r t i a l i d e r i v a t i v e s wi th r e s p e c t t o the n Is t o zero f o r i = 1 ,2 , ..., K i r e s u l t s i n t h e fol lowing s e t of equat ions . '1 - n = -f i , gas i , g a s (y) + ( ~ ) n + E ( n . a . )yi ; i = 1 9 2 , . . . , K Y j = l J l j (3-38) This g ives K e x p l i c i t equat ions f o r the moles of the gases - i n terms of t h e m + 1 unknowns, w ' s and n . Equation (3-38) j permi ts t h e e l imina t ion of n from t h e m a t e r i a l balance i equat ions (3-35). Note t h a t i n doing t h i s , equat ion (3-35) is i n terms of y I s , which a r e t he i n i t i a l guesses used t o i s t a r t t h e i t e r a t i o n . S u b s t i t u t i n g equat ion (3-38) i n t o equat ion (3-35) and de f in ing : Af te r some manipulat ions the fol lowing r e s u l t is obtained. where : and : Equation ( 3 - 4 0 ) r ep re sen t s m equat ions i n m f 1 unknowns, - the % and u, which apply t o gases only. An a d d i t i o n a l equat ion j i s ob ta ined by summing the K equat ions given by equat ion ( 3 - 3 8 ) . The a d d i t i o n a l s equat ions needed t o compute the amount of condensed phases present a r e obtained by equat ing the p a r t i a l d e r i v a t i v e of G( ; ) with r e spec t t o t he moles of the condensed s p e c i e s , ni, t o zero which gives: These equat ions , which a r e t o be solved s imultaneously, a r e given i n mat r ix form i n Table 3-2. When t h e mat r ix is so lved , va lues f o r t he moles of condensed spec i e s a r e obtained d i r e c t l y . Also t h e va lues n ' s and ; a r e obta ined . These va lues a r e 3 s u b s t i t u t e d i n equat ion ( 3 - 3 8 ) t o c a l c u l a t e the moles of t h e gas s p e c i e s , n . These ca l cu la t ed va lues , a f t e r appropr ia te i adjustment t o i n su re r ap id convergence, a r e used a s a s t a r t i n g va lue f o r t he next i t e r a t i o n . This process is repeated u n t i l the minimum f r e e energy is reached. Convergence Procedure: Normally i n the i t e r a t i v e procedure, t he amount of each s p e c i e s , n which is c a l c u l a t e d a t the i ' minimum of t he cons t r a ined quad ra t i c approximation, i s used a s t h e next e s t ima te . To in su re t h a t o s c i l l a t i o n s and over- c o r r e c t i o n s w i l l no t occur , t h e fol lowing convergence scheme, s i m i l a r t o t h a t of White (12), i s used, The va lues of t he moles of t h e gas s p e c i e s , i (new) ' f o r t he next i t e r a t i o n a r e ob ta ined us ing t h e fo l lowing express ion : - i (new) 'i(01d) + i where and 1 i s t h e parameter of t h e l i n e through n and y i i(o1d) ' S u b s t i t u t i n g equa t ion (3-45) i n t o (3-34) and t ak ing the d e r i v a t i v e wi th r e s p e c t t o 1 gives t h e fol lowing: where : and : The va lue of d ~ / d 1 must remain negat ive t o i n su re conver- gence t o t h e minimum f r e e energy. Sometimes i t becomes necessary t o meet t h i s requirement by reducing 1 t o a va lue l e s s than one. Once t h i s va lue i s found, equat ion (3-45) is used t o o b t a i n the numerical va lue of each y f o r the next i t e r a t i o n . i It t u r n s ou t t h a t a s t he minimum i s approached l a r g e changes i n 1 a r e necessary which causes t h e va lue of d ~ / d h t o become smal le r . This allows f o r a c o n t r o l l e d path of descent and convergence t o the minimum f r e e energy i s obtained. A t y p i c a l f r e e energy minimization s o l u t i o n g iv ing the composition of t he major components a s a func t ion of temperature a t atmospheric pressure is shown i n Figure 3-3. From t h i s s o l u t i o n t h e spec ies c o n t i n u i t y equat ion (3-30) can be solved f o r Ri , and, the energy absorp t ion by chemical r eac t ions K S 1 ( c H R ) can be ca l cu la t ed . i i i=l I n non-equilibrium flow, the form of the energy equat ion remains the same a s t h a t f o r equi l ibr ium flow. The d i f f e r e n c e i n t he two l i e s i n the manner i n which the energy absorp t ion by chemical r e a c t ion must be c a l c u l a t e d . Temperature, O F Figure 3-3. Equilibrium Composition of the Simulated Pyrolysis Products in Equilibrium with Solid Carbon (1:1 Ratio by weight of Phenolic Resin-Nylon Char). Non-Equilibrium Flow: The equat ions of change f o r non- - equi l ibr ium flow a r e t h e same a s those developed f o r equi l ibr ium flow. The eva lua t ion of t h e energy absorp t ion by chemical r e a c t i o n , however, i s dependent on t h e f i n i t e r e a c t i o n r a t e s of each r e a c t i o n occurr ing wi th in t h e char zone. Therefore, i n a d d i t i o n t o temperature and pressure , t h e r e a c t i o n r a t e , Ri, i s a l s o a func t ion of t h e mass f l u x and composition en te r ing t h e char l a y e r . This r e q u i r e s a knowledge of t h e s p e c i f i c r e a c t i o n s t ak ing p l ace wi th in t h e char and t h e assoc ia ted k i n e t i c da t a ; i . e . , frequency f a c t o r and a c t i v a t i o n energy. The fol lowing paragraphs w i l l p resent a method f o r determining t h e important r e a c t i o n s and t h e technique f o r us ing t h e k i n e t i c d a t a t o p r e d i c t t h e a c t u a l behavior w i th in t h e char zone. Reaction --- Rate and Rate Constant Equation: I n genera l , a chemical r e a c t i o n can be w r i t t e n i n t h e fol lowing form: For t h i s j - t h chemical r e a c t i o n , r and p a r e t h e stoichiome- i j i j t r i c c o e f f i c i e n t s of t h e r e a c t a n t s and products r e spec t ive ly f o r spec i e s A . There a r e a t o t a l of q chemical spec ies and m chemical i r e a c t i o n s i n t h e system. The r a t e of r e a c t i o n of t h e i - t h spec i e s , Ri, i s given by t h e fol lowing equat ion f o r t h e m chemical r eac t ions : where c i s t h e concen t r a t ion of component i and r ' and p ' i i j i j r ep re sen t t h e power on t h e concent ra t ions . It i s not necessary f o r t h e s e t o be equal t o r and p The forward and r eve r se i j i j ' r e a c t i o n r a t e cons tan ts a r e k and k This i s t h e equat ion f j r j f o r R . t h a t i s used i n t h e computer implemented numerical s o l u t i o n 1 of t h e t r a n s p o r t equat ions . Equation (3-51) i s a very convenient and genera l formulat ion f o r t h e r e a c t i o n r a t e of t h e j - t h spec ies i n m simultaneous chemical r eac t ions . The s t o i c h i o - met r ic c o e f f i c i e n t s and t h e powers on t h e concent ra t ions a r e each convenient ly represented a s a matr ix. I n a d d i t i o n t o t h e above, t h e r e a c t i o n r a t e cons t an t s a r e a l s o r equ i r ed . A genera l form f o r t h e r a t e cons tan t of t h e i , - th chemical r e a c t i o n i s : where A i s t he frequency f a c t o r and E t h e energy of a c t i - s j ' v a t ion . With these mathematical gene ra l i za t ions t h e a n a l y s i s i s resolved t o one of s e l e c t i n g t h e important chemical r e a c t i o n s t ak ing p l a c e i n t h e char zone along with p r e c i s e va lues of t h e r a t e cons t an t s . These equat ions and assoc ia ted r a t e cons t an t s can then be used i n equat ion (3-48) t o c a l c u l a t e t h e r eac t ion r a t e , Ri, which i s needed t o so lve t h e t r a n s p o r t equat ions. The non-equilibrium flow model i s an o rde r of magnitude more complex than t h e chemical equi l ibr ium computations. The l a t t e r c a s e involves t h e s o l u t i o n of a s e t of a lgeb ra i c equat ions with t h e energy and momentum equat ions. The former r equ i r e s t h e s o l u t i o n of a s e t of non- l inear , o rd inary d i f f e r e n t i a l equat ions ( spec i e s con t inu i ty equat ions) s imultaneously with t h e energy equat ion. There i s a l s o t h e a d d i t i o n a l d i f f i c u l t y of determining a l l of t h e important chemical r e a c t i o n s t h a t t ake p lace i n t h e system and t h e i n i t i a l composition of py ro lys i s products en t e r ing t h e char zone. For equi l ibr ium flow, only t h e elemental composition i s requi red . F i n a l l y , t h e r e i s t h e l abo r ious t a s k of c o l l e c t i n g and eva lua t ing r e a c t i o n k i n e t i c d a t a appearing i n t h e l i t e r a t u r e . Chemical Reactions i n t h e Char Layer: The genera l na tu re of t h e r e a c t i o n s occurr ing i n t h e char zone of a cha r r ing a b l a t o r has been q u a l i t a t i v e l y e s t ab l i shed (13) . Between 500°F and 3000°F, t h e primary r e a c t i o n s occurr ing a r e hydrocarbon cracking r e a c t i o n s of h igh molecular weight spec i e s t o lower molecular weight spec i e s (u l t ima te ly Hz , C02, CO, H20, e t c . ) . From 3000°F t o about 6000°F, f r e e r a d i c a l and recombination r e a c t i o n s t ake p l ace , wi th i o n i z a t i o n r e a c t i o n s beginning t o appear a t t he upper end of t h i s temperature region, This study i s concerned with t h e reac t ions occurring below 3000°F; i . e . , hydrocarbon cracking reac t ions , pr imar i ly . Free r a d i c a l , recombination and ion iza t ion reac t ions a r e not considered a s they do not take place. Fortunately, t h i s g r e a t l y s impl i f i e s t h e already complex system of r eac t ions t h a t could occur. Es tabl ish ing the f a c t t h a t r eac t ing flow i n t h e char zone can be accura te ly described i n the temperature range from 500" t o 3000°F es tab l i shes the b a s i s f o r extending t h e inves t iga t ion t o temperatures i n the 3000°F t o 6000°F range. Pike ( 1 4 ) , i n an e f f o r t t o condense the l a rge assortment of r eac t ion k i n e t i c da ta ava i l ab le i n the l i t e r a t u r e , has compiled a de ta i l ed l i s t i n g of reac t ions and the corresponding k i n e t i c da ta f o r the C-H-0-N system. I n a subsequent repor t (15) t h i s and o ther k i n e t i c da ta were analysed. The ca lcu la t ion of the isothermal conversion f o r each reac t ion poss ib le i n the char zone over a wide range of temperatures was included. This formed one method f o r determining the important r eac t ions taking place i n the char zone a s discussed below. Cr i t e r ion & Reaction Select ion: The r a t e of a chemical r eac t ion increases with temperature, For a p a r t i c u l a r r eac t ion , i f a s i g n i f i c a n t conversion of r eac tan t s t o products i s obtained with the char a t a uniform and speci f ied temperature, then it can be assumed t h a t the re may be a s ign i f i can t conversion when a temperature g rad ien t e x i s t s i n t h e char l a y e r with t h e f r o n t su r f ace a t t h i s spec i f i ed temperature. Thus, t h i s r e a c t i o n i s considered important . An example of t h i s behavior i s t h e r e a c t i o n i l l u s t r a t e d i n Figure 3-4 a s a p l o t of conversion versus tempera- t u r e . For another r e a c t i o n i f t h e r e i s no conversion i n t h e char a t a uniform higher temperature (3000°F), t h e r e w i l l be no eonversion when t h e r e i s a temperature g rad ien t i n t h e char . Therefore, t h i s r e a c t i o n can be omitted when t h e r e i s a tempera- t u r e g rad ien t i n t h e char with a f r o n t s u r f a c e temperature of 3000°F. However, t h e products formed by t h e r e a c t i o n may indeed be included a s important components sub jec t t o f u r t h e r r e a c t i o n s . This l o g i c forms t h e b a s i s of t h e i so thermal a n a l y s i s of r e a c t i o n k i n e t i c s d a t a i n t h e l i t e r a t u r e (15) . Although t h e r e a c t i o n s pos tu la ted t o t ake p l ace over a given temperature range (500°F t o 3000°F) could oecur , they a r e a l s o r e s t r i c t e d by t h e components i n i t i a l l y present i n t h e py ro lys i s gas stream. For example, t h e r e a e t i o n of butane and oxygen forming carbon d ioxide and water i s a l i k e l y candida te between 500°F and 3000°F; however, t h e absence of e i t h e r butane o r oxygen e l imina te s t h e r e a c t i o n from cons ide ra t ion , A considerable amount of cau t ion must be exerc ised t o make c e r t a i n t h a t t h e components a r e not formed a t some time w i t h i n t h e cha r , making t h e r e a c t i o n an important p a r t of t h e system. Composition of Pyrolys is Products: A s discussed above, t h e p y r o l y s i s product composition a t t h e back s u r f a c e of t h e char i s important i n reducing t h e t o t a l poss ib l e r e a c t i o n s l i k e l y t o occur w i th in a s p e c i f i e d temperature range. F i r s t a t tempts t o s tudy t h e non-equilibrium flow of p y r o l y s i s products through a porous char l a y e r r e l i e d on two sepa ra t e sources f o r es t imat ing t h e gas composition en te r ing the char a t t h e back sur face . The f i r s t method which served a s an o rde r of magnitude a n a l y s i s was t h e equi l ibr ium compositions ca l cu la t ed by t h e f r e e energy minimization method (10) . The second was ana lyses of t h e degrada t ion products of low dens i ty nylon-phenolic r e s i n compo- s i t e s by py ro lys i s gas chromatography (16,17) . Table 3-3 l i s t s t h e compositions obtained by each method. As noted, t h e u n a v a i l a b i l i t y of accu ra t e a n a l y t i c a l procedures and thermo- phys ica l d a t a f o r t h e high molecular weight p y r o l y s i s products ( i . e . , phenol, c r e s o l , to luene , e t c . ) l e f t a reg ion of d e f i n i t e unce r t a in ty . As a r e s u l t , t h e major components of t h e py ro lys i s products were i d e n t i f i e d a s methane, hydrogen, carbon d ioxide , carbon monoxide and n i t rogen by many (18,19) wi th unknown q u a n t i t i e s of water and high molecular weight r e s i d u e s completing t h e a n a l y s i s . Subsequent research by Sykes (20) confirmed t h e presence of phenol-based m a t e r i a l s a s primary c o n s t i t u e n t s i n t h e high molecuLar weight r e s idues . Table 3-4 r e p r e s e n t s a more p r e c i s e p y r o l y s i s gas composition obtained i n t h i s work. Very good Kr ae sc h (1 9) T ab le 3 -4 . P y ro ly si s P ro du ct s R es u lt in g Fr om t h e T he rm al D ec om po si ti on o f N yl on -P he no li c R es in C om po si te s In cl ud in g th e H ig h M ol ec ul ar W ei gh t S pe ci es . D im et hy lp he no l T ri m et hy lp he no l C ye lo pe nt an on e C ar bo n M on ox id e agreement was obtained by comparing t h e r epo r t ed experimental r e s u l t s wi th an o v e r a l l energy ba lance technique us ing h e a t s of formation and h e a t s of combustion d a t a f o r t h e v i r g i n p l a s t i c and t h e exper imenta l ly determined p y r o l y s i s product composition. Typical composition d a t a of t h e s imulated p y r o l y s i s products used i n t h i s r e sea rch a r e presented i n Table 4-3 of Chapter IV. The remaining p o r t i o n of t h i s chap te r s h a l l d i s cus s t h e p e r t i n e n t phys i ca l and thermodynamic p rope r ty r e l a t i o n s h i p s and t h e numerical techniques used t o o b t a i n a s o l u t i o n t o t h e equa t ions o f change. Phys ica l & Thermodynamic P r o p e r t i e s : I n any r e a l problem where t h e temperature g rad i en t v a r i e s over a wide range (>lOOO°K), changes i n t h e phys i ca l and thermodynamic p r o p e r t i e s a s a f u n c t i o n of temperature occur . For t h e multicomponent flow of a r e a c t i n g gas w i t h i n a porous cha r , composition change by chemical r e a c t i o n i s a l s o important . The equa t ions used i n t h i s r e sea rch f o r c a l c u l a t i n g t h e v a r i a t i o n s i n phys iea l and thermodynamic pro- p e r t i e s wi th temperature w i l l be d i scussed i n two p a r t s ; t h e gas phase p r o p e r t i e s and t h e char o r s o l i d phase p r o p e r t i e s . G a s Phase Phys ica l -- : The gas phase phys ica l and thermodynamic p r o p e r t i e s requi red f o r t h e s o l u t i o n of t h e equa- t i o n s s f change a r e t h e thermal conduc t iv i t y , v i s c o s i t y and h e a t c a p a c i t y , The phys i ca l p roper ty equa t ions a r e t hose presented by Sherwood and Reid (21) and t h e thermodynamic equat ions were ob ta ined from McBride, e t . a l . (22) . The thermal conductivi ty of a pure gas i s ca lcula ted using t h e equation shown below: For an i d e a l gas the heat capaci ty a t constant volume i s C - R P i and the c o l l i s i o n diameter, o, and c o l l i s i o n i n t e g r a l , "v ' a r e tabula ted f o r the individual gas components. The thermal conductivi ty of t h e gas mixture i s ca lcula ted as: The v i s c o s i t y of a pure gas i s given by a s imi la r equation: The v i s c o s i t y of the gas mixture i s ca lcula ted by an equation approximating the Chapman-Enskog Theory: where t h e parameter, qji , i s ca lcula ted by equation (3-57). j The thermodynamic proper t ies a r e ca lcula ted by empirical curve f i t t i n g equations (23). These equations a re : (1) For the heat capacity, ( 2 ) For the f r e e energy, and (3) For t h e enthalpy. The empir ica l cons t an t s f o r t h e above equat ions, along with t y p i c a l d a t a f o r t h e gas components s tudied i n t h i s research a r e presented i n Appendix C. Char Physical P rope r t i e s (Thermal Conductivity, Po ros i ty & - Permeabi l i ty) : The char po ros i ty and permeabil i ty va lues were assumed cons tant i n t h i s study. This assumption i s v a l i d when t h e temperature range i s r e s t r i c t e d t o va lues where l i t t l e carbon depos i t ion o r dep le t ion i s obtained. The po ros i ty va lue was assumed equal t o t h e average e f f e c t i v e po ros i ty of t h e m a t e r i a l s ; i . e . , char po ros i ty = 0.8 ( 3 ) , graph i t e po ros i ty = 0.5 (4) . The permeabil i ty va lues were average va lues obtained by a n a l y s i s of a v a r i e t y of experimental d a t a reported i n Appendix C , A Carmen-Kozeny p l o t of t h e d a t a was used t o es t imate t h e permeabi l i ty c o e f f i c i e n t s , % and $, which were needed i n t h e d i f f e r e n t i a l momentum equat ion (3-12). Char thermal conduet iv i ty va lues were obtained from exper i - mental d a t a shown i n Appendix C, The v a r i a t i o n with temperature was determined by a l i n e a r l e a s t squares f i t of t h e da ta . For t h e p a r t i c u l a r d a t a used, t h e experimental conduc t iv i t i e s were repor ted f o r an i n e r t gas (n i t rogen o r argon) wi th in t h e pores , These va lues a r e , t he re fo re , more r ep resen ta t ive of an e f f e c t i v e conduct iv i ty s i n c e t h e conduet iv i ty of t h e i n e r t gases i s approx- imately equal t o t h e pyrolys is gas conduct iv i ty . k c (experimental) Provisions a r e made i n t h e TEMPRE System f o r c a l c u l a t i n g t h e e f f e c t i v e conduct iv i ty when char c o n d u c t i v i t i e s a r e measured with t h e pores evacuated. I n t h i s i n s t ance equat ion (3-62) must be used, The use of t h e above phys ica l and thermodynamics property equat ions i n conjunct ion with t h e numerical i n t e g r a t i o n methods gives t h e v a r i a b l e p r o p e r t i e s so lu t ions t o t h e equat ions of change. Numerical Solu t ion of t h e Equations of Change P r i o r t o t h e s e l e c t i o n of a numerical method, t h e accuracy of t h e numerical s o l u t i o n des i red must be spec i f i ed . This determines t h e i n t e r v a l s i z e needed i n t h e a n a l y s i s which e f f e c t s t h e round-off e r r o r s assoc ia ted with t h e c a l c u l a t i o n of t h e so lu t ion . I f a r e l a t i v e l y small i n t e r v a l s i z e i s used, t h e round-off e r r o r s may be i n t o l e r a b l e . On t h e o the r hand, a very l a r g e i n t e r v a l s i z e could produce l a r g e t runca t ion e r r o r s which r e s u l t s i n a s o l u t i o n t h a t does not approach t h e t r u e so lu t ion . One technique used t o determine i f a s p e c i f i c i n t e r v a l s i z e i s a reasonable choice involves t h e computation of t h e so lu t ion f o r t h e p a r t i c u l a r i n t e r v a l s e l e c t e d , and i n t e r v a l s i z e s reduced by a f a c t o r of one h a l f of each preceeding value. Comparison of t h e s o l u t i o n s f o r each i n t e r v a l chosen should r evea l when t h e approximate s o l u t i o n approaches t h e t r u e so lu t ion o r when round-off e r r o r s make t h e ca l cu la t ed s o l u t i o n inva l id . I n genera l , increased accuracy r e q u i r e s inereased complexity i n ( o r o rde r o f ) t h e numerical method used. Therefore, t h e r e i s an optimum dec i s ion t o be made between t h e nearness of t h e approximate so lu t ion t o t h e r e a l s o l u t i o n and t h e computational time requi red t o ob ta in t h e so lu t ion . The b e s t approach i s obviously t h e one t h a t minimizes t runca t ion and round-off e r r o r s . Numerical Solu t ion of t h e D i f f e r e n t i a l Energy Equation: The energy equat ion descr ib ing t h e flow o f py ro lys i s gases through t h e char zone of a cha r r ing a b l a t o r i s a second o rde r , non- l inear d i f f e r e n t i a l equat ion with v a r i a b l e c o e f f i c i e n t s . I n o rde r t o ob ta in a s o l u t i o n t o t h i s equat ion, a numerical i n t e g r a t i o n technique must be used. This r e q u i r e s t h e equat ion t o be transformed i n t o a f i n i t e d i f f e r e n c e form which can be in t eg ra t ed s tepwise on a d i g i t a l computer, Of t h e var ious methods a v a i l a b l e , a l l r e q u i r e t h e s p e c i f i c a t i o n of t h e order and s t e p s i z e t o achieve t h e des i red s o l u t i o n . Two genera l types of numerical i n t e g r a t i o n schemes a r e commonly used; t h e s e l f - s t a r t i n g methods, ranging from t h e Euler equat ion t o t h e Runge- Kutta s e r i e s , and, t h e p red ic to r -co r rec to r methods which r e q u i r e t h e s p e c i f i c a t i o n o r c a l c u l a t i o n of s eve ra l i n i t i a l po in t s t o s t a r t t h e procedure. The number of po in t s i s propor t ional t o t h e o rde r of t h e p a r t i c u l a r equat ion used. Because of t h e accuracy and r e l a t i v e l y s t r a i g h t forward na tu re of t h e s e l f - s t a r t i n g methods, a fou r th o rde r Runge-Kutta formula was se l ec t ed . The genera l formulae, and t h e formulae a s they apply t o t h e d i f f e r e n t i a l energy equat ion a r e presented i n Table 3-5. 5 The t runca t ion e r r o r i s of t h e order O(h ) where h i s t h e s t e p s i z e (23) . The parameters A A2 , A3, and A i n equat ion (3-68) 4 correspond t o t h e Runge-Kutta cons tants generated by t h e numerical i n t e g r a t i o n of t h e energy equat ion. Therefore, i n t h e non-equilibrium flow a n a l y s i s , t h e s o l u t i o n of t h e energy and c o n t i n u i t y equat ions a r e ca l cu la t ed simul- taneously because of t h e interdependence of t h e temperature and t h e mole f l u x (composition). Numerical Solu t ion of t h e Species Continui ty Equation: I n t h e non-equilibrium flow a n a l y s i s , t h e spec ies con t inu i ty equat ion expressing t h e mole (or mass) f l u x of each species a s a func t ion of temperature must be solved simultaneously with t h e d i f f e r e n t i a l energy equation. Rewriting equat ion (3-30) i n terms of t h e mole f l u x , N of spec ies i gives: i' T ab le 3 -5 . F ou rt h O rd er R un ge -K ut ta Fo rm ul ae f o r S ol vi ng t h e D if fe re n ti al E ne rg y E qu at io n fo r Fl ow o f P y ro ly si s G as es T hr ou gh t h e C ha r Z on e. G en er al F or m ul ae h A4 = h f( \+ h, yM +h y; + p 3. Y; + A 3) where t h e temperature g rad ien t , d ~ / d z , i s ca l cu la t ed i n the energy equation so lu t ion . S u b s t i t u t i o n f o r R from equat ion i (3-51) r e s u l t s i n t h e f i n a l form of t h e equat ion used t o c a l - c u l a t e the spec ies mole f l u x , N i n t h e TEMPRE system. i' The s o l u t i o n of t h e K+1 f i r s t o rde r d i f f e r e n t i a l equat ions f o r t h e mole f l u x , N i s obtained by numerical i n t e g r a t i o n using i ' a f o u r t h order Runge-Kutta formula (23). where and M i s a l oca t ion wi th in t h e char l aye r . The interdependence of t h e energy and spec ies c o n t i n u i t y equat ions can be seen by not ing t h e presence of t h e A va lues i n t h e above equat ions (3-72). j These va lues a r e t h e Runge-Kutta parameters ca l cu la t ed f o r the energy equat ion s o l u t i o n a t t h e same p o s i t i o n wi th in t h e char . A one-to-one correspondence between t h e A and Bi va lues must j , j e x i s t t o ob ta in a non-equilibrium flow so lu t ion . To s t a r t t he i n t e g r a t i o n , t h e i n i t i a l composition, temperature and temperature g rad ien t a t t h e back su r face a r e used to c a l c u l a t e t h e f i r s t in te rmedia te temperature and Runge-Kutta parameter, . These A1 values a r e then used t o e s t ima te t h e mole f l u x of each species a t t h e same intermediate p o s i t i o n wi th in t h e char zone. The in termedia te f l u x va lues a r e then s u b s t i t u t e d i n t o t h e energy equat ion f o r t h e c a l c u l a t i o n of t h e next in te rmedia te temperature. This procedure i s continued u n t i l t h e four ( f o r a fou r th order a n a l y s i s ) cons tants assoc ia ted with each d i f f e r e n t i a l equat ion ( con t inu i ty and energy) a r e ca l cu la t ed . A t t h i s poin t t h e temperature and concent ra t ion a t a p o s i t i o n advanced one i n t e r v a l u n i t into t h e char are ca l cu la t ed using equat ions (3-66) and (3-70.). This technique i s repeated t o t h e second boundary of t h e problem. I f a n o n - i t e r a t i v e s e t of boundary condi t ions i s spec i f i ed ( i . e . , one boundary completely s p e c i f i e d ) , t h e s o l u t i o n t o t h e energy equat ion i s obtained i n one cyc le and t h e ca l cu la - t i o n of t h e pressure and hea t f l u x d i s t r i b u t i o n s can be s t a r t e d . I f , however, a two poin t boundary va lue problem i s being solved, a guessed va lue of t h e gradient must be used t o s t a r t t he s o l u t i o n . When t h e temperature a t t h e f r o n t su r face i s calculated, it must be compared with t h e spec i f i ed va lue . A ca lcu la t ed va lue which i s too high o r low requ i re s an adjustment of t h e i n i t i a l gradient and r e p e t i t i o n of t h e e n t i r e procedure. Therefore, i n a d d i t i o n t o t h e Runge-Kutta l o g i c , a convergence procedure t o approach t h e known f r o n t su r face temperature i~ a l s o requi red . Convergence Techniques f o r t h e I t e r a t i v e Runge-Kutta Analysis: The s p e c i f i c convergence scheme used i n t h e I t e r a t i v e TEMPRE System i s subdivided i n t o t h r e e main p a r t s . These include: (1) a gross c o r r e c t i o n procedure, ( 2 ) a f i n e c o r r e c t i o n procedure, and, ( 3 ) a l i m i t o r check procedure, Each method uses a s impl i f i ed formula which bases t h e cor rec ted adjustment on t h e r e l a t i v e overshoot o r undershoot of t h e f r o n t su r face temperature. Gross Correct ion Procedure: This method i s used when t h e abso lu te va lue of t h e d i f f e rence i n t h e ca l cu la t ed and t r u e f r o n t su r face temperature exceeds a spec i f i ed to l e rance l i m i t ( u sua l ly 2 5% of t h e spec i f i ed f r o n t su r face temperature) . When t h i s condit ion i s met, adjustment of t h e i n i t i a l s lope i s made using t h e following equation: L L = T I ( I + A [ t r u e ca lcula ted ';I 1) (3-73) new Oo ld T~ t r u e where h i s an adjus table parameter from 0 t o 1. Fine Correct ion Procedure: This method i s employed when - t he ca lcula ted f ron t surface temperature f a l l s between to le rance l i m i t s of 0.05 > 1 - T/T > 0.01 of the speci f ied value o r L when two complete cycles have been ca lcu la ted . I n t h i s case a more p rec i se adjustment i s used taking advantage of the pre- vious ca lcu la t ions t o rapid ly approach the speci f ied f r o n t tem- pe ra tu re and t o prevent o s c i l l a t i o n s around t h a t point . The s p e c i f i c equation used t o ad jus t t h e i n i t i a l gradient f o r the next i t e r a t i o n i s : I TA + - Lcalc. t h i s cycle new - T L ~ a l c . t h i s cycle 'calc. l a s t cycle I - l a s t cycle t h i s cycle ] (3-74) Very good convergence i s obtained with these simple equations over a range of f r o n t surface temperatures between 1500 - 3000°F Z and mass f l u x values between 0.00003 - 0 . 1 l b / f t -sec. Three i t e r a t i o n s a r e requi red t o o b t a i n a s o l u t i o n w i t h i n t h e s t a t e d t o l e r a n c e range. Limit o r Check Procedure: A l i m i t corresponding t o a --- 20% overshoot of t h e f r o n t su r f ace temperature i s used t o te rmina te t h e c a l c u l a t i o n s a t any poin t w i th in t h e cha r where t h i s cond i t i on i s v i o l a t e d . A reduct ion i n t h e i n i t i a l g rad ien t is made according t o equat ion (3-73.) and t h e procedure i s r e s t a r t e d . I n a d d i t i o n t o t h e above, s eve ra l checks a r e included i n t h e Runge-Kutta a n a l y s i s t o i n s u r e t h e c a l c u l a t e d and/or ad jus ted va lues of t h e g rad ien t remain non-negative and non- zero. The program l o g i c inc ludes an adjustment c a l c u l a t i o n s i m i l a r t o equat ion (3-73) which, on repeated v i o l a t i o n s , i n s t r u c t s t h e system t o p r i n t p e r t i n e n t information f o r diag- n o s i s of t h e problem. With t h e s e simple adjustment equa t ions , t h e i t e r a t i v e s o l u t i o n i s obtained very qu ick ly and wi th s u f f i - c i e n t accuracy t o i n s u r e a good approximation t o t h e r e a l so lu t ion . A comparison of t h e temperature p r o f i l e s obtained f o r t h e f rozen flow energy equat ion (3-29) a t va r ious i n t e r v a l s i z e s i s presented i n Table 3-6. Based on t h e presented r e s u l t s , a n i n t e r v a l s i z e of one hundred u n i t s (or 11400 t h s of an inch f o r a one-quarter t h i c k cha r ) was used. Ta bl e 3- 6. Co mp ar is on o f Va ri ou s Ru ng e- Ku tt a In cr em en t Si ze s fo r th e Fr oz en F lo w Va ri ab le P ro pe rt ie s Mo de l. Di me ns io nl es s Te mp er at ur e (O F) Ch ar D is ta nc e Ru ng e- Ku tt a In cr em en t Si ze s (A ) 50 0. 00 00 50 0. 00 00 50 0. 00 00 50 0. 00 00 63 1. 42 12 62 5. 62 82 62 5. 47 88 62 5. 42 02 82 4. 28 23 81 9. 55 01 81 9. 45 15 81 9. 39 08 11 06 .1 78 7 11 02 .8 11 1 11 02 .7 77 0 11 02 .7 14 1 14 94 ,5 63 6 14 92 .8 85 3 14 92 .8 26 0 14 92 .7 60 4 20 00 .o oo o 20 00 .0 00 0 20 00 .0 00 0 20 00 .0 00 0 Co nd it io ns : W = 0. 05 lb /f t - s e c L = 0. 02 08 ft E = 0. 8 Ga s Co mp os it io n: ( Mo le /M ol e Ga s) CO = 0. 24 5, C0 2 = 0. 04 6, N2 = 0. 07 3, CH 4 = 0. 57 0, C6 H6 = 0. 06 8 Numerical Solut ions of t h e Heat Flux and Momentum Equations The heat f l u x and momentum equations a r e solved a f t e r a v a l i d temperature p r o f i l e i s ca lcu la ted , Both hea t f l u x and pressure a r e uncoupled from the energy equation by considering the energy d issapat ion by PV work small i n comparison with o the r m ~ d e s of energy t r a n s f e r i n t h e system. The equations f o r t h e heat f l u x and pressure a r e f i r s t order d i f f e r e n t i a l equations with v a r i a b l e c o e f f i c i e n t s . A Simpson's Rule i n t e g r a t i o n technique i s used t o ob ta in so lu t ions f o r the i n t e g r a l terms i n these equations. The general fo r - mula f o r the Simpson's Rule ana lys i s i s (23): nh 5 where - f ( 4 ) represents the t runcat ion e r r o r . 9 0 I n terms of the hea t f l u x and pressure equations, the Simpson's Rule funct ions a r e : Once again the s t ep - s i ze i s an important parameter t h a t must be spec i f i ed . A s imi la r procedure a s t h a t described f o r the Runge-Kutta ana lys i s t o obta in the optimum value of t h e i n t e r v a l s i z e was used. This minimizes the e r r o r s and maximizes the accuracy of the approximate so lu t ion . A comparison of t h e so lu t ions f o r var ious s t e p s i z e s a s presented i n Table 3 - 7 . An i n t e r v a l s i z e of twenty s t eps was used i n t h i s ana lys i s . Calculat ion of the pressure p r o f i l e wi th in the char i s made from the f r o n t su r face where P = P t o the r e a r surface L pressure. Results a r e reported a s a pressure d i s t r i b u t i o n and a su r face heat f l u x which correspond t o the t o t a l heat t r ans fe r red within the char zone. Summary,of t h e Theoret ical Development of t h e Equations of Change f o r Flow i n t h e Char Zone ------ The equations of change (cont inui ty , momentum, and energy) T ab le 3 -7 . C om pa ri so n o f V ar io us S im ps on 's R ul e In cr em en t S iz es f o r th e Fr oz en Fl ow , V ar ia bl e P ro pe rt ie s M od el . D im en s i on le ss 2 P re ss ur e (l bl ft ) C ha r D is ta nc e Si m ps on 's R ul e In cr em en t S iz es 21 75 .5 92 1 21 75 .5 91 8 21 75 .5 91 3 21 75 .5 91 2 21 73 .4 14 7 21 73 .4 14 4 21 73 .4 13 9 21 73 .4 13 8 21 68 .7 37 3 21 68 .7 36 8 21 68 .7 36 4 21 73 .7 36 4 21 60 .0 00 0 21 60 .0 00 0 21 60 .0 00 0 21 60 .O OO O G as C om po si ti on : (M ol e/ ~o le Ga s) CO = 0. 24 5, C 02 = 0. 04 6, CH q = 0. 57 0, N2 = 0. 07 3, were developed f o r modeling t h e r e a c t i n g f low of p y r o l y s i s gases through t h e char zone of a cha r r ing a b l a t o r . The p a r t i c u l a r a p p l i c a t i o n t o f rozen , equi l ibr ium, and non-equi l ibr ium flow were d iscussed a long wi th methods f o r determining t h e hea t a b s o r p t i ~ n by chemical r e a c t i o n f o r t h e l a t t e r two models, A f r e e energy minimizat ion technique was employed f o r c a l c u l a t i n g t h e composition and hea t absorp t ion r e s u l t i n g from chemical r e a c t i o n s assumed t o occur a t equi l ibr ium. For t h e non-equilibrium flow, a d i scuss ion of t h e importance of t h e p a r t i c u l a r r e a c t i o n s considered i n t h e model, assoc ia ted k i n e t i c d a t a and i n i t i a l py ro lys i s gas composition en te r ing t h e char was presented . Typical boundary cond i t i ons were presented which led t o two s e p a r a t e s o l u t i o n s t o t h e d i f f e r e n t i a l energy equat ion. These were: (1) The i t e r a t i v e s o l u t i o n which r e s u l t e d by spec i fy ing t h e f r o n t and back su r f ace temperatures wi th t h e g rad ien t unknown at e i t h e r l o c a t i o n , and, ( 2 ) t h e n o n - i t e r a t i v e s o l u t i o n obtained by spec i fy ing t h e temperature and temperature g rad ien t (hea t of p y r o l y s i s ) a t t h e r e a r s u r f a c e of t h e char . A fou r th o rde r Runge-Kutta numerical i n t e g r a t i o n method was used t o achieve t h e so luqion a s a temperature d i s t r i b u t i o n ac ros s t h e char . S imi l a r ly , t h e momentum and hea t f l u x equat ions were in t eg ra t ed us ing Simpson's Rule. The s o l u t i o n s were presented as a pressure distribution across the char and a heat flux at the char front surface. A fourth order Runge-Kutta integration of the speciescontinuity equation, coupled with the energy equation, produced concentration gradients for each pyrolysis gas speciesas a function of the char distance. Specific values of the solutions will be presented and compared with experimental data obtained on the Char Zone Thermal Envir~nment Simulator in Chapter VI. A detailed presentation of the experimental apparatus and procedure follows in Chapters IV and V, respectively. REFERENCES 1. Peters, R. W. and K. L. Wadlin, "The Effect of Resin Composition and Fillers on the Performance of a Molded Charring Ablator," NASA TN D-2024, 9 (December 1963). 2. Weger, Eric, Jere Brew and Ronald Servais, "An Investiga- tion of Carbon Deposition in Chars - 11," Report SAMSO- TR-68-123, Washington University, St. Louis, Missouri, 96 pages (January 1968). 3. Wilson, R. Gale, "Thermophysical Properties of Six Charring Ablators from 140" to 700°K and Two Chars From 800" to 3000°K," NASA TN D-2991 (October 1965). 4. Clark, Ronald K., "Flow of Hydrocarbon Gases in Porous Media at Elevated Temperatures," M.S. Thesis, University of Virginia, 108 pages (August 1968). 5. Engelke, W. T., C. M. Pyron, Jr., and C. D. Pears, "Thermophysical Properties of a Low Density Phenolic- Nylon Ablation Material," NASA CR-809 (July 1967). 6. Nagler, R. G., "The Thermal Conduction Process in Carbo- naceous Chars," JPL Technical Report 32-1010, Jet Propul- sion Laboratory, California Institute of Technology, Pasadena, California (February 1967). 7 . Koh, J . C . Y . and E. P. d e l Casal, "Heat and Mass Flow Through Porous Matr ices f o r T ransp i r a t ion Cooling," Paper 16, Proceedings of t h e 1965 Beat Transfer and Fluid Mechanics I n s t i t u t e , Stanford Univers i ty P re s s , Los Angeles, C a l i f o r n i a , 263-81 (June 21-23, 1965). 8. Bi rd , R. B . , W. E. Stewart , and E. N , L igh t foo t , Transport Phenomena, John Wiley & Sons, Inc . , New York, 328-30 (1960). 9 . Scheidegger, Adrian E . , Physics of Flow Throuph Porous Media, Univers i ty of Toronto P res s , 68-76 (1960). - 10. d e l Val le , E. G . , R , W. Pike and G. C. Apr i l , "Transport Phenomena i n t h e Char Zone During Ablat ion. 11: Equil ibr ium Composition of Degradation Products of Ablation," Paper 13e, 63rd National Meeting of t h e A.I.Ch.E., S a l t Lake Ci ty , Utah (May 1967). 11. Zeleznik, F. J . and S. Gordon, "A General IBM 704 o r 7090 Computer Program f o r Computation of Chemical Equilibrium Composition, Rocket Performance, and Chapman-Jouguet Detonation," NASA TN D- 1454 (October 1962) . 12. White, W. B . , S. H. Johnson and G. B. Dantzig, "chemical Equil ibr ium i n Complex Mixtures ," Journa l of Chemical Phys ics , 28 (5) , 751-5 (May 1958). 13. Schmidt, D., "Thermal Parameters of Re-Entry Ablative Plastics," WADD Technical Report 60-90, Wright- Patterson AFB, Ohio, Aeronautical Systems Division (1960). 14. Pike, R. W., "Evaluation of the Literature for Chemical Reactions and the Reaction Rates for the Decomposition Products from Charring Ablators," NASA LWP-181, Langley Research Center, Hampton, Virginia (January 1966). 15. Pike, R. W., Gary C. April and E. G. del Valle, "Non- Equilibrium Flow and the Kinetics of Chemical Reactions in the Char Zone," NASA CR-66455 (July 1967). 16. Nelson, James B., "Determination of Kinetic Parameters of Six Ablation Polymers by Thermogravimetric Analysis," NASA TN D-3919 (April 1967). 17. Sykes, George F., Jr., "Decomposition Characteristics of a Char-Forming Phenolic Polymer Used for Ablative Composites," NASA TN D-3810 (February 1967). 18. Scala, S. M. and L. M. Gilbert, "Thermal Degradation of a Char-Forming Plastic During Hypersonic Flight," ARS Journal, 32 (6), 917-24 (June 1962). - 19. Kratsch, K. M., L. F. Hearne and H. R. McChesney, "Thermal Performance of Heat Shield Composites During Planetary Entry," AIAAINASA National Meeting, Palo Alto, California, 3 (September 30-October 1, 1963). 20. Sykes, G. F., Private Communication to R. W. Pike (March 14, 1968). 21. Reid, R. C. and Sherwood, T. K., T& Properties of Gases -- and Liquids, 2nd ed., McGraw-Hill Book Co., New York, - 395-519 (1966). 22, McSride, Bonnie J., Sheldon Heimel, J. G, Ehbens, Sanford Gordon, "Thermodynamic Properties to 6000°K for 210 Substances Involving the First Eighteen Elements," NASA SP-3001 (1963). 23. Abramowitz, Milton and I. A. Stegun, editors, Handbook of Mathematical Functions with Formulas, Graphs, and Mathema- tical Tables, 3rd Printing, National Bureau of Standards Applied Mathematics Series 55, Washington, D.C., 886, 896-7 (1965). 24. Freidman, H. L. , "Pyrolysis of Plastics in a High Vacuum Arc Image Furnace,'' Journal of Applied Polymer Science, 2, 1005 (1965). 25, Shulman, G. P . , and H . W. Lochte, "Thermal Degradation of P ~ l y m e r s . 11. Mass Spectrometr ic Thermal Analysis of Phenol-Formaldehyde Polycondensates," Journa l of Applied Polymer Science, 10, 619-635 (1966). 26 , Beecher, Norman, and Ronald E. Rosensweig, "Ablation Mechanisms i n P l a s t i c s with Inorganic Reinforcement," ARS Journa l , 2, 532-538 (1961). - , I V . CHAR ZONE THERMAL ENVIRONMENT S IMUUTOR - -- In t roduc t ion The experimental d a t a presented i n t h i s s tudy were obtained us ing an appara tus t h a t s imulated the flow of pyro- l y s i s gases through the char l aye r of a cha r r ing a b l a t o r dur ing r e e n t r y , Low d e n s i t y nylon-phenolic r e s i n cha r s , g raph i t e and carbon were obpained from the National Aeronautics and Space Admin i s t r a t i on ' s Entry S t ruc tu re s Branch a t the Laagley Research Center . These specimens were placed i n a meta l holder w i th the f r o n t su r f ace exposed t o a bank of i n f r a red quar tz lamps used t o s imula te t he high temperatures exper i - enced by a r e e n t e r i n g veh ic l e . Simulated py ro lys i s gases were passed through the char from the r e a r su r f ace t o the heated f r o n t su r f ace . The e x i t gases were sampled and analyzed f o r comparison wi th the i n l e t gas composition t o determine whether chemical r e a c t i o n s had occurred w i t h i n the char . These r e s u l t s were a l s o compared wi th the ca l cu la t ed e x i t gas compositions f o r f rozen , equi l ibr ium and non-equi l ibr ium flow cand i t i ons i n t h e TEMPRE system, This was t he method used t o determine t h e accuracy of the non-equi l ibr ium model f o r p r e d i c t i n g the hea t t r a n s f e r f o r t he flow of r e a c t i n g py ro lys i s products i n t h e char zone. A schematic diagram of the Char Zone Thermal Environment Simulator is shown i n Figure 4-1, For c o n v e n i e n c ~ , the system r - - - - - - - - - - - - - - - - - - - 0 0 - - - - C oo li ng W at er F ig ur e 4- 1. Sc he m at ic D ia gr am o f th e C ha r Z on e T he rm al E nv ir on m en t Si m ul at or has been divided i n t o f i v e sec t ions . These are: (1) The Char Holder (2) The Radiant Heating System (3) The Pyrolysis Gas Feed and Sampling System (4) The Analyt ical and Measuring Equipment (5) The Radioactive Tracer System Each of t h e above w i l l be discussed i n the following paragraphs. Char Holder -- The most important pa r t of the experimental apparatus i s the char holder . It was constructed t o permit t h e heat ing of one surface t o produce the temperature gradient experienced during reentry, an4 t o flow simulated pyrolys is gases through the char with c o l l e c t i o n of t h e e x i t gases f o r chemical analys is . Comparison of the e x i t gas composition with the i n l e t values determined whether chemical reac t ions occurred wi th in the char layer . Rapid cooling of t h e e x i t gases t o prevent f u r t h e r thermal decomposition was another important f ea tu re of the design. A sec t iona l diagram of t h e holder i s shown i n Figure 4-2. It was constructed of two s t e e l pipes arranged i n a concentr ic pa t t e rn . The outer sec t ion was s i x inches i n diameter ( O . D . ) and f i v e inches long. A f i v e and three-eighths inch diameter by one-eighths inch th ick quartz g lass cover p l a t e was attached t o the f r o n t surface by a f lange p l a t e and two asbestos gaskets . - Ga s E x it R ea r S ur fa c _ _ _ - - - - - - - a m ic M ou nt in g F ig ur e 4- 2. S ec ti on al D ia gr am o f th e C ha r H ol de r a n d A ss oc ia te d P ar ts . The qua r t z g l a s s p l a t e sea led the holder on t h a t f ace and was t r anspa ren t t o t h e r a d i a n t energy from the i n f r a r e d lamps. A r e a r p l a t e e i g h t inches square was welded t o t he o u t e r p ipe . There was a four inch diameter (O.D.) s l o t c u t i n t h e c e n t e r of t h i s f l ange f o r mounting t h e inner p ipe . I n s e r t i o n of the inner s e c t i o n sea led t h e holder a t t h e r e a r . The ou t s ide po r t ion of t h e l a r g e r p ipe was c o i l e d wi th one-quarter inch copper tub ing and covered wi th Thermon T-63 h igh temperature cement f o r maximum h e a t exchange. Water was used a s t he coo lan t , Also two one-quarter inch l i n e s were loca t ed a t t h e base of t he l a r g e r p ipe f o r the py ro lys i s gases t o flow from the annular t o the sampling system. The inner p ipe was four inches i n diameter (O.D. ) and four and th ree -qua r t e r s inches long. The f r o n t su r f ace was machined t o hold a two inch diameter char specimen which was cemented i n p lace wi th Mul l i t e No. 67-751 o r Sauereisan No. 29 cement. The r e a r su r f ace had a one qua r t e r inch machined l i p used t o s e a l t he inner and o u t e r s e c t i o n s of t he holder . A r ec t angu la r p l a t e was used t o hold the inner s e c t i o n f i rmly i n p lace . Two one-quarter inch l i n e s were loca ted i n t he r e a r f lange of t he inner p ipe s e c t i o n s f o r e n t r y of the s imulated py ro lys i s gas flow and back s u r f a c e temperature measurement. The char specimens were made from low d e n s i t y nylon-phe- n o l i c r e s i n composites which had been formed i n t he high vo l t age a r c image furnaces a t the Langley Research Center. They were about two and one-half inches i n diameter by one- q u a r t e r inch th i ck . These specimens were c u t t o g ive a c r o s s s e c t i o n a l a r e a of 0 .5 t o 1.5 square inches , and were mounted i n a two inch diameter mold us ing M u l l i t e o r Sauereisan cement. The cement was i n e r t and very s t a b l e a t t h e e leva ted temperatures experienced dur ing experimentat ion. In Figure 4-3 the va r ious s t e p s i n t he molding procedure a r e i l l u s t r a t e d , High d e n s i t y nylon-phenolic r e s i n composite cha r s , g raph i t e and carbon specimens were mounted i n t h e same manner, A l i s t of t h e var ious m a t e r i a l s used is shown i n Table 4-1. Radiant Heat i n g Sys tem The r a d i a n t hea t ing system was composed of s e v e r a l i n f r a r e d , qua r t z hea t ing elements (Figure 4-4) connected i n d e l t a on a t h r e e phase te rmina l block. A 220 v o l t (100 amp maximum c u r r e n t ) power source was used t o i l l umina te t he lamps. The quan t i t y , type and loca t ion of t h e elements from the specimen s u r f a c e a r e l i s t e d i n Table 4-2 f o r va r ious ranges of f r o n t s u r f a c e temperatures . The lamps were arranged i n two s taggered rows p a r a l l e l t o t h e specimen f r o n t su r f ace . The te rmina l blocks were cons t ruc ted of nylon and, a long wi th the meta l lamp t i p s , were cooled by fo rc ing d ry a i r ac ros s these a r e a s from a Le Roi, Model RX1, two s t a g e compressor. Ta bl e 4- 1. Id en ti fi ca ti on a n d Pr op er ti es o f th e Ch ar a n d Gr ap hi te S pe ci me ns T es te d in t he Ch ar Z on e Th er ma l En vi ro nm en t Si mu la to r. Re si n Ch ar Re si n Ch ar LR C- HP -G R( y) -2 5 LR C- LP -G R( y) -4 5 Ce nt er - NA SA ) . (2 ) H D = Hi gh D en si ty , L D = Lo w De ns it y, H P = Hi gh P or e, L P = Lo w Po re , GR = Gr ap hi te . (3 ) Th e n o ta ti on i n (x xx -x xx x) i s a dd it io na l LR C id en ti fi ca ti on ; e .g . C9 -S 10 2. (4 ) Th e n o ta ti on ( y) i s a c o de f or t he c a ta ly st (s ) u s e d in a pa rt ic ul ar t es t r u n ; T em pe ra tu re a t a S pe ci f i c V al ue . (2 ) 12 00 ~ 3/ C L la m ps o pe ra te d a t o n e a n d o n e h al f th e r a te d v o lt ag e. (3 ) T em pe ra tu re r a n ge i s a ls o a fu n ct io n o f th e a ir c o o la nt f lo w r a te . T he a bo ve v a lu es a r e fo r a n a ir f lo w r a te t h at m a in ta in ed th e la m p te rm in al s be lo w 4 00 °F . Type THW 600 v o l t copper w i re was used t o connect t he te rmina l leads t o t h e main power supply switch. Figure 4-5 shows a complete e l e c t r i c a l c i r c u i t diagram f o r t he r a d i a n t hea t ing system. A r e f l e c t o r cons t ruc ted of go ld-p la ted aluminum was mounted on the r e a r , s i d e s , top and bottom t o concent ra te t he r a d i a n t energy on the specimen, The r e a r , top , and bottom sec t ions were water cooled us ing three-e ighths inch copper tubing wi th a Thermon T-63 cement coa t ing f o r maximum hea t exchange. A one h a l f inch hole was loca ted i n t h e r e a r r e f l e c t o r f o r t he purpose of measuring the f r o n t s u r f a c e temperature wi th an o p t i c a l pyrometer. A complete s e c t i o n a l diagram of t he r a d i a n t hea t ing system i s shown i n Figure 4-6, Py ro lys i s Gas Feed and Sampling System The compositions of t he s imulated py ro lys i s gas used i n t he experiments a r e l i s t e d i n Table 4-3. Severa l of the s a r l i e r experimental runs repor ted were made wi th a s imulated py ro lys i s gas composed of methane, hydrogen, carbon monoxide, carbon d ioxide and n i t rogen (1 ,2 ) . La ter experiments included water and phenol i n a d d i t i o n t o t h e above mentioned gas s p e c i e s (3 ,4 ,5 ) . This l a s t mixture requi red the cons t ruc- t i o n of a two phase feed system ( l i q u i d water and phenol a t room temperature) wi th subsequent vapor i za t ion of the l i q u i d C ir cu it D ia gr am T er m in al B lo ck D ia gr am N ot e: L in d ic at es l am p A ,B ,C i n d ic at e v o lt ag e li n es F ig ur e 4- 5. E le ct ri ca l C ir cu it D ia gr am s o f th e R ad ia nt H ea ti ng S ys te m . R ef le ct o r B ac k- up PL at e G ol d- Pl at ed R ef le ct or P la te La m p S up po rt s w it h w it h 3/ 8" C op pe r T ub in g fo r (F ro nt S ur fa ce O nl y) A ir C oo la nt L in es W at er C oo li ng (I ns ul at ed w it h Th er m on T -6 3 ) F ig ur e 4- 6. S ec ti on al D ia gr am o f th e R ad ia nt H ea ti ng S ys te m . components p r i o r t o t h e i r e n t r y i n t o the char holder . The gaseous po r t ion of t h e py ro lys i s products were pre- mixed and s to red i n a two and one-half cubic f o o t gas c y l i n d e r a t a p re s su re of 250-500 ps ig . The gas was p re s su re fed through a one-quarter inch copper tube t o a ro tameter loca ted on the instrument board. The l i q u i d components were l ikewise p re s su re fed from i n d i v i d u a l l y c a l i b r a t e d feed v e s s e l s . The l i q u i d and gaseous streams en te red the inner s e c t i o n of t he char holder a t a junc t ion near t he back of the appara tus . The temperature of t he l i n e and t h e holder were maintained above the b o i l i n g po in t of t h e l i q u i d components. The py ro lys i s products flowed through the char and e x i t e d through the annular space. They then passed through an i c e water-cooled g a s - l i q u i d s e p a r a t o r where condensat ion of t he unreacted water and phenol, a s w e l l a s any l i q u i d products , were c o l l e c t e d and analyzed. The gaseous po r t ion continued t o a gas sampling manifold. This s e c t i o n was composed of a s e r i e s of one hundred cubic cent imeter pyrex sampling bombs mounted i n p a r a l l e l on the instrument board, A by-pass '' l i n e was used t o d i v e r t t h e e x i t gas flow around the sampling bombs, such t h a t t hese con ta ine r s could be removed dur ing a n experiment and rep laced wi th empty bombs. A wet t e s t meter was used t o measure t h e volumetr ic flow r a t e of t he e x i t gas s t ream. Figure 4-7 i s a photograph of the feed, e x i t gas and sampling s e c t i o n s of t he apparatus . The char holder and r a d i a n t hea t ing systems were t o t a l l y enclosed i n a f r a n s i t e ( s i d e s , top and bottom) and p l e x i g l a s s (doors) box which was connected t o t h e labora tory hood w i t h a four inch diameter f l e x i b l e pipe. Ana ly t i ca l Measuring Equipment Temperature: There were seve ra l l oca t ions i n t he system where temperature measurements were made dur ing an experiment. These are ind ica t ed i n Figure 4-1. I n a l l l oca t ions except t h e f r o n t char s u r f a c e , i ron-cons tan tan thermocouples were used. The f r o n t s u r f a c e char temperature was measured wi th a Leeds and Northrup Model 8891c Rayotube t o t a l r a d i a t i o n pyrometer. The pyrometer focused on a one-quarter inch diameter s e c t i o n of t he f r o n t char su r f ace a t a d i s t a n c e of t e n inches from t h e s i g h t i n g element. A one-half inch ho le was c u t i n the back s e c t i o n of the r e f l e c t o r p l a t e t o a l low focusing on the char s u r f a c e , A Leeds and Northrup Speedomax H recorder was used t o monitor the f r o n t su r f ace temperature. A Leede and Northrup Model 1549172 Galvonometer was used t o measure the temperature of t he o the r l oca t ions . The accuracy of t h e thermocouple measurements were checked t o + - 2%, and t h e o p t i c a l pyrometer t o + 1% a t a maximum temperature of 2500°F. Ca l ib ra t ion of t he temperature measuring equipment was made a t var ious i n t e r v a l s p r i o r t o experimental runs . Pressure : The p re s su re drop across t he char was measured w i t h a U-tube manometer. Water was used a s a manometer f l u i d and readings of + 0.05 inches (of water ) were ob ta inab le , Pressure gauges were loca t ed a t the top of t he l i q u i d feed v e s s e l s and i n t h e process feed l i n e t o make c e r t a i n the p re s su re g rad ien t was s u f f i c i e n t t o maintain flow from the v e s s e l s . Figure 4-1 i n d i c a t e s t he loca t ion of t he var ious pressure measuring devices used. Metering: The flow r a t e of the gaseous po r t ion of the py ro lys i s products was measured us ing one of two ro tameters . A Fischer -Por te r Model FP 112-21-6-10183 (2.55 scfm a i r ) rotameter tube was used f o r high flow condi t ions and a Schutte-Koernig Model SK 1/8-15-C-5 (0.5 scfm a i r ) rotameter tube was used i n low flow a p p l i c a t i o n s . C a l i b r a t i o n of these meters were made wi th a i r and helium flow us ing an American 0 .1 cubic foo t per hour wet t e s t meter . The rotameter va lues were readable t o + 2% of s c a l e . - Liquid flow was metered us ing c a l i b r a t e d twelve inches long by one q u a r t e r inch diameter (I.D.) Fischer -Por te r g l a s s c y l i n d e r s . These tubes were c a l i b r a t e d wi th water and were r eadab le t o + 1% of s c a l e . These v e s s e l s were r a t e d a t a 30 p s i g working p re s su re . A 0.1 cubic f o o t per hour wet t e s t meter was used t o measure the volumetr ic flow r a t e of t he gas po r t ion of the t o t a l product stream. This w a s done t o o b t a i n a m a t e r i a l ba lance on the system. Ma te r i a l balances f o r the experimental runs w e r e w i t h i n 95-102% un le s s otherwise ind ica t ed on the experimental d a t a shee t s i n Appendix D . Gas Analysis : The c o l l e c t e d e x i t gases from t h e char - l aye r were analyzed on a Packard Model 7800 gas chromatograph equipped wi th a Model 871 p ropor t iona l temperature c o n t r o l l e r and a Model 836 power supply, A Model 802 dual column oven w a s a l s o included i n t he chromatographic system. Figure 4-8 is a photograph of t h e a n a l y t i c a l equipment. Two columns were used t o determine the composition of t he sampled gases , A n ine f o o t by one qua r t e r inch diameter column packed wi th Hewletf-Packard BPL-20 a c t i v a t e d cha rcoa l was used t o determine hydrogen, carbon monoxide and methane compositions. A t y p i c a l scan of the var ious gas spec i e s is shown i n Figure 4-9, Approximately four teen minutes were r equ i r ed t o o b t a i n a complete scan. The second column was a s i x f o o t by one qua r t e r inch g l a s s column packed wi th Porapak S manufactured by Waters Assoc ia tes , Incorpora ted . This column sepa ra t ed methane, carbon d ioxide , e thy lene , ace ty lene and ethane. A t y p i c a l scan f o r t hese s p e c i e s is shown i n Figure 4-10. Approximately seventeen minutes were requi red t o complete t h i s a n a l y s i s . Duplicate and t r i p l i c a t e samples were used t o o b t a i n a n Da te : 12 -6 -6 8 Ac ti va te d Ch ar co al Ex pe ri me nt : XX VI Co nd Ct i on s 1. Ca rr ie r Ga s 3. Co lu mn T em pe ra tu re 28 0° F 4. De te ct or T em pe ra tu re 28 0° F 5. In le t Te mp er at ur e 6. Ou tl et T em pe ra tu re 27 0° F 7. Br id ge C ur re nt 8. Ch ar t Sp ee d Ti me D at e: 11 -2 3- 68 C on di ti on s 1. C ar ri er G as 2. C ar ri er G as F lo w 20 c c /m in 3. C ol um n T em pe ra tu re 15 0' F 4 . D et ec to r T em pe ra tu re 1 65 °F 5. In le t T em pe ra tu re 22 O 0F 6. O ut le t T em pe ra tu re 19 0° F 7. B ri dg e C ur re nt 8. C ha rt S pe ed average composition. Normalization of t he r e s u l t s from the two columns was made us ing methane gas a s a r e f e rence . A Honeywell E lec t ron ik 16 recorder was used t o record the peaks from t h e gas chromatographic system. The accuracy of t he gas chromatographic a n a l y s i s was r epo r t ed a s t he s tandard dev ia t ion a t a n ine ty - f ive per c e n t con£ idence l i m i t . Two d i f f e r e n t dev ia t ions a r e l i s t e d i n able 4-4. These a r e t he a n a l y t i c a l dev ia t ion which determines the accuracy of t h e gas chromatographic a n a l y s i s and the sampling p lus a n a l y t i c a l dev ia t ion which de f ines t he o v e r a l l accuracy of t he system. The c loseness of t he two dev ia t ions i n d i c a t e s the r ep roduceab i l i t y of the sampling procedure. Liquid Analysis : The separa ted l i q u i d phase from t h e e x i t stream was analysed f o r phenol conten t by a two-step t i t r a m e t r i c a n a l y s i s . This procedure, ou t l i ned i n ASTM B u l l e t i n D 2145 ( 6 ) , involved the r e a c t i o n of t he aqueous phenol s o l u t i o n wi th excess bromine t o form tribromophenol according t o the fol lowing r e a c t ion: 0"" Excess B The excess bromine was then mixed wi th potassium iodide forming f r e e iod ine . Ta bl e 4- 4. St an da rd D ev ia ti on o f th e Ga s Ch ro ma to gr ap hi c An al ys es . GA S CO MP ON EN T RA NG E OF C OM PO SI TI ON S ST AN DA RD D EV IA TI ON AT A 95 % AN AL YZ ED (M ol e %) Ca rb on M on ox id e Ca rb on D io xi de 0. 2 - 1. 1 0. 2 - 1. 5 Ov er al l An al ys is F ' m d excess KI 2KBr + I2 Br2 The f r e e iod ine was then t i t r a t e d wi th a s tandard sodium t h i o s u l f a t e s o l u t i o n t o a s t a r c h i n d i c a t o r end p o i n t . The amount of bromine s u b s t i t u t i o n t o the phenol r i n g determined the phenol concen t r a t ion i n s o l u t i o n . Any polymerized o r oxidized phenols were assumed t o be present i n small concent ra t ion and were accounted f o r a s equiva len t phenol. Resu l t s were accu ra t e t o + 0.7 per c e n t a t a 95% confidence l i m i t f o r a range of concent ra t ions from 2% t o 70%. Radioact ive Tracer Analyses I n a d d i t i o n t o t h e above a n a l y t i c a l procedures , r a d i o a c t i v e t r a c e r analyses of t h e e x i t stream were made t o determine: (1) t h e gas and/or l i q u i d products formed from t h e degrada t ion of a c e r t a i n carbon-14 labe led spec i e s i n the simulated py ro lys i s gas ( i . e . , methane and phenol) , and, (2) t he e x t e n t of carbon depos i t i on w i t h i n the porous char . These ana lyses determined the degree of thermal decomposition of methane and/or phenol t o carbon and lower molecular weight gases . A Packard Instrument Company Model 2002 l i q u i d s c i n t i l l a t i o n spectrometer wi th a Model 280A p rec i s ion ra temeter was used i n t he a n a l y s i s , A Model 325Tri-Carb combustion furnace was used t o combust t he separa ted gas components a s they e x i t e d the gas chromatographic column t o carbon dioxide and water . F a c i l i t i e s f o r counting carbon-14 ( l abe l ed CO combustion products) 2 and t r i t i u m ( labe led H obtained by reducing H 0 w i t h i r o n a t 2 2 e l eva t ed temperatures) were a v a i l a b l e i n t h i s system. The equipment is shown i n Figure 4-11. Rad ioac t iv i ty of t he Separated Gas Chromatographic E f f luen t Stream: The purpose of t h i s a n a l y s i s was t o determine which gas products were formed from the thermal degrada t ion of carbon-14 labe led methane and/or phenol contained i n a s imulated py ro lys i s gas s t ream. The a n a l y s i s involved the combustion of each sepa ra t ed gas component t o carbon d ioxide and water . Complete combustion was achieved by pass ing t h e gases over copper oxide p e l l e t s a t a con t ro l l ed temperature of 750°F. Water was removed by absorp t ion i n a s i x inch by one-quarter G3 inch diameter tube packed wi th Aquasorb . The dry carbon d ioxide was then bubbled through th ree cubic cent imeters of 1 molar hyamine hydroxide ( i n methanol) s o l u t i o n f o r absorp t ion and eventua l a n a l y s i s i n the l i q u i d s c i n t i l l a t i o n spec t rometer , A s t a t i c counting procedure was used f o r per iods of twenty minutes o r g r e a t e r . Comparison of the r a d i o a c t i v i t y of each c o l l e c t e d sample corresponding t o a gas chromatographic peak produced the des i r ed d a t a i d e n t i f y i n g which spec i e s were formed from the labe led py ro lys i s gas component. The r e l a t i v e @ Combustion Oven @ Rate Meter @ S c i n t i l l a t o r @ Sample Compartment @ Recorder F i g u r e 4-11. Photograph of t h e Liquid S c i n t i l l a t i o n Spec t romete r . Photo by J . R . Langley i n t e n s i t y of t h e r a d i o a c t i v e l e v e l of each sample gave a q u a l i t a t i v e i n d i c a t i o n of i t s concent ra t ion wi th r e spec t t o the t o t a l concen t r a t ion measured by the gas chromatographic a n a l y s i s , Figure 4-12 i s a t y p i c a l r a d i o a c t i v e a n a l y s i s p l o t of t he separa ted gas spec i e s . Rad ioac t iv i ty of Sol id Carbon and Liquid Products: It was a l s o important i n t h i s research t o determine the e x t e n t of carbon depos i t i on w i t h i n the char l a y e r . One method t o o b t a i n t h i s information involved the use of carbon-14 labe led methane and/or phenol which depos i ted r ad ioac t ive carbon w i t h i n the char a s a r e s u l t of thermal degradat ion of the simulated py ro lys i s products . Analysis of the char specimen f o r r a d i o a c t i v i t y determined the ex t en t of depos i t i on . Combustion of t he char specimen i n a muff le combustion f u r - nace wi th dry a i r a t 1400 - 1600°F produced carbon dioxide which was absorbed i n a one molar hyamine hydroxide ( i n a methano 1 ) s o l u t i o n . A diagram of the equipment is shown i n Figure 4-13. Sec t ion ing of t he char p r i o r t o combustion was used a s a means of determining depos i t i on a s a func t ion of char depth. This information was used t o l oca t e the p o s i t i o n (and thus temperature) where carbon depos i t i on became s i g n i f i c a n t . This a l s o ind ica t ed the p o s i t i o n where chemical r e a c t i o n s occur . A t y p i c a l p r o f i l e is shown i n Figure 4-14. Liquid product (or unreacted l i q u i d py ro lys i s companents) Ra di oa ct iv e An al ys is o f th e G C E ff lu en t St re am R e te mt io n T im e v s . No rm al iz ed Ra di oa ct iv it y a s (c pm 'c pm to ta l s c a n a pp ea r a s a Ga s Ch ro ma to gr ap hi c Sc an o f a n Ex it G as S am pl e (P or ap ak S C ol um n) i-' a 13 th e Ch ar S pe ci me ns f ro m th e Ch ar Z on e Th er ma l En vi ro nm en t Si mu la to r to W at er a n d Ca rb on D io xi de f or R ad io ac ti vi ty A na ly si s. c o m bu st io n Tu b ff le r Fu rn ac e Co mb us ti on B o a Ai r Ro t a m e t e r samples were a l s o analysed f o r r a d i o a c t i v i t y t o determine the ex t en t of chemical r e a c t i o n (conversion of t h e l abe l ed py ro lys i s component) w i t h i n the cha r . I n j e c t i o n of t he l i q u i d sample i n t o the i n l e t s i d e of t h e Tri-Carb combustion furnace, w i th water absorp t ion and CO c o l l e c t i o n f o r r a d i o a c t i v e monitor ing was 2 the technique used. In t h i s way the e f f e c t s of co lo r and water quenqhing were e l imina ted ( 7 ) . Accuracy of the Radioact ive Analyses: The accuracy of the l i q u i d s c i n t i l l a t i o n spectrometer is measured a s a s tandard dev ia t ion and i s approximately equal t o the square r o o t of t he number of counts above background a t a 68% confidence l i m i t . The percent e r r o r i s ca l cu la t ed a s t he s tandard dev ia t ion divided by the number of counts times one hundred, % e r r o r = (4-4) The percent e r r o r is thus reduced by inc reas ing the number of counts per sample. I n t h e case of t h i s r e sea rch where a l a r g e system d i l u t i o n was experienced, count ing times up t o 100 minutes were made t o i nc rease the counts , and thus reduced the e r r o r . The background count of the s c i n t i l l a t i o n f l u o r s o l u t i o n used i n t he r a d i o a c t i v e t r a c e r a n a l y s i s va r i ed between 15-20 cpm. The background count f o r each v i a l was c a l c u l a t e d a s the average of s i x r e p l i c a t e measurements f o r a per iod of 100 minutes each. The sma l l e s t counts above background were approximately 20 cpm counted f o r 100 minutes g iv ing 2000 counts . The percent e r r o r f o r t h i s ca se would be: 1 I2 % e r r o r = (L)IOO = N dx 100 = 2.2% 2000 which i s an unusual ly l a rge va lue . However, t hese l e v e l s were encountered only i n gas samples which had been c o l l e c t e d a f t e r being separa ted by gas chromatographic a n a l y s i s . For the purpose of i n d i c a t i n g which products were produced from c e r t a i n s imulated py ro lys i s products , the ca l cu la t ed e r r o r d id n o t s i g n i f i c a n t l y a f f e c t t he outcome of the a n a l y s i s . This is ind ica t ed i n Figure 4-12 i n which t h e measured r a d i o a c t i v i t y of each separa ted spec i e s i s p l o t t e d vs . r e t e n t i o n time. The do t t ed l i n e s i n d i c a t e t he s tandard dev ia t ion of t h e measured va lues . For t he case of s o l i d and l i q u i d samples, t he counts obtained per sample were always i n excess of 10,000 counts . The percent e r r o r a t 10,000 counts i s 1.0% and the s tandard d e v i a t i o n a t t he 68% confidence l i m i t is + - 100 counts . A more d e t a i l e d d i scuss ion of t he random e r r o r a s soc i a t ed wi th m a t e r i a l s undergoing r a d i o a c t i v e decay can be found i n the work of Wang and Willis (8). REFERENCES 1. Kratsch, K. M , , L. F, Hearne and H. R. McChesney, "Thermal Performance of Heat Shield Composites During Plane tary Entry," AIAA-NASA National Meeting, Palo Al to , C a l i f o r n i a , 3 (September 30-October 1, 1963). 2. Sca la , S, M. and L, M. G i l b e r t , "Thermal Degradation of Char-Forming P l a s t i c During Hypersonic F l igh t ,'I ARS Journa l , 32 ( 6 ) , 917-24 (June 1962). - 3. Ladacki, Michael, Jane t V. Hamilton aqd Samuel N . Cohz, "Heat of Py ro lys i s of Resin i n S i l ica-Phenol ic Ablator," AIAA Jou rna l , 4 ( l o ) , 1798 (October 1966). - 4. Nelson, James B . , "Determination of Kine t ic Parameters of S i x Ablat ion Polymers by Thermogravimetric Analysis ," NASA TN D-3919 (Apr i l 1967). 5. Sykes, George F. , J r . , frDecomposition C h a r a c t e r i s t i c s of a Char-Forming Phenolic Polymer Used f o r Abla t ive Composites," NASA TN D-3810 (February 1967). 6 9 American Socie ty f o r Test ing Mate r i a l s , "Phenol Content of Phenol-Water Mixtures," ASTM D 2145-632, P a r t 20, 978-80 (January 1967). 7 . Wang, C. H. and D. L. W i l l i s , Radiotracer Methodology Biologica l Science, P ren t i ce Ha l l , I n c . , Englewood C l i f f s , New Je r sey , 111-12 (1965). 8 . I b i d . , 186-206. V . OPERATING PROCEDURES FOR THE CHAR ZONE - THERMAL ENVIRONMENT S IMULATOR The procedure used f o r a l l experiments wi th the Char Zone Thermal Environment Simulator considered s a f e t y a s t he prime r e q u i s i t e , The recommendations f o r s a f e handl ing of hazardous m a t e r i a l s ou t l i ned i n Dangerous P rope r t i e s of I n d u s t r i a l Ma te r i a l s by N. I. Sax (1) and "Chemical Sa fe ty Data Sheets" by the Manufacturing Chemists' Assoc ia t ion (2 ,3 ,4) were used a s guides. Proper v e n t i l a t i o n of t he labora tory and va r ious s a f e t y devices inc luding exhaust hoods, eye wash bas in , s a f e t y shower, f i r e ex t ingu i she r and se l f -conta ined b rea th ing equipment were a v a i l a b l e and employed, The experimental procedure f o r t he ope ra t ion of the Char Zone Thermal Environment Simulator is d iv ided i n t o f i v e main po r t ions f o r convenience. These a r e : (1) Pre - s t a r tup phase (2) S t a r t u p phase ( 3 ) Experimental phase (4) Shutdown phase (5) Ana ly t i ca l phase These w i l l be d iscussed i n the fol lowing paragraphs. P r e - s t a r t u p Phase - The p r e - s t a r t u p phase involved a one hour check period of t he appara tus and a u x i l i a r y equipmept. During t h i s t ime t h e fol lowing i t e m s were checked: (1) I n s e r t i o n of t h e char ho lder s e c t i o n was made w i t h proper a l l ignment . (2) P re s su re and l eak t e s t i n g of a l l p rocess l i n e s , feed v e s s e l s and sampling con ta ine r s were made, (3 ) A l l r e co rde r s and o t h e r measuring devices were p rope r ly i n s t a l l e d and t e s t e d . (4) Coolant a i r and water l i n e s were checked f o r proper ope ra t ion and s u f f i c i e n t volumes. (5) Vent system and s a f e t y equipment were ope ra t i ve . Af t e r t he se items were s a t i s f a c t o r i l y checked, t h e second phase of the procedure was s t a r t e d . s t a r t u p Phase This phase of t h e procedure d e a l t wi th t h e f i n a l a d j u s t - ments t o t h e system p r i o r t o t h e experimental phase. During t h i s per iod t h e equipment was subjec ted t o f u l l power w i th on - l i ne checking o f t h e r eco rde r s and process supply l i n e s . The fol lowing items were checked during t h i s phase: (1) Helium (or Argon) gas a t t h e experimental flow r a t e l e v e l was s t a r t e d . ( 2 ) Temperature r eco rde r s and o the r measuring devices were turned on. (3) Water flow t o the r e f l e c t o r (and o u t e r char holder s e c t i o n when needed) was turned on. ( 4 ) A i r flow t o the te rmina l block coo l ing system was turned on. (5) Sample bombs were evacuated and i n s e r t e d i n t o the sampling manifold. (6) Hood ven t system was ad jus t ed t o p u l l d i r e c t l y from t h e apparatus hpod s e c t i o n wi th t o t a l exhaust through t h e vent s t a c k . ( 7 ) Heating lamps were turned on. A t t h i s p o i n t q f i n a l check was made t o make c e r t a i n t he pyrometer was focused on the char su r f ace and t h e temperature was record ing proper ly , Severa l on - l ine checks of t he pressure drop, te rmina l block temperatures and flow r a t e s were made t o make c e r t a i n t h a t opera t ion was normal. This phase of t he procedure continued u n t i l t he f r o n t and back su r f ace temperatures were cons t an t . A t t h i s p o i n t t he experimental phase s t a r t e d . Experimental Phase - The experimental phese began when s imulated py ro lys i s gas and l i q u i d spec i e s were s u b s t i t u t e d f o r t he helium (or Argon) flow i n t h e system. An a d d i t i o n a l check period was made f o r temperatures t o r e t u r n t o s teady s t a t e (about 5-7 minute$). Data were recorded and sampling of t he e x i t gases and l i q u i d s were made a t t h r e e t o f i v e minute i n t e r v a l s du r ing the run. The t o t a l time f o r a normal experimental run was from f i f t e e n t o twenty minutes i n length . Addi t iona l runs were made by changing condi t ions and al lowing s u f f i c i e n t time f o r t he system t o aga in reach s t eady s t a t e . During t h i s wa i t i ng per iod t h e e x i t gases were by- passed around the sampling manifold and t h e gas sampling con ta ine r s from t h e previous run were exchanged wi th empty bombs. This procedure was continued f o r a maximum of one hour and t h i r t y minutes t o t a l run time. This maximum was s e t t o decrease the p o s s i b i l i t y of s eve re damage t o t he h e a t i n g system and the char holder . Shutdown Phase The te rmina t ion of t h e experimental phase was made by fol lowing the ou t l i ned procedure l i s t e d below: ( I ) The p y r o l y s i s gas flow was stopped and helium ( o r argon) flow was begun, (2) The e x i t gas was by-passed around t h e sampling manifold, (3) The lamps were turned o f f . ( 4 ) A l l flows were l e f t on u n t i l a temperature of 200°F o r l e s s was a t t a i n e d by the char holder . (5) A l l r eco rde r s and o the r measuring devices were turned o f f . (6) A l l flows were stopped. ( 7 ) The hood system was placed i n t h e normal opera t ing cond i t i on wi th the apparatus hood i s o l a t e d from the system. (8) Equipment and recorder pens were cleaned and s to red f o r t he next experiment . (9) The char holder , lamps and r e f l e c t o r were inspected f o r damage a f t e r removing and l a b e l i n g the char specimens f o r char dens i ty a n a l y s i s . The e n t i r e experimental procedure r equ i r ed between th ree and four hours of p repa ra t ion and run time, excluding the a n a l y t i c a l phase of t h e opera t ion . This p a r t was done s e p a r a t e l y and u s u a l l y requi red a one t o two day period f o r a one hour experiment. Ana ly t i ca l Phase The a n a l y t i c a l procedures a r e subdivided i n t o four a r eas . These a r e the gas a n a l y s i s , the l i q u i d a n a l y s i s , the char a n a l y s i s and t h e r a d i o a c t i v e ana lyses . Each procedure w i l l be d iscussed s e p a r a t e l y i n t he fol lowing paragraphs. Gas Analyses: I n order t o o b t a i n accu ra t e ana lyses of t h e - gas c o l l e c t e d from the Char Zone Thermal Environment Simulator, t he gas chromatograph must be c a l i b r a t e d f o r the type and concen t r a t ion of each gas component contained i n the sample. Reagent grade gases (see Table 4 - 3 ) were used f o r t h i s purpose and c a l i b r a t i o n by the peak a rea technique was employed. C a l i b r a t i o n Procedure: The equipment used t o c a l i b r a t e the gas chromatograph is shown i n Figure 5-1. The method involved the in t roduc t ion of a pure gas sample i n t o the gas sampling va lve of t he chromatograph through va lve A wi th a l l o the r va lves c losed . Af t e r a s u f f i c i e n t flow of gas was noted e x i t i n g the system through t h e water "bubbler", va lve A was c losed and va lves B and C opened. A vacuum pump was used t o evacuate the system t o a s p e c i f i c p re s su re measured w i t h the manometer. A t t h a t po in t t h e manometer reading was recorded and the sample i n j e c t e d . The mole percent of t he pure gas i n the sampling loop was c a l c u l a t e d as : ' ~ a ~ o m e t e r - ' ~ a n o r n e t e r ) ~ ~ ~ Mole % = ( ' ~arometer A p l o t of t he peak a r e a a s a func t ion of t he mole percent pure gas i n j e c t e d i n t o t h e chromatograph gave the c a l i b r a t i o n curve d e s i r e d . An example c a l i b r a t i o n curve f o r methane is shown i n Figure 5-2. In o rde r t o cover the e n t i r e range of concent ra t ions obtained during the experimental program, i t was necessary , i n some cases , t o c a l i b r a t e f o r t he sample gas G as C hr om at og ra ph ic M an om et er c a li b ra ti o n F ig ur e 5- 1, E qu ip m en t U se d to C al ib ra te t h e G as C hr om at og ra ph ic S ys te m . Methane Calibration: Total Pressure 30.2 in Hg Outlet Temp. Detector Temp. 165OE Bridge Current 175 ma Carrier Gas Calibration Date: Mole % Methane Figure 5-2. Typical Calibration Curve for Methane on the Poropac S Column, component a t var ious chromatograph s e n s i t i v i t i e s . Once these curves had been prepared, however, it was a simple procedure t o c a l c u l a t e the composition of gas samples accu ra t e ly and quick ly . Determination of Reproduqib i l i ty : The gas ana lyses were r e g u l a r l y checked f o r r e p r o d u c i b i l i t y . One of two techniques were used. F i r s t , i n j e c t i o n of a pure gas used t o c a l i b r a t e t he instrument was made and the peak a r e a vs . concent ra t ion was compared wi th the c a l i b r a t i o n curve , Agreement w i t h i n the accuracy l i m i t a t i o n s of t he system c o n s t i t u t e d a reproducib le a n a l y s i s . Secondly, a s tandard sample, ( i . e . , one which contained a l l gas components a t o r near t he expected concent ra t ions i n t y p i c a l e x i t gas samples), was i n j e c t e d i n t o the chromatograph wi th comparison aga ins t t he a c t u a l composition of the mixture. Again, an a n a l y s i s w i t h i n the t o l e r a b l e l i m i t s c o n s t i t u t e d a reproducib le a n a l y s i s . Each of t he above methods were used f r equen t ly t o insure the proper and accu ra t e ope ra t ion of the instrument , Reca l i - b r a t i o n of the system was repea ted when e i t h e r of t he above t e s t s f a i l e d t o reproduce the s tandard ana lyses , Sampling Technique: In a d d i t i o n t o e r r o r s caused by changes i n t he system, q u i t e o f t e n changes i n sampling technique produced non-reproducible ana lyses . The p a r t i c u l a r chromatographic system was equipped t o minimize t h e e r r o r a s soc i a t ed with varying sample s i z e by using two one cubic cent imeter sampling loops. These loops where connected by a Ca r l e Sampling Valve, Model No. 2014, which a l t e r n a t e l y f i l l e d one loop wi th a gas sample whi le sweeping t h e o the r loop wi th c a r r i e r gas t o t h e d e t e c t o r of t h e gas chromatograph f o r a n a l y s i s . Gas samples were introduced i n t o t h e loops by fo rc ing mercury i n t o t h e con ta ine r s from t h e bottom, This compressed t h e gases i n t h e conta iner such t h a t flow i n t o t h e sampling va lve was obtained by opening t h e top stopcock. This method proved f a r supe r io r t o t h e gas bladder method of i n j e c t i o n wi th regard t o l eaks and ease of handl ing. The ope ra t ing procedure f o r t h e gas chromatograph i s s tandard information and r e fe rence i s made t o Figures 4-9 and 4-10 f o r t h e ope ra t ing cond i t i ons used i n t h i s research . Liquid Analysis: The method f o r determining phenol i n aqueous s o l u t i o n s i s repor ted i n ASTM B u l l e t i n D 2145 (59. A summary of t h a t procedure fo l lows . P repa ra t ion of Standard Solut ions: The fol lowing s tandard s o l u t i o n s a r e requi red i n t h e a n a l y s i s f o r phenol i n aqueous s o l u t i o n s . 1. Bromide-Bromate s o l u t i o n i s made by d i s so lv ing 10.2 grams of K B r and 2.8 grams of KBrO i n water wi th d i l u t i o n 3 t o one l i t e r . 2 . Hydrochloric ac id s o l u t i o n i s made by mixing an equal volume of concentrated HC1 ( sp . g r , 1.19) wi th water . 3 . Potassium Iodide s o l u t i o n is made by d i s s o l v i n g 150 grams of K I i n water wi th d i l u t i o n t o 1 l i t e r . 4 . Sodium Th iosu l f a t e s tandard s o l u t i o n is made by d i s s o l v i n g 25.0 grams of Na S 0 . 5H20 i n b o i l i n g water . 2 2 3 Add 0 . 1 gram of Na2C03 t o the cooled s o l u t i o n t o s t a b i l i z e and d i l u t e t o one l i t e r . S tandard ize a t f requent i n t e r v a l s t o i n su re a n accu ra t e normali ty . 5. S ta rch s o l u t i o n i s made by t i t r a t i n g 5 grams of so lub le s t a r c h and f i v e t o t e n mil l igrams of HgI wi th th ree 2 t o f i v e m i l l i l i t e r s of water . Add t h e suspension t o one l i t e r of b o i l i n g water and b o i l f o r f i v e t o t en minutes. Decant t he c l e a r supe rna t an t a f t e r cool ing . Ana ly t i ca l Procedure: The a n a l y t i c a l procedure f o r phenol de te rmina t ion fol lows: 1. Accurately weigh 0.5 - 0 .6 grams of the aqueous phenol s o l u t i o n i n t o a f i v e hundred m i l l i l i t e r volumeters f l a s k . (Take l a r g e r samples i f the concen t r a t ion i s l e s s than 85%). 2. Mark two 250 ml, iod ine f l a s k s a s "blank" and two a s samples. P ipe t 50 m l . of t he sample s o l u t i o n i n t o each f l a s k marked "blank", P ipe t 50 m l . of bromide-bromate s o l u t i o n i n t o each f l a s k . Measure 10 m l . of the H C 1 s o l u t i o n wi th a smal l graduate . Add t h e con ten t s t o one of t he f l a s k s a l l a t once and s topper quick ly s e a l i n g the top by pouring 5 m l s . of K I s o l u t i o n i n t o t he neck surrounding t h e g l a s s s toppe r . Swir l v igorous ly f o r t h i r t y seconds. Repeat f o r the remaining th ree f l a s k s . 3 . Allow each f l a s k t o s tand undisturbed f o r t en minutes. Cool i n an i c e ba th f o r one minute. Loosen the s topper and al low the f i r s t s o l u t i o n t o flow i n t o the f l a s k . Shake f o r t h i r t y seconds. Add K I i n t he peck, recool , a l low the second t o e n t e r t h e f l a s k and shake aga in f o r t h i r t y seconds. Repeat once more. (A brown co lo r i n t he vapor space of the f l a s k a f t e r each t rea tment i n d i c a t e s f r e e bromine. The a d d i t i o n of K I u n t i l t he bromine c o l o r is no longer v i s i b l e i n d i c a t e s succes s fu l r e a c t i o n w i t h KI.) 4. Rinse the s topper and f l a s k w a l l s wi th water . T i t r a t e t h e s o l u t i o n wi th Na S 0 When the co lo r changes 2 2 3' t o pa l e yellow, add f i v e m l . of s t a r c h s o l u t i o n . Continue t i t r a t i n g t o a c l e a r (from blue) end po in t . 5. The phenol concent ra t ion i n t h e o r i g i n a l sample is c a l c u l a t e d us ing t h e fol lowing equat ion: of Na S 0 so ln . . of Na S 0 so ln . Phenol (% wt . ) = e : i 1 d for2bfazks ] - 1"' 2 2 3 req 'd f o r samples C (Normality of Na2S203) x 1.569 grams of o r i g i n a l sample 3 (5-2) The s tandard dev ia t ion was ca l cu la t ed a s 0.7% at: a 95% confidence l i m i t over a phenol concen t r a t ion range of 2 - 70%. Char Analysis : In order t o analyze the char specimens - removed from t h e Char Zone Thermal Environment Simulator f o r r a d i o a c t i v i t y , combustion t o water and CO followed by 2 14 abso rp t ion of t h e labe led (C ) CO was r equ i r ed . To do t h i s , 2 a muff le r combustion furnace was used. Char specimens were placed i n t he combustion tube a t 1500°F and dry air was passed over t he carbon f o r 2 t o 3 hours . The e x i t gas was passed through a water absorber and then a C02 absorber f o r subsequent r a d i o a c t i v e monitor ing. In t h i s s tudy , the carbon depos i t i on a s a func t ion of char depth was des i r ed . To accomplish t h i s experimental ly , t h i n s l i c e s of t h e specimen were removed by l i g h t l y passing them over emery paper . The c o l l e c t e d "f ines" were placed i n t he combustion tube a f t e r record ing the weight l o s s of the o r i g i n a l cha r . This procedure was repea ted f o r up t o seven t o t e n s e c t i o n s wi th c o l l e c t i o n of t he CO (c14 labe led) e x i t 2 gas a f t e r combustion of each s e c t i o n . The samples were then prepared f o r r a d i o a c t i v e a n a l y s i s . Radioac t ive Analysis: A l l r a d i o a c t i v e analyses were made us ing gases combusted i n e i t h e r the Tri-Carb Furnace (gas chromatographic systems) o r t he muff le r combustion furnace (chars ) f o r h igher counting e f f i c i e n c i e s ( 6 ) . Samples were c o l l e c t e d i n 1 molar hyamine hydroxide ( i n methanol) s o l u t i o n wi th subsequent d i l u t i o n i n s tandard s c i n t i l l a t i o n f l u o r . The fol lowing procedures were used f o r each a n a l y s i s . Prepara t ion of the S c i n t i l l a t i o n Fluor: The concent ra ted l i q u i d s c i n t i l l a t i o n s o l u t i o n was made by d i s so lv ing 125 grams of 2,5-diphenyloxozole (PPO) and 2,5 grams of 1 , 4 - bis-2(4-methyl-5-Phenyloxozolyl)-benzene i n pure to luene d i l u t e d t o one l i t e r . Both compounds were obtained from the Packard Instrument Company. The s c i n t i l l a t i o n f l u o r used i n the r ad ioac t ive a n a l y s i s was made by adding 1 m l . of t he concentrated s o l u t i o n t o twenty-four m i l l i l i t e r s of to luene . Radioact ive Gas Analyses: The e f f l u e n t stream from t h e gas chromatograph was monitored f o r r a d i o a c t i v i t y t o a s c e r t a i n t he products and q u a n t i t i e s of m a t e r i a l s formed from the o r i g i n a l C14 l abe led spec i e s i n t he s imulated py ro lys i s gas . The e f f l u e n t gas was passed through t e s t tubes conta in ing about 3 cc of 1 molar hyamine hydroxide ( i n methanol) s o l u t i o n . A t 1 /2 and/or 1 minute i n t e r v a l s , t he t e s t tubes were changed, thus producing a d i s c r e t e sampling p a t t e r n of t he e f f l u e n t gas. This was continued f o r t he e n t i r e length of the gas chromatogram. The con ten t s of t he t e s t tube were emptied i n t o the s c i n t i l l a t i o n f l u o r s o l u t i o n f o r r a d i o a c t i v e counting. Comparison of the r a d i o a c t i v i t y i n each t e s t tube wi th the gas chromatogram, produced the necessary i d e n t i f i c a t i o n of t he components formed from r e a c t i o n s of t he labe led spec i e s i n the s imulated py ro lys i s gas . Repeated i n j e c t i o n of t he same gas sample was o f t e n done t o concen t r a t e t he r ad ioac t ive l e v e l i n the sepa ra t e t e s t tubes. Approximately t h i r t y minutes between i n j e c t i o n s were requi red t o reduce the r a d i o a c t i v i t y i n t he system t o a non-contamination l e v e l . Counting f o r 100 minutes was made t o decrease the e r r o r of t he a n a l y s i s . Radioact ive Liquid and Char Analyses: The l i q u i d and char r a d i o a c t i v e ana lyses were i d e n t i c a l t o t he gas ana lyses . The only except ions were: (1) t h e l i q u i d sample was i n j e c t e d by syr inge (1-1OW1) i n t o the gas chromatographic column ins t ead of e n t e r i n g through the sampling loop, (2) t he e n t i r e combusted e f f l u e n t s t ream from t h e l i q u i d and char combustions were c o l l e c t e d i n only one conta iner f o r r a d i o a c t i v e counting, (3) f o r t h e char samples, t he muff le r combustion furnace was used in s t ead of t he Tri-Carb furnace t o combust t he s o l i d carbon o r g raph i t e . Disposal of Radioact ive Samples: A l l samples conta in ing r a d i o a c t i v e carbon i n t h e gaseous s t a t e were disposed through the l abo ra to ry hood designed s p e c i f i c a l l y f o r t h a t purpose according t o Handbook 53 of the U.S. Department of Commerce and appraved by t he u n i v e r s i t y ' s h e a l t h p h y s i c i s t , Liquid samples and samples i n s c i n t i l l a t o r f l u o r were c o l l e c t e d i n a s p e c i a l con ta ine r f o r d i s p o s a l by the L,S.U. Nuclear Science Center. No s o l i d samples were r e t a i n e d i n t h a t s t a t e , A l l char specimens were combusted to CO and H20 with complete absorption of the labeled 2 carbon dioxide in 1 molar hyamine hydroxide (in methanol) soluti.on. REFERENCES 1. Sax, N. Irving, Dangerous Properties of Industrial Materials, 2nd. Ed., Reinhold Publishing Corp., New York (1963). 2. Manufacturing Chemists' Association, "Properties and Essential Information for Safe Handling and Use of Acetylene," SD-7, Washington, D. C. (1957). 3. Manufacturing Chemis~s' Association, "Properties and Essential Information for Safe Handling and Use of Phenol,'' SD-4, Washington, D, C. (1964). 4. Manufacturing Chemists' Association, "Properties and Essential Information for Safe Handling and Use of Cresol," SD-48, Washington, D. C. (1952). 5. American Society for Testing Materials, "Phenol Content of Phenol-Water Mixtures," ASTM D 2145-6311, Part 20, 978-80 (January 1967). V I . RESULTS OF THE NON-EQUILIBRIUM ANALYSIS 9 PYROLYSIS - GAS FLOW I N THE CHAR ZONE ------ In t roduc t ion The r e s u l t s of t h e non-equilibrium a n a l y s i s f o r py ro lys i s gas flow i n t h e char zone a r e presented i n t h i s chap te r . I n order t o ob ta in s o l u t i o n s t o t h e equat ions of change, t h e important chemical r e a c t i o n s occurr ing wi th in t h e cha r ; and, t h e p y r o l y s i s gas composition e n t e r i n g a t t h e back su r f ace must be s p e c i f i e d . The f i r s t p a r t of t h i s d i scuss ion i s , t h e r e f o r e , devoted t o t h e methods of s e l e c t i n g t h e c o r r e c t i n i t i a l compo- s i t i o n and important chemical r e a c t i o n s f o r non-equi l ibr ium flow. This i s followed by t h e s o l u t i o n s of t h e energy, momentum, hea t f l u x and spec i e s c o n t i n u i t y equat ions with comparisons t o t h e experimental d a t a obtained i n t h e Char Zone Thermal Enviorn- ment Simulator . Low d e n s i t y nylon-phenolic r e s i n cha r s formed under s imulated r e e n t r y condi t ions i n a r c j e t s a t t h e Langley Research Center were used i n t h i s phase of t h e r e sea rch . In t h i s way the accuracy of t h e non-equilibrium model f o r p r e d i c t i n g t h e r e a l behavior i s determined. Further comparisons wi th t h e two l i m i t i n g models of f rozen and equi l ibr ium flow a r e made t o determine t h e r e l a t i v e accuracy of each model i n p r e d i c t i n g t h e energy t r a n s f e r i n t h e char l a y e r . This i s followed by a d e t a i l e d parametr ic s tudy i n which the t h r e e flow models a r e compared over a wide range of mass f l u x , h e a t of py ro lys i s and f r o n t s u r f a c e temperature va lues . I n subsequent s e c t i o n s , t h e r e a c t i n g flow of t h e s imulated py ro lys i s gases through porous g r a p h i t e w i l l be compared wi th d a t a ob ta ined us ing cha r s formed from low d e n s i t y nylon- phenol ic r e s i n composites. The a b i l i t y of t h e non-equi l ibr ium f low model t o a c c u r a t e l y p r e d i c t t h e behavior i n each medium w i l l j u s t i f y t h e s tudy of carbon depos i t i on and py ro lys i s gas decomposition u s ing r a d i o a c t i v e t r a c e r technology wi th t h e more r e a d i l y a v a i l a b l e and workable s imulated cha r specimens. The e f f e c t of homogeneous and heterogeneous c a t a l y s t s on t h e chemical r e a c t i o n r a t e s and product d i s t r i b u t i o n s w i l l a l s o be determined and compared with t h e non -ca t a ly t i c d a t a . I n t h i s way t h e f e a s i b i l i t y of adding small q u a n t i t i e s of compounds t h a t c a t a l y t i c a l l y a f f e c t t h e h e a t abso rp t ion a t lower tempera- t u r e s can be determined, F i n a l l y , a s tudy of t h e e f f e c t of a i r i n j e c t i o n a t t h e f r o n t char s u r f a c e i s d iscussed . This work was aimed a t determining t h e e x t e n t of combustion of t h e porous media a t temperatures between 1500 - 2000°F. Non-Equilibrium Flow of Py ro lys i s Gases i n t h e Char Zone - -- The non-equi l ibr ium flow a n a l y s i s de sc r ibes t h e a c t u a l behavior w i t h i n t h e char zone i n which py ro lys i s gases and char r e a c t chemical ly a t f i n i t e r e a c t i o n r a t e s . I n o rde r t o a c c u r a t e l y p r e d i c t t h i s behavior , t h e p y r o l y s i s gas composition e n t e r i n g t h e cha r l a y e r and t h e important chemical r e a c t i o n s and c o r r e s - ponding r a t e d a t a must be a v a i l a b l e , The fo l lowing s e c t i o n s d i s c u s s t h e development of t h i s e s s e n t i a l in format ion , Py ro lys i s Products En te r ing t h e Char Zone: I n o r d e r t o s imu la t e a n a l y t i c a l l y and exper imenta l ly t h e char zone dur ing a b l a t i o n , a very accu ra t e d e s c r i p t i o n of t h e py ro lys i s p roducts r e s u l t i n g from t h e thermal degrada t ion o f low d e n s i t y , nylon- phenol ic r e s i n s must be known. Although t h i s has been t h e t o p i c o f a g r e a t dea l of r e sea rch (1 ,2 ,3 ,4 ,5 ) , t h e i n a b i l i t y t o d e t e r - mine t h e chemical composition of varying q u a n t i t i e s of l i q u i d r e s i d u e s prevented an accu ra t e d e s c r i p t i o n needed i n a non- equ i l i b r ium flow a n a l y s i s . The gas spec i e s (near room tempe- r a t u r e ) were i d e n t i f i e d , however, and t h e s e formed t h e b a s i s of e a r l y experimental and a n a l y t i c a l s t u d i e s of t h e cha r l a y e r phenomena (6,7,8,9,10) . Some t y p i c a l ana lyses a r e shown i n Table 6-1 f o r t h e s e s t u d i e s . Notable advances were made by Nelson (1 ) and Sykes (2 ,3) i n which a l a r g e p o r t i o n of t h e u n i d e n t i f i e d l i q u i d r e s i d u e was analysed. Their methods included p y r o l y s i s gas chromatography, d i f f e r e n t i a l thermal a n a l y s i s and thermogravimetric a n a l y s i s of nylon-phenol ic r e s i n , s i l i c o n e e las tomers , and composites of t h e s e polymers. Typical ana lyses a r e presented i n Table 6-2. (P he no li c Re si n On ly ) Di me th yl ph en ol Tr im et hy lp he no l Cy cl op en ta no ne Ca rb on M on ox id e Ca rb on D io xi de The i d e n t i f i c a t i o n of t h e s e prev ious ly unknown s p e c i e s ( i . e . , phenol, c r e s o l , xylene, e t c , ) was va luab le information i n t h e formula t ion of an accu ra t e non-equi l ibr ium flow a n a l y s i s f o r flow i n t h e char zone. I n t h i s r e sea rch , t h e ana lyses of Sykes (2) were used wi th one modi f ica t ion . The i d e n t i f i e d c y c l i c compounds, e , g . c r e s o l , xylene, which were 3% by weight of t h e t o t a l , were considered t o be phenol. This was done t o reduce t h e experimental d i f f i c u l t i e s encountered wi th t h e meter ing of l i q u i d phases i n t h e Char Zone Thermal Environment Simulator , and, t o keep t h e t o t a l number of s p e c i e s i n t h e system t o a smal l , bu t r ep re - s e n t a t i v e s i z e . I n so doing, t h e composition was ad jus ted t o t h e va lues l i s t e d i n Table 6-3. To determine whether t h i s simulated gas represen ted t h e a c t u a l pyso lys i s products a t t h e back su r f ace , an energy ba lance was made us ing experimental h e a t s of p y r o l y s i s (1 ,2 ) and com- bus t ion (10) d a t a f o r t h e v i r g i n p l a s t i c m a t e r i a l s , and t h e h e a t s of formation of t h e simulated gas s p e c i e s (12) . The r e s u l t s , presented i n Table 6-4 and d iscussed i n d e t a i l i n Appendix G, i n d i c a t e t h e r e l i a b i l i t y of t h e s imula t ion . A c a l c u l a t e d va lue of t h e h e a t of py ro lys i s of 213 B T U / P ~ was w i th in t h e experminetal accuracy s f t h e r epo r t ed va lue (200 + - 20 B T U / ~ ~ ) a s shown i n Table 6-4. The va r ious s imulated p y r o l y s i s product compositions used i n t h e experimental s t u d i e s Di me th yl ph en ol Ca rb on D io xi de Ca rb on M on ox id e T ab le 6 -4 . C om pa ri so n o f th e E xp er im en ta l H ea t o f P y ro ly si s w it h C al cu la te d V al ue s B as ed o n H ea ts o f F or m at io n o f th e R ep or te d P y ro ly si s G as C om po ne nt s, (3 ). A ve ra ge W ei gh t C ar bo n R es i d ~ e R ea ct an ts A H (C al cu la te d) = 21 3 B T U /lb a r e summarized i n Table 6-5. Important Chemical Reactions: The b a s i s f o r s e l e c t i n g o r omi t t i ng chemical r e a c t i o n s i n t h e non-equi l ibr ium flow model i s t h e i so thermal a n a l y s i s d i scussed i n Chapter P I 1 and developed i n Appendix F. For t h e p y r o l y s i s products l i s t e d i n Table 6-5 over a temperature range of 500 - 3000°F., t h e r e a c t i o n s and corresponding k i n e t i c d a t a desc r ib ing t h e non- equi l ib r ium flow i n t h e cha r zone a r e presen ted i n Table 6-6. The numbers under l ined i n t h e r e f e r ence column r ep re sen t t h e more r e l i a b l e sources of information wi th s p e c i f i c a p p l i c a t i o n t o t h i s r e sea rch . The c o n t r i b u t i o n and importance of each r e a c t i o n i s d i scussed i n t h e fo l lowing paragraphs: (1 ) Light Hydrocarbon Cracking Reactions; The f i r s t o rde r thermal decomposition of methane, e thane , e thy l ene and ace ty l ene represen ted i n r e a c t i o n s 6-1 through 6-4 i n Table 6-6 i s a very important and necessary s e t of r e a c t i o n s i f non-equi l ibr ium f low i s t o be accu ra t e ly desc r ibed , Although methane i s t h e only major l i g h t hydrocarbon i n t h e py ro lys i s product s t ream e n t e r i n g t h e cha r , r e a c t i o n s of e thane , e thy l ene , and ace ty l ene must be included t o account f o r t h e i r formation and subsequent r eac - t i o n w i t h i n t h e cha r . This was observed exper imenta l ly i n t h e Char Zone Thermal Environment Simulator i n which small q u a n t i t i e s (0 .1 - 1.5 mole %) of e thy l ene and ace ty l ene were i d e n t i f i e d i n t h e e x i t gas s t ream. No n o t i c e a b l e q u a n t i t i e s ( < 0 . 1 mole %) Ta bl e 6- 5, Si mu la te d Py ro ly si s Ga s Mi xt ur es U se d in E xp er im en ts o n th e Ch ar Z on e Th er ma l En vi ro nm en t Si mu la to r. Ca rb on M on ox id e Ca rb on D io xi de In de x o f Ex pe ri me nt s XI II -X VI II XI X- XX XI I of ethane were found even a t r e l a t i v e l y h igh methane conversion. The r e a c t i o n of carbon wi th hydrogen ( r e a c t i o n 6-5) forming methane was a l s o important over t h e tempreature range from 500°F t o 3000°F. ( a ) Methane Decomposition: The r e a c t i o n r a t e cons tan t f o r t h e thermal decomposition of methane t o ethane and hydrogen was based on t h e repor ted r e sea rch of Palmer and H i r t (13) and Kozlov and Knorre (14) . The a c t i v a t i o n energy 14 -1 of 95 Kcal/mole and t h e frequency f a c t o r of 7.6 x 10 sec used i n thk non-equilibrium flow model agreed c l o s e l y with t h e va lues r epo r t ed by Kozlov and Knorre (14) who c o r r e l a t e d t h e r e s u l t s o f s e v e r a l i n v e s t i g a t o r s . Their va lues were - 1 91 ~ c a l / m o l e and 4.5 x 10-13 sec . The range of a c t i v a t i o n energ ies i n t h e l i t e r a t u r e va r i ed from a low va lue of 73 Kcal l mole t o 103 Kcal/mole (15, 16, 17, 18, 19 ) . Values between 15 -1 4 .5 x 1013 and 1.0 x 10 sec were a l s o repor ted f o r t h e frequency f a c t o r , (b) Decomposition of Ethane: The ethane formed by r e a c t i o n (6-1) r e a c t s completely forming e thylene a s observed by i t s t o t a l absence i n t h e e x i t stream from t h e Char Zone Thermal Environment Simulator. This i nd ica t ed a somewhat f a s t e r r e a c t i o n r a t e than t h a t f o r t h e decomposition of methane and requi red t h e combination of a low a c t i v a t i o n energy and/or a high frequency f a c t o r . S t eac i e and Shane (27) and Kozlov and Knorre (14) repor ted va lues of 69 Kcal/mole and 1 x 10 14 - 1 sec f o r t he a c t i v a t i o n energy and frequency f a c t o r , respec- t i v e l y . The va lues used i n t h e non-equilibrium flow a n a l y s i s 13 were 70 Kcal/mole and 3 .1 x 10 sec - I and a r e i n good agreement wi th t h e l i t e r a t u r e d a t a , The range of a c t i v a t i o n energ ies and frequency f a c t o r s repor ted (14,20,27) were 64-78 Kcal/rnole and 10 14 - 1 1 3 * 5 - 1 ~ sec . ( c ) Decomposition of Ethylene: The thermal degrada t ion of e thy lene t o ace ty lene and hydrogen i s given by r e a c t i o n 8 - 1 (6-3). Values of 40 Kcal/mole and 2.6 x 10 sec were used i n t h e non-equi l ibr ium flow model a s t h e a c t i v a t i o n energy and frequency f a c t o r . These were t h e va lues repor ted by Kozlov and Knorre (14) who c o r r e l a t e d d a t a from seve ra l sources. Ethylene i n small concent ra t ions were observed i n t h e e x i t porduct s t ream from t h e Char Zone Thermal Environment Simulator . (d) Acetylene Decomposition: Like e thylene , ace ty l ene was i d e n t i f i e d i n small concent ra t ions (but t o a l a r g e r ex t en t than e thylene) i n t h e e x i t product stream. The r e a c t i o n r a t e should b e comparable t o t h e r a t e f o r e thylene r e a c t i o n o r perhaps s l i g h t l y f a s t e r due t o formation of ace ty l ene by benzene decom- p o s i t i o n ( r e a c t i o n 6-7) . An a c t i v a t i o n energy of 10 Kcal/mole 10 - 1 - 1 and a frequency f a c t o r of 5 .1 x 10 sec mole cm3 were used i n t h e second order r a t e equat ion i n t h e TEMPRE System. The range i n t h e energy of a c t i v a t i o n repor ted i n t h e l i t e r a t u r e va r i ed from 7 - 50 Kcal/mole (14,22,28,29). A frequency f a c t o r 10 - 1 3 of 5 .1 x 10 sec mole'' cm was repor ted by Happel and Kramer (28) . Reaction (6-4) i s t h e only major r e a c t i o n of ace ty l ene of importance i n t h i s system, due t o t h e absence o f t h e ace ty l ene polymerizat ion products , benzene, d i ace ty l ene and t r i a c e t y l e n e , i n t h e e x i t stream. ( e ) Methane Formation from t h e Reaction of Hydrogen and Carbon: I n a d d i t i o n t o t he above r e a c t i o n s involv ing t h e - l i g h t hydrocarbon products , r e a c t i o n (6-5) i n Table 6-6 i s a l s o important . Breisacher and Marx (30) and Corney and Thomas (31) observed an i n f l e c t i o n poin t i n t h e r a t e of methane product ion when hydrogen was passed over g raph i t e . This i n f l e c t i o n occurred near 1200 - 1300°F and r e s u l t e d i n a reduct ion i n t h e a c t i v a t i o n energy from 70 t o 12 ~ c a l / m o l e . The o rde r of t h e r e a c t i o n va r i ed between zero and one h a l f a s t h e temperature increased t o 2000°F. The r e a c t i o n k i n e t i c s d a t a f o r hydrogen atoms wi th carbon f i lms by King and Wise (32) i n d i c a t e a zero th o rde r r e a c t i o n and an a c t i v a t i o n energy of 7-9 ~ c a l / m o l e a t 440°F. A value of 17 ~ c a l / m o l e f o r t h e 9 a c t i v a t i o n energy and a frequency f a c t o r of 2 x 10 gm mole/ cm3-sec f o r t h e zero th o rde r r e a c t i o n were used i n t h e non- equi l ibr ium flow model. The va lue of t h e frequency f a c t o r was est imated from t h e k i n e t i c theory (57 ) s i n c e none was repor ted i n t h e l i t e r a t u r e . ( 2 ) React ions of Aromatic Hydrocarbons: The presence of aromatie hydrocarbons i n t h e py ro lys i s products i s a r e s u l t of t h e b a s i c phenolic r e s i n s t r u c t u r e of t h e v i r g i n p l a s t i c hea t s h i e l d . Sykes (2) repor ted such aromatic compounds a s benzene, to luene , xy lene , c r e s o l and phenol i n varying q u a n t i t i e s when phenolic r e s i n underwent thermal decomposition. Of these , phenol and t h e phenol-based ma te r i a l s form t h e major po r t ion of t h e aromatic compounds wi th benzene and to luene c o ~ t r i b u t i n g l e s s than 1 mole percent t o t h e t o t a l py ro lys i s gas composition. In o r d e r t o account f o r t h e chemical i n t e r a c t i o n of t hese compounds, two r e a c t i o n s a r e included i n t h e non-equilibrium flow a n a l y s i s . These a r e t h e phenol hydrogenation r e a c t i o n (676) and t h e benzene decomposition r e a c t i o n (6-7) . The absence of benzene i n t h e e x i t product stream from t h e Char Z ~ n e Thermal Environment Simulator makes t h e important products formed by t h e s e r e a c t i o n s water , hydrogen and carbon; t h e l a t t e r two r e s u l t i n g from ace ty lene decomposition by r e a c t i o n (6-4). ( a ) Phenol Hydrogenation: The c a t a l y t i c and non- c a t a l y t i c hydrogenation of phenol has been s tudied ex tens ive ly a s e a r l y a s t h e 1920's by many i n v e s t i g a t o r s (50,51,52,53,54) . However, no k i n e t i c d a t a has been repor ted f o r t h i s da t a . The products o f low p res su re , gas phase hydrogenation (50) a r e benzene and cyclohexanol i n varying q u a n t i t i e s . Liquid phase hydrogenation a t high pressures produce cyclohexanol and i n some cases cyclohexanone (50,51,52) . The y i e l d of cyclohexanol i s enhanced when a Raney Nickel c a t a l y s t i s used i n t h e l i q u i d o r vapor phase hydrogenat ion, I n o rde r t o determine t h e a c t i v a t i o n energy f o r t h i s r e a c t i o n , a comparison with t h e h e a t s of hydrogenation (49) f o r compounds r e l a t e d t o phenol were examined. These included e t h y l benzene (48.9 Kcal/mole), o-xylene (47.3 ~ c a l / m o l e ) , mesi tylene (47.6 Kcal/mole) and hydrindol (45.8 Kcal/mole). The a c t i v a t i o n energy used i n t h e non-equilibrium flow a n a l y s i s was 45 Kcal/mole which agreed with t h e va lues repor ted i n t h e l i t e r a t u r e f o r s i m i l a r compounds, The frequency f a c t o r was ca l cu la t ed from 3 t h e k i n e t i c theory (55) t o be 2 x 1013 cm /mole sec . (b) Benzene Decomposition: The decomposition of benzene t o ace ty l ene ,d i ace ty l ene , hydrogen and biphenyl a t 2000 - 2400°F was repor ted by Slysh and Kinney (34) t o be f i r s t o rde r . Hou and Palmer (33) descr ibed a more complex behavior made up of a mixed f i r s t and second order r a t e equat ion . The f i r s t o rder behavior was used t o desc r ibe ace ty l ene formation and r e s u l t e d i n an a c t i v a t i o n energy of 52 Kcal/mole with a 9.2 - 1 frequency f a c t o r of 10 sec . The second order c o n t r i b u t i o n descr ibed biphenyl formation wi th an a c t i v a t i o n energy of 14 - 1 -1 3 40 Kcal/mole and a frequency f a c t o r of LO mole sec cm . A f i r s t o r d e r r a t e express ion with an a c t i v a t i o n energy of 9 35 Kcal/mole and a frequency f a c t o r of 2 x 10 sec-' were used i n t h e non-equi l ibr ium flow a n a l y s i s . (3 ) Water-Gas Reactions: The water gas r e a c t i o n s a r e a very complex s e t of r e a c t i o n s which a r e c r i t i c a l l y dependent on the experimental condi t ions a t which they a r e s tud ied . These r e a c t i o n s inc lude t h e carbon-steam r e a c t i o n (6-8) , t h e water-gas s h i f t r e a c t i o n (6-9) and t h e carbon-carbon d ioxide r e a c t i o n (6-10). The genera l r u l e s of behavior f o r t h i s system of r e a c t i o n s a r e summarized below (36,37,38): ( i ) Inc reases i n t h e water concen t r a t ion inc reases the carbon consumption r a t e , ( i i ) Inc reases i n t h e hydrogen concen t r a t ion decreases o r r e t a r d s carbon consumption, and ( i i i ) A f i xed r a t i o e x i s t s between carbon d ioxide and carbon monoxide. The water gas s h i f t r e a c t i o n i s considered by many (35, 39,40) t o be a t equi l ibr ium and unaffected by concent ra t ion changes, temperature and p re s su re changes a t reasonably low pressures (-1 ATM) and moderate temperature (1000 - 1500°F). Walker (41) , on t h e otherhand, repor ted d e f i n i t e dev ia t ions from t h i s supposed equi l ibr ium below 2300°F. A d e t a i l e d d i scuss ion of t h e water gas r e a c t i o n s i s presented i n r e f e rence (42) . The r e a c t i o n k i n e t i c d a t a used i n t h e TEMPRE System f o r each of t h e above r e a c t i o n s a r e compared with t h e l i t e r a t u r e i n t h e fo l lowing sec t ions . ( a ) Carbon-Steam Reaction: The carbon-steam r e a c t i o n has been ex tens ive ly s tudied by many i n v e s t i g a t o r s (35,36,38,39, 40,43,44) . The r e a c t i o n i s f i r s t o rde r and a c t i v a t i o n ene rg i e s have been repor ted over a wide range of va lues (26-90 Kcal/mole). The more app l i cab le d a t a f o r graphi te-s team r e a c t i o n (42) i nd ica t ed an a c t i v a t i o n energy of 80 Kcal/mole. This i s i n agreement wi th t h e va lue of 83 Kcal/mole (47) , and 82 ~ c a l / m o l e was used i n t h e non-equilibrium flow a n a l y s i s of t h i s research . 12 - 1 A frequency f a c t o r of 1 x 10 sec was employed i n t h e nont equ i l i b r ium flow c a l c u l a t i o n s (55) . (b ) Water-Gas S h i f t Reaction: The water-gas s h i f t r e a c t i o n below 2300°F was considered t o be governed by a f i n i t e r e a c t i o n r a t e i n t h e TEMPRE System. A va lue of 30 Kcal/mole 12 a c t i v a t i o n energy and 1 x 10 sec-' frequency f a c t o r was used t o d e s c r i b e t h e r e a c t i o n of water wi th carbon monoxide, The dev ia t ion from equi l ibr ium below 2300°F i s repor ted by Walker (41) and a t t r i b u t e d , i n p a r t , t o a d i f f u s i o n con t ro l l ed mechanism, ( c ) Carbon-Carbon Dioxide Reaction: The r e a c t i o n of carbon w i t h carbon d ioxide i s b e s t descr ibed by a r a t e equat ion which i s f i r s t o rde r and r e v e r s i b l e . Values of t h e forward and r e v e r s e a c t i v a t i o n energ ies were repor ted a s 50 Kcal/mole and 60.6 Kcal/mole by Austin and Walker (45) and Glovina (46) . 6 - 1 The frequency f a c t o r s were 1 x 16 sec and 1 x lo-' s ec - 1 f o r t h e forward and r e v e r s e r e a c t i o n s , r e s p e c t i v e l y . These repor ted va lues were used i n t h e non-equi l ibr ium flow a n a l y s i s . Experimental Simulat ion of t h e Flow o f Reac t ing P y r o l y s i s Products i n t h e Char Zone ---- The purpose of t h e experimental program was t o o b t a i n s u f f i c i e n t d a t a f o r c ~ m p a r i s o n wi th t h e c a l c u l a t e d r e s u l t s of t h e non-equi l ibr ium f low model. Simulated p y r o l y s i s products were passed through r a d i a n t heated cha r s maintained a t a f r o n t s u r f a c e temperature of 1600 - 2300°F. Mass f l u x r a t e s were 2 va r i ed between 0.0001 - 0.10 l b l f t - s ec , and t h e back s u r f a c e temperature was measured a s a func t ion of t h e p a r t i c u l a r f r o n t su r f ace temperature and mass f l u x r a t e s t u d i e d , The back s u r f a c e temperature range was from 500 t o 1200°F. These va lues , a long wi th t h e p o r o s i t y , t h i cknes s and c r o s s s e c t i o n a r e a of t h e cha r were input parameters t o t h e non-equi l ibr ium flow model. The composition of t h e e x i t product s t ream was c a l c u l a t e d us ing t h e k i n e t i c d a t a f o r t h e important r e a c t i o n s l i s t e d i n Table 6-6 and compared with t h e exper imenta l ly determined compositions. The r e l a t i v e c lo senes s of t h e two compositions determined t h e accuracy of t h e model i n p r e d i c t i n g t h e flow o f p y r o l y s i s products wi th in t h e cha r over a tempera- t u r e range from 500 - 2300°F and mass f l u x r a t e s between 0.0001 - 2 0.10 l b / f t sec . The fol lowing paragraphs d i s c u s s t h e r e s u l t s of t h e s e comparisons. A d e t a i l e d summary of r e s u l t s f o r a l l experimental t e s t s i s presented i n Appendix D. of t h e Non- --- Flow Resu l t s wi th Experi- - mental Data Using Chars: The b a s i s f o r eva lua t ing t h e non- equ i l i b r ium flow model a s an accu ra t e a n a l y s i s of energy t r a n s f e r i n t h e cha r zone of a cha r r ing a b l a t o r i s by comparison of t h e exper imenta l ly determined e x i t product composition from t h e Char Zone Thermal Environment Simulator t o t h e ca l cu l a t ed composition i n t h e non-equilibrium flow a n a l y s i s . This i s done i n Table 6-7 i n which t h e non-equi l ibr ium e x i t product composi t ion, c a l c u l a t e d us ing t h e chemical r e a c t i o n s and co r r e s - ponding k i n e t i c d a t a i n Table 6-6, i s compared wi th exper i - mental d a t a f o r mass f l u x r a t e s between 0.0013 and 0.108 2 l b / f t -sec and f r o n t s u r f a c e temperatures of 1680°F t o 2300°F. The s imulated py ro lys i s gas composition e n t e r i n g t h e cha r zone i s a l s o shown ( f rozen ) , a long wi th t h e compositions p red i c t ed by t h e equi l ib r ium f low model. This s e t of experiments was conducted wi th c h a r s formed from nylon-phenol ic r e s i n compo- s i t e s under s imulated r e e n t r y cond i t i ons i n t h e e l e c t r i c a i r a r c j e t s a t t h e Langley Research Center (N.A. S.A.). A s seen i n Table 6-7, t h e experimental and c a l c u l a t e d composition p red i c t ed by t h e non-equi l ibr ium flow model agreed wi th in t h e experimental accuracy of t h e methods used. A summary of a l l low RU N NU MB ER d e n s i t y nylon-phenol ic r e s i n cha r expe r fmen~s a r e presented i n Appendix D. The r e s u l t s i n Table 6-7 w i l l be d i scussed i n d e t a i l i n t h e fol lowing paragraphs. The maximum temperature a t t a i n a b l e i n t h e Char Zone Thermal Environment Simulator was 2300°F. This r e s t r i c t i o n t o t h e tempera ture was caused by t h e l im i t ed power supply (70 KVA) t o t h e r a d i a n t hea t ing system, and by m a t e r i a l and economic f a c t o r s governing t h e des ign of h igh temperature equip- ment. A t temperatures between 1600 - 2300°F, mass f l u x r a t e s 2 of 0.01 l b / f t -see o r g r e a t e r d id no t a l low s u f f F e i e n t r e s idence t ime of t h e py ro lys i s products i n t h e cha r l a y e r . Therefore , t h e ex t en t of chemical r e a c t i o n s was l e s s than 1% and t h e f low was e s s e n t i a l l y f rozen . This f rozen behavior of t h e p y r o l y s i s gases i s i l l u s t r a t e d i n Table 6-8 f o r mass f l u x r a t e s of 0.0101 and 0.1080 1 b / f t L - s e e a t a f r o n t su r f ace temperature of 1600°F. The e x i t gas compositi.sn c a l c u l a t e d i n t h e non-equi l ibr ium flow model and t h e experimental ly determined va lues a r e compared wi th t h e i n l e t esmpss i t ion ( f rozen) and t h e composition pred ic ted by t h e equi l ib r ium flow model. Although t h e f rozen flow cond i t i on was accu ra t e ly des- c r ibed by t h e non-equilibrium flow model, t h e a b i l i t y t o p r e d i c t energy t r a n s f e r when chemical r e a c t i o n s occur remained un te s t ed . Therefore , i n o rde r t o ache ive cond i t i ons where chemical r e a c t i o n s would become an important mode of energy abso rp t ion , and, t h e non-equi l ibr ium model could be t e s t e d , t h e r e s idence t i m e of gases w i th in t h e char was increased by decreas ing t h e mass f l u x . The e f f e c t of changing t h e mass f l u x r a t e a t a cons t an t temperature of 1690°F i s shown i n Table 6-9. A t a mass f l u x 2 of 0.108 l b / f t - sec , t h e e x i t composition i s t h e same a s t h e composition of t h e s imulated py ro lys i s products e n t e r i n g t h e 2 char . Decreasing t h e mass f l u x t o 0.00208 l b / f t -sec causes a smal l , b u t d e t e c t a b l e composition change, p a r t i c u l a r l y i n hydrogen and methane r e s u l t i n g from chemical r e a c t i o n s between t h e s p e c i e s i n t h e char l a y e r . It should be pointed ou t t h a t t h e repor ted changes i n composition of t h e e x i t product s t ream a r e ~ r e d i c t e d by t h e non-equi l ibr ium flow model w i th in t h e accuracy of t h e experimental da t a . While t h e f rozen f low model p r e d i c t s t h e a c t u a l behavior a t t h e h igher mass f l u x r a t e s , t h e equ i l i b r ium flow model does no t a c c u r a t e l y d e s c r i b e t h e energy t r a n s f e r over t h e s e mass f l u x r a t e s . It erroneously p r e d i c t s l a r g e changes i n composition of a l l of t h e s p e c i e s even a t t h e h igh mass f l u x va lue of run XVIII-58 of 0.108 2 l b / f t - sec a s shown i n Table 6-9. The changes i n composition r e s u l t i n g from chemical r e a c t i o n s occur r ing i n t h e char l ~ y e r a r e b e t t e r i l l u s t r a t e d by i n c r e a s i n g t h e f r o n t s u r f a c e temperature. I n Table 6-10 a comparison o f t h e e x i t gas composition i s given f o r a f r o n t s u r f a c e temperature range of 1690 - 2300°F at an average mass 2 f l u x r a t e of 4 . 0 0 2 l b / f t - sec . The t r a n s i t i o n from a f rozen o r non- reac t ive s t a t e t o a s t a t e where chemical r e a c t i o n s become s i g n i f i c a n t i s c l e a r l y i nd i ca t ed by t h e change i n product concen t r a t i ons l eav ing t h e Char Zone Thermal Environment Simulator . Again t h e experimental e x i t product compositions ag ree wi th those pred ic ted by t h e non-equi l ibr ium flow a n a l y s i s w i th in t h e accuracy of t h e experimental d a t a . Again t h e equ i l i b r ium f low a n a l y s i s e r roneous ly pred ic ted t h e e x t e n t of r e a c t i o n s t o be much g r e a t e r than occur red . I n most of t h e above d i scus s ion , t h e i n i t i a l p y r o l y s i s product composition e n t e r i n g t h e char va r i ed over a small range, r a t h e r t han being cons t an t . These v a r i a t i o n s were a r e s u l t of v a r i a t i o n s i n feed ing t h e gas (CH4, CO, C02 and H2) and l i q u i d (phenol and H 0 ) phases a t t h e low mass f l u x r a t e s 2 r equ i r ed t o g e t chemical r e a c t i o n s among t h e spec i e s . Also, i n some c a s e s t h e composition was va r i ed purposely t o t e s t t h e a b i l i t y of t h e non-equi l ibr ium flow model i n p r e d i c t i n g t h e energy t r a n s f e r i n t h e char zone f o r a wide v a r i e t y of tempe- r a t u r e s , mass f l u x r a t e s and s imulated p y r o l y s i s product composi t ions. These compositions were repor ted i n Table 6-5, and i t shows how simulated product compositions were va r i ed i n t h e Ta bl e 6- 10 . F lo w o f Py ro ly si s Ga se s Th ro ug h L o w D en si ty N yl on -P he no li c Re si n Ch ar s. N f kind and amount of each spec i e s p re sen t . The phenol-water f r e e compositions ( feed mix 1, 2 and 3 ) were based on e a r l y s t u d i e s of p l a s t i c decomposition i n which t h e chemical ana lyses were l im i t ed t o spec i e s t h a t were gases a t a p a r t i c u l a r (u sua l ly near ambient) temperature (4 ,5 ,6 ) . The phenol-water-gas composition, which more a c c u r a t e l y represen ted t h e composition e n t e r i n g t h e char , was obtained a f t e r t h i s r e sea rch was s t a r t e d ( 1 2 3 ) . However, a s w i l l be d i scussed , t h e same conclusions r ega rd ing t h e phenol-water f r e e systems apply t o t h e l a t t e r Systems. I n Table 6-11 t h e e f f e c t of changing temperature (1575 - 2 2300°F) a t a cons t an t mass f l u x r a t e (- 0.001 l b / f t - s ec ) i s shown, whi le Table 6-12 shows t h e e f f e c t of changing 2 mass f l u x (0.00003 - 0.0170 l b / f t - s ec ) a t a f r o n t su r f ace temperature of 2000QF. f o r t h e va r ious s imulated py ro lys i s product compositions s tud i ed . I n each t a b l e , t h e t r a n s i t i o n from f rozen flow t o non-equilibrium f low i s c l e a r l y shown, a s i s t h e very e x c e l l e n t agreement between t h e pred ic ted e x i t gas compositions of t h e non-equi l ibr ium f low a n a l y s i s wi th t h e 2 experimental r e s u l t s . A t h igh mass f l u x r a t e s (> 0.01 l b / f t - sec) o r low f r o n t s u r f a c e temperatures (< 1800°F), t h e flow i n t h e cha r zone i s a c c u r a t e l y descr ibed by t h e f rozen f low model. Furthermore, a s seen i n Table 6-12 f o r experiment XVI-48, t h e equ i l i b r ium flow model i s only a p p l i c a b l e when t h e mass f l u x o f 20 35 OF a n d Va ry in g P yr ol ys is G as C om po si ti on s. L r a t e s a r e ve ry small (< 0,00003 l b l f t - see) corresponding t o very l a r g e r e s idence t imes w i th in t h e char l a y e r . I n summary, r e s u l t s have been presen ted f o r t h e flow of s imulated p y r o l y s i s products through a c t u a l low dens i ty nylon- phenol ic r e s i n cha r s under cond i t i ons approximating t h e r e e n t r y of a b l a t i v e hea t s h i e l d s . Using t h e non-equi l ibr ium flow model comparison of t h e c a l c u l a t e d and exper imenta l ly determined e x i t gas composition was made. I n a l l c a s e s , except t hose l i s t e d i n Table D-1 of Appendix D i n which unusual o r e r r a t i c behavior w a s r a t e d , t h e p red i c t ed va lues of t h e e x i t gas com- position .by t h e non-equi l ibr ium flow a n a l y s i s were w i th in t h e experimental accuracy of t h e measured v a l u e s , These r e s u l t s were r epo r t ed f o r f r o n t s u r f a c e temperatures between 1350 - 2 2300°F, mass f l u x r a t e s of 0.00003 - 0.1080 l b / f t -sec and va lues of t h e simulated py ro lys i s products e n t e r i n g t h e char zone shown i n Table 6-5. The non-equi l ibr ium f low model i s , t h e r e f o r e , a very a c c u r a t e and u s e f u l a n a l y s i s of t h e energy t r a n s f e r i n t h e char zone o f a char-forming a b l a t o r . I n ea se s f o r h igh mass 2 f l u x va lues of t h e o rde r of 0 .01 l b / f t -sec t h e f rozen flow model a c c u r a t e l y descr ibed t h e energy t r a n s f e r i n t h e char zone. Only 2 a t extremely low mass f l u x va lues of t h e o rde r of 0.00003 l b / f t - sec d id t h e equ i l i b r ium flow model approximate t h e changes i n composi- t i o n o f t h e p y r o l y s i s products a s they pass through t h e cha r zone. Comparison of t h e Non-Equilibrium Flow Resu l t s wi th t h e Resu l t s of t h e Frozen Equi l ibr ium Flow Analyses -- A s d i scussed i n Chapter 111, t h e f rozen and equi l ib r ium flow models bracke t t h e non-equi l ibr ium case . Frozen flow corresponds t o a system i n which no chemical r e a c t i o n s occur , whi le equ i l i b r ium f low r e f e r s t o a system of s p e c i e s under- going chemical r e a c t i o n s which a r e a t equi l ib r ium ( a func t ion of temperature and p r e s s u r e on ly ) . Since t h e non-equi l ibr ium flow model p r e d i c t s t h e a c t u a l behavior , comparison of t h e e x i t gas composi t ions, temperature and p re s su re d i s t r i b u t i o n s , and s u r f a c e h e a t f l u x f o r each model w i l l determine t h e accuracy o f t h e two l imi t ed f low ana lyses i n p r e d i c t i n g t h e energy t r a n s f e r w i t h i n t h e cha r l a y e r . These r e s u l t s a r e presented i n Figure 6-1 and Table 6-13 2 f o r a mass f l u x r a t e of 0.05 l b / f t wsec, a f r o n t s u r f a c e tem- p e r a t u r e o f 1500°F and a back su r f ace temperature of 500°F. The char p o r o s i t y i s 0.8 and t h e ohar t h i cknes s i s 0.25 inches. A s seen t h e temperature p r o f i l e of t h e non-equi l ibr ium f low a n a l y s i s i s i d e n t i c a l t o t h e f rozen flow temperature p r o f i l e , The r e l a t i v e c lo senes s of t h e s e two models i s l i k e w i s e seen by comparing t h e e x i t gas composition, p r e s su re drop ac ros s t h e char and s u r f a c e hea t f l u x i n Table 6-13. Therefore , a t t h e above cond i t i ons t h e r e i s l i t t l e evidence o f chemical r e a c t i o n s c = 0.8 (Nylon-Phenolic Resin Char) L = 0.0208 ft n-Equilibrium Dimensionless Char Distance ( z IL) Figure 6-1. Temperature Profile for the Frozen, Equilibrium, and Non-Equilibrium Flow of Pyrolysis Gases Through the Char Zone of a Nylon-Phenolic Resin Ablator. e n s it y Ny lo n- L = 0. 02 08 ft Fe ed M ix 4 No n- Eq ui li br iu m F lo w i n t h e cha r and t h e energy t r a n s f e r i s c l o s e l y predic ted by t h e frozen f low model. I n F igure 6-2 and Table 6-14 t h e same r e s u l t s a r e presented f o r a f r o n t su r f ace temperature of 2000°F. Although t h e repor ted non-equi l ibr ium va lues a r e aga in very nea r ly equal t o t h e f rozen flow r e s u l t s , a n o t i c e a b l e change, e s p e c i a l l y i n t h e concentra- t i o n p r o f i l e and s u r f a c e h e a t f l u x i s observed. This i n d i c a t e s chemical r e a c t i o n s among t h e spec i e s w i th in t h e char l a y e r . A con t inua t ion of t h e a n a l y s i s f o r a f r o n t s u r f a c e tempera- t u r e of 2500°F and 3000°F i n F igures 6-3 and 6-4 and Tables 6-15 and 6-16, r e s p e c t i v e l y , shows a more dramatic change which i s r e f l e c t e d by a downward s h i f t of t h e temperature p r o f i l e toward t h e equ i l i b r ium curve and corresponding r ap id changes i n t h e concen t r a t ion p r o f i l e . Chemical r e a c t i o n s a r e obviously a very important mode of energy c o n t r i b u t i o n under t h e s e l a s t two s e t s of condi t ions . It i s not p o s s i b l e t o extend t h e a n a l y s i s t o temperatures above 3000°F s i n c e t h e chemical behavior w i th in t h e char w i l l not be p red ic t ed by t h e chemical r e a c t i o n s of Table 6-6. I n t h i s event a d d i t i o n a l r e a c t i o n s must be included t o accu ra t e ly desc r ibe t h e energy t r a n s f e r w i th in t h e char zone, This ex- tens ion is d iscussed by d e l Val le , e t , a l . (55). I n a d d i t i o n t o t h e above comparisons, t h e temperature W = 0.05 lb/ft -sec e = 0.8 (Nylon-Phenolic Resin Char) Feed Mix 4 L = 0.0208 ft Nan-Equilibrium Dimensionless Char Distance ( /L) Figure 6-2. Temperature Profile for the Frozen, Equilibrium, and Non-Equilibrium Flow of Pyrolysis Gases Through the Char Zone of a Nylon-Phenolic Resin Ablator. C on di ti on s: L = 0. 02 08 ft Fe ed M ix 4 C ar bo n M on ox id e E = 0.8 (Nylon-Phenolic Resin Char) Feed Mix 4 L = 0.0208 ft Non-Equilibrium Dimensionless Char Distance (z/L) Figure 6-3. Temperature Profile for the Frozen, Equilibrium, and Non-Equilibrium Flow of Pyrolysis Gases Through the Char Zone of a Nylon-Phenolic Resin Ablator. P he no li c R es in A bl at iv e H ea t S hi el d C ha r a t 25 00 °F . C om po si ti on ( M ol e % ): C ar bo n M on ox id e F ro ze n Fl ow 3000 2500 F = 0.8 (Nylon-Phenolic Resin Char) L = 0,0208 ft 2000 1500 1000 500 0 0.0 0.25 0.50 0.75 1 .O Dimensionless Char Distance ( IL) Figure 6-4. Temperature Profile for the Frozen, Equilibrium, and Non-Equilibrium Flow of Pyrolysis Gases Through the Char Zone of a Nylon-Phenolic Resin Ablator. C ar bo n M on ox id e C ar bo n D io xi de N on -E qu il ib ri um Fl ow p r o f i l e , s u r f a c e hea t f l u x and p re s su re drop ac ros s t h e char a r e compared i n Figures 6-3 and 6-5 f o r two py ro lys i s product composi t ions. The r e s u l t s f o r t h e f i r s t s imulated p y r o l y s i s product c o m p ~ s i t i o n , which was based on exper imenta l ly measured and computed equi l ib r ium compositions excluding t h e h igh molecular weight c y c l i c compounds, i s shown i n Figure 6-5. The r e s u l t s i n Figure 6-3 a r e f o r t h e more accu ra t e composition based on p y r o l y s i s gas chromatographic ana lyses of Sykes ( 2 ) . 2 A mass f l u x r a t e of 0.05 l b / f t - sec , f r o n t and back s u r f a c e 1 temperature of 2500°F and 500°F, r e s p e c t i v e l y , and a one-quar te r inch t h i c k low d e n s i t y nylon-phenolic r e s i n char (C = 0.8) were t h e cond i t i ons f o r each c a s e presen ted . Comparison of t h e temperature p r o f i l e s f o r f rozen and non-equi l ibr ium flow show t h e same o v e r a l l behavior ; i . e . , a downward s h i f t by t h e non-equilibrium curves i n d i c a t i n g a h igher energy abso rp t ion due t o chemical r e a c t i o n s between t h e p y r o l y s i s p roducts . On t h e otherhand, a n o t i c e a b l e d i f f e r e n c e i n t h e equ i l i b r ium curves i s observed, For t h e more a c c u r a t e p y r o l y s i s gas composition (F igure 6-3) , t h e c h a r a c t e r i s t i c a l l y sharp downward s h i f t of t h e equi l ib r ium curve observed i n F igure 6-5 does n o t occur . The explana t ion f o r t h i s d i f f e r e n c e w i l l po in t ou t t h e inadequacy of t h e equi l ib r ium flow model i n p r e d i c t i n g t h e t r u e behavior w i t h i n t h e cha r zone. Because t h e r e s u l t s of Figure 6-5 = 0.8 (Nylon-Phenolic Resin Char) L = 0.0208 ft Frozen Flow Non-Equilibrium Equilibrium Flow Figure 6 - 5 , Temperature Profile, Pressure Drop and Surface Heat Flux for the Flow of Pyrolysis Gases Through A One-Quarter Inch Thick Nylon-Phenolic Char. were c a l c u l a t e d f o r a p y r o l y s i s product composition l a r g e l y based on equi l ib r ium c a l c u l a t e d va lues , t h e i n l e t gas compo- s i t i o n t o t h e char were very nea r ly equal t o t h e va lues ca lcu- l a t e d u s i n g t h e equi l ib r ium flow model. A s a r e s u l t , very l i t t l e energy abso rp t ion was omit ted from t h e a n a l y s i s due t o t h e very small change i n t h e i n l e t compositions which were a l r eady approximated a s an equi l ib r ium composition. This r e s u l t e d i n t h e r e l a t i v e l y f l a t curve over n e a r l y t h r e e q u a r t e r s of t h e t o t a l cha r t h i cknes s . On t h e otherhand, t h e more accu ra t e p y r o l y s i s product composition es t imated from experimental d a t a and dependent on f i n i t e r e a c t i o n r a t e s governing p l a s t i c decomposition, i s f a r removed from t h e equi l ib r ium c a l c u l a t e d composi t ions. However, a s t h e s e concen t r a t i ons of gases a r e introduced i n t o t h e equi- l i b r ium f low a n a l y s i s , an abrupt adjustment t o t h e equi l ib r ium compositions c a l c u l a t e d by minimizing t h e f r e e energy i s experienced, This i s e s p e c i a l l y noted f o r phenol and methane which have i n i t i a l compositions of 6 .2 mole % and 6,7 mole %, r e s p e c t i v e l y , bu t a r e immediately changed t o 0.0 mole % and 35.3 mole % a t t h e back su r f ace temperature of 500°F, This erroneous adjustment r e s u l t s i n t h e l o s s of energy absorp t ion which r e s u l t s from phenol decomposition a t f i n i t e r e a c t i o n r a t e s and causes t h e curve t o more c l o s e l y approach t h e f rozen and non-equi l ibr ium curves . These same conc lus ions regard ing t h e i n a b i l i t y o f t h e equi l ib r ium flow model t o a c c u r a t e l y p r e d i c t t h e t r u e behavior i s f u r t h e r shown i n Table 6-17. Here, t h e s u r f a c e h e a t f l u x va lues a r e compared f o r each model and f o r each s imulated pyro- l y s i s product composition. I n comparing t h e r e l a t i v e va lues , i . e . , t h e r a t i o of t h e hea t f l u x of any model t o t h e a c t u a l o r non-equi l ibr ium flow hea t f l u x , t h e c h a r a c t e r i s t i c under- p r e d i c t i v e n a t u r e of t h e f rozen flow model ( r a t i o = 0.818) and t h e extremely ove rp red i c t i ve behavior of t h e equ i l i b r ium flow model ( r a t i o = 1,445 ) a r e shown. It f u r t h e r i l l u s t r a t e s t h a t a l though t h e f rozen flow model can accu ra t e ly d e s c r i b e t h e t r u e behavior i n some cases (low temperatures o r h igh mass f l u x r a t e s ) , t h e equi l ib r ium flow model i s t o t a l l y inadequate over t h e temperature (500 - 3000°F) and mass f l u x (0.00003 - 0.10 l b / f t 2 - s e e ) va lues s tud i ed i n t h i s r e sea rch . Therefore , i n o rde r t o o b t a i n an accu ra t e p r e d i c t i o n of t h e energy t r a n s f e r , a non-equi l ibr ium flow model must be used wi th in t h e t r a n s i t i o n reg ion . This i s on ly p o s s i b l e by cons ider ing chemical r e a c t i o n s between t h e spec i e s t o occur a t f i n i t e r e a c t i o n r a t e s a s descr ibed by r e l i a b l e k i n e t i c d a t a . Again t h e importance and a p p l i c a t i o n of t h e non-equi l ibr ium flow model has been demonstrated and t h e l i m i t a t i o n s of t h e two i d e a l models shown. This d i s cus s ion forms t h e b a s i s f o r extending t h i s r e sea rch t o h igher temperatures involv ing more complex r e a c t i o n s and increased number of spec i e s . T ab le 6 -1 7. C om pa ri so n o f th e S ur fa ce H ea t F lu x V al ue s fo r E ac h Fl ow M od el a n d Tw o P y ro ly si s G as C om po si ti o C ar bo n M on ox id e C ar bo n D io xi de C ar bo n M on ox id e C ar bo n D io xi de N ot e: T he r e la ti v e h ea t fl u x i s d ef in ed a s t h e r a ti o o f th e h ea t fl u x c a lc u la te d b y a n y m o de l to t h e h ea t fl u x c a lc u la te d b y th e n o n -e qu il ib ri um fl ow m o de l. T he r e la ti v e Paramet r ic Study of t h e Flow of Py ro lys i s Gases i n t h e Char Zone A comparison of t h e non-equi l ibr ium flow r e s u l t s wi th t h e experimental d a t a was important i n determining t h e accuracy o f t h e flow model. However, very l i t t l e q u a n t i t a t i v e in format ion , beyond t h e d i s c r e t e s e t s of d a t a f o r each experiment , was assembled regard ing t h e e f f e c t of changing mass f l u x and/or temperature . A s a r e s u l t , a parametr ic s tudy was undertaken t o a c c u r a t e l y r e l a t e t h e changes i n t h e s e v a r i a b l e s with v a r i a t i o n s i n energy abso rp t ion wi th in t h e cha r . To do t h i s t h e n o n - i t e r a t i v e TEMPRE System (NIT) was used i n which t h e back su r f ace tempera- t u r e and temperature g rad i en t were s p e c i f i e d a s boundary cond i t i ons f o r v a r i o u s va lues of t h e mass f l u x . The r e s u l t s of t h e ca l cu - l a t i o n were i n t h e form of t h e n e t hea t t r a n s f e r a t t h e s u r f a c e , c a l l e d t h e approximate aerodynamic hea t ing , which was t h e sum o f t h e s u r f a c e hea t f l u x and r a d i a n t hea t f l u x r e s u l t i n g from t h e c a l c u l a t e d f r o n t su r f ace temperature: where a v a l u e of 0.95 was used f o r t h e emis s iv i t y . This in format ion i s shown i n F igure 6-6 i n which t h e mass f l u x i s p l o t t e d a g a i n s t t h e aerodynamic h e a t i n g f o r va r ious h e a t s of p y r o l y s i s , q~ ' ( func t ion of t h e temperature and g rad i en t 0 E q u i l i b r i u m F l o w @ Non-Equil ibrium F l o 0 0.01 0.02 0 ,03 0 .04 0.05 2 Mass F lux ( l b / f t -sec) a t t h e back s u r f a c e ) : where q i s t h e sum of t h e energy absorbed by t h e decomposition P of t h e polymer and t h e energy conducted through t h e v i r g i n p l a s - t i c . Resu l t s f o r t h e f rozen , equi l ibr ium and non-equilibrium flow models a r e presented . This form of p re sen t ing t h e r e s u l t s i s a very convenient and informative method a s w i l l be seen. I n a r e e n t r y problem one of t h e important ques t ions asked i s what i s t h e requi red hea t s h i e l d weight f o r p ro t ec t ion f o r a c e r t a i n mission. Spec i f i ca t ion of t h e type of hea t sh i e ld ma te r i a l t o be used (e .g . , nylon-phenolic r e s i n ) bracke ts t h e hea t of py ro lys i s va lue , while t h e t r a j e c t o r y c a l c u l a t i o n s determine t h e amount of aerodynamic h e a t i n g t h a t can be expected. For example, an approximate aerodynamic h e a t i n g r a t e of 500 BTU/ 2 f t -sec and a h e a t of py ro lys i s of 400 BTU/lb l o c a t e s t h r e e d i s t i n c t i v e p o i n t s on Figure 6-6; one f o r each of t h e frozen, equi l ibr ium and non-equilibrium flow models. This corresponds 2 t o t h r e e d i s t i n c t i v e va lues of t h e mass f l u x r a t e ; 0,017 l b / f t - sec 2 2 f o r f rozen , 0.002 l b / f t -see f o r equi l ibr ium and 0.009 l b / f t -sec f o r non-equilibrium. The non-equilibrium flow model accu ra t e ly predic ted t h e behavior and would spec i fy t h e exact hea t s h i e l d weight ( func t ion of t h e mass f l u x ) requi red . The frozen f low model shows an ove r -p red i c t i on because important endothermic r e a c t i o n s were omi t ted , and t h e equi l ib r ium flow model shows an under -pred ic t ion , because r e a c t i o n s were assumed t o occur a t a g r e a t e r ex t en t than t h e a c t u a l behavior . The r e s u l t s presented i n F igure 6-6 a l s o provide a way of determining a t what po in t t h e non-equi l ibr ium flow model changes from t h e f rozen flow behavior t o a t r u l y non-equi l ibr ium 2 flow cond i t i on governed by f i n i t e r e a c t i o n r a t e s (50 B T U / £ ~ - sec ) . This f i g u r e very g r a p h i c a l l y i l l u s t r a t e s t h e d i f f e r e n c e s i n each model and permits t h e p r e s e n t a t i o n of a l a r g e volume o f informa- t i o n i n a c l e a r and r e a d i l y a c c e s s i b l e manner, Ca l cu l a t i on of t h e Reacting Gas Heat Capacity I n a d d i t i o n t o t h e above information, t h e r e a c t i n g gas hea t c a p a c i t y f o r t h e non-equi l ibr ium flow of p y r o l y s i s products through t h e cha r has been determined a l s o . This t e r m i s very u s e f u l i n t h e c a l c u l a t i o n o f t h e one-dimensional, t r a n s i e n t response of an a b l a t i v e composite. The energy equa t ion f o r t h e t r a n s i e n t ca se can be put i n t h e fo l lowing form (56) f o r t h e char zone. K+1 where W i s t h e mass . f l ux of py ro lys i s p roducts a t z and W 0 i s t h e mass f l u x of py ro lys i s products e n t e r i n g t h e char . The term i n b racke t s i s r e f e r r e d t o a s t h e e f f e c t i v e r e a c t i n g gas hea t capac i ty . Hence, t h e flow wi th in t h e char zone can be considered f rozen (CH R # 0) by in t roduc ing t h e r e a c t i n g i i gas hea t capac i ty a s an input func t ion t o t h e t r a n s i e n t c a l c u l a t i o n s . I n Figure 6-7 a p l o t of t h e r e a c t i n g gas hea t capac i ty a s a func t ion of temperature i s shown f o r f rozen , equ i l i b r ium and non-equi l ibr ium flow w i t h i n t h e cha r l a y e r up t o 3000°F. These curves were c a l c u l a t e d f o r a mass f l u x 2 of 0.05 l b / f t - sec , a back su r f ace temperature of 500°F, and, cha r p o r o s i t y and th i cknes s of 0.8 and 0.25 inches , r e s p e c t i v e l y . The d i f f e r e n c e s i n t h e manner used t o c a l c u l a t e t h e energy t r a n s f e r by chemical r e a c t i o n (CH. R. ) f o r equi l ib r ium and non- 1 1 equi l ib r ium flow causes t h e curves t o s e p a r a t e a s shown. Flow of P y r o l y s i s Products Through Porous Graphi te -- There a r e two important reasons f o r u s ing porous g r a p h i t e t o s imu la t e low d e n s i t y , nylon-phenolic r e s i n c h a r s used i n a b l a t i v e h e a t s h i e l d a p p l i c a t i o n s . These a r e a v a i l a b i l i t y and machinabi l i ty of t h e g raph i t e . Nylon-phenolic r e s i n cha r s were obtained from t h e Nat ional Aeronaut ics and Space Administration's Lasgley Research Center f o r use i n t h e Char Zone Thermal Environment Simulator . L = 0. 02 08 ft Fe ed M ix 3 P = 1 a tm No n- Eq ui li br iu m Fr oz en a n d No n- Eq ui li br iu m Te mp er at ur e (O F) Fi gu re 6 -7 . Pl ot o f th e Re ac ti ng G as H ea t Ca pa ci ty f or F ro ze n, Eq ui li br iu m a n d No n- Eq ui li br iu m F lo w o f Py ro ly si s Ga se s Th ro ug h th e Ch ar Zo ne . E l e c t r i c a i r a r c j e t s were used t o char t h e nylon-phenolic r e s i n s , and t h i s represen ted a cons ide rab l e e f f o r t i n supplying j u s t a few specimens f o r use i n t h i s r e sea rch . Although two s e c t i o n s of char were u s u a l l y obtained from each specimen, t h e demand f o r a d d i t i o n a l cha r s could no t be met. I n a d d i t i o n t o t h e problem of ob t a iq ing t h e samples, t h e b r i t t l e n a t u r e of t h e cha r s caused s e r i o u s problems i n mounting on t h e cha r ho lder s e c t i o n . These complicat ions l ed t o t h e t e s t i n g and use of g r a p h i t e , e x p e c i a l l y , f o r use i n r a d i o a c t i v e t r a c e r and c a t a l y s t eva lua t ion s t u d i e s . However, f o r t h e succes s fu l s u b s t i t u t i o n of g r a p h i t e f o r t h e c h a r s t o be complete, t h e chemical behavior of t h e two must be e s s e n t i a l l y t h e same, This i s t o say t h a t t h e same r e a c t i o n s and k i n e t i c d a t a important i n p r e d i c t i n g t h e energy t r a n s p o r t w i th in porous cha r s , must a l s o do t h e same f o r energy t r a n s p o r t i n porous g raph i t e . This w i l l be shown i n t h e fo l lowing s e c t i o n s by comparing t h e e x i t gas compositions from t h e Char Zone Thermal Environment Simulator with t h e composition p red i c t ed by t h e non-equilibrium f low model, and, by d i r e c t comparison of char and g r a p h i t e experimental r e s u l t s over a range of mass f l u x r a t e s and f r o n t s u r f a c e temperature common t o both systems, Comparison of Reac t ing Flow Through Chars and Graphi te : Other than t h e d i f f e r e n c e s i n t h e s t r u c t u r a l p r o p e r t i e s of cha r s and g r a p h i t e , t h e one most important cons ide ra t i on t h a t must be accounted f o r i s t h e change i n mass f l u x r a t e s caused by d i f f e r e n c e s i n m a t e r i a l p o r o s i t y . Therefore , t o put t h e m a t e r i a l s on a common b a s i s f o r d i s cus s ion , t h e mass f l u x r a t e s p rev ious ly d i scussed i n terms of t h e t o t a l a r e a - sec) must be divided by t h e p o r o s i t y t o o b t a i n ( l b l f t t o t a l r a t e s w i t h i n t h e pores ( l b l f t - s ec ) . Even though t h e VQ i d s s u p e r f i c i a l mass f l u x r a t e s a r e d i f f e r e n t f o r each porous medium, t h e mass f l u x r a t e wi th in t h e pores w i l l be t h e same, Again, t h e p o r o s i t y of t h e cha r s and g r a p h i t e were 0 .8 and 0 , 5 , r e s p e c t i v e l y . The foregoing d i scus s ion i s no t intended t o mean t h a t chemical r e a c t i o n s w i l l no t be inf luenced by o t h e r s t r u c t u r a l p r o p e r t i e s b e s i d e t h e po ros i t y (e .g . , c r y s t a l l i d i t y , permea- b i l i t y , e t c . ) . However, it emphasizes t h a t t h e mass f l u x w i th in t h e pore spaces must be equiva len t f o r a v a l i d comparison. Di f fe rences i n t h e chemical r e a c t i o n r a t e s r e s u l t i n g from d i f f e r e n c e s i n s t r u c t u r a l makeup could e l i m i n a t e g r a p h i t e a s a s u i t a b l e s u b s t i t u t e . However, t h i s could on ly be determined by a comparison o f experiments conducted over t h e range of cond i t i ons f o r which t h e proposed flow model i s v a l i d . I n Table 6-18 f h e e x i t gas composition from t h e Char Zone Thermal Environment Simulator f o r t h e f low o f p y r o l y s i s products through g r a p h i t e a r e presented f o r mass f l u x r a t e s of 0.0034 2 t o 0.0059 l b / f t - sec a t a f r o n t su r f ace temperature of approxi- FR ON T TE MP mately 1950°F. A s i n t h e c a s e with c h a r s , t h e r e i s a s i g n i - f i c a n t amount of chemical r e a c t i o n s occu r r ing i n t h e porous 2 medium f o r t h e lower mass f l u x r a t e s (< 0.01 l b / f t - sec) . More impor tan t ly , however, i s t h e agreement w i t h i n exper i - ment e r r o r between t h e measured e x i t gas compositions and t h e p red i c t ed va lues by t h e non-equi l ibr ium f low model us ing t h e same k i n e t i c d a t a employed f o r t h e char experiments. A s i m i l a r comparison i s presented i n Table 6-19 f o r an average mass f l u x r a t e of 0.0035 l b / f t 2 - s e c and f r o n t su r f ace temperatures of 1950 and 2065°F. Again, e x c e l l e n t agreement w i th in t h e experimental accuracy of t h e ana lyses was obtained between t h e non-equilibrium f low model compo- s i t i o n s and t h e experimental va lues . However, a c l o s e r i n spec t ion of t h e g r a p h i t e experiments i n Table D-3 of Appendix D shows t h a t t h e non-equi l ibr ium pred ic ted compositions do oo t agree i n some c a s e s wi th t h e experimental d a t a . This i s e s p e c i a l l y t r u e f o r experiments XXI-66, XXIII-72, XXIII-73, and XXIV-76. These d i f f e r e n c e s were a r e s u l t of experimental d i f f i c u l t i e s a s soc i a t ed wi th maintaining a s t eady l i q u i d (water and phenol) feed r a t e a s ind ica ted i n t h e experimental summary s h e e t s of Table D-1; and, t h e r e f o r e , should no t be i n t e r p r e t e d a s a f a i l u r e of t h e model t o p r e d i c t t h e flow behavior i n porous g r a p h i t e . I n a d d i t i o n t o t h e s e i r r e g u l a r i t i e s i n t h e water-phenol- T ab le 6 -1 9. Fl ow o f P yr ol ys is G as es T hr ou gh G ra ph it e. E ff ec t o f C ha ng in g th e F ro nt S ur fa ce T em pe ra tu re a t a M as s F lu x R at e o f 0. 00 32 lb /f t2 -s ec . RU N NU M BE R M AS S FL UX gas experiments, s i m i l a r disagreement was a l s o observed i n s eve ra l water-phenol f r e e p y r o l y s i s product i n v e s t i g a t i o n s . I n experiments I X and X I shown i n Table 6-20, increased i n methane and corresponding decreases i n hydrogen concen t r a t ions c l e a r l y devia ted from t h e predic ted f rozen flow behavior . These observa t ions were a t t r i b u t e d t o problems a s soc i a t ed wi th t h e f a b r i c a t i o n of t h e g r a p h i t e specimens. I n t h e e a r l i e r experiments, t h e d u s t - l i k e g r a p h i t e " f ines" which r e s u l t e d from t h e m i l l i n g process were not removed from t h e pore spaces wi th in t h e p lug , These " f ines" provided addi- t i o n a l s u r f a c e a r e a which made them h igh ly s u s c e p t i b l e t o r eac - t i o n wi th hydrogen t o form methane. Af t e r complete r e a c t i o n of t h e " f ines" (about f i v e t o t e n minutes) , t h e hydrogen and methane concen t r a t ions i n t h e e x i t stream re turned t o t h e i r i n i t i a l compositions i n d i c a t i n g f rozen flow behavior , This i s i l l u s - t r a t e d g r a p h i c a l l y i n Figure 6-8 i n which hydrogen and methane concen t r a t ions ( i n mole p recen t ) a r e p l o t t e d aga ins t exper i - mental run time ( i n minutes) f o r experiment I X . Methane product ion of t h i s kind was el iminated i n subsequent experiments (XII , X I I I , and XV i n Table 6-21) by f i r s t pas s ing n i t rogen o r helium through t h e g r a p h i t e plugs p r i o r t o mounting i n t h e char ho lde r . This removed t h e " f ines" from t h e pore spaces and e l imina ted t h e sharp inc rease i n methane observed i n Figure 6-8. The c o n t r a s t i n g concent ra t ion p r o f i l e s a s a Ex pe ri me nt IX ( Gr ap hi te ) Fe ed M ix 2 W = 0. 00 1 lb /f t2 -s ec o ,c -- -- O -- -, - - - - - - - To = 89 0° F In le t Ga s Co mp os it io n - - - - - - - - & - - In le t Ga s Co mp os it io n - - - - - - - - 0 -- -- -- 0 -- - Fi gu re 6 -8 . Ty pi ca l Me th an e- Hy dr og en Co nc en tr at io n Pr of il e in t he E xi t Ga s St re am fr om t he c ha r Zo ne T he rm al E nv ir on me nt Si mu la to r fo r th e In cl us io n o f Gr ap hi te " Fi ne s" in t he P or e Sp ac es . R es u lt in g Fr om E xp er im en ts I n W hi ch T he " F in es " W er e C le ar ed F ro m T he f u n c t i o n of run time a r e shown i n Figure 6-9 f o r experiment X I I I . A s a f i n a l comparison, s e v e r a l char and g r a p h i t e experiments a r e examined i n Table 6-22, To accomplish t h i s t h e mass f l u x r a t e s based on t h e void a r e a were c a l c u l a t e d and a r e shown i n b r a c k e t s . The l i s t i n g i n Table 6-22 i s , a l s o , made i n o rde r of i n c r e a s i n g chemical r e a c t i o n s ; i . e . , low temperatures and h igh mass f l u x r a t e s appear f i r s t . A s seen, t h e char and g r a p h i t e experiments a r e indeed compatible and behave, from t h e o v e r a l l chemical viewpoint , a s one m a t e r i a l . This permi ts t h e use o f t h e more e a s i l y workable g r a p h i t e m a t e r i a l s i n experiments designed t o s tudy carbon d e p o s i t i o n and product d i s t r i b u t i o n us ing Carbon-14 t r a c e r s , and, t o inves- t i g a t e t h e e f f e c t of c a t a l y s t s i n a c c e l e r a t i n g t h e r a t e s of chemical r e a c t i o n s w i th in t h e char l a y e r . D e t a i l s of t h e r e s u l t s from t h e s e a d d i t i o n a l experimental i n v e s t i g a t i o n s fo l low. Radioac t ive Tracer S tud ie s Using Porous Graphi te Radioact ive methane and phenol were used i n s e p a r a t e experiments t o determine t h e s p e c i f i c p roducts of decomposition from each labe led s p e c i e s . Also, t h e amount and l o c a t i o n o f carbon depos i t i on i n t h e char due t o t h e thermal c rack ing o f each s p e c i e s was determined. The method used involved t h e sampling of t h e e x i t gas s t ream followed by gas chromatographic a n a l y s i s . The f r a c - Ex pe ri me nt X I1 1 (G ra ph it e) Fe ed M ix 2 w = 0. 00 1 lb /f t2 -s ec In le t Ga s Co mp os it io n TL = 17 00 °F To = 11 80 °F - - a - - - - - - - - - - - - - - 0 -- -- - - - , , - - - 0 - - - - - - - - U. I I I I I I I I I I I I I I I I m 0 0 U Ex pe ri me nt al R un Ti me (M in ut es ) Fi gu re 6 -9 , Ty pi ca l Me th an e- Hy dr og en Co nc en tr at io n Pr of il es i n th e Ex it G as S tr ea m fr om t he C ha r Zo ne T he rm al E nv ir on me nt Si mu la to r a ft er C le ar in g th e Po re Sp ac es o f Gr ap hi te " Fi ne s" w it h He li um o r Ni tr og en F lo w. t i ona fed gas chromatographic e f f l u e n t stream was then passed through a combustion furnace forming carbon d ioxide and water . Af te r t r app ing t h e water , t h e carbon d ioxide was absorbed i n a one molar hydroxide of hyamine ( i n methanol) s o l u t i o n . Co l l ec t ing t h e carbon d iox ide over small i n t e r v a l s (one h a l f t o one minute) produced r a d i o a c t i v e concen t r a t ions corresponding t o t h e separa ted gases i nd ica t ed on t h e gas chromatogram. By comparing t h e two curves f o r i d e n t i c a l r e t e n t i o n t imes, t h e r e l a t i v e amount of each carbon-containing spec i e s formed from t h e thermal degrada t ion of t h e labe led p y r o l y s i s product e n t e r i n g t h e cha r was determined. Typical r e s u l t s f o r Carbon-14 l abe l ed methane a r e shown i n F igure 6-10, i n which t h e gas chromatogram(s) and c o r r e s - ponding r a d i o a c t i v i t y curve a r e presented . The p a r t i c u l a r r e s u l t s a r e f o r experiment XXIX i n which t h e f r o n t s u r f a c e 2 temperature was 1935OF and t h e gas mass f l u x was 0,00591b/f t - sec . By comparing the two curves , t h e products of methane decomposition were found t o be unreacted methane, carbon monoxide, carbon d ioxide , e thylene and ace ty lene . These r e s u l t s f o r methane a r e very important i n t h e l i g h t of p r e d i c t i n g t h e manner i n which energy can be absorbed by chemical r e a c t i o n . Ethylene and ace ty l ene , f o r example, a r e i n d i r e c t products of methane decomposition predic ted by r e a c t i o n s (6-1) through (6-4) i n Table 6-7, whi le carbon monoxide and d iox ide a r e formed by t h e r e a c t i o n of steam with depos i ted carbon i n r e a c t i o n s (6-8) through (6-10). This information e s t ab l i shed t h a t t h e chemical r e a c t i o n s used t o p r e d i c t t h e phenomena occurr ing i n any system a r e c o r r e c t . A s i m i l a r d i scuss ion i s presented f o r labe led phenol. These r e s u l t s a r e l ikewise shown i n Figure 6-10. Condit ions f o r t h e presented d a t a were a f r o n t s u r f a c e temperature of 1960°F and a mass f l u x r a t e of 0.0034 l b / f t L - s e c . The e x i t gas products f o r phenol degradat ion a r e methane, carbon monoxide, carbon d iox ide , e thylene and ace ty l ene , a s we l l a s unreacted phenol analysed i n t h e l i q u i d phase, Once aga in i n s i g h t i n t o t h e kind of r e a c t i o n s necessary t o produce t h e products was obta ined . The formation of hydrogen and carbon by r e a c t i o n (6-6) and (6-7) i s probable by t h e observed carbon depos i t i on wi th in t h e g raph i t e . Hydrogenation of carbon by r e a c t i o n (6-5) t o form methane, followed by t h e steam-gas r e a c t i o n s (6-8, 6-9, 6-10) and t h e hydrocarbon cracking r e a c t i o n s (6-1, 6-2, 6-3, 6-4) accounts f o r each r a d i o a c t i v e spec i e s observed, I n both methane and phenol degrada t ion , thermal decompo- s i t i o n of t h e major spec i e s i n t h e s imulated p y r o l y s i s product s t ream was descr ibed and accounted f o r by t h e r e a c t i o n s considered important between 500 - 3000°F. I n a d d i t i o n t o t h e product d i s t r i b u t i o n r e s u l t i n g from t h e thermal degrada t ion of methane and phenol, deposi ted carbon was a l s o observed t o occur, The loca t ion of the carbon deposi t ion within t h e char l aye r i s important i n def in ing the temperature a t which reac t ions become s i g n i f i c a n t . This topic i s discussed i n d e t a i l i n the next sec t ion . Carbon Deposition Studies & Radioactive Tracer Methods The loca t ion and extent of c a r b ~ n deposi t ion r e s u l t i n g from methane and phenol decomposition was determined using Carbon-14 labeled methane and phenol. I n the s p e c i f i c cases s tudied , labeled methane and phenol were fed separa te ly a s components i n the simulated pyrolys is product stream enter ing t h e char. The char was removed a f t e r each experiment and sect ioned by removing t h i n l aye r s using emery paper. These l aye r s var ied between one and t en percent (by weight) of the t o t a l char and were combusted separa te ly with c o l l e c t i o n of the carbon dioxide i n one molar hydroxide hyamine ( i n methanol) so lu t ion . The r a d i o a c t i v i t y of each t h i n layer was determined and p lo t t ed a s a function of char depth. In Figure 6-11 such a curve i s shown f o r the thermal degradation of phenol and Figure 6-12 i s a s imi la r curve f o r the decom- pos i t ion of r ad ioac t ive labeled methane. The hashed-in rec tangular blocks represent the t o t a l percent r a d i o a c t i v i t y of t h e th ickness of t h e individual s l i c e s analysed, while t h e dotted curve represents the percent r a d i o a c t i v i t y per un i t th ick- T em pe ra tu re ( O F ) 11 10 13 38 15 53 17 59 19 50 E xp er im en t XX VI II Co nd i t i on s : W = 0. 00 34 lb /£ t - s e c L = 0. 02 08 f t = 0. 5 (P or ou s G ra ph it e) Fe ed M ix 4 (C l4 l ab el ed M et ha ne ) 0, O 0. 1 0. 2 0. 3 0 0 4 0. 5 0. 6 0. 7 0 ,8 0 ,9 1. 0 D im en si on le ss C ha r D is ta nc e (z /L ) F ig ur e 6- 12 , C ar bo n D ep os it io n P ro fi le f o r th e T he rm al D eg ra da ti on o f M et ha ne , a M aj or C om po ne nt in t he P y ro ly si s G as St re am . ness a t a p a r t i c u l a r char depth. The r e s u l t s i n F igure 6-1L a r e f o r phenol decomposition a t a mass f l u x r a t e of 0.0059 2 l b / f t - sec and a f r o n t su r f ace temperature of 1960°F. Depo- s i t i o n of carbon appears t o s t a r t a t a char depth of 0.38 corresponding t o a temperature of 1300 OF, and cont inues uniformly t o 0.925 where t h e temperature i s 1925OF. A t t h i s po in t a r a p i d decrease i s noted i n d i c a t i n g e i t h e r no f u r t h e r carbon depos i t i on o r disappearance of carbon by chemical r e a c t i o n . S imi l a r r e s u l t s a r e observed f o r carbon depos i t i on by methane decomposition i n Figure 6-12. Since carbon depos i t i on by methane and/or phenol degradat ion i s an inc reas ing func t ion of temperature, and, s i n c e a s u b s t a n t i a l amount of phenol and methane i s p re sen t i n t h e e x i t gas stream, i t i s u n l i k e l y t h a t carbon depos i t i on r e a c t i o n s have te rmina ted . In s t ead , t h e r e a c t i o n of t h e deposi ted carbon wi th steam ( o r carbon d ioxide) i s a more probable explana t ion of t h e d e c l i n e noted i n Figure 6-12, This i s a l s o subs t an t i a t ed by t h e rap id decrease i n water concen t r a t ion a t t he same temperature where carbon depos i t i on d e c l i n e s . Addi t iona l ly , carbon was observed on t h e qua r t z cover p l a t e and i n s i d e su r f aces of t h e o u t e r cha r ho lder s e c t i o n which ind ica t ed t h a t t h e carbon depos i t i on r e a c t i o n s were cont inuing a f t e r t h e gases had l e f t t h e char su r f ace . Therefore, a very comprehensive p i c t u r e of carbon depos i t i on wi th regard t o i t s l o c a t i o n , t h e causes f o r i t s appearance and disappearance, and i t s e f f e c t on t h e e x i t gas product d i s t r i b u t i o n was ob t a ined , This was one a d d i t i o n a l , important u s e o f an a c c u r a t e mathematical model i n p r e d i c t i n g phenomena ve ry d i f f i c u l t and o f t e n imposs ib le t o determine wi th expertmental techniques on ly . The combination of t h e r a d i o a c t i v e t r a c e r techniques and t h e non-equi l ibr ium f low a n a l y s i s w i l l be app l i ed i n eva lua t ing va r ious c a t a l y s t s f o r a c c e l e r a t i n g t h e chemical r e a c t i o n s and, thereby , i n c r e a s i n g t h e energy absorbed wi th in t h e char zone. The e f f e c t i v e n e s s o f each c a t a l y s t w i l l be determined i n t h e fo l lowing s e c t i o n by comparing t h e r e s u l t s wi th d a t a from n o n - c a t a l y t i c experiments. C a t a l y t i c React ions of t h e Py ro lys i s Products i n t h e Char Zone The d i s c u s s i o n . t h u s f a r ha s shown t h a t chemical r e a c t i o n s w i th in t h e cha r l a y e r a r e very important modes of energy ab- so rp t ion . It was a l s o pointed ou t t h a t chemical non-equi l ibr ium bec.omes important between 2000 - 2500 OF f o r a mass f l u x r a t e of 0.05 1 b / f t L - s e c (Tables 6-13 through 6-16). Below t h i s range , t h e f low of p y r o l y s i s p roducts through t h e cha r i s e s s e n t i a l l y f rozen , wh i l e above 2000 OF, t h e flow i s b e s t descr ibed by f i n i t e r e a c t i o n r a t e s f o r t h e important chemical r e a c t i o n s t ak ing p l a c e w i th in t h e cha r between t h e p y r o l y s i s p roducts , I n r e e n t r y a p p l i c a t i o n s where t h e temperature g rad i en t ac ros s t h e a b l a t o r may vary from 500 5000°F, t h e frozen s t a t e ( l e s s than 2000 OF) can extend over nea r ly one t h i r d t h e e n t i r e t h i ckness . Within t h i s reg ion h e a t absorp t ion by conduction and convect ion a r e t h e only important modes of energy t r a n s f e r . In orde r t o i nc rease t h e capac i ty of t h i s reg ion t o absorb h e a t , and thus p ropor t iona te ly reduce t h e t o t a l h e a t s h i e l d weight requirement , t h e i n t roduc t ion of a c a t a l y s t t o i n i t i a t e chemical r e a c t i o n s i n t h e lower temperature range (< 2000 OF) was evaluated. There a r e two types of c a t a l y s t systems: homogeneous and heterogeneous. The f i r s t involves t h e in t roduc t ion of a chemical compound which i s i n t h e same phase a s t h e p y r o l y s i s product stream. The homogeneous c a t a l y s t e f f e c t i v e l y reduces t h e energy of a c t i v a t i o n by i n t e r a c t i n g wi th t h e va r ious spec i e s p re sen t . To i l l u s t r a t e t h i s i n t e r a c t i o n t h e c a t a l y t i c c h l o r i n a t i o n of n i t r o u s oxide i n t h e presence of bromine i s used a s an example (58) of t h e a c t i o n of a homogeneous c a t a l y s t . The d i r e c t c h l o r i n a t i o n occurs by r e a c t i o n (6 -14) : In t roducing bromine r e s u l t s i n a two r e a c t i o n sequence a s f 01 lows : The r e a c t i o n with t h e g r e a t e s t a c t i v a t i o n energy between (6-15) and (6-16) i s t h e r a t e determining s t e p f o r t h e sequence. Bromine i s considered a c a t a l y s t i f , and only i f , t h e energy of a c t i v a t i o n of t h e r a t e determining s t e p i s smal le r than t h e energy of a c t i v a t i o n of r e a c t i o n (6-14). Such i s t h e ease f o r t h i s example. Other homogeneous c a t a l y s t s a r e i od ine , hydrogen bromide, hydrogen f l u o r i d e , n i t r i c oxide, c h l o r i n e and mercury (59,60,61,62,63). I n t h e c a s e of t h e halogens, i nco rpora t ion of an organic h a l i d e i n t o t h e composite which thermal degrades a t o r near t h e temperature f o r t h e nylon-phenolic r e s i n could be used t o inkro- duce t h e c a t a l y s t i n t o t h e py ro lys i s product stream, One example f o r bromine i s tribromobutane which vapor izes a t 225OC o r 5 4 0 " ~ (nylon-phenolic r e s i n a t 250°C ) and forms HBP and cracked products of an o l e f i n . The second kind of c a t a l y s t system wi th application t o flow of hydrocarbon products through porous media a r e t h e hetero- geneous c a t a l y s t s . These c o n s i s t of a t h i n d i spe r s ion of an a c t i v e meta l on a porous s o l i d , c a l l e d a c a t a l y s t support . Gases are thus absorbed on t h e metal su r f aces a s rhey flow through t h e porous s o l i d , undergo chemical r e a c t i o n s , and resorbed i n t o t h e gas stream. The kind of s o l i d suppor t s used vary from c l ays and alumina t o porous carbon. Heterogeneous c a t a l y s t s a r e widely used i n t h e petroleum and chemical i n d u s t r i e s f o r a c c e l e r a t i n g hydrogenation and dehydrogenation r e a c t i o n s , hydrocracking r e a c t i o n s and hydro- forming r e a c t i o n s . Some t y p i c a l a c t i v e metals used i n t h e s e a p p l i c a t i o n s a r e platinum, tungs ten , molybdenum, pal ladium, e t e . (64) . One example involves t h e c a t a l y t i c hydrogenation of benzene t o cyclohexane a t room temperature wi th platinum on porous carbon suppor t s (64) , Cyclohexane i s then cracked t o lower molecular weight compounds a t 84OoF (65) . D e t a i l s f o r t h e c a t a l y t i c c rack ing of numerous o rgan ic compounds a r e presen ted by Vogh (66) , I n many cases t h e use of heterogeneous c a t a l y s t s i s r e s t r i c t e d t o a p p l i c a t i o n s which do not con ta in compounds t h a t d e a c t i v a t e t h e metal su r f aces . Some of t h e s e s o c a l l e d poisons a r e carbon monoxide, s u l f u r and d e p o s i t s o f carbon o r coke. Although t h e r e i s no s u l f u r i n t h e py ro lys i s product s t ream, carbon monoxide and deposi ted carbon a r e p re sen t r e q u i r i n g a d d i t i o n a l sc reen ing of t h e heterogeneous c a t a l y s t cons idered , The a c t i v i t y and s e l e c t i v i t y of t h e c a t a l y s t chosen f o r t h i s a p p l i c a t i o n i s d i scussed i n a subsequent s e c t i o n . Because t h e heterogeneous c a t a l y s t e x i s t s i n a d i f f e r e n t s t a t e , t h e s o l i d phase, than t h e p y r o l y s i s p roducts , in t roduc- t i o n i n t o t h e system r e q u i r e s more d e t a i l e d planning. There a r e two p o s s i b l e techniques t h a t permit t h e placement of a f i n e l y d ispersed metal c a t a l y s t on t h e char of a cha r r ing a b l a t o r . The f i r s t t a k e s advantage of a nylon-platinum c a t a l y s t used t o hydrogenate benzene t o cyclohexane (67) . The i n c l u s i o n of t h i s plat inum impregnated nylon wi th nylon and phenolic r e s i n dur ing t h e molding process could be made. During a b l a t i o n , t h e nylon would degrade and r e l e a s e t h e metal c a t a l y s t which would be d i s t r i b u t e d on t h e s u r f a c e of t h e formed char l a y e r . The presence of water and hydrogen a t t h e lower temperatures ( <900°F) would prevent coking, leav ing t h e metal s i t e s exposed t o promote t h e py ro lys i s r e a c t i o n s , The second method i s s i m i l a r t o t h e method used f o r i n t r o - ducing a homogeneous c a t a l y s t i n t o t h e p y r o l y s i s product stream. I n t h i s c a s e an organo-metal l ic compound such a s n i c k e l s t e a r a t e (68) could be included which would vapor ize i n t h e decomposition zone wi th depos i t i on of n i c k e l on t h e char su r f ace . This a c t i o n i s commonly observed i n vapor phase c racking processes (68,69) i n which increased a c t i v i t y of t h e c racking c a t a l y s t r e s u l t s i n excess ive carbon and hydrogen formation, Other sfrni lar compounds a r e t h e carbonyl compounds of n i c k e l , i r o n and coba l t (70) . The combination of both c a t a l y s t s systems may aEsa be ~ o s s i b l e by us ing compounds conta in ing both rnecal and halogen atoms, such a s platinum iod ide , The advantage of t h i s type s f co -ca t a lys t would e x i s t only i f both groups were found t o a c c e l e r a t e chemical r e a c t i o n s wi th in t h e char l a y e r . The fol lowing sec t ions w i l l d e sc r ibe t h e r e s u l t s obtained i n t e s t s u s ing t h e Char Zone Thermal Environment Simulator . Each c a t a l y s t system w i l l be compared with non-ca t a ly t i c d a t a t o determine t h e ex t en t of chemical r e a c t i o n due t o t h e add i t i on of t h e c a t a l y s t . The prepara t ion of each c a t a l y s t and t h e procedure f o r in t roducing i t i n t o t h e experimental s imula t ion w i l l a l s o be d iscussed . Homogeneous Ca ta lys i s of t h e Py ro lys i s Products: Unlike t h e heterogeneous c a t a l y s i s systems, very l i t t l e information regard- ing t h e a c t i v i t y of va r ious homogeneous c a t a l y s t systems i s contained i n t h e l i t e r a t u r e . One source , however, repor ted t h e r e l a t i v e a c t i v i t y of s eve ra l o rganic h a l i d e s and Halogen c a t a l y s t s f o r t h e c a t a l y t i c degradat ion of hydrocarbons t o carbon monoxide, carbon dioxide and organic ac ids , aldehydes and ke tones . (71). A l i s t o f t h e r e l a t i v e a c t i v i t i e s of t h e s e c a t a l y s t s a r e presented i n Table 6-23 wi th iod ine a s a r e f e rence ( r e l a t i v e a c t i v i t y of 100). No r e l a t i v e a c t i v l . t i e s of n i t r o u s oxide o r mercury were found. Also hydrogen f l u o r i d e was omit ted from t h e above L i s t of r e l a t i v e a c t i v i t i e s . Although t h e above may indeed be e x c e l l e n t homogeneous c a t a l y s t s , c e r t a i n a spec t s of t h e a b l a t i v e process p r o h i b i t t h e i r use . For example, n i t r o u s oxide, whi le e x h i b i t i n g e x c e l l e n t T ab le 6 -2 3. R el at iv e A ct iv it y o f th e H al og en s a n d O rg an ic H al id es a s C at al ys ts i n th e T he rm al D eg ra da ti on o f P y ro ly si s G as P ro du ct s. C on di ti on s: O xi da ti on o f A ld eh yd he s a n d K et on es a t 4 00 -5 00 °C a n d o n e A tm os ph er e. C om po ne nt N am e Io di ne (R ef er en ce ) Is op ro py l Io di de E th yl I od id e M et hy l Io di de H yd ro ge n B ro m id e Is op ro py l B ro m id e E th yl B ro m id e D ib ro m oa ce ty le ne C hl or id es R el at iv e E ff ic ie nc y 10 0 7 0 40 3 0 20 5 4 3 0 c a t a l y t i c a c t i v i t y f o r t h e thermal degradat ion of c e r t a i n hydrocarbons r e q u i r e s a concent ra t ion too g r e a t t o be p r a c t i c a l l y included i n t h e composite (59) . S imi l a r ly , hydrogen f l u o r i d e and mercury a r e almost exc lus ive ly used a s l i q u i d phase c a t a l y s t s ( 7 2 , 7 3 ) , As a r e s u l t , a t t e n t i o n i n t h i s research was given t o t h e h a l i d e s which were not on ly repor ted a s good c a t a l y s t s i n hydrocarbon decomposition and ox ida t ion r e a c t i o n s ( 7 4 1 , bu t a l s o requi red i n small enough concen t r a t ions t o be convient ly and economically f e a s i b l e f o r a b l a t i v e h e a t s h i e l d a p p l i c a t i o n s . Experimental Resu l t s for Homogeneous C a t a l y s i s of t h e P y r ~ l y s i s Product Reactions with Bromine: As a mat te r of con- venience i n t h e experimental s imula t ion appara tus , bromine was se l ec t ed a s a r e p r e s e n t a t i v e h a l i d e c a t a l y s t . It was convenient t o d i s s o l v e bromine i n t h e water and feed t h e r e s u l t i n g s o l u t i o n t o t he char holder wi th phenol and t h e gaseous p y r o l y s i s products , The concen t r a t ion of bromine i n t h e water s o l u t i o n was va r i ed from 1.0 t o 4.0% by weight, The s e l e c t i o n of bromine a s a s u i t a b l e and t y p i c a l c a t a l y s t was based on evidence of s t rong aromatic r i n g a t t a c k , such a s with phenol, t o form tribromophenol a t ambient cond i t i ons . I n a d d i t i o n it has e x c e l l e n t o x i d a t i v e p r o p e r t i e s i n decomposing hydrocarbons such a s propane t o carbon monoxide, carbon d ioxide and o t h e r organic spec i e s such a s organic a c i d s , aldehydes and ketones ( 7 4 9 , Furthermore, t h e formation of HBr from hydrogen and bromine occurs a t moderate temperatures (200 - 300°C) by t h e fo l lowing mechanism (75) . This g ives t h e a d d i t i o n a l c a t a l y t i c b e n e f i t of HBr being p re sen t . B r + H2 HBr + H H i- B r 2 4 H B r + B r H i- H B r 4 H2 + B r Also it e s t a b l i s h e d a r e f e rence t o t h e remaining h a l i d e c a t a l y s t s contained i n Table 6-23 and thus makes an exhaus t ive inveski - ga t ion unnecessary i f s i g n i f i c a n t promotion of chemical r e a c t i o n r a t e s a r e found, The above mechanism i s favored by low p res su re and l a r g e s u r f a c e a r e a , both o f which e x i s t i n t h e char zone dur ing r e e n t r y . Resu l t s s f s e v e r a l experiments a r e shown i n Table 6-24. The experimental e x i t gas compositions a r e no longer pred ic ted by t h e non-equi l ibr ium flow model w i th in t h e experimental accuracy a s observed f o r t h e non-ca t a ly t i c experiments. Also t h e r eace ions a r e not a t equi.l ibrfum a s seen from t h e t a b l e . The e f f e c t of bromine a s a c a r a l y s t i s be%%er i l l u s t r a t e d by comparing experiment XXVEII-92, i n which t h e mass f l u x was 0.0044 l b / f t 2 - s e c , t h e f r o n t su r f ace temperature of 1920°F and no bromine, wi th experiment XXV-81 (mass f l u x of 0,0038 Z l b / f t - see , a f r o n t s u r f a c e temperature of 1995°F and 4%(wt) bromine c a t a l y s t ) in Table 6-25, The cond i t i ons a r e almost t h e same, and t h e ex t en t of r e a c t i o n i s g r e a t e r f o r t h e experiment with bromine p re sen t . The add i t i on of bromine acce l e ra t ed t h e chemical r e a c t i o n s a s seen by t h e f a c t s t h a t s i g n i f i c a n t l y more of t h e water (17.6% r a t h e r than 25.4%) and phenol (7.2% r a t h e r than 9.5%) had been consumed than would have been i f bromine had not been p re sen t . 'This i s a l s o seen by d i r e c t comparison o f t h e experimental e x i t gas esmposi t ions from each of t h e s i m i l a r experiments, A measured decrease i n t h e water and phenol concen t r a t ions , wi th corresponding increases i n methane, carbon monoxide, carbon di.oxide, e thylene and ace ty l ene a r e obtained i n t h e bromine ca t a lysed experiment, These same t r ends a r e observed i n a l l i n v e s t i g a t i o n s wi%h bromine and a r e independent of t h e c a t a l y s t concent ra t ions used(l ,O t o 4,0% by weight ) , The e f f e c t of t h e bromine c a t a l y s i s i s a l s o seen by in spec t ing t h e carbon deposi, tfon p r o f i l e s f o r t h e thermal decomposition s f phenol i n t h e simulated p y r o l y s i s product stream. This i s presented i n Figures 6-13 and 6-14. The carbon depos i t i on p r o f f l e f o r the non-ca t a ly t i c experiment i s shown i n Figure 6-13 2 f o r a mass f l u x of 0,0059 Eb/ f t -see and 1935'F. Deposition T ab le 6 -2 5. Fl ow o f P y ro ly si s G as es T hr ou gh G ra ph it e. C om pa ri so n o f B ro m in e C at al yz ed a n d N on -C at al yt ic E x it G as C om po si ti on s. FR ON T TE MP begins a t a d i s t a n c e of 0.38 i n t h e char where t h e temperature i s 1310 OF with a uniform inc rease t o a maximum value a t 0.925 o r 1915OF. A t t h i s po in t t h e p r o f i l e decreases . I n c o n t r a s t t o t h i s curve, Figure 6-14 r e p r e s e n t s t h e carbon depos i t i on p r o f i l e f o r t h e bromine ca t a lysed experiment i n which t h e 2 mass f l u x was 0.0075 l b / f t - see and 1900°F. There i s a d e f i n i t e s h i f t i n t h e carbon depos i t i on eurve wi th t h e maximum va lue moving from 0.925 t o 0.71 o r from a temperature of 1915°F t o 1630°F. Deposition aga in s t a r t s a t a d i s t a n c e of 0.38 (1300°F). Also a d d i t i o n a l carbon depos i t i on was noted near t h e f r o n t s u r f a c e a t a temperature of about 1925°F. S imi l a r p r o f i l e s a r e shown i n Figure 6-15 and 6-16 f o r carbon-14 l a b e l l e d methane decomposition. Although t h e r e s u l t s a r e not a s pronounced a s t h e phenol d a t a , a d e t e c t a b l e s h i f t i n t h e carbon depos i t i on p a t t e r n i s aga in observed. Deposi t ion begins a t 0.48 (1555°F) f o r t h e non-ca t a ly t i c experiment compared wi th 0.42 (1500°F) f o r t h e bromine ca ta lyzed case . The p o i n t of maximum depos i t i on i s s h i f t e d away from t h e f r o n t s u r f a c e t o a p o s i t i o n corresponding t o 1893OF o r 0.85, The peak f o r t h e bromine-free experiment i s loea ted a t 0.98 (1930°F). I n summary t h e s e r e s u l t s show t h a t bromine i s an a c t i v e c a t a l y s t f o r t h e c a t a l y t i c c racking of phenol i n t h e presence of hydrogen (hydrocracking) and t o a l e s s e r ex t en t f o r t h e hydrocracking of methane. A s i m i l a r d i scuss ion regard ing t h e cracking of t h e p y r o l y s i s products us ing heterogeneous c a t a l y s t i s presented i n t h e fol lowing s e c t i o n . Heterogeneous C a t a l y s i s of t h e Py ro lys i s Product React ions Using a Tungsten-Molybdenum =-Catalyst : A g r e a t d e a l of r e sea rch i n t o heterogeneous c a t a l y s t s , t h e i r a p p l i c a t i o n s and a c t i v i t i e s has been repor ted i n t h e l i t e r a t u r e (64,65,66,67) . These c a t a l y s t a r e e x c e l l e n t hydrogenation a c c e l e r a t o r s f o r a number of hydrocarbons common t o t h e petroleum and chemical i n d u s t r i e s . However, they a r e a l s o s u s c e p t i b l e t o d e a c t i v a t i o n by r e a c t i o n , adsorpti.on o r coa t ing by seve ra l poisons. The two poisons which a r e present i n t h e py ro lys i s gases a r e carbon monoxide and coke ( o r carbon) formation. These two poisons a r e present i n t h e char zone and must be considered when s e l e c t i n g p o s s i b l e heterogeneous c a t a l y s t s . These poisons r u l e out t h e use of platinum, paladium, rhodium, n i c k e l and selenium s i n c e t h e s e a r e a l l poisoned by carbon monoxide. I n l i g h t of t h i s d i scuss ion , tungs ten , because of i t s r e l a t i v e l y good a c t i v i t y i n systems conta in ing carbon monoxide, and molybdenum, because of i t s h igh s e l e c t i v i t y i n t h e thermal degrada t ion of hydrocarbons, were se l ec t ed a s co -ca t a lys t s . The method used t o d i s p e r s e t h e s e metals on t h e g r a p h i t e specimens was t h e s tandard procedure t o p repa i r heterogeneous c a t a l y s t s and is a s fo l lows . F i r s t , t h e metals were obtained a s metal ac ids (anhydrous) and added t o ho t (80°C) s u l f u r i c ac id . Molybdenum was completely d isso lved whi le tungs ten formed a s a t u r a t e d s o l u t i o n . The g r a p h i t e specimens were placed i n t h e ho t s o l u t i o n and s t i r r e d v igorous ly f o r t h i r t y minutes. The second phase of t h e procedure involved t h e pas s ing of carbon d i s u l f i d e vapors through t h e g r a p h i t e t o conver t t h e metal oxides t o s u l f i d e s which inc reases t h e c a t a l y t i c a c t i v i t y o f t h e metals . The specimens were then d r i ed a t l lO°F and r e - weighed t o determine t h e weight of c a t a l y s t d i spe r sed w i t h i n t h e pores . The c a t a l y s t concen t r a t ion va r i ed from 5 t o 6 percent (by weight) of t h e co -ca t a lys t (50:50). This i s t y p i c a l of t h e d ispersed (metal) phase composition of he t e - rogeneous c a t a l y s t s . The e f f e c t of t h i s c a t a l y s t on t h e r e a c t i o n s of t h e pyro- l y s i s products i n t h e char zone i s shown i n Table 6-26. Although t h e r e a r e n o t i c e a b l e d i f f e r e n c e s between t h e exper imenta l ly measured e x i t gas compositions and t h e computed va lues f o r t h e uncatalyzed case , they a r e no t a s pronounced a s t h e r e s u l t s f o r bromine. This i s b e t t e r i nd ica t ed by comparing t h e r e s u l t s of non-ca t a ly t i c experiments (XXVIII-92 and XXIX-94) wi th t h e va lues obtained i n t h e heterogeneous co -ca t a lys t systems (XXXII-99 and XXXP-98). The e x i t gas compositions a r e shown i n Table 6-27 f o r an average mass f l u x r a t e of 0.0048 l b / f t 2 - s e c and a f r o n t su r f ace temperature range of 1860" t o 1945OF. No d e t e c t i b l e d i f f e r e n c e between t h e f o u r experiments i s determined. S i m i l a r l y , FR ON T TE MP RU N NU M BE R N O N -E QU IL IB RI EX PE RI M EN TA L EX PE RI M EN TA L EX PE RI M EN TA L a comparison of t h e carbon depos i t i on p r o f i l e s f o r carbon-14 labe led phenol (XXVIII and XXXII) and methane (XXIX and XXXI) show no s u b s t a n t i a l s h i f t i n t h e p o s i t i o n of t h e maximum depos i t i on o r t h e l o c a t i o n where carbon depos i t i on begins . These a r e shown i n F igures 6-17 through 6-20. A s l i g h t d i f f e r e n c e i n behavior near t h e f r o n t su r f ace i s observed. However, t h i s r e p r e s e n t s no s u b s t a n t i a l change from t h e non-ca t a ly t i c behavior . A s e r i e s of experiments wi th a platinum c a t a l y s t d i spersed on t h e g r a p h i t e specimens was a l s o conducted us ing phenol- water f r e e p y r o l y s i s gases having a r e l a t i v e l y low carbon monoxide concent ra t ion . These s t u d i e s showed no c a t a l y t i c a c t i v i t y over a temperature range of 1370' t o 1755OF. The r e s u l t s of t h e s e t e s t s a r e summarized i n Table 6-28. The flow remained f rozen i n each experiment s tud ied . Summary of the C a t a l y t i c S tudies Increase React ions i n t h e Char Zone -- Resu l t s f o r adding bromine t o t h e py ro lys i s product stream a s a homogeneous c a t a l y s t i nd ica t ed increased chemical r e a c t i o n s wi th in t h e char zone. This a c c e l e r a t i o n was shown by comparison of t h e e x i t gas composition from non-ca t a ly t i c and c a t a l y t i c experiments with t h e c a l c u l a t e d e x i t gas composition based on t h e non-equilibrium (non-catalysed) flow model. Furthermore, T em pe ra tu re ( O F ) 11 10 13 38 15 53 17 59 19 50 D im en si on le ss C ha r D is ta nc e (z /L ) F ig ur e 6- 17 . C ar bo n D ep os it io n P ro fi le f o r th e T he rm al D eg ra da ti on o f M et ha ne , a M aj or C om po ne nt i n t he P yr ol ys is G as St re am . T em pe ra tu re ( O F ) 11 63 14 08 16 65 36 32 E xp er im en t X X IX 28 C on di ti on s : 24 L = 0. 02 08 f t = 0. 5 (P or ou s G ra ph it e) 20 T = 93 0° F 16 Fe ed M ix 4 ( C1 4 la be le d P he no l) 12 8 4 0 D im en si on le ss C ha r D is ta nc e ( z IL ) F ig ur e 6- 19 . C ar bo n D ep os it io n P ro fi le f o r th e T he rm al D eg ra da ti on o f P he no l, a M aj or C om po ne nt i n t h e P y ro ly si s G as S tr ea m . m 6 13 'rl cd U Ta bl e 6- 28 . F lo w o f Py ro ly si s Pr od uc ts T hr ou gh P or ou s Gr ap hi te . Ex it Ga s Co mp os it io ns o f Pl at in um C at al ys ed E xp er im en ts . carbon depos i t i on p r o f i l e s were used t o l o c a t e t h e p o s i t i o n and temperature where depos i t i on r e s u l t i n g from methane and phenol thermal degrada t ion occur red . The use of bromine (o r HBr) a s a r e p r e s e n t a t i v e homogeneous c a t a l y s t made a d e t a i l e d i n v e s t i g a t i o n unnecessary because o f t h e r e l a t i v e a c t i v i t y of va r ious h a l i d e s t o hydrogen bromide i n Table 6-23. By comparison, i od ine and organic i od ides should have a g r e a t e r i n f luence on t h e py ro lys i s product r e a c t i o n s , whi le c h l o r i n e o r t h e organic c h l o r i d e s should have a l e s s e r in£ luence. No d e t e c t a b l e change i n t h e e x i t product composition, and, t h e r e f o r e , i n t h e r a t e s of chemical r e a c t i o n of t h e p y r o l y s i s p roducts , were observed f o r tungs ten and molybdenum c o - c a t a l y s t s and plat inum over a temperature range of 1845' t o 2300°F. Oxidat ive Degradation of Low Density Nylon-Phenolic Resin Chars i n an A i r Stream at Elevated Temperatures --- The o x i d a t i v e degrada t ion of low d e n s i t y nylon-phenolic r e s i n c h a r s i s important i n r e e n t r y a p p l i c a t i o n s a s a r e s u l t of t h e h o t , shock heated a i r s t reams f lowing ad j acen t t o t h e char f r o n t s u r f a c e . It i s be l ieved t h a t a po r t i on of t h i s a i r s t ream p e n e t r a t e s t h e char f r o n t s u r f a c e forming l a r g e c a v i t i e s and i r r e g u l a r shaped, erroded a r e a s on t h e s u r f a c e o f t h e h e a t s h i e l d dur ing r e e n t r y o r i n models t e s t e d i n a r c j e t s . I n o rde r t o determine t h e ex t en t of a i r ox ida t ion , experiments were made i n t h e Char Zone Thermal Environment Simulator i n which a i r , a t r a t e s corresponding t o r e e n t r y va lues , was i n j e c t e d i n t o t h e char a t t h e f r o n t su r f ace . These exper i - ments simulated a maximum a i r mass f l u x , because t h e r e i s pyro- l y s i s gas flow counter t o t h e a i r dur ing a b l a t i o n . To determine whether a i r reac ted a t t h e su r f ace o r i n depth , samples of t h e e x i t gas s t ream were taken a t s h o r t i n t e r v a l s t o determine t h e oxygen conversion wi th in t h e cha r . The r e s u l t of t hese ana lyses f o r two sepa ra t e experiments a r e shown i n Figure 6-21. A t an a i r mass f l u x of 0.0057 l b / f t L - s e c and a f r o n t su r f ace temperature of 1485°F. The maximum conversion of oxygen a t t h e back su r f ace was 53% corresponding t o an oxygen concent ra t ion of 10 mole percent leav ing t h e back su r f ace . A back su r f ace temperature of 747°F was measured f o r t h e 118 inch t h i c k cha r . Increas ing t h e a i r 2 flow r a t e t o 0.035 l b l f t -sec and a f r o n t su r f ace temperature of 2047"F, increased t h e maximum conversion a t t h e r e a r s u r f a c e t o 81% o r a concent ra t ion of fou r percent leav ing t h e char back su r f ace . The back su r f ace temperature was measured a t 304°F. The char th ickness was 114 inch . The r e l a t i v e l y low back s u r f a c e temperatures i n d i c a t e t h a t t h e h ighly exothermic r e - a c t i o n probably occurs near t h e f r o n t su r f ace . Although oxygen conversion a t t h e back su r f ace was never complete i n d i c a t i n g t h e presence of oxygen w i t h i n the pores a t a l l char depths , the e x t e n t of ox ida t ion i n depth appears small i n comparison t o t he s u r f a c e ox ida t ion . A photograph of the f r o n t su r f ace a f t e r 11 minutes exposure t o an a i r mass f l u x of 0.035 l b / f t 2 - s e c and a temperature of 2047OF (Experiment XVII) i s shown i n Figure 6-22. The t h r e e l a r g e erroded a reas i n d i c a t e s t rong su r f ace a t t a c k . The rounded edges near t he e r r o s i o n s f u r t h e r support t h e concept t h a t ox ida t ion occurs where t h e r e i s the l e a s t r e s i s t a n c e t o flow. The time f o r t hese holes t o be formed can be es t imated by comparing t h e length of time necessary to o b t a i n near zero oxygen conversion a t t h e back su r f ace i n Figure 6-21. In a d d i t i o n t o the experimental d a t a , a modi f ica t ion t o t he i so thermal a n a l y s i s (Appendix F) was made by cons ider ing temperatures w i t h i n the char t o vary l i n e a r l y wi th char d i s t - ance. This approximation premits the c a l c u l a t i o n of t h e oxygen convers.ion f o r a given char depth ( res idence time) and f r o n t su r f ace temperature, A comparison of t he c a l c u l a t e d and measured maximum conversions i s shown i n Table 6-29. The conversion of oxygen wi th char depth i s a l s o presented i n F igure 6-23 f o r t he l i n e a r approximation of the temperature and a l s o t h e isothermal eva lua t ions a t t he f r o n t and back su r f ace temperatures . The d a t a used t o desc r ibe the a i r ox ida t ion of g raph i t e i s presented i n Table 6-29. Agreement of the ca l cu la t ed and experiment con- ve r s ions a t t he back su r f ace is wi th in the experimental (I] (d aJ 2 (I] aJ U .rl aJ ik k 0 5 b (I] 4 0 0 e* W Cu 0 h aJ (I] rl aJ aJ M 5 3 C U k (d G U d .A (d E : 8 P;; $ E? 3aJ '7 aJ H rl W (d h m '44 (I] 0 m g g (b (d k M U 0 a U Ta bl e 6- 29 . Ai r Ox id at io n o f Lo w De ns it y Ny lo n- Ph en ol ic R es in C ha rs . A De ta il ed Ca mp ar is on o f th e Ca lc ul at ed a n d Me as ur ed O xy ge n Co nv er si on a t th e Ch ar B ac k Su rf ac e (E xi t Su rf ac e) . Co nd it io ns : Ba ck T em pe ra tu re , O F Ch ar T hi ck ne ss , ft Ex pe ri me nt R un T im e, M in . Me as ur ed M ax im um C on ve rs io n: @ ) Ca lc ul at ed M ax im um C on ve rs io n: (1 ) a t th e Fr on t Te mp er at ur e (2 ) a t th e Ba ck T em pe ra tu re (3 ) a t a Te mp er at ur e w hi ch v a r ie d li ne ar ly w it h c ha r de pt h (4 ) a t th e Av er ag e Te mp er at ur e W w 03 Dimensionless Char Distance ( 2 1 ~ ) ; 1 = Char Back Surface Figure 6-23. Conversion of Oxygen f o r t he Flow of A i r Through a Low Densi ty Nylon-Phenolic Resin Char a t a Mass Flux of 0.035 l b / f t 2 - s e c and a Temperature of 1 4 8 5 ' ~ ' . accuracy of t h e ana lyses . Values of 3 0 ~ c a l / m o l e f o r t h e a c t i v a - - 1 t i o n energy and 1 x 1017 sec were used f o r t h e f i r s t o rder a i r ox ida t ion of carbon, Energies of a c t i v a t i o n between 8 and 43 ~ c a l / m o l e , frequency f a c t o r between 1016 and 1018 and r e a c t i o n o rde r s of zero, one h a l f and one a r e reported i n t h e l i t e r a t u r e (42) . REFERENCES 1. Nelson, James B., "~etermination of Kinetic Parameters of Six Ablation Polymers by Thermogravimetric Analysis", NASA TN D-3919 (April 1967). 2. Sykes, G, F., Private Communication to R. W, Pike (March 14, 1968). 3. Sykes, George F., Jr,, "~ecomposition Characteristics of a Char-Forming Phenolic Polymer Used for Ablative Composites," NASA TN D-3810 (February 1967). 4. Freidman, H. L., "Pyrolysis of Plastics in a High Vacuum Arc Image Furnace, " Journal of Applied Polymer Science, - 9, 1005 (1965). 5. Ladacki, Michael, Janet V, Hamilton and Samuel N. Cohz, "Heat of Pyrolysis of Resin in Silica-Phenolic Ablator , " A I M Journal, (PO), 1798 (October 1966). - 6. Kratsch, K, M., L. F. Hearne and H. R. McChesney, "Thermal Performance of Heat Shield Composites During Planetary Entry," AIM-NASA National Meeting, Palo Alto, California, 3, (September 30-October 1, 1963). 7 . Sca l a , S . M. and L. M. G i l b e r t , " ~ h e r m a l Degradation of a Char-Forming P l a s t i c During Hypersonic F l i g h t , " & Jou rna l , 32 ( 6 ) , 917-24 (June 1962). 8. Shulman, G . P , , and H. W. Lochte, "Thermal Degradation of Polymers. 11. Mass Spectrometr ic Thermal Analysis of Phenol-Formaldehyde Polycondessates," Journa l of Applied Polymer Science, l0, 619-635 (1966). 9. Beecher, Norman, and Ronald E. Rosensweig, "Ablation Mechanisms i n P l a s t i c s wi th Inorganic Reinforcement," ARS Journa l , 2, 532-538 (1961). - 10. d e l Va l l e , E. G . , R . W. Pike and G . C. A p r i l , "Transport Phenomena i n t he Char Zone During Abla t ion . 11: Equil ibr ium Composition of Degradation Products of Abla t ion ," Paper 13e, 63rd National Meeting of t he A.I.Ch.E., S a l t Lake Ci ty , Utah (May 1967). 11. A p r i l , Gary C . , E . G. d e l Va l l e , Simon Hacker and R . W. Pike , "Comparison of Methods f o r Determining t h e composition of Py ro lys i s Products from the Degradation of Nylon-Phenolic Resin Abla t ive Composites," NASA-RFL-9, Louisiana S t a t e Un ive r s i t y , Baton Rouge, Louisiana (March 1969). 1 2 . Pe r ry , John H . , ed . , Chemical Engineers ' Handbook, 3rd ed . , New York: McGraw-Hill, 1950, pp. 236-243. 13, Palmer, H, B. ; and H i r t , T. J . : "Thermal Decomposition Kine t i c s of Carbon Suboxide," J . Am. Chem. Soc., 84, 113-4 (Jan. 1962). 14. Kozlov, G. I,; and Knorre, V. G . : "Single Pulse Shock Tube Studies on the K i n e t i c s of t he Thermal Decomposition of Methane," Combustion and Flame, 6, 253-263 (Dec. 1962). 15. H i r t , T. J . ; and Palmer, H. B. : "Kinetics of Deposi t ion of Py ro ly t i c Carbon Films From Methane and Carbon Suboxide," Carbon, 1, 65-70 (1963). 16. Kozlov, G. I. ; and Knorre, V, G. : "Kinet ics of Thermal Decomposition of Methane by the S ingle-Pulse Shock Tube Method," Russian Jour . Phys. Chem., 37 ( 9 ) , 1128-1130 (Sept . 1963). 1 7 . Bradley, J. N,: Shock Waves i n Chemistry and Physics , John Wiley, Inc . , New York (1962). 18. Thon, N. , ed. : Table of Chemical K ine t i c s Homogeneous Reac t ions , N.B.S. C i r c u l a r 510 (Sept . 1958), Supplement 1 (Nov. 1956); N.B.S. Monograph 34, v o l . 1 (Sept 1961), v o l . 2 ( Ju ly 1954). 19. Palmer, H. B . ; and H i r t , T. J.: "The Ac t iva t ion Energy For t he Pyro lys i s of ethane , " Journa l -9 Chem - 67 ( 3 ) , 709-711 (March 1963). 20. B a r t l i t , J. R. ; and B l i s s , He: "Kinetics of Ethane Pyro lys i s , " A . 1.Ch.E. Journa l , 2 ( 3 ) , 562-572 (May 1965), 21. Quinn, C . P.: he Thermal D i s soc i a t ion amd Pyro lys i s of Ethane," Proc. Royo Soc, , 275 1361 (Sept , 1963). 22. Cumings, G. A . McD.; Ha l l , A. R . ; and S t r a k e r , R . A . M.: "Decomposition Flame of Acetylene and Methyl Acetylene," Eighth I n t . Syrnp. on Combustion, Williams and Wilkins Co., Bal t imore, 503-510 (1962). 23. B l a i r , J. D.; and Seschske, A , : "Graphite-Hydrogen Methane Kine t i c s Above 1600" K," A.E.C. Contract W-7405 ENG 36, LASL2896 (May 1962). 24. Hedden, K . , Proceedings of the F i f t h Conference on Carbon, Macmillan Co., New York, 125-31 (1962), 25. Gulbrasen, E . A.; Andrews, K. F.; and B r a s s e r t , F. A . : "The React ion c.£ Hydrogen With Graphi te a t 1200" t o 1650°c," Jour . Electrochem. Soc., 112 ( I ) , 49-52 (Jan. 1965). 26. King, A. B e ; and Wise, H . : "Reaction Kine t ics of Hydrogen Atoms With Carbon Films," Jour . Phys. Che., 67 ( 6 ) , 1163-9 (June 1963). 27 . S t e a c i e , E. W. R . , and Shane, Gerald, "The Kine t ics of t h e Decomposition React ions of t he Lower Pa ra f f in s , " Canadian Journal of Research, 2, 203-16 (1940). 28. Happel, John, and Kramer, Leonard, "Acetylene and Hydrogen from t h e Pyro lys i s of Methane," I n d u s t r i a l Engineering Chemistry, 59, 39-50 (Jan. 1967). 29. Chase, J. D , , and Weinberg, F. J . , "The Acetylene Decomposition Flame and the Deduction of React ion Mechanism from ' ~ l o b a l ' Flame Kine t ics , " Proc. Roy. Soc. A . , -, 275 411-429 (Apr i l 1963). 30. Breisacher , P. , and Marx, P. C . , "The Hydrogen-Graphite React ion Between 360' and 800°," 85, 3518-9 (Nov. 1963)- - 31, Carney, N. S . , and R. B. Thomas, "Reactor of Carbon and Graphi te Below 950" C . , " B r i t i s h Report AERLE-C/R 2502 (June 1958). 32. King, Bruce A . , and Henry Wise, "Reaction Kinet ics of Hydrogen Atoms wi th Carbon Films," The Journal of Phys ica l Chemistry, 67 ( 6 ) , 1163-70 (June 1963), 33. Hou, K . C . , and Palmer, H. B . , "The Kinet ics of Thermal Decomposition of Benzene i n a Flow System," Jour . Phys. Chem 69 (3 ) , (March 1965). -9 - 34. Slysh, R . S , , and C , R . Kinney, "Some Kinet ics of t he Carbonizat ion of Benzene, Acetylene and Diacetylene a t 1200" ," - The Journal of Phys ica l Chemistry, 65, (June 1961). 35. S c o t t , G . S . , "Mdchanism of the Steam-Carbon Reaction," I n d u s t r i a l and Engineering Chemistry, 33, 1279-84 (1941). 3 6 . Lewis, W. K . , E. R . G i l l i l a n d , and Howard Hipkine, "Carbon-Steam Reaction a t Low Temperatures," I n d u s t r i a l and Engineering Chemistry, 45, 1697-1703 (August 1953). - 37. Haslam, R . T . , F. L. Hitchcock, and E . W. Rudow, "The Water- Gas Reactions," I n d u s t r i a l & Engineering Chemistry, IS, 115-121 ( February 1923). 38. Thie le , E . W . , and R . T. Haslam, "Mechanism of the Steam- Carbon Reactions," I n d u s t r i a l & Engineering Chemistry, 19, 882-7 (August 1927). - 39. Mayers, Martin A., "The Rate of Oxidation of Graphite by Steam," Journal of the American Chemical Society, 56, 1879- 1884 (September 1934). 40. Warner, B. R., "Mechanism of the Steam-Carbon Reaction," Journal of the American Chemical Society, 60, 1447 (Aug. 1943). 41. Walker, P. L., Jr., Chemistry & Physics of Carbon, Volume 1, Marcel-Dekker, Inc., New York, 203-64 (1965). 42. Walker, P. L., Jr., F. Rusinko, Jr., and L. G. Austin, Gas Reactions of Carbon, Advances Catalysis, ll, Academic Press, Inc., New York (1959). 43. Johnstone, H. F., C. Y. Chen, and Donald S. Scott, "Kinetics of the Steam-Carbon Reaction in Porous Graphite Tubes," Industrial and Engineering Chemistry, Volume 44, No. 7, 1564-69 (July 1952). 44, Binford, Jesse S., Jr., and Henry Eyring, "Kinetics of the Steam-Carbon Reaction," Journal of the American Chemical Society, 60, 486-491 (April 1956). 45. Austin, L. G., and P. L. Walker, Jr., "Effect of Carbon Monoxide in Causing Nonuniform Gasification of Graphite by Carbon Dioxide," A.1.Ch.E. Journal, 9 (3), 303-6 (May 1963). 46. Glovina, E. S . , and G. P . Khaustovich, "The I n t e r a c t i o n of Carbon wi th Carbon Dioxide and Oxygen a t Temperatures Up t o 3000°K': Eighth I n t . Symp. OJ Combustion, Williams and Wilkins Co., Baltimore (1962). 47. Walker, P. L. Jr., Chemistry and Physics of Carbon, Volume 4 , Marcel Dekker, I n c , , New York, 287-383 (1965). 48. Maak, Robert O . , "High Temperature Gas Reactions," MIT Of f i ce of Ordinance Research, Contract DA-19-020-ORD- 4268 (June 1961). 49. Berkman, Sophia, J . C, Morrel l and Gustov Eglof f , Ca ta lys i s : Inorganic and Organic, Reinhold Publ i sh ing Co., New York, 572 (1940). 50. Car le ton , E l l i s , Hydrogenation of Organic Substances, 3rd Edi t ion , D. Van Nostrand Co., I n c . , New York (1930). 51. Augustine, R. L. , C a t a l y t i c Hydrogenation, Marcel Dekker, I n c . , New York (1965). 52. S a b a t i e r , E. N . and J. H. Reid, C a t a l y s i s _14n Orqanic Chemistry, D. Van Nostrand Co., I n c . , New York, 216 (1922). Diwoky, F. F. and Homer Adkins, "Competitive Hydrogenation," Journal of the American Chemical Society, 53, 1868 (1931). Adkins, Homer and H. I. Cramer, "The Use of Nickel as a Catalyst for Hydrogenation," Journal of the American Chemical Society, 52, 4349 : (1930). del Valle, E. G., R. W. Pike and G. C. April, It~odeling for a Set of Complex Chemical Reactions at High Temperatures," Sixty-First Annual Meeting (A.I.Ch.E.), Preprint 8F, Los Angeles, Calif. (1968). Swann, R. T., Claud Pittman and J. C. Smith, "One Dimensional Numerical Analysis of the Transient Response of Thermal Pro- tection Systems," NASA TN D-2976 (September 1965). Benson, Sidney W., Thermochemical Kinetics, John Wiley and Sons, Inc., New York, 60 (1968). Beekman, op.eit., 166, Laidler, K. J., Chemical Kinetics, 2nd Ed., McGraw Hill Book Co., New York, 484 (1965). Kondrat'ev, V. N., Chemical Kinetics of Gas Reactions, Pergamon Press, New York, 36 (1964). Emmett, P. E., Catalysis, Reinhold Publishing Corp., Baltimore, Maryland, 5, 388 (1957). Minkoff, G. J. and C. F. H. Tipper, Chemistry of Combustion Reactions, Butterworths Publishing Co., Ltd., London, 249 (1962). Emmett, op.cit., 5, 184. Emmett, op.cit., 6 , 427. Emmett, opecite, 6, 407. Harrison, D. P. and H. F. Rase,"Nylon-Platinum Catalysts with Unusual Geometric and Selective Characteristics," Industrial and Engineering Chemistry - Fundamentals, 6 (2), 161 (May 1967). - Emmett, op.cit., 5, 217. Emmett, s.cit., 6, 486. Emmett, op.cit., 2, 98. Schwab, Georg-Maria, H. S, Taylor and R. Spence, Catalysis, D. Van Nostrand Co., New York, 26-27 (1937). Simons, J. H., Fluorine Chemistry,.Volume 1, Academic Press, New York, 2,78 (1964). Laidler, opecite, 8. Jolles, 2. E., ed., Bromine and Its Compounds, Academic Press New York, 74, 102-3 (1966). 75. Schwab, op.cit., 58. VIP. CONCLUSIONS - Based on t h e experimental and t h e o r e t i c a l r e s u l t s of t h i s r e sea rch t h e fo l lowing conc lus ions a r e drawn: Reac t ing Flow of Py ro lys i s Products i n t h e Char Zone 1. The r e a c t i n g f low of p y r o l y s i s products from nylon-phe- n o l i c r e s i n composites i n t h e char zone i s a c c u r a t e l y descr ibed by a non-equi l ibr ium model employing r e a c t i o n k i n e t i c d a t a of t h e important r e a c t i o n s occur r ing i n t h e system, For t h e s imulated py ro lys i s product compositions i n Table 6-5, mass f l u x va lues 2 between 0,00003 - 0.10 l b / f t - sec and a f r o n t su r f ace temperature range of 1350 - 2300°F, t h e r e a c t i o n s and a s soc i a t ed k i n e t i c d a t a i n Table 6-6 a c c u r a t e l y d e s c r i b e t h e energy t r a n s f e r i n t h e char zone. These r e a c t i o n s a r e v a l i d up t o 3000°F. Above t h i s temperature , a d d i t i o n a l r e a c t i o n s must be considered t o accu- r a t e l y d e s c r i b e t h e r e a c t i n g flow system. 2 2 . Under cond i t i ons of h igh mass f l u x e s (;, 0.01 l b / f t - sec) and/or low temperatures (." 2000°F), t h e flow of p y r o l y s i s p roducts i s e s s e n t i a l l y f rozen . These cond i t i ons d e f i n e t h e upper l i m i t a t i o n o f t h e f rozen flow model, 3 , The equi l ib r ium f l ~ w model e r roneous ly p r e d i c t s t h e behavior i n t h e cha r f o r a l l cond i t i ons except t hose i n which 2 t h e mass f l u x r a t e i s smal le r than 0.0001 l b l f t - s ec , Mass f l u x r a t e s g r e a t e r than t h i s va lue r e q u i r e t h e use of a non- equ i l i b r ium flow a n a l y s i s t o d e s c r i b e r e a c t i o n s occu r r ing a t f i n i t e r a t e s . Reac t ing Flow of Py ro lys i s Products Through Porous Graphi te 1. The same r e s u l t s a r e ob ta ined f o r t h e r e a c t i n g flow of p y r o l y s i s products i n porous g r a p h i t e . The same important r e a c t i o n s and k i n e t i c d a t a t h a t appl ied t o t h e low dens i ty nylon-phenol ic r e s i n c h a r s , l i kewi se apply t o t h e g r a p h i t e 2 between 1350 - 2300°F and 0.00003 - 0.10 l b / f t - sec . This permi ts t h e s u b s t i t u t i o n of g r a p h i t e f o r t h e b r i t t l e c h a r s i n s t u d i e s r e q u i r i n g post-experimental ana lyses of t h e porous media; i . e . , carbon depos i t i on s t u d i e s . 2. I n o r d e r t o compare t h e r e s u l t s from cha r and g r a p h i t e experiments , t h e mass f l u x i n t h e pores must be i d e n t i c a l . This c o r r e c t s f o r d i f f e r e n c e s i n t h e po ros i t y of each m a t e r i a l . 3 . The inc lus ion of g r a p h i t e " f ines" i n t h e pore spaces , dur ing t h e f a b r i c a t i o n procedure, r e s u l t s i n r e a c t i o n s w i th hydrogen forming methane. Purging t h e g r a p h i t e wi th helium o r n i t r o g e n p r i o r t o an experiment i s s u f f i c i e n t t o remove t h e s e d u s t - l i k e p a r t i c l e s from t h e pore spaces and e l i m i n a t e t h e methane formed from t h i s more r e a c t i v e form of g raph i t& . Carbon Deposi t ion S tud ie s 1. The use of r a d i o a c t i v e t r a c e r s i s a very e f f e c t i v e method of determining t h e ex t en t of carbon depos i t i on wi th in t h e char from t h e c racking of t h e p y r o l y s i s gases . A p l o t of t h e percent r a d i o a c t i v i t y a s a func t ion of char depth very g raph ica l ly determines t h e p o s i t i o n where depos i t i on s t a r t s , ends and i s maximum. 2 . Carbon i s depos i ted a s a r e s u l t of t h e thermal degra- da t ion of methane and phenol. Deposi t ion s t a r t s near t h e middle of t he char ( Z / L = 0.5) where the temperature i s 1400°F and inc reases uniformly t o a maximum value near t h e f r o n t su r f ace a t a temperature of 1900 O F . Degradation Product D i s t r i b u t i o n 1. The products o f methane degradat ion were determined by comparing r a d i o a c t i v e t r a c e r concent ra t ion p r o f i l e s with t h e gas chromatograms of t h e e x i t gases leav ing t h e Char Zone Thermal Environment Simulator . The spec i e s i d e n t i f i e d were carbon monoxide, carbon d ioxide , e thylene , ace ty lene and unreacted methane. 2 . S imi l a r ly , t h e products of phenol degradat ion were determined. The spec i e s were i d e n t i f i e d a s methane, carbon monoxide, carbon d ioxide and unreacted phenol, 3 . The above methods provided e x c e l l e n t suppor t ing evidence t h a t t h e r e a c t i o n s considered important i n t h e mathe- mat ica l model were c o r r e c t . C a t a l y s t s Evaluat ion ,S tud ie s 1. The e f f e c t of adding homogeneous c a t a l y s t s (such as bromine) t o t he py ro lys i s product stream t o a c c e l e r a t e chemical r e a c t i o n s and, t h e r e f o r e , t he h e a t absorp t ion i n the system was determined. Bromine (and the organic h a l i d e s and o the r halogens) produced a c a t a l y t i c e f f e c t which reduced the tempera- t u r e a t which carbon depos i t i on s t a r t s from 1400°F t o 1200°F. The p o s i t i o n of maximum depos i t i on was l ikewise s h i f t e d 300°F. A sharp dec l ink i n t he carbon depos i t i on probably ind ica t ed r ap id dep le t ion of carbon by r e a c t i o n s wi th water and/or carbon d ioxide . The product concent ra t ions of the e x i t gas stream i s l ikewise d i f f e r e n t from the non-ca t a ly t i c experiments and not p red ic t ed by t h e non-ca t a ly t i c k i n e t i c d a t a , 2. Molybdenum and tungsten heterogeneous c a t a l y s t s did not a f f e c t a measurable change i n t he behavior of the system. A s l i g h t s h i f t i n t he carbon depos i t i on p r o f i l e s were observed; however, the r e s u l t s were ou t s ide the experimental accuracy of the a n a l y t i c a l equipment, Platinum was used i n e a r l i e r s t u d i e s and, l i kewise , f a i l e d t o produce a change. A i r Oxidat ion S tudies - The e f f e c t of i n j e c t i n g a i r i n t o low densFvy nylon-phenolic r e s i n cha r s a t t he f r o n t su r f ace i s r ap id e r r o s i o n near the edge r eg ions of t h e chars . These experiments were conducted by pass ing a i r i n t o t h e char from t h e f r o n t su r f ace wi th no counter flow of py ro lys i s products from t h e r e a r . The experimental r e s u l t s were bracketed by t h e isothermal a n a l y s i s and va lues ca l cu la t ed us ing a l i n e a r d e s c r i p t i o n of t h e tempera- t u r e p r o f i l e wi th in t h e cha r . Symbo 1 A area NOMENCLATURE Description species identification in a general expres- sion for a reaction Runge-Kutta parameter in the energy equa- tion numerical solution method ratio of system parameter defined in equation (2-13) a formula number for chemical compounds coefficients in the polynomial defined in equation (2-28) B Runge-Kutta parameter in the species continuity numerical solution method ratio of system parameter defined in equation (2-14) b mass of a chemical element coefficients in the polynomial defined in equation (2-29) C ratio of the fluid to matrix thermal conductivity molar concentration defined in equation (2-38) heat capacity of a pure component at constant pressure heat capacity of a mixture at constant pressure none T none none none none M none none mole/L 3 Symbol C Descr ip t ion t o t a l number of atoms o f a chemical element i n t he system def ined by equat ion (3-41) c o e f f i c i e n t s i n t he polynomial def ined i n equat ion (2-35) s u b s t a n t i a l d e r i v a t i v e mass d i f f u s i v i t y energy of a c t i v a t i o n f r e e energy f r e e energy a t a s tandard s t a t e of 298OK and 1 atom f r e e energy func t ion def ined i n equat ions (3-31) and (3-33) any mathematical func t ion augmented func t ion of the quadra t i c approximat ion t o the f r e e energy func t ion defined i n equat ion (3-37) fo rce of g r a v i t y en tha lpy enthalpy a t a s tandard s t a t e of 298OK and 1 atom hea t t r a n s f e r c o e f f i c i e n t i n equat ion (2-3) numerical i n t e g r a t i o n increment s i z e s 337 Uni t s none none none L2/ t 2 2 ML / t - mole M C ~ / ~ ~ M L ~ / ~ ~ M L ~ / C 2 none 2 2 ML / t L / t 2 M L ~ / t2 M L ~ / ~ ~ M / t 3 t none Descr ip t ion Un i t s molar f l u x mass f l u x t o t a l number of gas spec i e s i n t h e system thermal conduct iv i ty r e a c t i o n r a t e cons t an t frequency f a c t o r char th ickness mobi l i ty of a porous mat r ix def ined i n equat ion (2-84) molecular weight t o t a l number of chemical r e a c t i o n s i n t h e system molar f l u x of spec i e s i n t h e char zone n moles of spec i e s - n mole f r a c t i o n of spec i e s P p re s su re P s to i ch iome t r i c c o e f f i c i e n t of t h e products i n a chemical r e a c t i o n P I power on t h e concen t r a t ion terms f o r products i n a chemical r e a c t i o n Q volumetr ic flow r a t e quadra t i c approximation of t h e f r e e energy func t ion (3-36) (4"' h e a t genera t ion by chemical r e a c t i o n none *func t ion o f r e a c t i o n o rde r . L none M/moles none mole/tL 2 moles none M / L ~ ~ none none L~ / t M L ~ / ~ ~ 339 Units Symbol number of gas plus so l id (condensed) phases i n t h e system none energy t r a n s f e r by conduction, convection o r r ad ia t ion i d e a l gas constant mole chemical r eac t ion r a t e e f f e c t i v e chemical reac t ion r a t e f o r gas and s o l i d species defined i n equation (3-21) m o l e l t l 3 none Reynold's number dimensionless mole f l u x defined i n equation (2-43) none mole / t l 3 chemical r eac t ion r a t e of a chemical species s to ichiometr ic c o e f f i c i e n t of the r eac tan t s i n a chemical r eac t ion none radius of a c y l i n d r i c a l graphi te t e s t sec t ion included i n equation (2-83) power on t h e concentrat ion terms f ~ r r eac tan t s i n a chemical r eac t ion none power on t h e temperature i n the r a t e equation (3-52) none T T/L t temperature temperature gradient time r a t i o of the ac tua l t o estimated mole f r a c t i o n i n t h e f r e e energy minimization ca lcu la t ion (3-42) none volume Descript ion Units ve loc i ty mass f l u x based on t h e s u p e r f i c i a l ve loc i ty mass f l u x based on t h e ve loc i ty i n the pores spaces of chars and graphi te M / L ~ ~ none mass f r a c t i o n of t h e species d is tance i n the a x i a l d i r e c t i o n (Chapter 11) d is tance i n the r a d i a l d i r e c t i o n (2-82) estimated moles of species i n t h e f r e e energy minimization ca lcu la t ion none estimated mole f r a c t i o n i n t h e f r e e energy minimization ca lcu la t ion none d is tance i n the a x i a l d i r e c t i o n (Chapter I1 and 111) L none compressibi l i ty f a c t o r Greek r a t i o of the mass f l u x t o t h e mass d i f f u s i v i t y used i n equation (2 -44 ) viscous c o e f f i c i e n t i n t h e modified Darcy's law equation (2-82) i n e r t i a l c o e f f i c i e n t i n the modified Darcy's law equation ( 2 ~ 8 2 ) permeabil i ty of a porous medium Kronecher Delta none a d i f ference between two parameters none de l operator none Symbo 1 Description € porosity of a porous medium - Q emissivity af a porous medium 7 dimensionless char distance defined in equation (2-15) 8 dimensionless temperatures defined in equations (2-11) and (2-12) X parameter of a straight line (0-1) PJ viscosity 7 3.1416 P density - B Stefan-Boltzmann constant o collision diameter T shear stress @ dimensionless parameters defined in equations (2-25), (2-26) and (2-27) parameter used to calculate the viscosity of a gas mixture in equation (3-57) h6 collision integral n Lagrangian multipliers in equation (3-37) Subscripts c convection or conduction d carbonaceous deposit e effective or overall value Units - nQne none none none none M/ Lt none M/L~ M/t3T4 none none none none f fluid or gas phase Symbo 1 Description g gas phase L f ron t su r face of a char m matrix o r so l id phase o i n i t i a l o r i n l e t condit ion P pressure pyrolys is pores r rad ia t ion s so l id phase T temperature t o t a l Y dis tance i n the r a d i a l d i r e c t i o n z dis tance measured from the char back surface 00 f r e e stream condit ion 1 ins ide surface of a c y l i n d r i c a l tube 2 ou t s ide su r face of a c y l i n d r i c a l tube Superscr ip ts .fr a standard o r reference condit ion 0 a standard o r reference s t a t e I der iva t ive A. INTEGRITY OF THE CALCULATIONS I N THE TEMPRE SYSTEM - Introducf i on The TEMPRE System i s a gene ra l a n a l y s i s implimented i n FORTRAN I V f o r s tudying t h e energy t r a n s f e r i h t h e cha r zone of a c h a r r i n g a b l a t o r . Three s e p a r a t e flow models and two boundary cond i t i on op t ions a r e contained i n t h e system. The I t e r a t i v e TEMPRE System so lves t h e two po in t boundary va lue prablem obtained by spec i fy ing t h e back and f r o n t char s u r f a c e tempera tures . An i t e r a t i v e s o l u t i o n f o r t h e c o r r e c t i n i t i a l ( o r f i n a l ) temperature g r a d i e n t requi red t o match t h e known f r o n t (o r back) s u r f a c e temperature i s necessary . The Non- I t e r a t i ve TEMPRE System so lves t h e energy equat ion wi th back s u r f a c e temperature and h e a t of p y r o l y s i s of t h e v i r g i n p l a s t i c (and t h e r e f o r e t h e temperature g rad i en t ) s p e c i f i e d . Since any f r o n t su r f ace temperature i s accep tab l e , a paramet r ic s tudy i s necessary t o i n v e s t i g a t e t h e wide range o f back and f r o n t s u r f a c e cond i t i ons on t h e system. I n bo th of t h e above op t ions t h e type of flow can be s p e c i f i e d a s f rozen , equi l ib r ium, o r non-equi l ibr ium. These t h r e e models g ive t h e upper (equi l ib r ium) and lower ( f rozen) l i m i t s on t h e system and t h e degree wi th which t h e a c t u a l (non-equi l ibr ium) behavior d i f f e r s from t h e two i d e a l ca se s . A b lock flow diagram of t h e TEMPRE System i s given i n Figure A - 1 . A s i n d i c a t e d , t h e system i s composed of one primary s e c t i o n and e igh t secondary sec t ions . The func t ion of each p o r t i o n w i l l be analyzed i n d e t a i l i n t h e fol lowing pages. Each s e c t i o n r ep re sen t s an independently t e s t e d u n i t of t h e e n t i r e system forming t h e b a s i s f o r t h e o v e r a l l i n t e g r i t y of t h e TEMPRE System. Frozen Flow Model The f rozen flow model i s t h e s imples t and forms t h e b a s i c s t r u c t u r e of t h e TEMPRE System. A fou r th o rde r Runge-Kutta numerical i n t e g r a t i o n scheme was used t o so lve t h e energy equat ion and is t h e important p a r t of t h e primary sec t ion . So lu t ions of t h e Energy Equation by a Fourth Order Run,ge- Kutta Analysis : The s tandard form f o r t h e s o l u t i o n of a second o rde r d i f f e r e n t i a l equat ion us ing a fou r th o rde r Runge-Kutta a n a l y s i s i f shown below (1). The va lues of t h e next temperature and temperature g rad ien t a r e given by equat ions (A-1) and (A-2). and The values of A . ( i = 1,2 ,3 ,4) a r e obtained by the following 1 s e t of equations: Therefore, t o begin the numerical so lu t ion , values of the temperature (T )and the temperature gradient ( T ' ) must be n n speci f ied a t one surface of the char. This reduces the problem t o a second order i n i t i a l (or f i n a l ) value problem. I n t h e I t e r a t i v e TEMPRE System t h e temperature g rad ien t a t t h e s u r f a c e must be guessed such t h a t t h e temperature cond i t i ons a t t h e back and f r o n t su r f aces a r e s a t i s f i e d . This r e q u i r e s an i t e r a t i v e s o l u t i o n accompanied by a s u i t a b l e convergence scheme t o i n su re e f f i e c i e n t and accu ra t e approaches t o t h e r e a l so lu t ion . The Non-I te ra t ive TEMPRE System i s an i n i t i a l (o r f i n a l ) va lue problem and r e q u i r e s no i t e r a t i v e scheme, and, t h e r e f o r e , no convergence l o g i c . Convergence Technique: The convergence technique i n t h e TEMPRE System i s purposely simple because of t h e r a t h e r complicated problem a l r eady e x i s t e n t wi th t h e numerical so lu t ion . It i s composed of t h r e e main p a r t s . The f i r s t o r check p o r t i o n l i m i t s t h e c a l c u l a t i o n s made i n t h e numerical a n a l y s i s t o va lues which a r e non-zero, non-negative and below an a r b i t r a r y c e i l i n g on t h e des i r ed ( s p e c i f i e d ) f r o n t s u r f a c e temperature. I f e i t h e r of t h e condi t ions mentioned above a r e v i o l a t e d , t h e temperature and g rad ien t a r e p r in t ed f o r r e f e rence , t h e g rad ien t i s ad jus ted t o c o r r e c t t h e s i t u a t i o n , and t h e a n a l y s i s i s r e s t a r t e d a t t h e i n i t i a l p o i n t . The second type of l o g i c w i th in t h e convergence scheme i s a g ros s c o r r e c t i o n t o t h e g rad ien t made when t h e f i n a l c a l c u l a t e d temperature i s g r e a t e r than an a r b i t r a r y increment (lOO°F, f o r example) p lus t h e des i r ed f i n a l temperature. This involves t ak ing t h e r a t i o of t h e a c t u a l t o ca l cu la t ed f i n a l temperature and d e f i n i n g t h e new g rad ien t a s t h e product of t h i s r a t i o and t h e old gradient value. The t h i r d type involves a f i n e r convergence scheme and i s used when the f i n a l ca lcula ted temperature i s wi th in the a r b i t r a r y increment speci f ied (100°F) o r when two o r more i t e r a t i o n s have been made. This scheme involved the adjus t - ment of t h e gradient by a l i n e a r in te rpo la t ion using the f i n a l temperature r a t i o ( ac tua l t o ca lcu la ted ) , t h e r a t i o of the ca lcula ted temperatures f o r the l a s t and next t o l a s t i t e r a t i o n , and the r a t i o of the g rad ien t s ( i n i t i a l ) of the l a s t and next t o l a s t i t e r a t i o n s . This method converges i n th ree t o f i v e i t e r a t i o n s (30 seconds computer time) f o r frozen flow, Although t h e r e a r e many e labora te convergence techniques a v a i l - able t o insure e f f i c i e n t and accurate approaches t o the desired condit ion, no r e a l incent ive beyond the above simple scheme was j u s t i f i e d i n the Tempre System. Overal l Runge-Kutta S t a b i l i t y Accuracy: A comprehensive inves t iga t ion i n t o t h e s t a b i l i t y and accuracy of the Runge-Kutta analys is i s e s s e n t i a l t o any program where t h a t method i s used t o give numerical so lu t ions t o d i f f e r e n t i a l equations. Beyond t h e d iscuss ions by Ames ( 2 ) and Collatz (3) regarding t h e mathematical development of the Runge-Kutta equations, the most important quest ion which must be answered i s what increment s i z e i s necessary and s u f f i c i e n t t o insure a s t a b l e , ye t accura te so lu t ion . Results of an increment study made i n the Frozen Flow TEMPRE System f o r Constant Physical Proper t ies and Variable Physical P roper t i e s a r e presented i n Tables A - 1 and A-2. A very l a r g e increment s i z e i s s u f f i c i e n t f o r the Constant Physical P roper t i e s case; however, a very c r i t i c a l decis ion a r i s e s f o r t h e Variable Physical P roper t i e s case. A value of 100 appears t o be the point above which no r e a l accuracy i s gained f o r t h e investment of computer time. This value seems reasonable over t h e e n t i r e system, including the equil ibrium and non-equilibrium flow cases . Frozen Flow, Constant Physical P roper t i e s Analysis: For the case where gas and char physical p roper t i e s a r e assumed independent of temperature, an a n a l y t i c a l so lu t ion of the energy equation i s obtained (4) . This so lu t ion out l ined i n Table A - 3 forms a b a s i s f o r t e s t i n g the accuracy and r e l i a b i l i t y of the numerical method. Since no subroutines a r e required t o generate physical proper ty da ta , a d i r e c t comparison of the Runge-Kutta ana lys i s t o the a n a l y t i c a l so lu t ion i s obtained. Table A-4 contains t h e values of the temperature f o r various dimensionless char depth values (z/L) f o r the a n a l y t i c a l so lu t ion and two numerical so lu t ions ( s t ep s i z e s of 10 and 100). Excellent agreement i s noted a t t h e smaller increment s i z e a s well a s t h e l a r g e r . Frozen Flow, Variable Physical P roper t i e s Analysis: I n order t o handle the v a r i a b l e physical p roper t i e s (with tempe- r a t u r e ) op t ion , th ree subroutines a r e added t o the TEMPRE Ta bl e A- 1. Co mp ar is on o f Va ri ou s Ru ng e- Ku tt a In cr em en t Si ze s fo r th e Fr oz en F lo w Co ns ta nt P hy si ca l Pr op er ti es M od el Di me ns io nl es s Te mp er at ur e (O F) Ch ar D is ta nc e Ru ng e- Ku tt a In cr em en t Si ze 50 0. 00 00 50 0. 00 00 50 0. 00 00 50 0. 00 00 60 9. 46 15 60 9. 45 97 60 9. 45 97 60 9. 45 97 77 5. 94 48 77 5. 94 13 77 5. 94 13 77 5. 94 14 10 29 .1 54 3 10 29 .1 49 7 10 29 .1 49 7 10 29 .1 49 8 14 14 .2 68 3 14 14 .2 64 2 14 14 .2 64 3 14 14 .2 64 3 20 00 .0 00 0 20 00 .0 00 0 20 00 .0 00 0 20 00 .0 00 0 Co nd it io ns : W = 0. 05 lb /f t - s e e L = 0. 02 08 ft C = 0. 7 B T U /~ ~- 'F ke = 1. 0 B ~ ~ / f t - h r - ~ F 6 = 0. 8 Ta bl e A- 2. Co mp ar is on o f Va ri ou s Ru ng e- Ku tt a In cr em en t Si ze s fo r th e Fr oz en F lo w Va ri ab le P hy si ca l Pr op er ti es M od el Di me ns io nl es s Te mp er at ur e (O F) Ch ar D is ta nc e Ru ng e- Ku tt a In cr em en t Si ze 50 0. 00 00 50 0. 00 00 50 0. 00 00 50 0. 00 00 63 1. 42 12 62 5. 62 82 62 5. 47 88 62 5. 42 02 82 4. 28 23 81 9. 55 01 81 9. 45 15 81 9. 39 08 11 06 .1 78 7 11 02 .8 11 1 11 02 .7 77 0 11 02 .7 1 41 14 94 .5 63 6 14 92 .8 85 3 14 92 .8 26 0 14 92 .7 60 4 20 00 .0 00 0 20 00 .0 00 0 20 00 * 0 00 0 20 00 .0 00 0 L = 0. 02 08 f t c = 0 - 8 Ga s Co mp os it i on ( Mo le /M ol e Ga s) : Ta bl e A- 4. Co mp ar is on o f th e An al yt ic al S ol ut io n o f th e Fr oz en F lo w, C on st an t Ph ys ic al Pr op er ti es M od el w it h th e Ru ng e- Ku tt a So lu ti on f or T wo In cr em en t Si ze s Di me ns io nl es s Te mp er at ur e (O F) Ch ar D is ta nc e An al yt ic al Nu me ri ca l So lu ti on s So lu ti on 10 I nc re me nt s 10 0 In cr em en ts , 50 0. 00 00 50 0. 00 00 50 0. 00 00 60 9. 45 97 60 9, 46 15 60 9. 45 97 77 5. 94 13 77 5. 94 48 77 5. 94 13 10 29 ,1 49 7 10 29 .1 54 3 10 29 .1 49 7 14 14 .2 64 2 14 14 .2 68 3 14 14 .2 64 3 20 00 .0 00 0 20 00 .0 00 0 20 00 .0 00 0 L = 0. 02 08 ft C = 0. 7 B T U/ ~~ -' F ke = 1. 0 B ~ ~ /f t- hr -' F (d ~/ dz )~ = 21 18 0 O ~ /f t System. These a r e c a l l e d PROPT, which c a l c u l a t e s t h e phys ica l p r o p e r t i e s of t h e gas mixture, t h e o v e r a l l thermal conduct iv i ty and t h e conduct iv i ty gradient f o r s p e c i f i c va lues of temperature; CHAR, a curve f i t t i n g program used t o es t imate t h e char thermal conduc t iv i ty from tabula ted d a t a ; and OMEGA, a genera l Lagrangian i n t e r p o l a t i o n program. Each w i l l be discussed i n d e t a i l i n t h e fol lowing paragraphs. I n a d d i t i o n t o t h e checks made on each ind iv idua l sub- rou t ine , t h e o v e r a l l Frozen Flow Variable Physical P rope r t i e s Model i s compared with so lu t ions obtained i n M I M I C ( 5 ) , an ana log-d ig i t a l s . ~ n u l a t o r . These techniques e s s e n t i a l l y represent two d i s t i n c t i v e pa ths t o t h e same so lu t ion and add confidence t o t h e c a l c u l a t i o n s made i n t h e system. Table A-5 compares t h e temperature a t var ious dimensionless char depths f o r t h e var ious numerical so lu t ions . Copies of t h e M I M I C programs and s o l u t i o n s a r e given i n Appendix H, PROPT: The c a l c u l a t i o n of t h e gas and char phys ica l proper- t i e s a r e made i n subrout ine PROPT with a s s i s t a n c e from OMEGA and CHAR. For a given temperature supplied from t h e main program, t h e hea t capac i ty , thermal conduct iv i ty and v i s c o s i t y of t h e pure gases and gas mixture a r e ca l cu la t ed . The equat ions used a r e described i n Chapter 111. From subrout ine CHAR, t h e thermal conduct iv i ty of t h e char i s obtained and t h e e f f e c t i v e conduct iv i ty (Equation 3-20) i s ca l cu la t ed . The thermal conduct iv i ty gradient i s l ikewise Ta bl e A- 5. Co mp ar is on o f th e Ru ng e- Ku tt a So lu ti on f or t he F ro ze n Fl ow , Va ri ab le Ph ys ic al P ro pe rt ie s w it h Tw o So lu ti on s Ob ta in ed U si ng M IM IC Di me ns io nl es s Te mp er at ur e (O F ) Ch ar D is ta nc e MI MI C (a ) MI MI C (b ) Ru ng e - Ku t ta So lu ti on So lu ti on 62 6. 52 62 7. 11 82 1. 89 82 1. 95 11 05 .7 6 11 04 .9 0 14 92 .9 5 14 94 .8 9 20 00 .0 0 20 00 .0 0 Ga s Co mp os it io n (~ ol e/ ~o le Ga s) : CO = 0. 24 5, C 02 = 0. 04 6, N 2 = 0. 07 3, C H4 = 0. 57 0, C 6H 6 = 0. 06 8 (a ) So lu ti on o f Eq ua ti on (H -1 ) (b ) So lu ti on o f Eq ua ti on ( H- 2 ) calcula ted i n PROPT f o r use i n the general energy equation, Subroutine OMEGA supplies the c o l l i s i o n i n t e g r a l a s a function of temperature f o r c a l c u l a t i n g the v i s c o s i t y and conductivi ty of the pure gases. Figure A-2 i s a comparison of the ca lcula ted values of the various physical p roper t i e s and experimental values reported i n t h e l i t e r a t u r e (6,7). Excellent agreement was found f o r a v a r i e t y of gases over a wide range of temperatures. OMEGA: The in te rpo la t ion of input and ca lcula ted da ta i s e s s e n t i a l i n the TEMPRE System. I n the frozen flow ana lys i s , i n t e r p o l a t i o n f o r the c o l l i s i o n i n t e g r a l a s a function of temperature i s performed f o r use i n ca lcu la t ing the pure gas v i s c o s i t y and conductivi ty. A standard Lagrangian i n t e r p o l a t i o n formula i s used. The degree of the formula and the s i z e of the a r ray a r e required input parameters, These may be var ied over a wide range of va lues ; however, t h e bes t combination must be determined f o r an accura te and e f f i c i e n t analys is . I n subsequent d iscuss ions , OMEGA i s used t o i n t e r p o l a t e values of char d is tance a s well a s mass f lux , molecular weight of t h e gas mixture, heat of r eac t ion and concentrat ion values a s funct ions of temperature. Reliable values a r e obtained over a wide range of parameter values of l a rge and small magnitude. CHAR: This ana lys i s can be any general curve f i t t i n g - technique t h a t bes t descr ibes the ava i l ab le thermal conduct iv i ty < F ig ur e A -2 . C om pa ri so n o f C al cu la te d P hy si ca l P ro pe rt y V al ue s w it h E xp er im en ta l V al ue s in t h e L it er at u re . P ar t (a ) : V is co si ty ( Ce nt ip oi se x 10 0) L, 3 70 ( 19 58 ). T em pe ra tu re (O K ) Fi gu re A -2 . Co mp ar is on o f Ca lc ul at ed P hy si ca l Pr op er ty V al ue s w it h Ex pe ri me nt al V al ue s in t he L it er at ur e. Pa rt (c ) : Th er ma l Co nd uc ti vi ty (~ al /c m- se c- OK ) Pe rr y, J. H. , ed ., Ch em ic al E n gi ne er s1 -H an db oo k, 2n d Ed it io n, M cG ra w- Hi ll , 0 Me th an e A Ni tr og en o Be nz en e Ca rb on M on ox id e Q , Ca rb on D io xi de Te mp er at ur e (O K) I I da ta of t h e char mater ia l . I n the present analys is a l i n e a r l e a s t squares f i t i s used. Values of the c o r r e l a t i o n c o e f f i - c i e n t and standard devia t ion a r e 0.97169 and 0.000234 ( a t an average value of 0.0044) u n i t s r e spec t ive ly , ind ica t ing a very good f i t of the da ta (8). A p l o t of the ava i l ab le char conductivi ty da ta vs . temperature (9) i s shown i n Figure A-3 with the corresponding l e a s t squares curve. A s more da ta becomes ava i l ab le a t higher temperatures it i s an t i c ipa ted t h a t higher order regress ion analyses might be necessary. Such changes a r e e a s i l y made by s u b s t i t u t i n g the appropriate curve f i t t i n g technique as subroutine CHAR. From t h e slope and in te rcep t (and o ther pe r t inen t information f o r a mul t ip le regress ion analys is ) the conductivi ty and gradient a r e obtained f o r use i n PROPT t o c a l c u l a t e e f f e c t i v e conductivi ty values. Equilibrium Flow Model The primary d i f fe rence between the frozen flow and equi- l ibrium flow models i s the change i n species concentrat ions with temperature i n t h e l a t e r case , These changes, a s ca lcula ted by a f r e e energy minimization technique ( l o ) , a r e only a function of temperature and pressure and a l l pe r t inen t r e s u l t s can be tabulated ou t s ide of the Runge-Kutta numerical procedure. I n addi t ion t o the subprograms required i n the frozen flow a n a l y s i s ( i . e . , PROPT, CHAR, OMEGA) t h r e e a d d i t i o n a l ope ra t ions must be added. MOLFRA performs t h e f r e e energy minimizat ion c a l c u l a t i o n s and t a b u l a t e s p e r t i n e n t va lues t o be t r a n s f e r r e d , a s needed by t h e Runge-Kutta a n a l y s i s , using OMEGA. ENTALl and MATINV a r e used t o gene ra t e enthalpy d a t a a s a func t ion of temperature and f o r mat r ix i nve r s ion , r e spec t ive ly . Once aga in each a d d i t i o n a l method w i l l b e discussed i n d i v i d u a l l y wi th emphasis on t h e accuracy and r e l i a b i l i t y of t h e c a l c u l a t i o n s . MOLFRA: The a n a l y s i s contained i n t h i s subrout ine uses t h e f r e e energy minimization technique t o p r e d i c t t h e e q u i l i - brium composition of a r e a c t i n g gas-so l id mixture. It employs a search technique t o compute t h e number of moles of each chemical spec i e s requi red t o g ive t h e minimum f r e e energy of t h e mixture. A d e t a i l e d d e s c r i p t i a n i s presented by d e l Val le (11) . To v e r i f y t h e c a l c u l a t i o n s made by t h i s program, s e v e r a l l i t e r a t u r e examples were used f o r comparison, Table A-6 i n d i c a t e s t h e r e p r o d u c i b i l i t y and accuracy with which t h e equi- l i b r ium model reproduced experimental and o the r numerical s o l u t i o n s , Once aga in r e f e rence t o t h e work by d e l Val le (11) i s made f o r d e t a i l e d d i scuss ions of t h e r e s u l t s . MATINV: This subrout ine i s a s tandard method f o r f i n d i n g t h e i n v e r s e of a noncsingular n x n matr ix. The IBM Share Library i s t h e source f o r t h i s p a r t i c u l a r program (12) . The inve r s ion i s performed i t e r a t i v e l y by reducing t h e o r i g i n a l ma t r ix t o an i d e n t i t y mat r ix by a s e r i e s of row opera t ions . The method i s then repea ted wi th t h e r e s u l t i n g i d e n t i t y matr ix . ENTALI: The e n t h a l p i e s of t h e va r ious s p e c i e s a s a func t ion of temperature a r e c a l c u l a t e d i n subrout ine ENTALI. It i s c a l l e d by MOLFRA and KINET a f t e r t h e s p e c i e s compositions a r e c a l c u l a t e d . Values of t h e enthalpy a r e c a l c u l a t e d a t a r e f e r e n c e temperature of 298°K and modified by t h e hea t capac i ty term a s i s u sua l ly done. Non-Equilibrium Flow Model - Like t h e equi l ib r ium f low model, t h e concen t r a t i ons and h e a t s of r e a c t i o n vary wi th t h e temperature . However, i n t h e non-equi l i - brium flow model, changes i n t h e mole f l u x wi th temperature must be c a l c u l a t e d a s p a r t of t h e Runge-Kutta a n a l y s i s . That i s , f o r each temperature generated i n t h e RungecKutta a n a l y s i s , a corresponding set of concen t r a t i ons , h e a t s of r e a c t i o n , e t c . must be c a l c u l a t e d . Because of t h e added complexity, a Runge-Kutta s t a b i l i t y a n a l y s i s , i d e n t i c a l t o t hose methods descr ibed f o r t h e f rozen f low models, was made. The r e s u l t s shown i n Table A-7 f o r s t e p s i z e s of 100, 200, 400, 1000 show s l i g h t l y h ighe r d i f f e r e n c e s i n t h e va r ious temperature p r o f i l e s a s compared wi th t h e f rozen f low r e s u l t s i n Tables A - 1 and A-2. However, t h e r e s u l t s a r e w i th in t h e convergence t o l e r a n c e of 1% and t h e s o l u t i o n f o r 100 s t e p s i s v a l i d . Over the t empera ture range from 500" t o 3000°F, t h e r e i s no i n c e n t i v e i n a sma l l e r increment f o r t h e added investment i n computer t ime. The s u b s t i t u t i o n of KINET f o r MOLFRA and INOUT f o r MATINV completes t h e necessary t ransformat ions r equ i r ed t o make t h e non- equ i l i b r ium flow ca lcu la t ioms . KINET func t ions a s MOLFRA, but u se s a k i n e t i c a n a l y s i s i n s t ead of t h e equi l ibr ium t rea tment f o r c a l c u l a t - ing t h e mole f l u x of each spec i e s . A l l p e r t i n e n t k i n e t i c d a t a a r e entered through INOUT, a genera l input-output r o u t i n e . A d e t a i l e d d i scuss ion fol lows on each new add i t i on t o t h e TEMPRE system. KINET: This program uses t h e k i n e t i c d a t a read i n t o t h e system i n INOUT f o r c a l c u l a t i n g t h e change i n t h e spec i e s mole f l u x e s a s a func t ion of temperature. The new mole f l u x va lues a r e then used t o c a l c u l a t e t h e hea t of r e a c t i o n , which f o r endothermic r e a c t i o n s , r e s u l t i n energy abso rp t ion , This absorp t ion i s accounted f o r i n t h e energy equat ion which so lves f o r t h e next temperature based on t h e change i n composition and h e a t of r e a c t i o n va lues c a l c u l a t e d . The interdependence between t h e mole f l u x and temperature r e q u i r e s a simultaneous s o l u t i o n of t h e d i f f e r - e n t i a l energy and spec i e s con t inu i ty equat ions . KINET i n t e g r a t e s t h e spec i e s c o n t i n u i t y equat ion us ing a f o u r t h o rde r Runge-Kutta method. INOUT: This subrout ine conta ins t h e k i n e t i c d a t a needed t o i n - t e g r a t e t h e spec i e s c o n t i n u i t y equat ion. The s p e c i f i c r e a c t i o n s , a c t i v a t i o n ene rg i e s , frequency f a c t o r s and s to i ch iome t r i c c o e f f i c i e n t s a r e t y p i c a l d a t a read . The system i s designed t o handle any number of chemical r e a c t i o n s and chemical spec ies . I n summary, t h e d i scuss ion thus f a r has been concerned with t h e development 05 a genera l computational system f o r ana lys ing the energy t r a n s f e r a s soc i a t ed wi th t h e flow of p y r o l y s i s gases through t h e char zone f o r f rozen , equi l ibr ium and non-equilibrium cond i t i ons . I n addi- t i o n t o t h e s o l u t i o n s of t h e energy equat ion which r e s u l t s i n a temp- e r a t u r e d i s t r i b u t i o n , t h e p re s su re d i s t r i b u t i o n and su r f ace h e a t f l u x areneeded t o f u r t h e r d e s c r i b e t h e phenomena t ak ing p l a c e w i th in t h e cha r l a y e r . This i s t h e t o p i c of t h e fo l lowing s e c t i o n s . Ca l cu l a t i on of the Pres su re D i s t r i b u t i o n and Surface Heat Flux The p re s su re d i s t r i b u t i o n ac ros s t h e cha r zone, and, t h e f r o n t s u r f a c e hea t f l u x a r e c a l c u l a t e d by a Simpson's Rule i n t e - g r a t i o n o f t h e d i f f e r e n t i a l momentum and hea t f l u x equa t ions , (3 -12) and (3 -23) . Because t h e s e equa t ions a r e uncoupled from t h e energy equa t ion , t h e i r s o l u t i o n s a r e c a l c u l a t e d a f t e r a v a l i d temperature d i s t r i b u t i o n h a s been obta ined . Therefore , t h e i n t e g r a t i o n method i s t h e same i n t h e i t e r a t i v e and non- i t e r a t i v e c a l c u l a t i o n s . I n t e r p o l a t i o n u s ing subprogram OMEGA of both cha r d i s t a n c e and c o l l i s i o n i n t e g r a l a s a func t ion o f t h e temperature d i s t r i b u t i o n ac ros s t h e cha r i s requi red . These o p e r a t i o n s al low t h e c a l c u l a t i o n of t h e gas mixture v i s c o s i t y a s a func t ion of char d i s t a n c e . I n a d d i t i o n t h e s to red r e a c t i o n r a t e and h e a t c a p a c i t y d a t a needed i n t h e h e a t f l u x c a l c u l a t i o n a r e a l s o i n t e r p o l a t e d f o r us ing OMEGA. A t t h e end of t h e s e c a l c u l a t i o n s , a l l p e r t i n e n t i npu t and output information a r e p r in t ed f o r comparison wi th experimental o r o t h e r a n a l y t i c a l d a t a . Simpson's Rule I n t e g r a t i o n : A s d i scussed i n Chapter 111, t h e Simpson's Rule formula i s used t o i n t e g r a t e t h e s p e c i f i c terms i n t h e momentum and hea t f l u x equa t ions , A s i n t h e c a s e of t h e Runge-Kutta a n a l y s i s , a s t e p s i z e must be s e l e c t e d t o produce an accu ra t e , y e t e f f i c i e n t , s o l u t i o n t o t h e t r u e s o l u t i o n . Table A-8 compares t h e s o l u t i o n of t h e momentum equat ion f o r va r ious i n t e r v a l s i z e s . As no ted , t h e s o l u t i o n becomes s t a b l e f o r a s t e p s i z e of twenty. A s i m i l a r comparison f o r t h e h e a t f l u x c a l c u l a t i o n l i kewi se i nd i ca t ed twenty u n i t s a s a v a l i d s t e p s i z e t o i n s u r e accuracy. I n t h e ca se of t h e p r e s s u r e d i s t r i b u t i o n , t h e s o l u t i o n f o r one ca se was compared wi th a g raph ica l i n t e g r a t i o n us ing a desk c a l c u l a t o r and ve ry good agreement was ob ta ined . Summary This appendix introduced t h e TEMPRE System and d iscussed t h e v a r i o u s func t ions o f each subprogram used i n t h e a n a l y s i s . More impor tan t ly , however, was t h e f a c t u a l information presented which insured t h e c a l c u l a t i o n s t o be accu ra t e , e f f i c i e n t and func t ion ing a s expected. This formed t h e b a s i c proof of t h e i n t e g r i t y of t h e TEMPRE System, I n Appendix B a complete l i s t i n g of t h e TEMPRE System w i l l be presen ted wi th i n s t r u c t i o n s regard ing t h e use and i n t e r p r e - t a t i o n o f t h e input and output s p e c i f i c a t i o n s . S p e c i f i c examples w i l l be i l l u s t r a t e d f o r c a l c u l a t i o n of t h e tempera ture , p r e s su re and concen t r a t i on p r o f i l e s w i th in t h e cha r zone, t h e s u r f a c e h e a t f l u x and change i n mass f l u x f o r f rozen , equ i l i b r ium and non-equi l ibr ium flow of p y r o l y s i s gases . T ab le A -8 . C om pa ri so n o f V ar io us s im ps on 's R ul e D im en si on le ss C ha r D is ta nc e s im ps on 's R ul e In cr em en t S iz e 21 75 .5 92 1 21 75 .5 91 8 21 75 .5 91 3 21 75 .5 91 2 21 73 .4 14 7 21 73 .4 14 4 21 73 .4 13 9 21 73 .4 13 8 21 68 .7 37 3 21 68 .7 36 8 21 68 .7 36 4 21 68 .7 36 4 21 60 .0 00 0 2 1 60 .0 00 0 21 60 .0 00 0 21 60 .0 00 0 L = 0. 02 08 ft G as C om po si ti on (~ ol e/ ~ ol e Ga s) : REFERENCES 1. Abramowitz, Milton and I. A. Stegun, e d i t o r s , Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 3rd P r in t ing , National Bureau of Standards Applied Mathematics Se r i e s 55, Washington, D. C . , 896-7 (1965). 2. Ames, W. F., m - L i n e a r Ordinary D i f f e r e n t i a l Equations i n Transport Processes, Academic Press, New York, 218-228 - (1968). 3 , Co l l a t z , Lothar, Numerical Treatment of D i f f e r e n t i a l Equations, 3rd Edit ion, Springer-Verlag, New York, 61-78 (1966). 4. Pike, R. W . , "Evaluation of t h e L i t e r a t u r e f o r Chemical Reactions and t h e Reaction Rates f o r t h e Decomposition Products from Charring Ablators ," NASA LWP-181, Langley Research Center, Hampton, Virg in ia (January 1966). 5 . Pe tersen , H. E. and F. J . Sansom, "MIMIC - A D i g i t a l Simulator Program," SESCA INTERNAL MEMO 65-12 (May 1965). 6. Reid, R. C. and T. K. Sherwood, The Proper t i e s of Gases and Liquids, 2nd Edit ion, McGraw-Hill Book Co., New York, 395-519 (1966). 7. Hougen, R. A., K, M. Watson and R. A. Ragatz, Chemical Process P r i n c i p l e s , P a r t I , John Wiley and Sons, Inc . , New York, 250- 258 (1959). 8. A p r i l , G. C . , R. W. P ike and E. G. d e l Va l l e , "Solu t ion of t h e Frozen Flow Energy Equation," NASA- CR-77026 ( J u l y 1966). 9 . Wilson, R. Gale , "Thermophysical P r o p e r t i e s of S ix Char r ing Abla tors from 140" t o 700°K and Two Chars from 800' t o 3000°K," NASA TN D-2991 (October 1965). 10. d e l Val le , E. G . , R. W. P ike and G , C, A p r i l , "Thermo- dynamic Equi l ibr ium o f a React ing Gas-Solid Mixture. I: Der iva t ion o f Equation and Convergence Procedure," NASA CR-79677 (October I., 1966). 11. d e l Va l l e , E. G . , R. W. Pike and G. C . A p r i l , "Thermo- dynamic Equi l ibr ium o f a Reacting Gas-Solid Mixture , 11: Computer Implementation and Resul t , " NASA CR-66309 February 1, 1967). 12. Sadaka, R. N . , "Double P r e c i s i o n Matr ix Invers ion wi th S e l e c t i v e Pivot ," IBM Share L ib ra ry , No. 7090-F1, 3181 INV2 (1965). B . ITERATIVE AND NON-ITEWTIVE TEMPRE SYSTEMS - A s d i scussed i n Appendix A, t h e TEMPRE System i s comprised o f two main programs and e i g h t subprograms. The i t e r a t i v e main program i s f o r t h e a n a l y s i s of a two po in t boundary va lue problem r e q u i r i n g an i t e r a t i v e s o l u t i o n technique , and t h e n o n - i t e r a t i v e main program i s f o r an i n i t i a l ( o r f i n a l ) va lue problem which i s n o n - r e p e t i t i v e i n n a t u r e . These two d i s t i n c t i v e main programs a r e c a l l e d "IT" and "NONIT" f o r obvious reasons . The complete a n a I y s i s i s t hus genera l ized wi th t h e except ion o f t h e main programs which must be interchanged f o r a s p e c i f i c a p p l i c a t i o n . F igure B - 1 g r aph ica l ly i l l u s t r a t e s t h e com- p l e t e TEMPRE System. The remaining s e c t i o n s o f t h i s appendix i nc lude a complete l i s t i n g o f t h e TEMPRE System wi th t y p i c a l input and ou tpu t formats f o r us ing and i n t e r p r e t i n g t h e system, The fol lowing o u t l i n e w i l l h e lp l o c a t e t h e p a r t i c u l a r programs i n t h e system. L i s t i n g B-1 I t e r a t i v e TEMPRE (blain) Program L i s t i n g B-2 Non-I te ra t ive TEMPRE (Main) Program L i s t i n g B-3 TEMPRE Subprograms a - PROPT (Phys ica l P rope r t i e s ) b - OMEGA ( I n t e r p o l a t i o n ) c - CHAR (Char Thermal Conduct ivi ty) d - MOLFRA (Free Energy Minimization) e - MATINV (Matrix Inve r s ion ) f - ENTALL (Enthalpy of Gas Mixtures) g - KLNET (@hemi.cal Reaction Rates) h - INOUT (Kine t i c Data) L i s t i n g B-4 Input Format L i s t i n g B-5 Output Format ON- ITERATIVE ON- ITEK4T IVE F igure B - 1 , TEMPRE System f o r Calculat ing the Energy Transfer i n the Char Zone of a Charring Ablator , - * - Y - Ln C; * W C n N n r I u - 0 - C I-- D I r C I - 3 * m > - - U - 0 0 - ! - l o LI 3 - 0 ?LNCIIO * v) -3 c -0- a r - ~ n D U- rn * N O - O Z r r \ O N r >- CL \ f - N - P - U - 0 rn u 3 o a u - *a- ~ m m L - UJ 3 I- , o u c ( L U - u - d L 3 - I c a - C - - A O X V w - a m . j - O m c f o a u = . n u ro - 0 - c , u m x a a u k d U m c J - - I - - - * a Q L * 0 m - 0 x D Z - o - - Z G U L U u N W - X O r - O - '3 W 0 * u - - a~ - N - 0 b - LLJ C v) -u Z ~ - ~ O O -I 'U - v, a d U1 3 - u * = - 0 f i o m q L Y u 3 m Z - Q L L - 0 0 ~ 9 - 0 - UJ Cr: 0 > 0 N h ' c V \ N 4 > - > W - U 0 < J k' t y - - d-- - O h ! !2 ,7 L Q > 4 d - 0 0 * 3 Y LIJ z clC -WNC.LnO13OCY- U - v) In Z r - r - O . 4 U J Z N N o o - m I- -v) x Z LL 5 0 Q - O d - + X - - N > - r O Y - U U CnK LU *--4CwNSUJO - G O - I- - - Z a 0 C LU 0 4 - - J & N - - C Q --J u U- c; (3 0 m I N Q U - W Z - c - m - u a w >-I- --eon * M O O - - - a - a r 11 m a - - N - - W I - ( N N O C - ,-. a C: +I- z 44----~na-- - 0 4 3 --r LL 0 - - w - - . - O ~ O ~ - W O - ~ ~ ? - L Y a .n lz l~ > - V \ C U - r V * - h c z o - o w m - * v) ~l x c v ) - - a - - o c ~ - o o x r ~ ~ ~ ~ ~ LL 3 lx ,Y !- UJ N ern * > ~ N x x o N ~ ~ c . ~ ~ Q 4 k - L I ~ C - D U - L C U D b D C D 0 x co 4 q ~ O - O Y - - + - % L Y ~ Y X X ~ i 7 n n w z a - - ~ o r n m c o o o n r * , ~ ~ u Y 1-2 C U - I . ; t O - h l % r O N 3 O O m L -yCL lu Z - I LLLL 0-4 a a v ) ( v ~ - c - - m u e r n > - - J - M - Z I- c c I- IU J - - ~ - ~ _ ) - i n r ; c - . ~ c r - - * r 7 - Z X Z TI /> -p > 2 4 v) G ; t o ; cJt4-a r O u O - C - -uJ < ( 1 . d S - C - 3 d v) N - L - L L;Y - - . m S - l r r - . 2 c n g y . > ; ~ i - - . - l - Y LU a - A - 0 - m a - O - a - - N D Q Z Q . ~ Z Z Z > . Z z UJU7ONO-4 - 0 O C r Y X Z N - U J r 1 O W L l J u - E w o - ~ - - ~ - - o m ~ n ~ r a o -o 3 5 c c 5 0 0 O - - U - U O C C ) - - J r C C ~ - ~ I- ~ ) Z U J ~ I ~ z ~ & u - - h c ( f i ~ - t ~ - - u v ) d ~ - a 3 a o d 3 1 ) 1 4 c - - - ~ C ~ ; U J I Y - ~ C O G X Z - - ( ~ ; ~ ~ * O . 3 i l Y C A O G E N - - U - 0 0 - - - X = - - U Z Z Z - E UJ > z ~ , z - - z L u z - ~ ~ z ~ cur^ A L L C L I ~ ~ o - cr r 3 G - T O O ~ O ~ O - - C Z ~ ~ ~ Y Y - 3 0 3 g 0 7 ? - 4 a tr' - - - u N ~ J - O - O Y , P : - v) LA - 11 E UJ m e m - - w - - v , n - o v ) r l L Z Z Z , c a * d ~ W T W z Z - Z ~ - ' z O Z ~ X 3 z ~ ~ 9 3 9 UJ C C O ll ll 3 t UJ U J ~ W r - , > U J i L U + 4 Z U J X . f i E F . X ,Y 7 % Z & J i L i L T E v ) I < X - Z C - t Q X Z - i T Z I I I! 11 5 3 < - U C - 3 33C) L ) f i Z , Y Z LL]u C1, C: C' v? z 0 !3 C' U .lA T( 2F 15 .6 ,A 4) IT 6 9 1 8 F O R M A T( Fl 5. 5) C C 4L P H A =V IS C O U S C O E FF IC IE N T IN D AR CY E Q U AT IO N ( 1/ FT I G B E T A =I N E R T IA L C O E FF IC IE N T IN D AR CY E Q U AT IO h (1 /F T2 ) C R E A D 22 sA LP H A tB E TA C C UD AT A= NO . OF XT KE VS e ZO M GA D A TA P O IN TS C Y D IM 1= N O o GF D IM E N SI O N ED L O C AT IO N S FO R E Q U IL IB R IU M P RO GR AM C AL C U LA C IN S UB PR O G RA M O ME GA C VD IM Z= N O . OF D IM E N SI O N ED LO C AT IO N S FO R TE M P E R A TU R E- D IS TA N C E C AL C U L C IN S UB PR O G RA M OM EG A C Q D 1 ~ 3 = i~ 0 ~ CF D IM E hS IO N E D L O C AT IO N S FO R P H Y S IC A L PR O PE RT Y C A LC U LA TI C IN S UB PR O G RA M O PE G A C K E Y = 1 ( FR OZ EN F LO W ) C K EY = 2 (E QU IL IB RI UM F LO W ) C K E Y = 3 (N ON -E QU IL IB KI UM FL O W ) C M TY PE = TY PE OF PR O BL EM B E IN G C O dS ID ER ED C 1 = E X P E R IM E N TA L C 2 = TH E O R ET IC AL C ~ E A ~ ~ ~ ~ '~ D A T A ~ N D IM ~ ~ N D IM Z ~ N D IP ~ ~ K E Y ~ ? J ~ T Y P E C C < TK E= PK O D U C T OF TE M PE R AT UR E AN D 1 /E K VA LU E C 70 M G 4= C 3L LI S IO N IN TE G R AL TA B U LA TE D VS X TK E C ~ < E A 32 4, (X TK E( I) ~Z OM GA (I )t I= 11 ND AT A) 22 F O R 4A T( LE l5 .5 ) 2 3 F O K 4A T (6 16 ) 2 4 F O R ,I A T (L FL ~. ~I C C I' Q IM ~K Y P A R A A E Tt :S Ir U' IT IA LI ZE I) C \J CP SR =l K 6 = 1 Z( 1 )= 0, 0 I J K L= 1 EP S- CH AR P O R O SI TY TL =T EP PE R AT U R E A T Z= L (O F) T( l)= TE MP ER AT UR E AT Z = 0 ( OF ) D T( 1) =T EM PE RA TU KE G R AD IE N T A T Z= 0 (O F/ FT ) ZL =C HA R TH IC KN ES S (F T) H I- R U N G E- KU fT A IN C R EM EN T S IZ E (F T) H S IY P I- S IM P S O N R U LE IN C R EM EN T S IZ E [ FT ) W I= IN IT IA L G AS M AS S FL U X V AL U E A T 2= 0 (L B/ FT 2- SE C) PL =* R ES SU R E A T Z= L (L B/ FT 2) R R =G AS CO NS TA NT (1 ,9 87 BT U /L B- M O LE /O R ) TZ ER O =R EF ER EN CE TE M PE R AT U R E (2 98 .2 O K) D EL TK =T EM PE SA TU R E IY C YE M EN T U SE D T O C AL C U LA TE D KC /D T (O K) FW =4 O LE CU LA R & E IG H T Y I= IN IT 'I A L 4O LE FR A C TI O i4 U F G AS ES AT Z= 0 &L PA =C O W PO NE NT ID E N T IF IC A T IO N I C 0 9 E = 0 ( GA S1 9 = 1 (S OL ID ) I)E Lt i= Eh dT tiA LP Y Of - FO AM AT IU N A T 2 98 O K D U 1 2 7 I = lr N C IT 1 4 0 1 2 7 Y I( I) =Y I( II /S U M IT 1 4 1 Y I( tq SI =Y I( NS )/ SU M IT 1 42 R K S S =Z L/ H I IT 1 43 SR SS =H S/ H SI M PI IT 1 44 JR KS S= (R KS S* 1O e0 +5 .r) )/1 0. O IT 1 45 J SR SS =( SR SS *1 0e 0+ 5e 0) /1 0. 0 IT 1 4 6 C IT 1 4 7 C IN IT IA L IZ A T IO N O F PA R AM ET ER S IT 1 48 C IT 1 49 C A LL E R K SE T (2 07 g2 56 r- 1* 1) IT 1 5 0 C A LL E R M E T ( 20 8g 25 6r -l rl ) IT 1 5 1 C A LL E R R SE T (2 09 g2 56 g- lr l) IT 1 52 U 0= 1 IT 1 53 l'J N4 =N C+ 4 IT 1 54 YO UN T= L IT 1 55 T P l= T ( 1 ) IT 1 56 K 7= 1 IT 1 57 4 0 V = l IT 1 58 TE ST =5 00 .0 IT 1 5 9 W =W I/ EP S IT 1 60 3U 31 I= l, NC IT 1 61 Y (I )= Y I( I) IT 1 62 3 1 C bh T Ih U E - r * . C IT 1 6 3 t* =b rI IT 1 64 Y N = 1 IT 1 65 Y A X IS ( 1 )= Oe O IT 1 66 Y 4 X IS ( l )= Oe O IT 1 67 5 0 7 ( 1 )= 0. 0 IT 1 68 C IT 1 69 C ?U UG (;E -K UT TA A Q AL YS IS FO R TW O PO IN T B O U N D AR Y V A LU E P R O BL EM IT 1 7 0 C (T G AN D TL KN tiW Np L) T/ DZ 4T Z= 0 AS SU M ED ) IN V O LV IN G A N O N -L IN EA R IT 1 7 1 C SE C dU D C r? DE R D IF F E R tY T Ib L E O U AT IO Q ( EN ER GY B A LA N C E) IT 1 7 2 L k IR S T P C IN T E S T I M A T t O B t tU LE R hE TH O D IT 1 7 3 C IT 1 74 55 IF (N -G T- 1) GO T O 1 0 1 IT 1 7 5 5 6 T (N +l )= H* DT (N )+ T( N) I T 1 76 D T (N +l )= OT (N ) I T 1 7 7 GO T O 13 8 IT 1 78 1 0 1 T C =T (N ) IT 1 79 TP R E V =T (N -1 ) IT 1 80 TH E TA =T tN ) IT 1 8 1 1 0 2 D TC =D T( N) IT 1 8 2 D TH E TA =D T( N) IT 1 83 Y X =1 IT 1 8 4 IF (D T( 1) oG To Oe O) GO T O 10 3 IT 1 8 5 A 10 9 D T (1 )= DT (l )/ (( 1e O+ 0. 5* (t TL -T CH EC K) /T L) ~* 2~ O) IT 1 8 6 GO TO 40 IT 1 8- 8 1 0 3 AR K = H *D TC I T 1 19 8 8 8 8 T NC W =T C IT 1 8 9 2A N K IN =T C +4 60 .0 IT 1 9 0 TV AR =R AN K IN /1 .8 IT 1 9 1 I)E LZ =H I T 1 9 2 G O T O (5 81 60 r6 1) rK EY IT 1 93 5 8 A V G Fh =O -0 IT 1 94 I)U 59 I = lp N C IT 1 95 4V C FW =A VG FW +Y (I) *F K( I) IT 1 96 5 9 C O N TI bt U f IT 1 97 GO T U 1 04 IT 1 9 8 6 0 I F( KC I~ IN T. EI ).Z )G O TC i 7 1 0 IT 1 9 9 C IT 2 0 0 C U SE M O LF KA TO G EN ER Al E P O LE FK A C TI O N I AV ER AG E M O LE CU LA R W EI G HT IT 2 0 1 C 4P dP R kA C TI O N R A TE t X P 2E S S IO N F O R U SE IN T EM PR E IT 2 0 2 C TR AN SF ER VA LU ES TA B U LA TE D IN M LI LF RA FO R A S P E C IF IC T EK PE R AT U R E IT 2 03 C IT L O 4 C A LL ~ IO L F K A (K O U XT IK PT ~~ K~ *T PL IT 2 0 5 I( T= 2 IT 2 0 6 KM AX =K PT 3 IT 2 0 7 JN S =N N 4+ 1 IT 2 0 8 7 1 0 U O 7 C 7 K L= 2r N N 5 IT 2 0 9 C AL L O M E G A (T VA R, TA BL E( l,l ), TA BL E( lq KL ), Kt JI AX ~N DI ~I ~V AR Y) IF (k L. GT .2 1G O TO 7 04 R EA CT =\ JA RY GO T O 70 7 7 0 4 IF (K Le GT e3 )G 0 r0 7 0 5 AV G FW =V AR Y GG TO 7 07 7 05 IF (K Le GT e4 )G O TO 7 0 8 W =V AR Y GO TO 70 7 7 0 8 Y (K L- 4) =V AR Y G C AY =Y (K L- 4) IF (G CA Y. GT ,O .C )G O 13 7 C 70 7 0 6 Y /K L- 41 ~1 -O E -1 0 7 07 0 dR I& N l= A i3 S (T VA R- T( 2) ) IF (Y RI AN le GT ~1 eO )G O T O 7 07 KY C SV P= KL -4 Y CO MP (K YC OM P, l) =Y (K YC UM P) 7 0 7 C O N TI N U E G O T3 10 4 C C LJ SE K iN E T T O G EN ER AT E M OL E F R A C TI C N * AV ER AG E M O LE CU LA R W EI G HT C 4N C R E A C TI O N K A T t E X P R E SS IO N F O K US E IN T EM P C TR AN SF ER V A LU ES C AL C U LA TE D F O R A S P E C IF IC T EM PE R AT U R E C 6 1 D E LZ =H C A LL K II J E T (T P ~~ TV A Y ~I ~E LZ ~K N ~K ~~ D TC ~R E A C T~ W ~K P T~ ~A V G FW ) :< N =2 i(M AX =K PT 3 - ', 7 = 2 IF ( ~ ~ K IA I; ~ ,G T .~ .O ~ G C ~ Ti 1 1 0 4 9 0 1 3 4 0 IO U= LI NS I Z K = IO U +4 YC O l4 PL I O U *l )= TA UL E( L e I C K ) 1C 40 C CP .T I N U E US E PR O PT T O G EN ER AT E NE ED ED P W Y Sl C A L PR O PE RT Y D A TA (H EA T C A PA C If Yc EA S AN D CH AR C O N D U C TI VI TY A ND D E R IV A TI V E O F O VE RA LL TH ER M AL C O N D U C TI VI TY V A LU ES ) CA LL P ~ O P I ~ T V A R ~ J C H A R ~ K 0 O E t N C A T A t X T K E ~ Z O M G A ~ N D I ~ 3 ~ C P ~ X ~ C D O t D C O O ~ JC HA R= 2 G AS CP =E CP HX /A VG FH I* RR G C A A T= A B S( T( NI -T C) IF fG C A A Te G Te O -0 00 01 )G O TO 10 7 C A PA C iN I= G AS CP C A PA C I1 1= C A PA C (2 1 6 0 T O t6 2 *6 3 ~ 6 3 ) ,K EY GR O9 P= EH *E PS *G AS CP /C DO )- (D CD C? *D TC /C DO f GO TO 6 5 G R O U P = t ~ + E P S * G A S C P /C DO ~- ~D CD O* DT C/ CD O~ +( RE QC T/ CD O~ DA =4 RK *G RO UP TP R EV =T C G C TO (ll O pI 20 91 30 p1 35 19 M X C A LC U LA IE PA R A M El ER S IN F O R TH O RD ER R UN G E- KU TT A A N A LY SI S IF TZ BE CO M ES N E G A TI VE q EA D JU ST AS SU M ED V A LU E O F D T/ D Z AT 2= 0 AN D R ES UR N TO Ih !I TI A C IZ A TI O N S TE P D TC =D TH ET A+ O a5 *0 A2 I T 2 80 M X= 3 IT 2 81 IF (T C )1 33 ~1 33 i1 03 IT 2 82 1 3 0 43 =A R K IT 2 83 D A3 =D A IT 2 84 TC =T H ET A+ A3 +0 eS *D A3 *H I T 2 85 D TC =D TH ET A+ D A3 IT 2 86 M X =4 IT 2 87 IF (T C1 13 3r 13 3r 10 3 I T 2 88 1 3 3 P R IN T 2 22 21 TC IT 2 89 22 22 F O R ? ~ A T (~ H O ~ ~ H T C = ~ ~ X ~ F ~ ~ -~ ~ ~ X O ~ H N E G A T IV E ) IT 2 90 D T (l) =D T( 1) *0 .5 IT 2 91 GO T O 4 0 I T 2 92 13 5 A4 =A R K I T 2 93 D A4 =D A IT 2 94 C IT 2 95 C C AL C U LA TE N E X T TE M PE R AT U R E AN D D E R IV A T IV E P O IN T U S IN G F O U R TH IT 2 96 C O RD ER R U N G €- KU TT A E Q UA TI O NS IT 2 97 C IT 2 98 T (N +1 )= T( N) +( la 0/ 6. 01 *~ DA 1+ DA 2+ DA 3) *H + A 1 IT 2 99 D T (N +l )= DT (N )+ (1 ~0 /6 eO ~* ~D A1 +2 eO *D A2 +2 ~O *O A3 +D A4 ~ I T 3 00 C IT 3 0 1 C TE ST N EW TE M PE R AT U R E P O IN T I F G RE AT ER TH A N 5 0 0 O F( 20 00 -3 00 0 O F IT 3 0 2 C SU RF AC E TE M P E R A TU R k) A D JU ST D T /D Z AT Z= @ A ND R ET U R N T O IT 3 0 3 C IN IT IA LT IC IN S TE P IF N EW TE M PE R AT U R E P O IN T IS N A G A TI V E R ET U R N T O IT 3 04 C IN IT IA L IZ A T IO N S TE P. AF TE R AO JU ST D E R IV A T IV E ( DT /D Z AT T= O ) I T 3 0 5 C IT 3 06 fL IM IT =T L+ S O O .O IT 3 0 7 A N L Y l = T (N +l ) IT 3 08 IF (P ND Y1 ,G T. TL IM IT )G O TO 6 0 0 0 IT 3 0 9 50 00 IF ( 1 N D Y le G Te O aO )G O TO 13 8 IT 3 10 1 3 6 P K Ir IT 13 79 T (N +l ) IT 3 1 1 13 7 FD R fv lA V( 1 H O ~ 7 H T (N +L )= i1 X9 F1 5~ 69 8X ,8 HN EG AT IV E~ IT 3 1 2 D T (l )= DT 11 )+ 0, 5 IT 3 1 3 S O TL I 4G IT 3 14 6 0 0 8 P R I N T 8 00 0r T[ N+ ll pT LI MI T IT 3 15 PR IN TR OO lt DT (N +l ), N I T 3 16 80 00 F O R M A T (~ H ~ V ~ H T (N + ~ )= ~ ~ X ~ F ~ ~ ~ ~ ~ ~ X ~ ~ H E X C E E D E ~ X ~ H T L IM IT VA LU E OF IT 3 17 lr l Xt FL 5. 6) I T 3 18 80 01 F O R M A T /l H O t8 H D T (N +l )= ~1 X ~F 20 ~5 ~8 X ~2 H ~l X ~I 6) IT 31 9 IJ KL =I JK L+ l IT 3 20 IF (I JK L* GE al O) GO T0 30 IT 32 1 TR AT IO =( TL -T (N +l )I /T L IT 32 2 D T (1 ~= DT (1 )* (1 ~O +O e5 *T RA TI O~ I T 3 23 TC HE CK =T (N +1 1 IT 32 4 IF (O T( 1) )1 0t 10 t4 0 IT 3 25 13 8 Z( N+ l) =Z (N )+ H IT 3 2 6 XA XI S( N+ l) =Z (N +l )/ ZL IT 3 27 IF (N eE Q- 20 1) GO T0 14 0 IT 3 28 Y A X IS (N +l )= IT IN +l )- T( l) )/ IT L- T( 11 1 I T 3 29 GO T0 14 4 I T 3 30 14 0 D Ol 41 N= lr 20 1 IT 3 31 P R I NT l4 2t N, XA XI S( Nl 9T (N )t CA PA C( N) IT 33 2 14 2 FO RM AT ( 1H 0v I 69 3F 10 .4 ) I T 3 33 14 1 CO NT IN UE I T 3 34 DT (l I= DT (2 00 ) IT 33 5 T ( 1 )= T( 20 0) IT 3 3 6 DT (2 )= Dr (2 01 ) IT 33 7 T (2 )= T( ZO l) IT 33 8 w = 2 IT 3 3 9 GO T0 10 1 IT 3 4 0 C IT 34 1 C IF NU N- NE GA TI VE A N 0 L E SS T H A N 50 0 OF , TE ST F OR CH AR D I ST AN CE IT 34 2 C IT 3 43 C IF Ch AR D I ST Ak CE L E SS TH A N CH AR TH IC K N ES S GO T O N E X T ST EP IN IT 3 4 4 C KU NG E- KU TT A A kA LY S I S IT 3 45 C IF C tl kR D I ST AN CE E QU AL S CH AR T H I CK NE SS T E ST F OR T- FI NA L IT 34 6 C (C AL CU LA TE D) V S (A CT UA L) IT 34 7 C IT 34 8 i4 4 n N D Y 2= A D S( ZL -Z (N +1 ) ) IT 3 49 IF (A ND Y2 eL E~ Oe OO OO l)G O TO 1 5 0 1 4 5 N = N + l GO TO 1 0 1 1 5 0 Q T( NO )= T( N+ l) Q D T( NO I= DT (l) C A P A C (N +I )= CA PA C( N) P R IN T lS O l~ D T (l )v TI N +l ) 1 5 0 1 F O R M A T (lH O vl 4H IN IT IA L S LO P E =9 F1 5- 5q 4X 91 8H FI N A L TE M P E R A TU R E= *F 15 .5 ) D IF F = A B S (T L- T( N+ l)) S T E P = (1 Oe O* ~L L/ HI )+ 5~ 0~ /1 0~ 0 L S TE P= ST EP LC H AR =L ST EP + 1 C C IF T -F IN A L (C AL CU LA TE D) IS N OT EQ UA L TO + r - 1 OF T -F IN A L C (A CT UA L) A D JU ST IN IT IA L S LO PE AN D R ET U R N T O IN IT IA L IZ A T IO N S TE P C IF T -F IN A L (C AL CU LA TE D) IS + * - 1 OF T -F IN A L (A CT UA Ll *S TO RE T H E C TE M PE R AT UR E P R O FI LE C IF (O IF F- 25 -) 15 5* 15 5* lS 3 1 5 2 T R A T IO = (T L- T( N+ l)I /T L D T (l )= DT I1 )* (1 -0 +0 .9 *T RA TI O) T C H E C K =T (N +l ) hO =r JU + 1 GU TO 4 0 1 5 3 I F (N O. Lt .1 )G O TC I 1 5 2 1 5 4 ?A TI O= (T L- QT (N O) )/ (Q T[ NU -1 )- QT (N O) ) ?U AS H= RA TI C* (Q DT (N O- l) -b ~O rI NO ) P T (l )= DT (l )+ RD AS t+ > u o = YU + 1 " 0 T O 40 C C C C A IC bL A TI U N O F PR ES SU R E P R U FI LE U S IN G S IM PS O N R U LE IN TE G R AT IO N C 3 F M UM EN TU V E Q ~I A TI O ~~ J (k I T H R ES U LT S FK U P EN ER GY E Q U AT IO N ) C C IT 3 85 1 5 5 D E LT T= (T L- TI 11 1 IT 3 86 C I T 3 87 C IN IT IA L IZ A T IO N S TA TE M EN TS , NO TE S IN C E P -A T T HE CH AR S UR FA CE IS IT 3 88 C SP EC IF IE D e IN TE G R AT IO N M ET HO D W IL L PR OC EE D FR OM E =L TO Z =O * IT 3 89 C IT 3 90 SI M P1 =O eO IT 3 9 1 S IM P 2= 0- 0 IT 3 92 S IM P3 =0 .0 I T 3 93 S IM P 4= 0- 0 IT 3 94 ZS =Z L/ HS I T 3 95 C IT 3 96 C D E FI N E J S A S TH E TO TA L NO , OF SL IC ES I N T HE C HA R IT 3 97 C IT 3 98 JS =( lO -O *Z S+ 5e O) /L Oe O I T 3 99 LS =J S +l IT 4 00 W FL U X (l) =W I/E PS I T 4 01 Z X (L S) =Z L IT 4 02 TP (L S) =T L I T 4 03 P (L S) =P L IT 4 04 AC O Nl =2 *6 69 3* 10 ,* * (- 3) IT 4 05 A C O N 5= 2a 42 /3 60 0. IT 4 06 A C O N 7~ 77 8e 16 /3 2. 2 I T 4 07 DO 2 60 N = l* JS IT 4 08 N BA K= N- 1 IT 4 09 HN =N BA R IT 4 10 LO =L S- NB AR IT 4 1 1 ZX (L O) =Z X( LS I-H N+ HS IT 4 1 2 ZS IM P= H S/ H SI M PI IT 4 1 3 M S= (l Oe O+ ZS IM P+ Se 0) /1 0, 0 IT 4 1 4 C IT 4 15 C D E FI N E M P A S T H E TO TA L NO , OF P O IN TS O VE R W H IC H SI M PS O N' S R U LE IT 4 1 6 C IS T O B E A P P LI E D IT 4 17 C IT 4 1 8 M P= M S+ 1 IT 4 19 Z Y (M PI =Z XI LO ) IT 4 2 0 PO 24 0 M =l qM P IT 4 2 1 M BA R= M - 1 IT 4 2 2 HM =M BA R IT 4 2 3 M U= M P- M tlA R IT 4 2 4 ?Y (M O) =Z Y( MP )-H M* HS IM PI IT 4 2 5 Z V AR =Z Y 4 M O ) I T 4 26 I TE M P= LC HA R IT 4 2 7 C IT 4 2 8 C FO R A S P E C IF IE D C HA R D IS TA N C E (S TA RT IN G AT Z = L AN D P R O C EE D IN G IT 4 2 9 C BA CK TO P = O ) O B TA IN T H E CO RR ES PO ND IN G TE M PE R AT U R E FR OM TH E IT 4 30 C TE M P tR A TU R E P R O FI LE IT 4 3 1 C IT 4 3 2 C A LL O M E G A I Z V A R ~ Z I T ~ I T E H P * N D I M ~ ~ T V I S ) IT 4 3 3 20 5 T K = (T VI S+ 46 0- 0) /1 .8 IT 4 3 4 20 9 0 0 2 16 I= l, N C IT 4 35 T K E = (L .O /E K( I)) +T K IT 4 36 IP A X =N D A TA IT 4 37 C IT 4 38 C FO P TH E VA LU E OF TH E TE M PE R AT UR E F IN D T H E C O KR ES PO N D IN G IT 4 39 C C U LL IS IO N IN T tG R A L TU C AL C U LA TE TH E PU RE G AS V IS C O S IT Y IT 4 4 0 C C AL C U LA TE V IS C O S IT Y U F G AS M IX TU R E U S IN G M ET HO D OF W IL K E - IT 4 4 1 C JO HN SO N IT 4 42 C IT 4 4 3 2 1 1 C A LL O M E G A (T KE ,X TK EI ZO MG A~ IM AX *N DI M~ ~O MG A) IT 4 4 4 4 C O N 2= Fh (I) *T K IT 4 45 V IS (1 )= AC ON l* SQ RT (A CO N2 )/ IS IG (I )* *2 )* 0M GA IT 4 46 2 1 6 C O N TI N U E IT 4 47 I F (N C. LE e 1 )G OT 02 38 IT 4 4 8 2 2 0 ( - 1 0 T 0 (2 22 92 21 12 21 ) , K EY IT 4 49 2 2 1 T V/ \K =T K IT 4 5 0 \! N f; =N h4 + 1 IT 4 5 1 90 31 7 K LZ Z9 N N 5 IT 4 52 C IT 4 5 3 C IN T E K P U LA TE FU K 0, IT A G EY EK AT FD IN M O LF RA AN D /O R K IN E T F R O M IT 4 5 4 =a C I X v) z l-4 .'d 01 0 r a - PC d 4 'A rr% Ic: N Q Q - (3 r - 4 c h3 - 4- l5 a' u Md '-4 4 I 0 d N cd etd 0 k- (U t-4 PO 0 - 9 L4 & a a 0 P L L 5- 9 b-4 hi-- b !- 0 0 a -. - L' @- e- s - 4 98 ha -- ea 3 C3 -8 1 P9 >- > - >d a .-.?a a '4 >P" e8LU 0. UI C- 3 z m k r - m - d 1 !=--a 2E bL C-( L L 3 AN$- P7> =$ < d o Q '3 c (A ".- O bkf w $ & ? : u B P - fa S > ) a 1 4 U - 0 - a I W + e t = i $ = - e - 4 b - = I1 - m It t ri 0 A * P d a " % N L 9 > r 4 e - N - > > - - s N w7 - - a2 c I t r $1 -$ I IO-4++ - N 9 .-. - 3 9 c ~ ~ I - B J X O ~ C C Q I ~ Z I ~ >- N M > - j & Z ex C % L O P k i & C & 4 C d > Q . A N II 01 N - 4 - 3 y o - g '-4 rn bbl m l - 0 w & L L U G & > r n & 11 O - Z & - - 9 0 cy a 0 35: - c s i 9 i d B d g O - Q Q - S O l d u > C A rJ UJ I- b- >0- m F* w k c , ~d e a r n + Q I- 0 €L ~ ! - J Z P O UJ --.E C - c 3 r ~ z CIS: F* 6 ~ 3 I- T k - C Z 4 - - I 1 I 0 N I I P i 4 - .B -=-%'A Ca 0 -=+-dU N a I I 1 1 - 3 0 d U i C . 3 ' 4 - u ~d ~ C J ? L + L U O ~ ~ ~ T ~ , A e r n 3 &-LO B Cf 3z C J I I S 9 * - A U N LI 0 0 a - Q - 2 0 - b d O Z I I O - C- * X E Q - II O X F ? II PI e 3 4 ah] l l v9 S 2 0 2 E C X C S N Z N J P Cd Z Z T d --dUC3ZU Pr - C O I L 4 U - J > O C . ¶ E Q L L O W 0 L 3 4 U 3 U ~ P Y > U > O S O C C ~ ~ e= -9 1-- 4- & 05 COO-' t C N 8" 5 d 4 4 -=lF-rC d N N N Pq LP\ N C C 4 a 0 V) 63 Y h W U I- 0 JJ N I E a U e' 0 a z a C a I- - 3 r Z) a3 LL W a z 0 c c 3 - > u 2 - N u 7 N @ - >- - Y a - - te\u UJ cu st .I >- Z Y 1 4 Il k! 3 c \ a x4t.a - I u \ - --cf - LU * m a - c v, x .-.I J Q A C m - - G O 4 U I -;3 v \ Z 3 0 - 3 0 L O m c 3 3 3 * >- - i> V I L l m + - 9 4 - 3-4 I B - 1 & - -7 U 2 0 - aL 1 4 - - 0 +t - a o > > v ) < -+- V)O - * a - N > > V) 9 U Q Y U C O ~ U UI o - c 3 w C u u I. d\V)>ao< 3u.J A d 1 - c c = > " * v , u c u \ f u J iI -1- x a s a - - u p - 11 N ~ Y a c x c o &3\+ + 3 W % C < n - l l > N C A + m > z X ~ - ~ E C I l ~ J O O n * I1 I1 -- 0 9 C L Y : ~ J J + ? U ~ > ~ > - - - J H \ ~ ~ U uv) - - C L cr r ( 3 1 1 3 I I ) N I I N I I I I O Z - N Z 3 X 7 ddt- I I N I - C Z > Z ~ - Z O L - - E 3 I I 11 a l l ll 11 - M u 3 3 0 0 O W U O E - C > 0 0 U Z > > ~ C X C I - U ~ V ~ ~ J ~ C Q I - m D J d C C C " a Z u Z rn V ) - - 3 J O O Z -+---I O O X Y 3 E 3 3 ~ 0 ~ C C L Q C f O ( y : 3 XQLU a r ~ i - u > u ~ ~ ~ ~ c . n ~ n ~ ~ a o N C S rC a3 CT' 4 0 ~ c o o e n m m o & 1 I N r n r n C J r n N & & V N ' V nl U 0 U c ) O SU M8 =@ .0 IT 52 5 H E VE N= MP -1 IT 5 26 00 25 5 K P = Z r M E V E N g2 IT 5 27 SU M1 =S UM 1+ 4e 0* PR OD (K P) IT 5 28 SU M3 =S UM 3+ 4, 0* TT (K P) IT 52 9 25 4 SU M b= SU M 5+ 4e O *P R U D C P( KP ) IT 5 3 0 6 0 T O( 25 5r 25 40 r2 54 0) qK EY IT 5 31 25 40 S UM 7= SU M7 +4 ,O *P RO OR (K PI IT 5 3 2 L 5 5 CO NT IN UE IT 5 33 IV IU DD =M P- 2 I T 53 4 00 25 6 K P = 3v MO OD q2 IT 5 35 SU MZ =S UM 2+ 2e C* PR OD (K P) IT 5 3 6 SU M4 =S UM 4+ 2. O* TT (K P) IT 5 37 25 7 jU M6 =S UK 6+ 2e O+ PR OD CP ( K P ) IT 5 38 G O T O (2 56 ~2 57 0q L5 7O )q KE Y I T 5 39 25 70 S UM 8= SU H8 +2 .O +P RU DR (K P) IT 5 4 0 25 6 CO NT IN UE IT 54 1 S I M P l = (( hS IM PI /3 ~0 )* ~P RO O~ 1) +P RO O~ MP ~+ SU Ml +S UM 2~ +S IM Pl ~* EP S* *2 IT 54 2 SI MP 2= (( HS IP PI /3 ,0 )* (T T( l) +T T( MP )+ SU M3 +S UM 4) +S IY P2 )* EP S IT 5 43 P (L O- 1) =S QR T( PL *+ 2+ (2 .* KR )3 :( 77 8. 16 /3 2. 2) *A LH A* SI M Pl +B ET A* SI M 2 IT 5 44 S lM P 3= D E LT F *H S IN P I/ (H 53 :3 ~O )* (P RO DC P( 1) +P RO CP M P+ SU M +S UM 6+ SI P3 I T 54 5 12 0 T O( 26 0q 25 8r 25 8) rK EY IT 54 6 2 5 8 S I Y P 4 = D E L T F + H S I M P I /( HS ~~ 3~ O) ~( PR UD R( l) +P K~ @R (M P) +S UM 7+ SU M8 )+ SI MP 4 I T 54 7 2 6 0 C U hT IN U E IT 54 8 b O T C( 26 00 q2 60 1q L6 CL )v KE Y IT 54 9 L OO 0 CL =E PS *S IM P3 IT 5 5 0 G O TG 26 03 IT 55 1 25 01 J L = E P S* (S IM P3 +S IM P4 ) IT 55 2 L IT 5 5 3 L Pf !I hT I N P UT P n R A M F T ER S IT 55 4 C IT 5 55 2 6 0 3 P R Ib T 5 97 IT 55 6 7 F U R X A T ( l hl // // // // ) I T 55 7 LC 7 T( l( 59 80 q5 38 1~ 59 82 )r Kt Y IT 55 8 5 1 80 0 K IL T 5 9 8 IT 5 5 9 8 FO RM A1 ( 11 X vS 9H F R OZ EN F LO W M O DE L - 1 T EW PF -? E/ ) G O TO 5 9 8 9 5 9 8 1 P R I U T 5 9 8 3 5 9 8 3 F O R M AT ( 1 1 X v6 1H E Q U IL IB R IU M F LO J M OD EL 1 - TE M PR E/ ) GO TO 5 9 8 9 5 1 8 2 P R IN T 5 98 4 5 3 8 4 F O R M A T( 11 Xv 63 H N O N -E Q U IL IR R IU M F LO d M OD 1E L - TE flP R E /) 5 9 8 9 G U T 0 (5 ~8 5p 59 86 lr M TY PE 59 85 P R IN T 5 9 9 5 9 9 F O R M A T( 12 Xe Sl H E X P E R IM E N TA L/ I/ 1 ;ti TO 5 0 9 1 5 3 8 6 P R IN T 5 9 9 0 39 9C F 2R Y A T ( 1 2X ,5 1H TH E O R ET IC AL / 11 1 5 9 9 1 P K IN T 6 0 3 ,T (l) vN C b0 0 F O R M A T (1 8X v2 6H IN IT IA L TE M PE R AT UR E (O F) = * lX tF 7 -1 ~ 1 4 X v2 6 H Y U M B E R O F lG A S C G M FU NE NT S = r 1 x1 I2 /) P R IT 4T 6O Lv D T( 1 ) ~ 3 1 b0 Q M A T( !U X1 23 hI lV IT IA L SC OP E IQ F/ FT ) = , 1X 1F lO .l, 14 X v2 9H U O e CO M PO NE L" JT M O Lt /M O Lf G A S /) P K I~ JT O C L ~ T L IA L P A (~ ) r Y l( 1) b 32 tO R K A T( 18 X1 24 HF iN AL T EM PE R AT U R E (O F) = v lX vF 9. 1, 15 Xv lH Lv 3X 1A 4p 6X pF 1 1 (? .4 / \' R I~ IT L O ~ ,P L IA L P A (~ ) v Y I ( 2) b d 3 I- IJ RY AT ( 1 8 X 1 2 5 ti F I~ ~ A L PR E- SS UR E (L B/ F T i) = * LX r1 -8 .1 ,1 5X r lH Z v3 X rA 4 r6 X rF 1 1 0. 4/ ) " K II J T ~ O ~ ,V ~ I~ A L P A (~ ) tY I ( 3) 6 0 4 F O K M A T( l8 Xv 24 HM AS S FL U X (L P/ FT 2- SE C) = r l X , f 9 . 4 ~ 1 5 X v L H 3 v 3 X v A 4 ~ 6 X v F L 11 1 - 4 1 1 ~ ' K Ip ~ T O ~ f~ Z L q A L P A (4 ) ? Y I ( 4 ) b: ) 5 F u K ~ ~ A T (~ ~ X ~ ~ ~ H C H A R TW IC KU ES S (F T) 1 4 / 1 IT 5 95 P R I Y T t 06 *E PS *A LP A( 5) .Y I( 5) IT 5 9 6 60 6 F O R M A T( ~~ XI LS HC HA R P O R O SI TY = r l X ~ F 1 8 ~ 2 ~ 1 5 X ~ l H 5 ~ 3 X v A 4 ~ 6 X ~ F 1 0 ~ 4 / ) IT 5 97 P R IN T C 07 vA LP A (6 ) 9 Y I (6 ) IT 5 9 8 6 0 7 FO R M AT (1 8X pS OH 6 .3 IT 5 99 lX *A 4 ,6 X *F 10 -4 /) IT 6 00 P R It 'd Tt O C O pA LP AI 7) ,Y I (7 ) IT 6 0 1 b 0 8 0 F OR MA T( l8 X, SO HP ER ME AB IL IT Y C C E FF IC It N TS 7. 3 IT 6 02 lX .A 4. 6X ,F 10 -4 /) IT 6 03 P R I N T 60 8, AL PH A. AL PA (S )9 YI (8 ) I T 6 04 60 8 FO R M AT (lS X. 19 H AL PH A (F T- 2) = r l X ~ E 1 4 . 2 ~ 1 5 X ~ l H 8 ~ 3 X , A 4 ~ 6 X ~ F 1 0 ~ 4 / IT 6 0 5 1 ) IT 6 06 P R I N T 6C 3, BE TA ,A LP A( 9) ,Y I( 3) IT 6 07 6 3 3 FO R M AT ( 1 8X ,1 8H B E TA (F T- 1) = ~ l X ~ E l 5 - 2 ~ 1 5 X ~ l H 9 ~ 3 X t A 4 , 6 X ~ F l O - 4 / ) IT 6 08 P ~ I~ 4 T 6 1 0 ~ A L P A (l O lt YI (l O ) IT 6 09 bP O FO R M AT ( 1 8X v5 0H 10 93 I T 6 1 0 lX .A 4 th X 9F 10 -4 /) IT 6 1 1 P R I N T 6l lr AL PA (l l) ,Y I( ll ) IT 6 12 61 1 FU R M AT ( 1 8X .5 O H 11 .3 IT 61 3 lX vA 4, 6X ,F 10 .4 /) IT 6 1 4 P K I N T 61 2~ JR KS S, AL PA (l L) rY 1( 12 ) IT 6 1 5 61 2 FO R M \T IlS Xp 23 H R U N G E- KU TT A ST EP S IZ E = ~ l X , I 1 0 ~ 1 4 X v 2 H 1 2 r 3 X ~ A 4 , 6 X ~ F l O IT 6 16 1. 4/ 1 IT 6 1 7 P R I \T 61 3v JS RS S, AL PA (1 3) ~Y I( 13 ) IT 6 1 8 6 1 3 FO K Y A T' (1 8X ~2 5H SI MP SO NS KU LE ST EP S IZ E = ~ l X 1 1 8 , 1 4 X ~ 2 H l 3 ~ 3 X ~ A 4 ~ 6 X ~ F l IT 6 1 9 lf ? - 4 1 1 IT 6 2 0 P E II U T5 86 IT 6 2 1 5 3 6 FO K PA 4T ( 1 H l) IT 6 2 2 C IT 6 2 3 C P ri IN T O UT PU T PA KA M ET ES S CO RR ES PO NO IY G T O JS t G R ID S IZ E IT 6 2 4 L IT 6 2 5 IK E = l IT 6 2 6 4 iK E =5 IT 6 2 7 1 I K t = i IT 6 2 8 L bG L t'K I'd T 5 9 7 IT 6 2 9 G O TO (2 66 0q 26 61 q1 66 2) rK EY L 66 0 P R I N T 59 8 G O T O 26 63 d6 61 P R I N T 59 83 GO TO 26 63 26 62 P R I N T 5 98 4 26 63 G Q T O( 26 64 r2 66 5) tM TY PE 2 6 6 4 P R I N T 5 9 9 G O T 0 2 61 26 65 P R I N T 59 90 26 1 IF (L Ik E. GT o1 )G O TO 26 5 P R I N T 26 50 tD EL TT 26 50 F O R M A T( 35 Xt 23 HT EM PE RA TU KE D R OP (O F) = ll Xt F2 0- 1/ ) DE LP =( P( l) -P L) P R I NT 26 51 tD EL P 26 51 F OR MA T( 35 Xq 24 HP RE SS UR E UR UP (L B/ FT 2) = ql Xt F1 9o l/ ) Pt ? I NT 26 52 tQ L 2 6 5 2 F OK MA T( 35 X* 33 ti SU RF AC E H E A T F L U X (B TU /F T2 -S EC ) = ~ l X q F l 0* 2/ /) 26 5 P3 1r 4T 27 20 t ( ZX (K K) ,K K = I K E qM IK E) 27 20 F OR YA J (1 4X ,1 5H CH AR D E P T H (F T) t6 Xr 5F l3 .4 ) P R I Y T 2 7 2 1 t (T P( KK )t KK =I Kf tM IK E) , 27 21 tO R M A 7( 14 Xq 16 HT EM PE KA TU RE ( Ot ), 5X tS F1 3. 1) P R I ? d T 2 7 2 2 , (P (K K) ~K K= IK E~ MI KE ) 27 .2 2 F dR YA T( 14 Xt l7 HP RE bS UR E (L B/ FT 2) g4 Xq 5F 13 .1 ) " 4I VT 27 L3 r( NF LU X( KK )* KK =I KE tM IK E) 2 7 2 3 F OK MA T( 14 Xt Zl HM 4S S F L U X (L H/ FT Z- Sf C) q5 F1 3- 4/ ) ?I ? I' JT 27 24 2 7 2 4 F U R M AT ( 1 4 X ~ 6 h H b AS C O PP UN EN T lh Af lL E/ b! UL E G A S 1 / :;U TL I( 2 72 6. 27 2 I r 27 27 ) p K iY ~ 1 2 0 !) U? 72 8 Y. IC K= l* LS I1 02 72 bL L= L 1 N S Y CC l~ lP (L L~ KI CK )= YI (L L) L li o C l~ li TI Pi lt C i7 .2 7 t! U 27 2' 9L L= l VN S IT 6 3 0 I T 6 3 1 I T 6 3 2 I T 6 3 3 I T 6 3 4 IT 6 3 5 IT 6 3 6 I T 6 3 7 I T 6 3 8 IT 6 3 9 IT 6 4 0 IT 6 4 1 IT 6 4 2 I T 6 4 3 IT 6 4 4 IT 6 4 5 IT 64 6 IT 6 4 7 IT 64 8 IT 6 4 9 I T 6 5 0 IT 6 5 1 IT 6 5 2 IT 6 5 3 IT 6 5 4 IT 6 5 5 IT 6 5 6 CO MP OS IT IO N IT 6 5 7 IT 6 5 8 IT 65 9 IT 6 6 0 IT 6 6 1 IT 6 6 2 IT 6 6 3 LT 6 6 4 Y C O M P (L Lv lI= YI (L L) P K IN T ? ~ ~ ~ ~ A L P A (L L) ~( YC O M P( LL ,K K) ~K K) ~K K= IK E, KK )~ M IK E) 2 7 2 5 F U R M A T (1 8X rA 4~ 11 Xv Sf 13 ~4 ~ 27 79 C O N TI N U E IF (M IK E. GE eL S) GO T G 2 80 0 L IK E= L I K E + l M I K t = M I K E + S IK E =I K E +5 G O TO 2 6 0 2 2 6 0 0 P R IN T 5 8 6 2 7 8 GO TO 3 0 3 0 0 ST O P EN D t C t e C k C ~ ~ I - t C k C C ~ e t t C t t . t - k C - C C C + b b t C - p W C n C w u ~ ~ C * ~ ~ I H u C H U C ~ C C " C . u C C H k H c L b I C L - Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z T Z Z Z ; 7 Z Z Z Z P Z 1 Z Z Z Z ; 9 Z Z U! C 3C Q - P b- C I T e - U- I T h . - . * C Q - C - c e g r ( 9 - 0 c > Z - - - C C n m r. 5 ' $ - c U - h l P O V] P e c - 0 E ' -C)Z(C - u F vi N D. (n CL J - r v - F U - LO cl C U u - m u - m i - m u Cf I- r oc d u - m t-l c a - C A O X WI - c M LL J 4 - 0 P a c e - - - a o u. - C - +ai-% a c t &I w e r n N - u k - e O U - PI u W - 0 X r Z - r - 2 ' C h W LL 4 + N L i . - X C - U c U E >. C - u - n ~ \ . - r u o n u I- .d A - -- Z+-- C C LL LL W C 2 4 W 4 - H r -Owl yC\ -3 - (Y K ' 2 V 2 7 - C U - 0 C c - r U (Yt o a - N - V I N ~ , > z u I-, u r d Crl hl - r t u - - oh' c, c - a > PC, r e c c - 2 d - - 0 c c cx LL P 4 Cr: - b f i - U n C C O - C r r/. w 2' C- C e - r - C t d U Z C \ C C C' c c I- H C T H (r I ^eFMN.I * C C l W O L C- 2 LL > U 4 - C u u X - h > - V ' Y * U U Vt. $ t f ) * d N U , T I L C * L C ; ' - - 7 Q C LL C . 4 - * d O : N - c d h 5 n LL c C G -4 LL I N < ~ - u J Z - C - Q r LL a u U C (d > I - - - C C C - a c c ; a - - c - r 9 T T &I U U - m h * r . L L d f i C O C o c r e kt- P) t 2 U J - - r r ( h P R - - ~ C . 4 c Y U L) C- - u a - - - C u C . 4 r L c C ~ - ( r o m d w 3 1% H CI: - U i r \ ! r h - - s Z C - C U , U 2 - c LTI LL a C W - C - I T C ~ - C C X N ~ ~ W ~ C - u 5 (I o w t LL & - 3 - > C . - ( h X U P T , h - C - < C S d C C < z b.. LL - - L C C-- c 01 rQ. L c L L I I I IJ- C $ - C - U C - - - C - F o r ~ ~ I x V c r W L U 2 Z C U - - ~ ' C W W O G C C O ~ & U -ILL c c 2 N C u - ~ \ ~ c . - - N c . ~ O N C Y C L -6 - L O u- 7 - L - I , I % oc. Q ( / ' C \ ) w r r - ~ V ' - - Q C R > . d * w C z k U C CTC In k c L - c c * c C - Q ,- - G V , U r * U- L .J - - M C ' ~ ( r C I I - C : - C n - C C * Z ) C 3 C C > C M d C Ln CeCT - L n d - C , c O C j C w < c rU C C U ' V C I - C .d a u; h - -- r - a r - C G - 3 - C ' c r c r c 5 ~ ' C - I - k u U 4 - f n - C o V \ < - ~ ~ c - - N * C L ? a C 7 1 ~ > > - (0 Z Z L L n C h t C + c C G - c r % > &MU. - 0 L L L c - 2 .rl u c - ~ \ - f i ~ . - - - c n ~ n ~ ~ a ~ - c r ~ + b 3 d C3 C C - - u - C ; C , c r , - * ."J,, CCv, V 7 L L C O - 7 u $ ~ - Y M ~ - c - - L v + u - c < C J = Z v, I a - - - a c r u ~ u - - t - + ~ o ~ ~ - - r r w J c a c - L U - c c z N r r & - Q C r C r r C 5 7 .. x Kl w \ t w - - ( r , - y : F c C : V \ Z - 2 7 2 4 * * * d P . + ~ ~ 7 ~ h Z C z - x c ' Z C . f C C C u- C C C II II -- u d L L c > L L h f I L I - < C : U Z L O Z F X 0. Z ; ; - L lU - C I- u Z W , F U X ~ S ~ ~ ~ Z - S E S T II II 11 c LI c u b. ' - u - c-.C C C t U r n 5 C C U C C C V; C C C C C L Z Z F Y Y a 4 tdN d -P.w, td C3 .-.. PL =P R FS SU PE AT Z- L [L R/ FT Zj N IT 0 3 5 RR =G AS CO NS TA YT (1 .9 87 B TU /L S- YO LE /O R ) N IT 0 3 6 TZ FR O =R EF ER FN CE TE M PE R AT U R E (2 98 .2 O K) N IT 0 3 7 D EL TK =T EM PE PA TI JR E I NC RE M FN T IJ SE D TO C AL C U LA TE D KC /D T (O K 1 N IT 0 3 8 N IT 0 3 9 RE AD 12 vP Lp R R pT ZE R O pD EL TK N IT 0 40 D O 15 J= l, M Y N IT 0 4 % S l TH R U S 5= E M P IR IC A L CO NS TA NT S FO R H EA T C AP AC IT Y O F EL EM EN TS N IT 0 4 2 (U P TO 1 0 0 0 O K) N IT 0 4 3 N IT 0 4 4 R E A D 14 rS l( J) rS Z( Jl ,S 3( J) 1S 4( J) ,S 5( J) N IT 0 45 N IT O G 6 A 11 T H SU A 55 =F M P IR IC A L C flN ST AN TS FO R H E A T C AP AC IT Y O F EL EM EN TS N IT 0 4 7 4 4 BO VE 1 0 0 0 O K ) N IT 0 4 8 N IT 0 4 9 P E A 0 1 4 ,A L l( Jl vA 22 lJ 1 9A 33 4J I p A 44 (J ), A5 5( Jl N IT 0 5 0 CO NT f N U € N IT 0 5 1 00 16 I= l, R JS N IT 0 52 N IT 0 53 AA =F O RM UL A NU M PF K N IT 8 54 N IT 0 55 P E A R l4 ,I A 4 (I ~J )~ J= l, M M ) N IT 0 5 6 N IT 0 5 7 A 1 Tt iR U G I= FM pI R IC A L CO NS TA NT S FO R H EA T C AP AC IT Y f A BO VE 1 00 0 O K ) N IT 0 5 8 N IT 0 5 9 R E A D 1 4 ~ A I ~ I ~ q 9 I ~ l ) ~ C I ( I ) 1 D I ( I ~ ~ E I I I ~ v F I ( I ~ ~ G I ~ I ~ N IT 0 6 0 N IT 0 6 1 A 11 T H P U G II =E M P IP IC A L C llN ST AN TS FO R H EA T C AP AC IT Y (U P Ti 3 10 00 O K ) N IT 0 62 N IT 0 6 3 R F A ~ ~ ~ ~ A I I ~ I ) T P I I I T ) ~ C T I I I ) ~ I ) I I ~ T ~ ~ E I I ~ I ~ ~ F ~ ~ ~ I ~ ~ G ~ I ~ I ~ N I T 0 4 4 C O N TI N U F N IT O h 5 N IT 0 6 6 FK =P rlT rF ,T I AL ~ A R A M E TE R /S O LT ZY AY C O NS TA NT N IT 0 67 SI r;= CC II L IS In h f ?T AI VI ET FR (3 A) N IT 0 68 N IT 0 6 9 XT KE =P R O DU CT OF TE YP ER A TI J3 E AN D l/ EK VA LU E 70 Y G A= C flL LI S IU R IN TE G R AL TA BI JL AT ED VS XT KF E M I S= CH AR E N IS S IV IT Y SI G M A= ST FP H AN -R nL TZ M AN CO NS TA NT (0 .4 81 X 10 -1 2 B TU /F T2 -S EC -O F4 1 R E A D ~ ~ v E M IS , SI G M A OP Y IN =L D W ER L IM IT O N T H E H EA T OF P Y R O LY SI S I R TU /L R ) Q PI NC =l NC RE M EN T BY W H IC H TH E H E A T O F P Y R O LY S IS I S V A R IF O QP P4 AX =U PP FR 1 I M IT O N TH E H EA T CJF P Y R O LY S IS W IY IN =L O W EQ L IM IT O N T H E G AS M AS S FC U X (L RS fF T2 -S EC ) Y II N C =I N C R E M €N T B Y W H IC H TH F G AS YA SS FL U X IS V A R IE D W IM AX -IJ PP ER L IM IT O N TH E G AS Y AS S FL U X Fl d= M O l FC lJ LA P W E IG H T Y I= Iq IT IA L M nL t F R A C TI oh O F GA SE S A T L= O AL "A =C Cl M P3 VF YT II )E NT IF IC AT IO U fC l' 7f = ? (G AS 1, = l (S OL II) ) , > FL H =F N TH A l- P Y C F Fr )P MA TI SN A T 2 9 3 n K N IT 1 05 N IT 2 06 N IT 1 07 N IT 1 08 N IT 1 09 N IT 1 10 N IT 1 1 1 N IT 1 12 N IT 1 13 N IT 1 14 N IT 1 15 N IT 1 16 N IT 1 17 N IT 1 18 N IT 1 29 Q IT 1 20 N IT 1 2 1 N IT 1 7 2 N IT 1 23 Y IT 12 4 N IT 12 5 N IT 1 26 N IT 1 2 7 Y IT 1 2 3 N IT 1 29 N IT 1 3 0 N IT 1 31 N IT 1 3 2 N IT 13 3 N IT 1 3 4 N IT 1 35 N IT 1 36 N IT 1 37 N IT 1 38 N IT 13 9 4 0 N = l N IT 1 76 H =H I N IT 1 77 K N =1 N IT 1 78 % A X IS ( l) =O .O N IT 1 7 9 Y A X IS ( 1 )=O .O N IT 1 8 0 5 0 Z (l) =O *C ) N IT 1 8 1 C N IT 1 82 C R UN G E- KU TT A A R A LY S IS FO R IN IT IA L S LO PE AN D IN IT IA L T EM PE R AT UR E N IT 1 8 3 C S P E C IF IE D A T TH E BA CK SU RF AC E. N O N -L IN FA R * SE CO ND O RD ER N IT 1 8 4 C D IF F E R E N T IA L EQ !J AT IO N (E NE RG Y B A LA N C E) e F IR S T P O IN T N IT 1 85 C E S TI M A TF D R Y EU LE R M ET HO D N IT 1 86 C N IT 1 87 1 3 1 T C =T (N I N IT 1 8 8 TH E TA =T (N ) N IT 1 89 M X =1 N IT 1 90 1 0 3 R A N K Ih =T C +4 hO .O N IT 1 9 1 TV A R =R A N K Ih / 1. 8 N IT 1 9 2 C N IT 1 9 3 C U SE PK fIP T TO G EN ER AT E N EE D ED P H Y S IC A L PR O PE RT Y D AT A N IT 1 9 4 C (H EA T CA PA C IT Y T G A S A ND CH AR C nN D U C TI V I T Y AN D D E R IV A T IV E O F N IT 1 95 C O VC P4 LL T H ER M AL C nN D U C TI V IT Y V A LU ES ) N IT 1 96 C N IT 1 97 1 04 C A LL D ~ ~ ~ ~ ( TV A R TJ C H AR ,K O O FT N D AT AT ~ T K E ,~ ~ M G A ,N D IP ~ ,C P M Y ,C ~ ]O ,D C ~~ ~ NI T 1 9 8 JC H A 9= 2 N IT 1 9 9 55 IF (N *G T. l)G O T n 1 0 1 0 R IT 2 0 0 5 5 D T( N) =O FL UX /C nO N IT 1 0 1 T (N +l )= H* DT (N )+ T( N1 N IT 2 02 D T (W +l )= OT (N ) Y IT 2 0 3 TP R E V =T ( 1 ) N IT 2 04 GC T O 1 35 N IT 2 05 1 91 0 49 K = H *D TC N IT 2 06 9 3 3 TY O 'r! '= TC N IT 2 07 D FL 7= Ii N IT 2 13 8 Gf l Tn (5 8, 60 y5 1) ,K FY N IT 2 09 r NI T 21 0 AV GF W =O .O W IT 21 1 AV G FW =A VG FH +Y ( I )+ FW ( I1 N IT 2 1 2 C O VT IN U F N IT 2 1 3 GO TO 10 40 N IT 2 1 4 IF (K ~U YT oE Q o2 ~G 0 TO 7 10 N IT 2 15 N IT 2 1 6 LJ SF M O LF RA T O G EN ER AT E M O LE F R A C TI O N q AV ER AG F M O LE CU LA R W EI G HT N IT 2 1 7 A(V D R E A C TI O N R A T E E X P R FS SI O N F OR US E IN T EM PR E N IT 2 1 8 TR AN SF ER VA LU ES TA BU LA TE D IN V O LF RA FO R A S P E C IF IC T EM PE R AT UR E N IT 2 1 9 N IT 2 2 0 C AL L M O L F R A (K PU NT rK PT 3q KG qT Pl ) N IT 2 21 YM AX =K PT 3 N IT 2 2 2 N N 5= N N 4+ 1 N IT 2 23 7 0 7 K L= 2, N N 5 N IT 2 24 C AL L Ill tlE G A( TV AR qT AB LE ( 1 r 1 ) ? T A B LE ( 1 rK L) qK MA Xq ND IM Lr VA RY ) N IT 2 2 5 IF (K L- GT o2 )G O TO 7 04 N IB 2 26 Q FA CT =V AR Y N IT 2 2 7 G O T O 7 0 7 N IT 2 2 8 IF [K L, GT o3 )G 0 Tf 7 7 0 5 N IT 2 29 AV G FW =V AP Y N IT 2 30 GC I TO 70 7 N IT 2 31 IF (K L. GT .~ IC ~ ~ n 7 09 N IT 2 32 'r l= VA RY N IT 2 33 G O T0 70 7 N IT 2 3 4 Y ( K L- 4) =V AR Y N IT 2 35 G CA Y- Y (Y L- 4) N IT 3 3 6 IF (G C4 Y. GT .O .O )G O TO 7 0 7 0 N IT 2 3 7 Y (K L- 41 =1 .3 F- 13 N IT 2 38 9 R I A q l = A H S t T V 4 P - T (2 ) 1 N IT 2 39 IF (B R IA Nl .G T. L. 01 GO TO 7/ 17 N IT 3 40 Y Y C O M P- KL -4 N IT 2 4 1 YC QV P( KY CQ MP , 1 )= Y (< YC Dp f') N IT 2 42 Cf lh lT IN IJ F N I Y 24 3 GT ; T'! 13 40 N IT 2 44 ' V IT 24 5 C U SE K IN F T T O G EN ER AT E M O LE FR A C TI O N T AV ER AG E M O LE C U L4 R W EI G HT N IT 2 4 6 C AN D R E A C TI O N R A TE E X P R E SS IO N F O R U SE IN T EM P N IT 2 4 7 C TP AN SF ER V AL U ES C AL C U LA TE D FO R A S P E C IF IC T EM PE R AT U R E N IT 2 48 C N IT 2 49 6 1 I )E LZ =H N IT 2 50 C AL L K JN FT (T P1 ,T VA R TD FL Z ' IY N ,K ~ ~ D T C ~ P E A C T ~ W tK P T3 9A V G FH I N IT 2 5 1 KN =2 N IT 2 52 K M A X =K P T3 N IT 2 5 3 K 7= 2 N IT 2 5 4 IF (B RI AN l.G T. 1e O) GO TO 1 0 4 0 N IT 2 55 D O 10 45 I O U =l vN S N IT 2 56 TC K= I O U +4 N IT 2 5 7 Y CO MP tI OU ~l )= TA RL E( L, IC K) N IT 2 5 5 1 0 4 5 C O N TI N U E N IT 2 59 10 40 G AS C P= (C 0M X/ AV GF h) *R R N IT 2 60 3 0 8 8 F O R M AT I L H O, 1 2 ) N I T 26 1 G C A A T= A S S IT 4N )-T C) N IT 2 62 IF (G CA AT .G Te O, OO OO l)G C TO 1 0 7 N IT 2 63 1 0 6 CA PA C (N )-G AS CP N IT 2 64 C AP AC t l )= CA PA C( 2) N IT 2 65 1 0 7 G O T fl (6 2r 63 yb 3l rK EY N IT 2 66 ti 2 G PU UP = (W *E PS *C AS CP /C DO l-I OC DI 1* DT C/ CD O) N IT 2 6 7 GC I TO 6 5 N IT 2 68 6 3 G R! llJ P= ( W *F P5 *G AS CP /C ~~ ~- (D CD Of OT C/ Cr )O l+ ~~ EA CT /C DO ) N IT 2 6 9 5 5 OA - AP Kf G RO UP N IT 2 70 TP R EV =T C N IT 2 7 1 1 0 5 GO T O ( 1 10 9 1 7 0 ~ 1 3 0 , 1 3 5 ) , PY N IT 2 7 2 r W IT 2 7 3 r CR LC OL A TE P A R A Y FT E Q S Ir V F '3 R TH O Qr lE P R U N G F- KU TT A A N A LY S I S N IT 2 7 4 C. N IT 2 7 5 I1 0 A l= A R K N IT 2 7 6 PA 1 = P A N IT 7 7 7 TC =T H FT A+ 0. 5* Al +O . 12 5* D A l* H N IT 2 7 3 '> TC =D T H CT A+ O 5* D P 1 N IT 2 7 9 M X =7 N IT 2 5 0 IF (T Cl 13 3r 13 3r 10 3 NI T 28 1 A2 =A R K N IT 2 82 D A2 =D A N IT 2 8 3 TC =T H ET A +O e5 +A 2+ 0, 12 5* D A 2* H N IT 2 84 DT C= DT HE TA +O .5 +D A 2 N IT 2 85 M X= 3 N IT 2 86 N IT 2 87 I F TC SF C R YE S N E G A TI V E R E ID JU S T AS SU M ED VA LU E O F D T/ D Z AT L= O N I T 2 8 8 AY D R ET U R N T fl IN IT IA L IZ A T IO N S TF P N IT 2 8 9 N IT 2 9 0 IF (T C 11 33 ,1 33 9 10 3 N IT 2 9 1 A3 =A R K N IT 2 9 2 DA 3= DA N IT 2 9 3 TC =T H FT A+ A3 +O 0 5* 0A 3* H N IT 2 9 4 D TC =D TH ET A+ D A3 N IT 2 95 Y Y =4 N IT 2 96 IF (T C) 13 3 r1 3 3 q 1 0 3 N IT 2 97 P R IN T 22 23 qT C N IT 2 9 8 FO SM AT ( l H O ,3 H Tf =? l X rF 15 .6 98 Y t8 H N E G A T fV F 1 N IT 2 9 9 A4 =A Q Y N IT 3 00 l3 44 =0 A N IT 3 01 N IT 3 92 CA LC IJ I- AT F VE YT TF M PE R AT lS RF AN D D FQ IV A T IV E P O I Y T U S IN G F fl U R TH N IT 3 0 3 D Q DF R P U N G F- YU TT 4 F 30 4T In V S N IT 3 0 4 N IT 3 05 T [~ ~+ 1) =T tN )+ (L .G /f ~. O~ *( QQ l+ DA 2+ @ A3 )r H + A 1 N IT 30 6 3T (t\ J+ 1 ) =n T( V) +( 1 .9 /6 e ~ )* (~ A i+ 2. ~* 3A 2+ 20 0* ~A 3+ r) A 4) N IT 3 0 7 N IT 3 05 TF ST L 4 S T T FY P rF A Tl JQ E C 4L C U l AT Er ) A G AI N ST TH E 'IA XI YL JM VA LI IF . N IT 3 09 I F T r I ~ X 1 S EX CF ED lr l), P R Ii\ lT Y lJ G G ES TT n AD JU ST M EV T Tr ) i4 AS S FL U X N IT 31 0 4'J D P 2q C TE f3 T D U FX T JC R (0 3 C A 5 tl o IF T FM 4x IS V QT EX CF ED EI ) N IT 3 1 1 P R O C FF C T n f Y G P flT ST AF !C .E C H FC Y T 3 S FE IF P P P F IL F IS C O sY PL ET Er ). N IT 3 1 2 V IT 3 1 3 IF (T t N + l)- Tf \4 AX ) 1 3 8 7 1 3 h v 1 3 5 N IT 3 1 4 " 2 I h! T 5 Yf , r\ lIT 3 L5 W c.l I- C C 0 - u < t 0 Cr: I- qZ. e I (n c3 LU 0 - W I -4 i b Z I- k- \ 0 cJ 0 2 - 0 . . - c u cr: s c c n + I- < * 3 G F c( a r e rl M i e a w v : - N ~ I I m + 3 m,F S T UUJh: "7 L'7 3'\4 --(.. I .J" II G N r 4 J d U r 3 C O O C L +A A 4 ' C f o C I I C u . * l e m Z v n r u C J * *PIC- - I-U O O C O I c * r l - r l l 11 & a h + 1 a I! - - W d II II II I I \ LL C + - - 0 - 1 1 II II I I C Z U I- Z O l l ZNfOaA L - = i W Y f A V l - ~ U ' ~ ~ l l f c n a a c ~ . , c - 7 3 ~ + m z z ~ - ~ i - F E Z I - I1 I1 II i - - - J C C ! , U II UJ r u r n ( n ~ O U X P - U U G C C - . I C V ) m m V ) N - J J S N I - 3 . Q U < C 2 Z I I u.. C= Y Z t - J c l c w b- c: I- LL, - x (YLLG Y V IS lI )= AC ON l*S OR T( A C PN 21 /( SI G ( I )* *2 )+ nM GA 2 1 6 C O N TI N U F IF (N C. LE . 11 G O T0 23 8 2 2 0 G O T O (2 22 t2 21 t2 21 )r KE Y 2 2 1 T VA P= TK N N 5= N N 4+ 1 00 21 7 K Lz 29 N N 5 C P ,, IN TE R P O LA TF F f'R D A TA G ER FY AT FD IN P IO LF RA AN D/ O R K IN E T F RO M C, ST O RF D TA BL F A T TH E S P E C IF IC C HA R D IS TA N C E I N Q U ES TI O N C C 4L L O M E G A (T V4 R~ TA BL E( lt l) ~T AE LE (l ~K L~ rK MA Xr ND IM l~ VA RY ~ IF (K Lo GT e2 )G D TO 2 1 4 R EA C T= VA R Y GO T O 21 7 2 1 4 IF (K L. GT .3 )G O TO 2 15 4V G FW =V AR Y GP TO 2 1 7 7 1 5 IF (K Lo GT .4 1C f' TO 2 1 9 i.I =V AR Y GC I TC 1 2 1 7 2 1 9 Y (K L- 4 1= V 4K Y AN DY 3 =Y (K L- 4 1 IF (A N3 Y3 .G T. O. O) GD T p 2 17 0 3 1 8 Y (F L- 4) =1 .0 F- 10 2 1 7 0 IF (Y .G l.l )G D Tc 2 1 7 7 1 7 1 M F LU X (L fl1 -d KY CO Pl P= KL -4 Y C ,n hl P( KY C, r~ P, l n ) = Y (K YC OY P) ? 1 7 C I~ X T I' U II ~ 3 7 2 V "I Y =O .O GO T 3 (? 2? 0r ?2 71 12 7? 1) , K tY ?? ?? I M FL !IY I L1 li )= W I ' 7 7 1 01 7 2 37 J = l, N C T rR 'J =l . CI N IT 4 2 1 N IT 4 2 2 N IT 4 2 3 N IT 4 2 4 N IT 4 25 N IT 4 2 6 N IT 4 37 N IT 4 2 8 N IT 4 2 9 N IT 4 30 N IT 4 31 N IT 4 3 2 N IT 4 3 3 N IT 4 3 4 N IT 4 35 N IT 4 3 6 N IT 4 3 7 N IT 4 3 8 N IT 4 3 9 N IT 4 4 0 N IT 4 4 1 N IT 4 4 2 N IT 4 4 3 Y I T 4 4 4 N IT 4 4 5 Y IT 4 4 6 Y IT 4 4 7 N IT 4 4 8 N IT 4 4 9 N IT 4 5 0 N IT 4 5 1 N IT 4 5 2 N IT 4 5 3 " Jl T 4 5 4 N IT 4 5 5 22 3 Do 23 C L = lr N C N IT 4 56 IF (L .N E. J) GC l TI 7 22 6 N IT 4 5 7 22 5 GO T O 23 0 N IT 4 5 8 C N IT 4 59 C C AL C U LA TE TH F V IS C O S fT Y O f TY E G AS M IX TU R E N IT 4 60 C N IT 6 61 22 6 A C O N 4= V IS (J )/ VI S/ LJ N IT 4 62 AC O NZ O =S QR T( S Q R T( FH (L I/F W ( J l 1 ) N IT 4 63 TO PV =( l. +S Q RT ( A C 0N 4) *A CO N2 01 ** 2 N IT 4 6 4 2 7 7 A C D N S= l.+ FW (J )/F W (L 1 N IT 4 6 5 R flT V= Z. *S O ST (2 . )*S OR T( A CO Y8 1 N IT 4 6 6 22 8 P H IV =T @ PV /R O TV N IT 4 67 T E R M =T F R M +P H IV *( Y( CI /Y (J )) N IT 4 68 2 30 C O N TI N U E N IT 4 6 9 V Y T X = V M IX + (V IS (J l/T ER V) N IT 4 7 0 23 7 C O N TI N U E N IT 4 71 GO T n 23 80 N IT 4 7 2 2 3 8 V IS C O 5= V IS (I )* AC ON 5 N IT 4 7 3 GO Tf l 23 0 N IT 4 7 4 2 3 5 0 V IS C O S= VY I X *A CO Y5 N IT 4 7 5 7 39 T T( MO )= (T Vl 5/ AV GF bd )* W ** 2 N IT 4 76 ~ s n v ( vr ?) = TV I S* VI S C ~S *W /A V G FW NI T 47 7 C AL L O M E G A lT VI S IT ? CA PA C IT E M P pb in I P 2, CP RA R) N IT 4 7 8 PR O Q CP (V O) =C F3 AR *W N IT 4 7 9 GO T f> t2 4 3 ~ 2 4 0 1 ~ 2 4 0 1 ), KE Y N IT 4 R 0 ' 2 4 0 1 P R O Q R( W 3) =P FA CT Y IT 4 81 24 0 C 3K TI N fJ E N IT 4 8 2 C N IT 4 83 C ST Cr ?F V AL U FS [ lF T H E O O TP lJ T PA R AY ET FR S AT IN T F K V A LS S P F C IF IF D N IT 4 8 4 C B Y JS , TH F G R I? S I7 F N IT 4 85 C N IT 4 86 7 X (L O- l)= ZX (L fl) -H S N IT 4 87 T P ( L O -l )= JT ( 1 ) * AV G FN /I. i*> :7 N IT 4 -8 8 n F C T F = rP (L r? )- TP (l o- l) VI T 4 5 9 f, Y IT 4 9 0 - n-l - 8 ruz .$ C L - a Ern F- ' -* c w - v, * a + cz- - l-3 cD Lv, H m + " + m WJ I-( dr + -. >- n u - - Y Y C L n - r k z - n - v - 0 U O o l ( v n x n ~ n - C - O ~ O ZolCtZNCY: LLICLCO *a > * u * G Y u 0 0 0 4 - 0 T * . * U \ * - * 4 - * c u * d h l + + + * + cY 1 l l d F W a m + N I I N + Q Q Q v ~ L C W - O J 3- 0 O O O C O O O O ~ O . ~ Z Z f l E L L I Q E E f L P Z % I I I1 L L J \ C U . L \ ~ V : LU * * * * * Z Y 3 3 Z N 3 3 Q Y 3 7 , - Q ~ I > - - - C N C 5 3 h i t C C O O O O O O O n m l A m - m z 2 E w > w W - m z 11 11 11 - 11 2 - W GO TO 26 1 2 6 0 1 % =E P S *( S IM P 3+ S IM P 4) 2 6 1 QR =E M IS *S IG M A *T L* *4 QA =Q C+ QP C. C P R IN T IN P U T PA R AM ET FR S C 36 33 P R IN T 59 7 59 7 F O R M A T I1 H L/ // // // /) GO T O (5 98 09 59 81 ~5 98 2) qK FY 5 9 8 0 P R IN T 59 8 5 98 F O R M A T( lL X9 59 H F9 fl ZE N F LC IW YD DF L - 1 TE Y P R E /) GO Tf l 5 9 8 9 5 9 9 1 P R IY T 59 H 3 5 98 3 FC l? F' AT ( 1 lX , 61 H F Q U IC I B R I U M FL OW YO DE L 1 - TE Y P Q F/ ) GO TO 59 89 5 9 8 2 P K IY T 5 95 4 59 54 Ff lR Y A Tt l lX v 6 3 H N O N- FQ UI L I R R IU M F LO k M OD 1E L - T rM P R E /) 59 49 Gn TO ( 5 98 5, 59 96 1 q* TY PF 5 9 9 5 P R IN T 5 99 5 9 9 F O SM AT ( 1 7 xr 5 1 H EX PE R [M EN TA L/ 1 /) GO T I1 5 9 9 1 5 Q 46 P R IY T 5 9 3 0 5 9 9 0 F 09 Y A T (l? X, 51 Y TH E O R E TI C A L/ I /) 5 0 9 1 P P JN T 60 0r T (1 1r NC b3 13 FO K Y A TI 1 8 X r2 6 H IN IT IA L TE vP E R 4T U R E (O F 1 = , lX vF 7. 1 r 14 X r2 6H rV U M BE P [? f lG bS C O YP IV E? :T S = , 1Y I Z/ 1 P R lU T 6 0 lr Q P 6 9 1 F O rl N A T (l RX ,2 5M PY R7 LY SI 5 I- JF dT ( (3 TI I/L B) = rl X pF 3. 1~ 14 X q2 91 -1 P \1 3. Cf JY P' 3N 1 FV T V! -I. F /Y ,7 LF G & S / 1 N IT 5 2 6 N IT 5 27 N IT 5 28 N IT 5 2 9 N IT 5 30 N IT 5 31 VE T 53 2 N IT 5 33 N IT 5 34 N IT 5 35 N IT 5 36 N IT 5 37 N IT 5 38 N IT 5 39 N IT 5 40 W IT 5 4 1 N IT 5 4 2 N IT 5 43 N IT 5 4 4 N IT 5 4 5 N IT 5 4 6 V IT 54 7 % IT 5 48 N IT 5 4 9 N IT 5 5 0 N IT 5 5 1 N IT 5 52 W IT 55 3 N IT 5 5 4 V IT 5 5 5 N IT 5 5 6 W IT 55 7 N IT 5 5 8 N IT 5 59 V IT 5 60 N I- C - 3 X d 0 a: I rc 9.4 t - 03- z I- l n t - u - c a OL z\zx 0, P R IN T2 72 l? (T P( KK )? KK =I KE ph rl IK €) 27 21 F OR YA T( 14 X? 16 HT EM PE RA TU RF (O F) ?S X? 5F 13 .1 ) OR IN T2 73 0p (P tK K) ? K K = I Y E ? M I K F ) 27 30 F OR YA T( L4 Xp 17 HP YE SS UR E (L R/ FT 21 r4 Xp 5F 13 .1 1 P R I Y T 27 23 ?I WF LU X( KK l pK K= IK E? MI KE l 27 23 F OR Y4 T( 14 Xp Zl HM AS S FL UX (L B/ FT Z- SF C) ?5 FL 31 6/ ) P R I N T 27 24 27 24 F OR YA T4 1 4X ?6 6H GA S C O M P O N E N T lM OL E/ MQ LE G AS )/ ) GO T O( 2 72 6? 27 27 ?2 72 7! ? K E Y 7 7 26 9 02 72 8 K I C K = lp LS OQ 27 28 LL =l eN S Y Cn MP (L L? YI CK )= YI IL LI 27 25 C ON TI NU F 27 27 D 02 72 9L C= lp NS Y CO l~ P( LL ?l )= YI (L Ll P R I N T ~ ~ ~ ~ ? A L P A (L L) ,( YC OM P~ LL ?K K) VK K= TK E, MI K€ ) 2 7 2 5 F OR VA T( 1 8X ?A 4, 11 X? 5€ 13 .4 ) 27 29 C ON TI NU E IF (Y IK E. GF .L S) GO TQ 7 80 0 L I K E = L I KF +l M I Y E = M I K F + 5 I K E = I K € + S Gn TO 26 92 3 8 9 9 P R I N T 58 6 7 7 5 QP =f ?P +Q PI NC Y P f9 I FI Q P- Q PM AX ) 23 72 99 2R O 29 '3 !? P= QP Y IY H I = WI +d I IN C IF ( d I- 'r lI M A X )2 9, 29 r2 72 2 ?7 ?2 G O TO 20 33 0 ST 3P " = Y 0 NI T 6 3 1 N I T 6 3 2 N I T 6 3 3 N I T 6 3 4 N I T 63 5 N I T 63 6 N I T 6 3 7 CO MP OS IT IO N N I T 6 38 N I T 63 9 N I T 6 4 0 N I T 64 1 N I T 6 4 2 N I T 6 4 3 N I T 6 4 4 N I T 64 5 N I T 6 4 6 N I T 6 4 7 NI T 6 4 8 NI T 6 4 9 NI T 6 5 0 N I T 65 1 N I T 6 5 2 N I T 6 5 3 NI T 6 5 4 N I T 65 5 NI T 6 5 6 N I T 6 5 7 N I T 6 5 8 N I T 65 9 N I T 6 6 0 N I T 66 1 N I T 6 6 2 NI T 66 3 Li st in g B- 3. TE MP RE S ub pr og ra ms . (a ) PR OP T C PR 1 C PR 2 1, SU H R O U TI N E PR O PT (H EA T C A P A C IT Y AN D C O N D U C TI V IT Y VS e TE M PE R AT U R E) PR 3 i; PR 4 i PR 5 SU BR O U TI N E P R U P T (T VA R~ JC HA Rv KO DE ~N DA TA ~X TK Ev ZO F1 GA vN IM vC PX tC DO PR 6 1 II C D U ) PR 7 D IM E N SI O bJ I C O O E (Z O) ~A LP A( 20 )~ AA (2 0~ 61 ~ PR 8 1 5 1 ( 4 ) 1 S 2 ( 4 ) r ~ 3 ( 4 ) v S 4 ( 4 ) v ~ ' 5 ( 4 ) A 2 v t v PR 9 D IM E N S IO N A I ( ~ ~ I ~ B I ( ~ ~ ) ~ C I ~ ~ ~ ~ ~ O I ~ ~ O ) ~ E I ~ ~ ~ ) ~ ~ F I ( ~ ~ ~ ~ G I ~ ~ O ~ ~ P a 10 1 ~ I I ( L O ) ~ B I I ( ~ ~ ) ~ C I I ( ~ O ~ ~ O ~ ~ ( ~ ~ ) ~ F ~ ~ ( ~ ) G I I ( ~ O F ~ PR 11 2 Y I (Z O) ~E K( 20 )~ SI G( 20 )t Y( 20 )~ DE LH (2 0) PR 12 IJ IY E N S IG N R S C ( ~ S ~ ~ ~ ) ~ P S C ( L ~ ~ ~ ~ ) ~ ~ J R E X ( ~ ~ ~ ~ ~ ) ~ N P E X ( ~ ~ T ~ S I ~ ~ F ~ ~ O ~ ~ PR 11 3 ~ S F ~ ~ O ) ~ A E F ( ~ ~ ) ~ A R ( ~ O ~ ~ S R ( ~ O ) ~ A ~ R ( ~ ~ ) ~ E Q N ~ ~ O ~ ~ ~ ~ ~ T A B ~ E ~ ~ O ~ ~ O ) PR 1 4 IjI M EN SI ON C P ( ~ ~ ) ~ C ' J ~ ~ ~ ) ~ C O N D ( ~ ~ ~ ~ X T K E ( ~ ~ ~ ) ~ Z O M ~ A ( ~ O O ~ PR 1 5 CO M M ON ~ ~ C 9N S 1M Y ~W I~ P L ~R t? ~T Z E R O ~D E L T K vI C O D E vA L P A vA A vS 19 S 29 S 3v P R 1 6 1 S 4 *. i5 ~ A ll ~ A 2 2 v A 3 3 ~ A 4 4 ,A 5 5 PR 1 7 CU M M DN A I ~ B I ~ C I Q D I ~ E I ~ F I ~ G I ~ A I I v H I I ~ I I E I I v F I I ~ G ~ I ~ F d v Y I PR 18 CU M M ON ~ K ~ S E G Q E P S ~ Y ~ Q E L H PR 1 9 CU M M UN R S C p P S C ~ N K t X p V P L X q A F ~ S F , A E F v A R v S R v 4 E R v E QV tT AB LE PR 2 0 R AN K IN ;L o8 *T dA K PR 2 1 FA Y E N zK A N K IN -4 60 .0 PR 2 2 T= TV A K PR 2 3 T c= T+ r)! =L F K PR 24 A A A =Z o6 69 3* 10 .* *( -5 .) PR 2 5 t, C O N =3 00 4H /( 25 L .+ l, 8) PR 2 6 f4 l= T C PR 2 7 C Z= A l* T C PR 28 43 =A 2* TC PR 23 A 4= .1 3* TC PR 30 55 0 n o 51 6 I= L~ PI C P R 3 1 T K E = (l ou /t V (l )) *T ~ PR 32 1 F 1& X= FJ UA T A PR 33 F - I-' PR 34 W G O TC j( 5 3 4 9 5 0 3 1 , K C j3t * a * n w - 4 m a u * CU - + 0 - m u u a u c 3 U U J 5 - + 0 - h - a m u * - I - 4 - + - 3 - \r a + - - Z r y - .JT - 4 0 + X S ( 4 - a - (V rn L? G S - a - - n a - - u > UI u 0 * u - L) 0 1 a m - - o 0 3 0 U - * rl s t s + u c. C Y 4 39-4 0 -4 1 % a - 3 N O 4 4 Z 7 Lx U I w 4 L7 m u 4- o - a a I- o c z - 0 LUG-- aotu u c W Z O - ? Q IZ > Q z -a g1-4- Y 9 0 a d o O Y U - o ;)- + Q c m C Z ) w - 4 3 - 0 1 0 3 1 . H * X ?>- - Z r I 0 X Q - - l Y C Z \ g - 7 3 * 3 * - 3 0 - 0 0 s r - u -- - g D s ! - u ' -U" - C l - W e C D -un-U2(0 - O + T + 3.0 + Q O Z + U g o + Q - V \ U V ) I U C S Z X - x 00 O L Y * o c o n b O - + h & - U Y I1 0 C Q m O Z Q . Z L q d O C C f m 3 V ) I *L' -0-1 - - O V \ 3 Q O L - * e Z V \ U Q C ) h LMUJrJ=U - C 3 t - t - arc- - w r L Q - u 00 r c I I U I I O o D W b + O X O ?\ r+ t UIU-1c: (3 e ~ r - - + 9 \ a u ~ 11 I I - A ~ O I I Q II ~ ~ \ C * : J Z ~ A V C ~ O X ~ A * I - : U C u O ~ C L : C ( U I I - P L $ % X I1 * C I X I C - ) X ~ b ~ , ? d - J U ~ 3 Z \ + ~ s f ) \ f * Z ~ U L I U ~ L L ~ ~ ~ ; ~ ~ X ~ : Z ~ L ~ ~ ~ X ~ - ~ I ~ 11 O O U L - ~ ~ < ~ ~ J o ~ I I 11 1 1 - I I O ~ O Z O O 1 . ~ 0 3 a z U H I I C L H - I v d U - 3 - - 0 d C V ) O u L ) ~ b O ~ U M O r O L x 6 4 k L 5 U 3 1 1 C 3 2 d C ~ b ~ ~ b Z 11 t rh C C C J U U ~ f Y C 11 C Y , z > < l - A - - -5. 3 C Z V\ 2 J X I V Q Cl * - O - - U L L 5 3 Q > O U 0 0 0 0 O O U U O O I : 3 ~ 3 < 5 7 U L U -uC3U00d CL: U 3 t3 U O O ~ > - O O . 3 ' 3 . ' e c ' c r + + - 54 1 CD OP =C DL ) TC =T -D EL TK JC HA R= 2 GO TO 50 0 55 0 CD O Y= CD O D E LT F= O EL TK *l -8 D CD O= (C DO P- CO ON )/ (O EL TF +Z IO ) TC =T GO TO 50 0 56 0 R ET UR N € NO L is ti n g B- 3. TE M PR E Su bp ro gr am s. (b ) OM EG A. OM EG A - G E N E R A L I N T E R P O L A T I O N S U B P R O G R A M S U B R O U T I N E O M E G A (V AR tX vF vI MA X~ NA ME vS OM ) D I M E N S I B N X (Y AM EI ~F (N AP E) ~X N( 30 0) tF N( 30 0) PJ PT S= 3 X U P= 1. E3 0 D O 61 1 I= lr I M A X T = V A K - X (1 ) I F (T *G Ee Oo O) GO T O 6 0 9 T= -T I F (T eG Eo XU P) GO T 0 61 1 I P = I X U P = T CO iJ T I N UE I N = l N P P = U P T S + l D 0 6 1 8 I = l ~ N ? P F( 41 I )= F( IP I A N ( I ) =A ( I P ) I F (I N- GT e0 )G O TO 6 1 3 IU =I P- I SU r 0 6 1 5 I Q= IP +I IF fI YA X- LE .I Q) GO T D 6 1 5 IP =I P- 1 G O TO 6 1 8 IF ( I G. GT oO )G n T O 6 1 7 I P = I P + l I;C Tr 3 6 1 8 I P = I W IN =- If 4 A 1 + rY w a I > - u Z St CL I- d-;, + I1 u ?-L IZ I W I I ~ w r e I > ' I -L11--CI a z ~ w z r U . , L X L U Li st in g B- 3. TE M PR E Su bp ro gr am . (c ) CH AR C C H 1 C C H 2 C LE A ST S Q UA RE S F IT O F E X P E R IM E N TA L CH AR C O N D U C TI VI TY D AT A C H 3 C C H 4 C C H 5 SU BR O U TI N E C H AR (S LO PE ~Y IN TC PI KO DE ) C H 6 D IM E N S IO N X CO ND ( 1 0 0 ) r Y C O N D ( 1 00 ) C H 7 C C H R C M D AT Az N O . OF XC ON D VS . YC ON D D AT A P O IN TS C H 9 C KO DE = 1 (D AT A W IT H IN E R TS I N P O RE S) = 2 (D AT A W IT H E VA CU AT ED P O RE C H 1 0 C C H 11 R E A D 70 0r M D A TA ~K O D E C H 1 2 C C H 13 C XC O ND =T €M PE RA TU RE I O K) C H 1 4 C YC ON D= CH AR C O N D U C TI VI TY TA BO LA TF D VS TE M PF R AT UR E (C AL /C M- SE C- OK ) C H 1 5 C C H 1 6 K E A D 70 lv (X CO N@ ( I ) * YC O N D ( 1 ) t I =l vM D A T A ) CH 1 7 7 0 0 F O RM AT ( 2 1 6 I C H 18 7 0 1 F O R M A T( Fl 5* 0, €1 5. 5) C H 19 SU M X= O. O C H 20 SU M Y= O 0 C H 7 1 SU M XY =O .O C H 72 SU M X2 =O . 0 C H 23 SU M YZ =O ,O C H 24 TN =Y D 4T A C H 2 5 00 71 0 J = l r M DA TA t H 2 6 SU M X= SU M X+ XC O ND ( J CH 7 7 SU PY =S U M Y+ YC O N D (J ) CH 28 SU M XY =S UM XY +X CO ND ( J * YC I? Nn ( J ) C H 2 9 SU M XZ =S U M X2 +X C O N @ (J )** 2 CH 3 0 SU M Y2 =S U VY Z+ YC O Yn (J )** ? T H 3 1 7 1 0 C O N TI N U E CH 7 2 7 2 0 SL O PE = ( S UM XV - I S UM X* Sl JM Y/ TN f f / (S IJM Y2 -( S U Y X ? /T N ) 1 CH 33 7 30 Y IN TC P =( S U M Y- (S LO P€ *S UM X) 1 / TY C H 3 4 - 'F TI I$' J T h 3 7 c r EV I' Li i 3 L t m L is ti ng B -3 . TE MP RE S ub pr og ra m s. (d ) MO LF RA C C M OL FR A CA LC UL AT ES T H E C OM PO SI TI ON vR AT Et AN D H E A T O F R E A CT IO N F OR C T H E E QU IL IB RI UM M OD EL C C CH EM IC AL E QU IL IB RI UM IN C OM PL EX M I X T UR E- ME TH OD OF WH IT E- JO HN SO N- DA C R A ND M E T H OD lS TE EP ES T D ES C EN TI qJ O U R N AL -C H EY IC AL PH YS IC S- VO L- 28 -N 05 - L C SU BR OU TI NE M O LF R A (K OU NT qK PT 3t K6 rT PL ) D I M E NS IO N I CO DE 12 0) VA LP A( 20 ) q AA ( 20 96 ) 9 1 S 1 ( 4 ) ~ S 2 ( 4 ) ~ S 3 ( 4 ) ~ S 4 ( 4 l ~ S 5 ( 4 ) r A 1 1 ( 4 ) r A 2 2 ( 4 l w A 3 3 ( 4 ) ~ A 4 4 ( 4 ) t A 5 5 ( 4 ) D I M E NS IO N A I ( 2 0 ) t B I ( 2 0 ) r C I ( 2 0 ) t D I ~ 2 O ~ ~ E I ( 2 0 ) ~ ( 2 0 ~ 1 G I ~ 2 O ~ r 1 A I I ( 2 0 ) q B I I ( 2 O ) ~ C I I ~ 2 O l ~ D I I ( 2 0 ) , E I I ( 2 0 ) ~ F I I ( 2 O ~ ~ G I I ~ 2 O ~ v F ~ ~ 2 O ~ v 2 Y I ( 2 0 ~ 9 E K ( 2 0 ) ~ S I G ( 2 0 ) 9 Y t 2 0 ~ t U E L H ~ 2 0 ) D I M E NS IO N R S C ( L ~ ~ ~ ~ ) ~ P S C I ~ S ~ ~ S ) ~ N R E X ( L ~ ~ ~ ~ ~ ~ N P E X ~ ~ ~ ~ ~ ~ ~ V A F ~ ~ O ~ ~ ~ S F ~ ~ ~ ) ~ A E F ~ ~ ~ ) ~ A R ~ ~ O ) ~ S R ~ ~ O ~ ~ A E R I ~ O ~ ~ E Q N ~ ~ O ~ ~ ~ ~ ~ T A B L E ~ ~ O ~ ~ O ~ D I M E NS IO N X M W / 2 0 ) ~ X ~ 2 0 ) q F Y ( 2 0 ) ~ C ~ 2 O ~ q F O R T ( 2 0 ) ~ R I 6 ~ 6 ~ ~ ~ ~ 6 ~ l ~ ~ P I ~ 6 ~ p ~ I P I V O T ( ~ ) ~ B B ~ ~ ) ~ ~ N D E X ( ~ V ~ ~ V B B P I ~ ) O D E L T ( ~ ~ ~ ~ E N T ~ ~ O ~ ~ D ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 2 D O T A l ~ 7 0 ~ 2 0 ) q C P D T ~ 2 O ~ ~ C P D T 1 ( 2 0 ~ ~ F S U M ~ 2 O ~ ~ Y S U M ~ 2 O ~ ~ X Y ~ 2 O ~ ~ X ~ A S S ~ 2 0 ~ 3 q Y X (2 0) ~P E R C ~2 0) qH O ~4 )~ Y P R E V 1( 20 )~ M (2 0~ ~Y Y ~2 0~ CO MM ON N C ~ N S q M M ~ W I q P L ~ R R q T Z E R O ~ D E L T ~ ~ I C O D E I A L P A v A A t S l q S 2 t S 3 ~ 1 S4 tS S. Al lt A2 2t A3 3t A4 4r AS 5 CO MM ON A I ~ B I ~ C I I D I I E I I F I ~ G I V A I I I R I I V C I I V D I I I E I I ~ ~ I I ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ CO MM ON E K, SI Gv EP Sp Yv DE LH CO MM ON R S C ~ P S C ~ N R E X ~ Y P E X V A F ~ S F ~ A E F ~ A R V S R V A E R IE Q N ~ T A B L E IF (K 6. GT .l )G OT U3 17 4 C C X T = I NI TI AL T E M P E R A T UR E AT WH IC H E QU IL IB RI UM P R OG RA M I S ST AR TE D C TM AX -F IN AL T E M P E R A T UR E AT WH IC H E QU IL IB RI UM P R OG RA M IS E Y D E D C T I NC =T EM PE RA TU RE I NT ER VA L IN E QU IL IB RI UM P R OG RA M CA LC UL AT IO NS C CR IT -C RI TE RI ON FO R CO NV ER GE NC E I N E QU IL IB RI UM P R OG RA M C R E A D 7* TM AX vT IY C, CR I T 7 F OR MA TI 1 OX 14 E1 0. 4) X T= (? P1 +4 60 . )/ lo 8 c C NM AX =M AX IM UM S IZ E O F TH E SQ UA RE M A TR IX C N FR EQ tN Oe A FT ER W H IC H TR AC E CO M PO NE NT S AR E CH EC KE D C K E Y =2 R eA D 2r N M A Xs N FR EQ 2 FO R M A T( 21 6) 31 74 K 6= 2 DO 3 I= lr N S Y II l= Y I( I) XM W ( I )= FW 1 I ) 3 CO NT IN UE DE BA R= O* W= W I / EP S NN =N C NQ =N S M A =l NA =M M +l +N Q- NN P =P L/ 21 60 -0 K PT =O K P ?l =O M AX NT =L OO KC O DE -0 KR EA D= O T= XT K O S= NN +4 LL =N N +l M= MA N= NA K X= O X B E TA =C R I T 10 00 0 03 20 J= lt M M R B ! J l= O oO DO 3 2 0 I = l p N Q B B (J )= BB IJ )+ AA II IJ )* Y( I~ 32 0 CO NT IN UE 50 0 DO 4 33 I =l ,N Q I F (I CO DE (I ~e EQ eO ~G OT 04 33 KC OD E* l 4 33 C ON TI NU E 45 N T E ST rN FR EQ N T = 1 C C I F I T e GT e 10 00 e lG OT 06 20 5 D O 4 1 I = l* NQ F O R T (I )= AI I~ I) *( le -A LO Gi T) )- BI I~ Il *T /2 ~- CI I~ I~ *~ T* *2 ~/ 6- 1 ~ D I I ~ I ) * ~ T * * 3 ) / 1 2 ~ ~ E I I ( K ~ * ( T * * 4 ~ ~ 2 O e + F I I ~ 1 ~ / T ~ G I I ~ I l 4 1 C ON TI NU E G O T 01 02 0 62 05 D O 6 2 0 6 I = lr NQ F O R T (I )= AI ~I )* (1 ~- AL OG fT )) -B I( I) *T /2 ~O -C I~ I~ *~ T* *2 ~/ 6e O 1 ~ 0 1 ~ 1 1 * ( T * * 3 ~ / l 2 e 0 ~ E I ( I ) * ( T * * 4 ) / 2 O ~ O + F I ( I ~ / T ~ G K ~ I ~ 62 06 C ON TI NU E 10 20 C ON TI NU E 30 0 Y B A R = Oe O D O S O I = l ~ N N 50 Y B A R = Y H A R * Y (I ) D 01 01 =1 9N N C( I) =F OR T( I) +A LO G( P) F A G= Y 4 I 1 / YB AR I F lF AC eL Te l oE -3 8) FA C= l* f- 38 F Y (I )= Y1 11 *( C( I) +A LO G( FA C) ) 10 C ON TI NU E ' I F I K CO DE oE Qe O) GO TO 11 1 D O 11 I = L L r N Q F Y (I )= YI I) *F OR T( I) 11 C ON TI NU E 11 1 D 03 0J =l rM M K K = M M + l K L = J J I F I K C O D E o E Qo O) GO TO lO 50 D O 2 9 I = L L r N Q K K = K K + l D O 2 9 J = l* MM R I J I K K )= AA (I IJ ) C O N T I N U E KL -N Q- NN +J J K K = M M + 2 D O 9 5 K = K K q K L D O 97 J = lr MM R t K 9J )= R( Jf Kl C QN T I N U E K M = M M + l D O 10 52 J = lr MA DO 10 53 I= LL .N Q K M = K M + l ~ (K MI J) =F OR T( I) C O N T I N U E C O hT I N U E D O 1 04 4 J = J J w K L DO 10 45 K= JJ ,K L H (J ~K )= Ca O C U N T I N U E N = N A M =M A C A L L M A T I N V ~ R QN ~~ ~M ~N MA X, IP IV OT ~I ND EX ~I SC AL EQ DE TE RM ) D Ol OO I= l; JJ P I I I )= BI IP M) C O N T I N U E U = P I (J J) X B A R = U * Y B A R I F 4K CO DE aE Qa O) GO T0 59 KK =M M +2 H O 1 4 0 Y O 14 1 Y O 1 4 2 M O 1 4 3 M O 1 4 4 Y O 1 4 5 MU 1 4 6 M D 1 4 7 M O 14 8 YO 14 9 Y O 1 5 0 M O 15 1 M O 1 5 2 M O 15 3 MO 15 4 M O 15 5 M O 15 6 YO 15 7 Y; l 1 58 M O 15 9 M O 16 0 Y O 16 1 YO 1 62 M D 1 63 Y O 1 64 MO 1 65 Y 3 1 6 6 M il 1 67 M O 16 8 Y O 1 69 Y 3 1 7 0 M D 17 1 M O 17 2 YO 1 7 3 YO 1 7 4 - d 4 m W L3 0 a m z 4 -1 - X - + c) cr: cy a a u U. eD a - X C t - 0 Y 9 0 C u \ CT CC Y C 0 4 - u r - L + - a3 - 4 4 m - a n - > 7 03 J a3 - 0-4 6 \ m 0 - x 0 t. -- Y 1 u + Q u * I-- -J 9 0 0 Y V CI O W -0 - O W N - U. - a - 0 0 t-coo Y 0 a a I * )C 2. a - B --I- ~ r m - -+fa UJ-- - - u - 3 u e o u a z I- d o e ~ o - - J + - u r n -00 C . J U J d ) O m e - r w x - 7 > - t > .- \ X . J W C Y Z C 3 T ~ C C .. k4 - u + ( W . - - x o w e - a 9 - 1 J g - - W E - U - 0 0 r - - + S ( + - 1 e d b U J w % Z > Z T O 3 - M o e L n v Z C d - X O X O Q (3 II * f lLZ E + V ) - O ~ U - I - N > ~ ~ 2 Q C U u + vO O + + 7 7 c X Q Z * d X " u I 1 I @ Z a O Z - - C - - @ O - . J J - * = I t s d t t 1 1 - e u I I a o u J 0 - u - + a e c O 3 a ~ r n c l . 4 . - II e II m a m II u n + - e n II II 3040 e 4 0 - r 11 x u u O U + tt - - w O ? a r ~ O U J - ~ - O O Z I1 N I1 0 I1 O t U O Q O ~ O A O e X ~ - O I1 0 I l w I1 m a - - U J r c I I V U I ~ W ~ Y I Y 1 ~ U w U C O - I II CD I1 J ~ ~ ~ o ~ ~ ~ ~ ~ E - ~ ~ ~ o x - ~ ~ ~ c - ~ ~ c ~ J ~ ~ ~ I I L L ~ x J o ~ 11 . A ~ I ~ D ~ ~ A ~ D W ~ ~ u - - a a ~ z ~ ~ m ~ a - ~ - a u o ~ ~ 3 0 - 3 O V ) O M O ~ M - ~ O ~ ~ L ~ J d J O ~ 3 W U , O U Q ~ ~ U U . O C L A O X ~ O ~ O ~ O ~ ~ X X O C U ~ X X X X U ~ ~ O C I ~ ~ ~ ~ X ~ C ~ ~ N d ' O 0 0 0 Q F- V7 9 C O - 4 N h Ou\S N 4 4 e4 CC 6 6 0 4 6 a3 a3 0 d d h 6 4 C O N T I N U E I F t D F D L . L T . O~ 01 )G OT 08 08 1 X L A M B D = * 9* XL AM BD IF ( X L A M B Oe GT el eO E- 61 GD T0 93 I F (D FD L- LT mO el GO T0 89 P R I N T 22 22 ,D FO Lv NT F O R M A T ( / / / ~ X ~ L E ~ O ~ ~ I 1 X @ l I 6 ) D 0 7 6 1 = l r N Q Y (I )= YI I) +X LA MB D* DE LT (I ) TF IY [I ). LT .l .E -2 5I Y( I) =1 .E -2 5 C O N T I NU k SU MY =O . D 03 70 1- 1 r NN SU M Y= SU M Y+ Y1 1) D0 34 0I -1 ,N Q P E R C1 I) =I Y( I) /S UM Y) *l OO . BE TA =O . D OR 51 =l ,N Q B E T A = B E T A + A B S (@ EL T( I) ) IF (B ET A, LT ,X BE TA )G OT 08 00 IF IN T. GE .H AX NT IG OT 06 00 N T = N T + l I F (N T. GT e5 1) GO T0 80 1 G O T 03 00 X B E T A = X B E T A + O - 00 1 M A X N T = M A X N T + lO N T = N T + l G O T 03 00 N N = N C . K X = K X + l I F (K Xe LT .2 )G OT U3 00 N T = N T + l D O 3 2 1 J =L pM M P R I N T 32 2, 88 (J ) F OR MA T( lX ,6 HB B( J) =r Fl 2. 6) BB ( J )* O- 0 MO 28 0 DQ 79 I* lr NQ MD 28 1 BB (J )~ BB (J )+ AA (I eJ )* Y( I) NO 28 2 79 CO NT IN UE MO 28 3 GO T0 17 1 1 Pi0 28 4 82 3 WG =W Pi0 28 5 RO UT =P ER C4 NQ 1/ lO Oe *X MW (N Qj /X MW GA S MO 28 6 RA TI O* ( le +R IN J/ Il .+ RQ UT ) MO 28 7 W= WG *R AT IO MD 28 8 R I Nt RO UT Pi0 28 9 17 11 T A B L E I K P T I ~ )= W MO 29 0 c MO 29 1 C CA CC UA LT IQ N OF TH E I ND IV ID UA L MA SS F L UX ES YD 2 92 C Pi0 29 3 DO 17 12 Is lr NN MO 29 4 FL UX =W /X MW GA S* PE RC (I )/ lO O. *X MW II ) MO 29 5 17 12 D OT AI KP Jr I) =F LU X MD 29 6 FL UX =U *R OU T HO 29 7 DO TA (K PT gN Q) =F LU X MO 29 8 DO 4 4 4 I = Sr KO S YO 2 9 9 T A B L E I K P T I I )= PE RC ~I -~ I/ ~O O* MO 30 0 6 4 4 C ON TI NU E MD 30 1 NY =K OS +l MO 30 2 T A B L E I K P T I NY I= PE RC (N Q) /~ QO - MO 30 3 I F (T aG E- TM AX lG OT 03 33 YD 30 4 T= T+ T I N C MO 30 5 K X = O 14 0 3 0 6 GO TO 50 0 MO 3 0 7 33 3 KP T3 =K PT -3 YO 3 08 K OU NT S2 . M O 3 0 9 DO 80 00 J zl rK PT 3 NO 31 0 IF I J - GT *l )G OT O 7 32 M O 31 1 DO 80 01 I= lp NQ YO 31 2 Y ~ R IM E = ~ 1 ~ /( 60 o* TI N C ~~ ~( -1 37 ,s D O TA ~J 11 )+ 30 0D O TA J+ 1I 3O 0* D O TA MO 31 3 1 (J +2 rI )+ 20 0~ *D 0T A( J+ 3, I) -7 5o *D OT Af J+ 4~ I) +l 2~ *D OT A( J+ 5e I) ) MO 3 1 4 3 L ..o 7 a - C 4 0 C P 0 * D 0 u 0 * N 0 d N + .a I - CI. m M 0 3 - d - L I - 5 4) 7- t 4 U c.I 0 7 Q m Q I- m ++ a 0 + r C 0 3 - m o Y - U 9 0 0 u w I * 0 C 3 - r cr\ 0 L S u m 1 0 > X - 1 - * W \ - 4- u r Y - u I * N L ln - 7 r N 4 L 0 , 3 - m I - 3 UJ x a + 7 w V) u L I x c. 7 >- 0 \ 0- a N rn r ln 0 4 f- 4 Q rt h 4) tc 0 3 ..J - UJ e 0 a- 5 * u N 0 * Q C CI C d + * C z n m I * m Q w w u - 0 - 0 L b C + N Y Y I- Z Z - 4 - r Z U J W n C a m W VII( Y 0- 4.J e-4 r 0 1 LI Z e Z I 4 0 0 w - N u - C € 0 - r CU m + + W t u t u 4 -3 -3 s n + ? I + * E m UJ 0- v u p r - r e p t u k S C . . d d W OL Q ~ O Q C Y 0 0 4 a Q c w a a x Q C..Z9+P. 2 9 7 0 Y C Z O C I C 2 * 0 *--0s- * C I > c-- c o o 0 cn H n @ d \ a 11 -J\4 11 d d d e - 4 - 0 0 It - - I ) 0 9 - I r C - it * d 1 1 C Y + 9 4 - u g N u d r u . $ - d o n - ' 3 - " 9 U w Z N O N N ' * u o e - 0 O W 0 -0 LLUL4JW --C . 5 0 r C L I LLU 7 ~ 0 ~ ~ ~ 9 = 3 3 0 4 1 1 ~ = 3 3 3 3 o ~ ~ z ~ I - - ~ ~ z I ~ - , z , r Z 9 0 C 3 O U d ( - f Q ) ) r . W r - Z Z % O O - I W O d V ) V ) Z - Z Z 4~ 0 O E a - J - O X O d m - w II Ob) 0 r II 0 11 m w - a u C 0 7 Q ~ ~ 4 ~ 0 ~ ~ 9 a C C ~ N ~ a A ~ - N c . M e - A C 3 C Z + - b ~ c f - z + ~ Y + C . Z Z Z ~ A w rzrnzc-a O ~ ~ G ~ ~ ~ ~ Q ~ ~ Q ~ O O ~ O ~ O I I ~ O G ~ O ~ O Q O W ~ ~ U ~ ~ 0 ~ + O U ~ ~ > - ~ Q U U V V ) O C U 0 ~ V ) O M U I - - O c L L U d d rl N N m 44-0 In9 P 0 cn 0 m b o o O D 0 B b $ P- o b o m o B a z s 8 Li st in g B- 3. TE M PR E Su bp ro gr am s. (e ) MA TI NV c C C M A TR IX I N V E R S IO N W IT H A CC O M PA NY IN G SO LU TI O N O F LI N E A R E Q UA TI O NS L C SU BR O U TI N E M A T I N V (A qN ~B qM ,N MA X~ IP IV OT tI ND EX ~I SC AL Eq DE TE RM ) D IM E N S IO N A (N M A XV N )* B IN M A X~ M )~ IP IV ~T (~ ~) ~I N D EX (N M A X~ ~) E Q U IV AL FN C E I I R O kp JR O W I q ( I CC IL UM r J C O LU M I q (A PA XI TI SH A P) C C IN IT IA L IZ A T IO N C 5 IS C AL E= O 6 R l= 10 .0 ** 18 7 R Z= l. O /R l 1 0 D ET ER M =l .O 1 5 DO 2 0 J = lq N 2 0 IP IV O T IJ )= O 3 0 D O 5 5 0 I = lq N L C SE AR CH F O R P IV O T FL EM FN T c 4 0 AM AX zO .0 4 5 00 1 0 5 J z1 .N 5 0 IF ( IP IV fl T( J) -1 )6 0q 10 5~ hO 6 0 DO 10 0 K = lr N 7 0 I F ( I P IV O T (K )- 1) 80 91 00 (7 40 SO IF ( AH S( AM AX )- AB S( A( J~ K) )1 85 tl OO ~l 00 S 5 I? O W =J 9 0 IC CI LI JM =K 9 5 A Y A X =4 (J ,K ) 1 00 C O N TI N U E 1 0 5 C O N TI N U F IF ( AV AX ) 1 1 0 ~ 1 0 6 ~ 1 1 9 1 0 6 D ET ER M zO -0 IS C A L E = O GO T O 7 40 11 0 I P I V t lT (I CO LU M~ =I PI VO T~ IC r? LU MI +l C C I N T E P C H A N G E R O W S T O PU T P IV O T E L E M E N T ON D I A G D N A L C 1 3 0 I F (I PO W- TC OL UM l1 40 ~2 60 91 40 1 4 0 D ET FR M =- D FT FR M 15 0 DO 20 0 Lz 1. N 1 6 0 S WA P= A( IR OW ,L ) 1 7 0 A (I RO W, L) =A (I CO tU M~ LI 2 00 A 1 I CO LU Mv L )= SW AP 2 0 5 I F (Y )2 60 r2 60 ,2 10 21 0 DO 2 5 0 L = L t M 2 2 0 S W A P = B 1I PO kr L) 2 3 0 R ( I R OW ,L )= B( I C O L U Y I L ) 2 5 0 R ( I C O L U M * L ) =S WA P 7 6 0 IN D FX f 1, 1 )= IR DW 2 7 0 I ND EX (I ,Z )= IC CI LU Y 3 1 0 P I V O T = A ( I CO LU V, I C O L U Y ) c C SC AL F T H E D F T E P Y I Y AW T C 1 00 0 P I V O T I = P I V O T 1 0 0 5 I F l A R S I D F T ~ K ~ )- 91 1 1 0 3 0 ~ 1 0 1 0 ~ 10 10 10 10 D E T E R M = U E T F F Y /Q l I T C A L E = I S C A L F + l IF (< 'lB S( DF TE RV )- 31 )1 06 C) pI r? 20 ~1 02 0 1 0 7 0 ' > E T F R P = D F T E R M /F 1 I S C A L F = J S C A L € + l G O Tr ) LC hC 10 30 I F (9 3S (D El FY Y) -K ?) 1 0 4 0 ~ 1 C 4 0 ~ 1 3 h O lr /+ o ~ E T F ~ P -I -D F T E -P Y *~ 1 I Y CA LF =l SC AC F- 1 IF (A RS (r 'E TF Pp 4) -R 2) 1 05 0p 1 0 5 0 ~ 1 O I ~ ~ D IV ID E P IV O T 9 ?W B Y P IV O T E LE YE N T C L * - LL - C K I L C C - 2 2 * m r \ - I - U rr. d - c C % W U - r r , r f C L > * Lr - C L L - C r" 0 l LLe c U r \ l w ? 1 u - C : - 6 . C I.& U C C I & h a C - C h r T C .*-C\. - F U? c I- c- 7 u u - L r - c C U z' c -LC:* d U ! 3 <' - U < - w r_, IA a C' * U' & I - C ' L r m * h < I- G - C r d < + C 7 7 = F P 1 - - + c L r C u t F - C X - * - T - - z < 4 - h L L - C: r CI - I + C O - U - C h C c LL C u n u - .U U_ . c - C S C * c c C < . 0 C. > L C 5 - S U - c n * U .7 a Ah . - p W - U 6 L 2 c Y - U ' L i.,!-- ,d -& , .C t r Y t- r 0 L s ~ ~ ~ n u , ~ u c C t . - - P- X c C C + - ~ d f f h I r \ ~ c LL L Cl r , t uC-U tZ - -LL f f i U C : d L Z v : - - C C C * c r ' C C - C V, T c U 1 d - r h c - U 1 7 r cl r 2. - I- IP a * - - - t r e u c L P c I < O - O - C I - - C L a -I 7 I A C C 3 - m h ' r W c - - U p - c O u ~ - c - ~ c O h m ~ u C U U L C * c t U I U n 4 0 - C > d N h l - C C 4 r' J --I-.!+ C V Y - C C e L C L t- a k k < \ t ~ G - - U S - C Z & - ~ X U! 4 I?C Q w - N O I P V C Q U L L J U ' P- LL L: L L -14-C-hO. rc2 - U * U P C L L I J Z C ~ V N - V r - Q a e m C Z * r r\ A c C C r r - C , ~ - C ~ C j G F U L c hlP$V' 4 Cf c uc12 - - - C U U L P ~ r r * - > x \ \ \ \ C- r v +r C & C r W , + - - r e + R U - - - - I- V, ~ Q Q N - ,- C C ( G - Z - C I A O : N ~ U W ! C 9 J 4 x 0 - - P - - c ) - ~ c N - N O Q Z + t * + + $ + e L' < UCI W ( / i O N O + - - Z h - U r 45 i ( O 4 I - W C k c > C *R-hl"cCPuU - u C C C , C C' Z Z U . b C - U U Y C ; C C C - CCIP, c I ' O I _ l Y C C - LL U LL J U & u w g V , N Q W H c u & LUWLLLCt C T U,U c - a e r w a i - u ; P r r c w r A ~ W N & ~ ( c c c L L L C I A, 0 r U. - 4 : c - U C C t - C - k - * Z C 7 2 I- Z V \ z - - - - Z U , Z L : * ~ Y ~ ~ l I I I ~ 0 L L r w C Z C L O O O C U O Z ( ~ , ~ U L L C L W ( V ~ \ $ ~ ~ ~ . d o I- c t - < & - - c ( \ l h ~ - - s ~ Y * + t $ I . C u c r : * O l I t c: 3 3 u J m 4 - L o - u r n - W Z c Z P Z l - O * % * I I U ' c 1 1 - - A s 0 C I U I Z - Z m c Z o Z C - & C r C I I - C C l - t OW, 11 3Q) 0 = w cf .J u ' 4 L c > L L w ~ L ' z V , 5 T F C - - - - a d 7 + C b k C m b i u ~ r n r m r e 5 - x r X F F 11 I I I I 11 I I LL I I I I x c - -r 3 3 l c r * c U u C C C C d & F * U h E C , F U C U Q IA c C* C W C U U U U d U 4 d 6 C q Z W , I C + ' C 4 '-4-1 4 .-' + * 0 3 C 3 - * WJ + m 4 4$ C -? c. m m + ru a 3 C 7 c. tu Ln 4. rl ci . w a Lt G c S I kt- z - LL x C L u - -1 Y cC C) c - v; C- Z - b L Y m t x c Z) CT. g z : u - L L r c w II LLI u - w A -I 11 t a a 1 1 - Z C T II C.V) * I I - = - w ~ ~ c I I m .-+-u LL o 3 ~ ~ 3 0 . - at- b-3736 4 ~ , - u c 1-1133 m n h * ccrc b r 4Z G 9 - z W - L L c A Z o ~ t r z W Z I I o a C a c - u . c I I C . l u g 3t tr DL! . f - L J W L C 1 1 6 L \ I I C u c u z -h t t r u u I- u z Y G C C T C C L Z - P ~ ~ C U! D J U - dZk- J W C J k - h t C Z " U 3 - - Oc a u L L C b C C < a O 4-l U C C i C GI-r. (rCLUv,C. m L2 U U - a v U c ' U W 0 U U - C U U f x 4 c E . C - t i c 9 t- r- i 6 C 0 0' CL h h! h' J: a U U G U U C U C U C U G L CI1 +F I v, C h u Ln Lid w o u t b O - c 3 C I ? C C c at- - U O O W + C C + - 0 4 nCGOL ----a+ Z * . - d b it 0 - c - G L T C e h . - m f i . - - Ss 4 - c , e 3 Y U - '3 r c t - U - > cr 1-li - Q X - - - cc' C > 4 . c - L c ' x e c o LT 3. - 0 - C c * N h r r U - * N o r C C - - W e W &scN -1ChJl.le LT - I- 4 - - V\---b: r r U Q * C C c ~ L J ~ G - - P A Y - - u - a > d J CT - a - a-C: LC\ CT * C' U- C H C 13: - C r & a - r r < * I - U en--- - k c " - - d L L .. 2 C r - C x -wee - - 2 3 6 r h L L I L - - & C \ < 6 - C - - L L - GC\rLL-- C * L C c +I.- Z d I - I - r J L d e - w - * d O z C * C L - C , U - C C i d 2 r c L L I hhJ - L C & - U J U u d c r,J-0 d - - - . & C C - U 4 - C - Z E - - C - 0 I- - U , ( \ ' - K b C 6 P \ f G - C ^ Y V C * - cucH!=L-PL 'c c t r c 0 - J - - c l P \ - e x - h - L C F Q - O r Y X - t Y C - y r c Y - z n A L I L C . * 7 N t c 0 - C d u - d r y h - L L X d ' - k Z N U c - U Z w G - 3 U 6. LL Y Y - @ O C - P ~ ' c - J C L d r e - o h ' - - lb -ou L C ( - N U \ f - - - - - m d Y h l - - C u U A c - G - 0 4 *L- - - C a C rr; ~ ~ ~ . = - m n ~ r u r - ~ C C F L L J ~ ~ - C G m - C w W O - S h - h P W U - N c u r > d C u C U - r - l U C - < o Q C r : - - L I - - - - N + r l Q' r c r w ~ a + ~ u - - u ~ Y - > x c c u * - r w > P - - & C V W V - = C C . ~ U - , I L L ! 0 - J v, - 4 - u c r d V ) N c u DL--CLL Z - : r m C 7 i r O ~ C C T , . - C O C U c e a r & c 6. r r r . ~ L \ r P h N c c - c c F , r > % CC&CCI c V J d w - L C ? - C u Q I . - c U a --hrcr r ~ L ~ : u ~ N C P P . ~ ; e n w a cC C C - m - o - ~ n a z ~ r : - ~ n - rtw - a z O N - L L W O N O ~ c x u - - - e z r w c ~ - O O C ~ ~ 11 ZC. - N - - N - - 3 C X t U , Z d U r U I I 11 3 li LL - 0 C u U - U 0 . J 3 m b - c 0 c o r n &t'd 11 - d * Y U & - - X W N U d l . b U t C + - c Q Y Y 3 * I - C - - e c f u , c r - w U . C - ~ Z ~ C C V ) - -.-.-o-- U: N r r L - - 4 - r L d C O I T \ C C z ~ ~ z - ~ z ~ I o ~ ~ I ~ u L W Y W . . a . * . . + C ~ C C O C = Z N ~ O C C Z W ~ W C L C C * O + c o C C ( - - u h N r r rcu-o- V) I/? LLU-U.+LLL 3 m * * $ - - - w l - c m v , m m v , Z c Z Z 2 Zc; . * .a 0 * ~ Z - Z ~ ~ Z O S Z Z Z Z ~ ~ C C C ~ I I Z Z ~ C C - ~ ~ ~ U ' ~ W ~ > U , ~ X U l L ~ ! - L Z ~ E F S I1 d I f Y Y Y - Y Y a 3 X w l T < Z - 3 I T X X Z T F T Z Q C - - - - l t - - 3 - - r U . . J - - c - C t C C ~ ~ w ~ U U u h u u W O 0 D W u O C 6 C v U U L ~ X Y ~ - - I - - ~ 6-4 .=-I& --'N 4 - 3 LL >z C 4 > L L' 7 M I- C c u 7 4 * (r, a 4 c, V! -a c Y C V) - C m n v x a3 \O CI. dD--+- *I--- I t - r > t @ e - & u 3 - l I Z e C X * u r - c 9 r - r n . - r ~ - + M > - Z ~ - ' $ & * - C N - l l v r + N O C P h l C * 4 - - Q d \ @ * d a d - r z d Y d N - - i W £ Y C X - U - J I I ~ C 11 c a - ClU. d C < d ll ll CI' ll C U. X > > U g P Q N I U . - P- 4- VI h P- f- '4 C. C CA LC UL AT E R E A C TI O N R A TE CO NS TA NT c D 0 7 I= l~ N F (S T F (S FI I ) e EQ eO . )G OT 09 00 FK (I )= AF (I )* T* *I -S F( I) l* FX PI -& EF II )* RQ P! G O T0 90 1 90 0 FK (T )= AF (I )* FX P( -A EF (I )a RR R) 9 0 1 IF (K N. €Q el )G OT n9 0? 90 2 IF (S R( I)o EQ oO .IG OT Q9 03 R K (I) =A R( I) *T ** (- SR [II l)* FX P( -A FR R( I) *P nQ ) GO T O 7 9 0 3 Q K( T) =A R[ T) *E XP (- AE Ri I) *F ;9 R) 7 Cf lN TI NU E C C C A LC U LA TI O N O F R FA C TI O N R A TC O F S P FC TF (J 1 C D C l1 2J =l vK S P l SU M 2= Om D O 11 I= lt N E Q XM U CT R= 1. 0 XP UL T P = 1 .0 D C ?l O K =I 9K SP 1 I F lC IK ) . t- T ,l .E -3 7) C( K) =l .F -3 7 N FW =N R EX ( T 9 K ) T F (N E W .F ~ .O ~ G ~ T O ~ ~ O X Y U LT R =X Y U LT Q *( C( Ul *fr Y FW l 97 0 N E W =Y P E X /I TK ) IF IN F W .F Q eO )G ~T f3 10 X M U CT P= XM UC TP *( CI K) ** NF W 1 In C nM TI N U F. RA TE R ( I )= FK { I )* XM llL TQ -R KI ? l* X M tI LT P X V FW l= P SC ( I rJ ) XY FW '2 =R SC (? v J ) IF (X ~! FH l.F Q, XU EW 2) G7 Tt 71 1 + - 7 - v w 3 2 U- +$ fi + C 3 I N X .-. i L L +C * C\ + C -7 V rr C X u C C 7 L 3 3 J & X - CC u LL, Z 1-4 h L- C - X X C1 +t a - I, 3 -7 C tn 0: -.-J -- - * rl * C 3 L L -,LL 3 F 3 6 G - 0 - * - * trx cr\ I2 4 c\] r = r m 3 m IZ, x * C- x c L L . u * L L A u d 0 C w r x o x o X L L X U C- + 2 0 * + & + * + * + - X C C I - C - C 1- C * C C I n F3-3 3 3 7 3 3 3 3 C 0 4 C rl -3 C u - -- -.I SLW w e CI a at- 3 - & & + @ u u & - ! A 3 - r 7 - L C T Q * a 3 @ G W J O I - ~ , I- LL X P 3 - 5 3 1 . 7 C x ( n ~ ~ u , ~ ~ * - r C U : V; a I L ~ J , J . J - J c u z s - & & a Y d % c o w - . u. '-4 - x u n u u a x - z - A L O e l l - 11 ( " I w w - I1 I- II In C - I I v , + + v,x>- C O u 4 m + J n d ~ - I f Q e 3 ~ 1 1 - * c - J e Y f - 3 Y 3 l l C L U II II Q C X Z Y U J . J V ) C - aauu I I T L U a I - I-a - X I I W - X - 3 o r v , a ~ 3 3 - - - ~ ~ ~ @ @ ~ t . . a ~ z z 4 ~ - , ~ v , 4 N L U ~ ~ ~ ; ~ ~ ~ I I L U C L , C Z ~ ~ ~ ~ + * O C L L I W ~ Z II 1 1 - J a a ? C C X - . i Z r ~ C " C @ X C ~ C Z C ~ W % . X 11 II CPZ II 11 u 3 ~ ~ 3 P CT ~ w X X U X C ~ ~ X ~ X C - t u X t r 5 3 r " ~ x 3 m 7 P ~ 7 b U - Y L C - - - 3 - 3 2 u J - - ~ Z Z I - 3 Z I l - U ! € 3 - - T b Z - - c c -4.A * O ~ U J U J C C ~ & & ~ O O Q ~ C ~ X U Z ~ ~ ~ ~ ~ Z C C W ~ < C - C X ~ U ~ & U ~ X ~ ~ U ~ O ~ U U S ~ ~ V ) D U U V ~ : L ~ C > Q U m > r, d- 40 4 4 CC r - 9 de! e .-I d d pd d G L C U SU M =O no 11 1 I= I,K SP SU W =S UM +X FW ( I) Q Y 1l I 1 1 1 1 C O N TI N U E AV GF W =S UY D O 66 06 I K = l NC Y( TK I= Yl (I Y) 66 06 C Q N TI N U F CA LL E N T A L I l T I H F A T l q FM Ty SI .IM 7q RA TE q KF Y1 C C CO NV ER T TH E U N IT S O F TH E H EA T n F R FA C TI O N T E R M C TO TH O SF N EE D ED IN G R n U P C H E A T = ~ H E A T ~ / ~ ~ ~ - I Q ~ ~ ~ O ~ S * * ~ ) /m K P T3 =K 2 IF ( T eL T, Tl )G OT f1 37 T I= T l+ T IN I: KO S= K SP +4 K 2= K 2+ 1 00 17 I z 5 q K O S T A R L E (K 2~ I) =Y l( I- 41 1 7 C O N TI N U E N Y =K O 5+ 1 T A R C F( K2 ,N Y? =Y IIK TP 1) 60 21 T A B L E (K 2~ l) =T T4 B C Et K 29 2 )= HF AT TA B LF {K 29 3) =A VC FW T A B L F (K 21 4) =W VF W T F =T +L 18 -4 60 .0 3 7 5U M =O 0 11 2 C O N T I N U F R FT !J PN EN D Li et ln g B- 3. - RE Su bp ro gr am . (h ) IN OU T GE NE RA L I N P UT -O UT PU T SU BP RO GR AM F O R K I N E T I C A N A L Y SI S SU BR OU TI NE I N OU T( KS Pl rN EQ ~T IN C* Yl *X FW ) D I M E N SI ON IC OD Ea 2 0) rA LP A( 20 ) eA A( Z0 16 )r 1 ~ 1 (4 )r S2 (4 )e S3 (4 )r S4 (4 )r S5 (4 le Al l( 4~ eA 22 (4 )e A3 3( 4) *A 44 (4 )* A5 5f 4) OI ME NS IO N A 1 ( 2 0 ~ q 8 1 ~ 2 0 1 r C I ( 2 O ~ ~ D I ~ 2 O t ~ E I ( 2 0 ) e F I I 2 O ~ ~ G I ~ 2 O ~ r 1 A I I ( ~ O ) ~ B I I ( ~ ~ ) ~ C I I ( ~ ~ ) ~ D I I ( ~ ~ ) ~ E I I ~ ~ O ~ ~ F I ~ ( ~ O ~ ~ G I I ~ Z O ) ~ F U ~ ~ O ~ ~ 2 Y I ( Z O ) ~ E K ( ~ O ) ~ S I G ( ~ O ) ~ Y ( ~ O ) ~ D E L H ( ~ O ) D I %E NS IO N R S C (1 5~ 15 )r PS C~ 1S q1 5) eN RE X~ L5 el 5l rN PE X~ 15 ~1 5~ ~A F~ 3O ~e ~ S F ( ~ ~ ) ~ A E F ~ ~ O ) ~ A R ( ~ O ~ ~ S R ~ ~ ~ ) ~ R ~ ~ ~ ~ ~ E Q N ~ ~ O ~ ~ ~ ~ ~ T A % L E ~ ~ O ~ ~ O ~ ~ 2Y 1( 20 )r XF W1 20 ) C O M M O N N C v N S ~ M M ~ W I ~ P L q R R ~ T Z E R O r D E L T K ~ I C O D E t A L P A ~ A A r S l ~ S Z q S 3 ~ 1 . S 4 * S 5 r A l l ~ A 2 2 r A 3 3 r A 4 4 r A 5 5 CO MM ON A I ~ B I ~ C I ~ D I ~ E I ~ F I ~ G I ~ A I I ~ ~ I I ~ C I I ~ D I I ~ E I I ~ F I I ~ G I I ~ F U ~ Y I CO MM ON E K v SI Gr EP Sv Yt DE LH C O M M O N R S C r~ ~C ,N R E X tN P E X tA Fv S Fp A FF rA R ~ S R O A E R I E QN VT AB LE R E A D EQ N 1 C H 4 = ti 2 + 0. 5C ZH 6 J= 1 R EA D Z l, (E QN (J eI )t I= 1t lZ I QE AD T H E ST OC YI OC ET RI C CO EF IC IE NT S OF T H E E QU AT IO Y R E A D T H E E X P OY FN TS OF T H E R A T E E QU AT IO N R FA D T H E C O E F E C I F N T S OF TH E F O R W A R D A ND R E V E R SE R E A CT IO N R A T E CO WS IJ V IT S n F 4F AN D AR AR E IN G Y- MO LF St CU SI C- CM 9A UD SF CO ND S U Y IT S O F AE F A ND AE R A R E IN K CA L PE R GM -M OL E C R E A 9 2 3 rA F ll )r SF (l ) v A E F (1 ) R E A D 23 ?A R( l) ~S P( 1) 9I \E Ri l) C C R EA D FQ N 2 C 2H 6 = Y 2 + C 2H 4 C J= J+ l RE AD 2 l? (~ ~ fd (J ? I) rI = l~ 1 2 ) R E A 02 2t R S C (2 93 ) , P S C (2 ?1 ] ~ f' sC t2 94 ) R E A D 2 5 , N R E X I 2 ~ 3 l v M P E X (2 ?1 ) ~ N P F x (2 14 ) R E 40 23 ? A F ( 2 1 , S f 4 2 ) r 4 E F ( 2 1 R E A O ~ ~ ~ A R ( ~ ) ~ S R ( ~ ) T A E R ( ~ ) 2 1 FO R M A T( 12 44 1 22 F O R Y A T( 6F 4- GI 23 FO R M A T( ER .O ? L X v2 F 6. 0) C C R EA D F G N 3 C ?H 4 = 9 2 + C 2H L C J= J+ 1 R EA D 2 1 ? 4 E O N (J ,I )r I= l? lZ ) R E A D 22 ? R S C (3 r4 ) ? P S C (3 ?1 ) vP S C (3 15 ) R F ~ D ~ ~ ? N R F X (~ ~ ~ )~ N P E X (~ ~ ]. ~ tN P F x( 31 5) R E A D 23 ? A F (3 ) v S F (3 ) t A E F I3 1 ~ E A D ~ ~ ? P R (~ )T S R (~ )T A E R ( 31 C C R EA D EQ N 4 C 2H Z = 2C + i-4 2 r, J= J+ l R FA D 2 1 ,( EQ fV (J ,I )~ I= lv 12 ) R FA D 22 9. R S C 14 95 ) p P S C (4 9 1 3) vo S C (4 rl ) R F A D 2 5 r N P E X (4 r5 )q YP EX (4 v1 3) ,h pE X( 4, 1) Q E A ~ ~ ~ ~ A F (~ I~ S F (~ )P A F F O Q FA !l 73 ~4 R (4 ) r S F (4 )9 AF R( 4) C, C R E A P E QN 5 C hH 6 = 3C ?H ? J = J + l R E A D 2 lr (E QN (J qI )r I= 1, 12 ) R E A D 22 rP SC (5 rb ) v P SC (5 tS ) R E A D Z S, NR EX (5 ~6 ), NP EX (S r5 ) R F A D ~ ~ , A F (T ~, SF (~ ~, AE F( ~I R E A D 23 ,A R (S )q SR (S )t AE R( S) R F A n E QN 6 N H 3 = 0. 5N 2 i1 .5 H2 J = J + l R E A D 2 1r (E ON (J ,I ) ,I =1 ,1 2) R E A D Z Z p P SC (6 q8 ) v P SC (6 t7 ) ~ p S C (6 t 1 ) R E A D 2 5 ~ N K E X (h ~R I~ NP EX (6 t7 )~ NP EX (6 rl ) R E A D 23 ,A F( 6) p SF (6 ) r A E F (6 ) R E A D 23 rA R( b) q SR (6 ) v A E R (6 ) R E A D E QN 7 C 6H 60 + H 2 = H 2f l + C 6H 6 R EA D E O U 4T IC N 8 C. + H 20 = C O + 14 2 0 Z C c C1- d d C I -00 O O d d 4 4 - v * " - - L L Q NUXUILU 4u)ulau c u t x - 0 d 2-- I1 - -00 u - - d 4 c m m - Y - 4 - ( L L C U c-r r * W L A C O O - - 7448-- - - - G O Z O X - J c ' QOLU- - C C drr d G C d Ccr C d C . 0 CC' O L L C I W U Q W L u O U L L . LLLL U IC UU2 L L L ' * + UJO3 d L C N D . 0 d L m d ~ t n o m r P - IXP a : d N W 6-9 tu F LLI U! & rr + at' 4 h C d D C' . 0 (r3 r* I I r, * 0 0 0 LU Lu m 4 m 4 m re m V\ 9 0 . 9 (V 4 r) 0 LU LU Ln N P P a c u m 4- r) . a d d d + '44 d W 4 4 4 d I 1 I 1 I I I I I I U W LUUJ W L U LULL' L U U . m m 4-a P-e 6 N rld r-N E C l d @ F mCC 0'6 (CN C c h ' d P C O . . .b r \ P . . e dr, + . g . d N N N I d I I a m o 8 c k o & & o o e c c ( 1 r 1 1 W d 1 1 U d 1 0 - 0 e C C W C * O C C O C C C C C . . . * . * . . * a u r r ~ . c t n c c c c a O C C 1 4 . 4 ~ C . ; f ~ C F C Q * U P - Q - O . - t C . l F - i 3 - ' l l , - - l 0 0 d.4 40 C 3 a 3 C C O C O C o u 0 1 K I L L C L L C LLLL L L U I LUO Uo? LUJ & + U ' W H W C h 6 0 - - L L a + 9 w o w r -F W l n m r N115 6 4 * - O W COG a m 4 - 0 + C C b m u - 9 4 m t 00' G m + C 9 9 6 C C F C r e C V d m a * L O d d a ? W , h h\f d e * * u . l 0 . .(r . . . * I I d e a * n ~ I - - a n o r I "P- I I + h r ~ m e o C m v o o c ~ r r r F ~ C c u O W 00 OUI o c lLU1 L u u U L L U . 4 ' W 9 U i U J U I Q O W C O Q & a d m c 9 00 6 a L I P C O F-c 0 4 C P W a m c c K C + w , o c .-IN & a m c r n o d-h+ rrh c c C \ C C ~ C U'a c c 00 Inn-, g c C C P C J'F- o r 0 . r r p l p e . . r e * a (Z6 6 4 O C O a h C C o71w .CQ, I 1 I I LP T\r I 1 I I g d - ~ ~ h l u \ . $ m ~ @ N 4 - N e n 1 4-6, e m cr- I r-3 d-nr F-Id.4-4,-i.ddH d d 4 4 d,-i d ? 4 d +.-I - d 4.4 1 1 1 1 I l l 1 1 I I I 1 I I I 1 I I I l l U J L L . U L L I I W U ~ U UL!J UU, LLLL U.Ui U.U: u:LL! I L L : L L L ' e(\i O . U I ( C ~ ~ P P C7-m 0 0 rcfc O W r , ~ n U:P- A P - 4 t d C - + d d I L L d C C d I I.! I I L L + I U d I I I C c c d U . @ I U. I I I I I I I U O I I U I u C u u ~ I u . C I L C ~ U C I I c j l L L C L L U ~ U I U ~ L C U ~ ~ C W U ~ C I L ~ L P O O ~ ~ U ~ : ~ ~ c . c r . ~ u u - c u P C ~ ~ F ~ S t 0 6 C P ~ F O ~ d O N W C ~ ~ C 4 L n C . O C C ~ * O O C q P ' O + C ~ . d G O 0 O C N C ~ + C F ~ C Q m C u 7 C O f - C > C C . C C 3 ' i C &in * ~ . ( F I c ~ - ~ c * ~ ~ c ~ w c o ~ ' ~ c o ~ C C ~ C L T L C . C W ~ C ~ " ~ C LP e h p d r ( L l - 4 r r r . d * O a - 4 o f - e r c I - 6 e O C C I * C + C \ r O e d O P - + G e h C . P - C * P C . O - F + l d - I o I - 1 I n V + I - - I * I ~ 9 0 9 F 9 + C 0 0 9 C 9 L O 0 9 W 0 ~ d C , . C L T C L " I . G C F .CC?d.CC I l l 1 I l l l L l I C I I U I I U I I U C I L I I L L 1 I U ~ I C U U I U W U ' U L L u U I O U I W U I ~ L u o U L u C W u O I L L O U U C U J L C U I C u r r u ~ ~ a - + + ~ o ~ r ~ c o c u o ~ t c m c c o u ~ t ~ n ~ c .O- - .GU;LLC ~ ~ ~ ~ ~ ~ c r o u ~ ~ ~ ~ c e - 3 ~ .j.ncrr*c-3r- C U - F C O f i ~c ~ N ~ + ~ c ~ F O ~ ~ C C ~ ~ ~ ~ C ~ U P ~ C C C ~ ~ C L C ~ C ~ ~ C ~ G L P * a n ~ m n l a , c . s c o c c c t c c r c + \ c c a r r c i e c n u c n r - c e e + . e & ~ i . ~ a + e e r e r . d e e r e . e o s . o * . \ L * e C ~ b U \ I O \ O e N r C I O C & K O + e C - 4 - h C - C " C + b h . C * r c N * C I I I l r u l c c I I I d I I I I I I R I D F ~ ~ ~ F P ~ F c Q ~ ~ c ~ ~ c N ~ c ~ ~ c ~ ~ ~ ~ c K ~ I c I ~ c ~ c ~ ~ c I I I C 1 1 1 1 ~ 1 2 C I I u I I ~ C I k l l ~ l l u l I U I I U + L L L I u W U J U C U J I u & u C u u C I U G L U C L L U C L U C U U C W ~ + U ~ S ~ ~ ~ G F L ~ O O ~ C ~ C C L L ~ C C I . C C ~ \ O O C ~ C ~ ~ L T ~ C C ~ m h F - ~ m 9 C m n ! G w f i o ~ ( \ ~ c p c c ~ ~ c o o c ~ c r c a 6 c Q ~ + W G ~ ~ ~ O ~ ~ ~ C O ~ C ~ ~ C L T , O . C \ U ~ C C ~ ~ ~ C ~ C ~ \ ~ C ~ ~ ~ ~ ~ ~ ~ ~ C ~ ~ C C P O ~ F C ~ ~ C ~ ~ F G C L T C L T C ~ C O ~ C C O y s .d * . a r *r r . 0 . C C C ' a l l l . e O C r r 0 r .. Cn l r Q s d ~ * r \ l ( L 9 r & d r C Q e e \ t c l + h V ~ \ * C a C . 4 - W 0 4 - 4 + - - t + O l b l d- I +-rrc h r- I C 1 C ~ C c O c O C O O O O O O C C O O C c C C . 4 C O ~ O C C C c C C I 1 U l d 1 W d 1 1 0 - 4 0 U W C I W O l W Q l U L l l F ~ O u J N G L u ~ O k O O k W ~ Q O L A ~ O ~ ~ ~ ~ C C P ~ O & & C F O ' C d ~ C ~ b O P - ~ O O d ~ * o * * O ~ & C d n O d m h & 9 ~ N 9 ~ ~ m I T \ r C C N N * 8 - e 8 e 8 e em * I I I I I X Z I O C : U C \ I 9 .NN e - t . - ( r n c l - 4 & 0 e - 4 ~ N ~ N Q Z I C ; x 4 d 9 I I - ' uc) .CL ' a ~ m 0 9 ~ 0 + 6 0 b Q Q P 9 9 Y W M " C ~ N O G C P L " N I I L L I I U I ! I L L I ~ O I I X N ~ F N ~ * ~ V O C T O - ~ C ~ w o w w o w ~ o u ~ w w u ~ m ~ ~ ~ ~ ~ + ~ ~ ~ ~ + \ C Q O C O \ f C I 4 m G C j L b c m L n * * . . * r r * * . * . L L C 0 0 6 ~ 0 d b G 0 N 0 b 9 N F & & ~ O ~ * h L T F I y C K C d ~ O N + O Q l n O W ~ C ~ h N N O . C J C d b O @ . O O r n e * d e a r 0 * C ? b 9 0 * m l n o 1 4 0 9 0 0 1 .of-tn o c o c o EX P V Il I EX P V II I EX P V II I EX P V IX I EX P V II I EX P V If I EX P V II I EX !' V II I 00 d.4 d o C d 0 9 - 4 C - 4 C O G O O W G I UJUI O W U O WUt U W LLC u d a UhW * r UJa d U C N Q O F ' L L a7-l a m O F . r-r- elf' a + hlP c i f & d o m C O Q V 4 - 0 P C C b W l n 9 4 ) wr- c s G P ~ 4 - 0 -04 s a n c * N + u ' m 4-rn c l cia rc,h f i d 4 4 e b .+LT a * 0 0 r O . e e e e I 6 . r N r , rn& d . .h h + I dr- I I - NN m * 0 0 m m 44- 0 0 h v m r l O b O W 0 0 CUJ C O L b UILU W L u e U ~ J W e o u 0 0 e r l 6 0 d W 6 6 OC2 C'a W W G O P-U? G-' CPN P O 3 O C mCf? t-p G O -+N d C d'b rn-4 00 & N m N C C O d C h u'a 00 o e F P a a o o s c i f * . . r * , * * e m u - l . 0 0 Q . * * m e Q d O C 4- . erC\i 0 0 a,.r 4-0 1 1 1 1 In N I 1 I 1 - 9 4 - l n N u ' * I n N m N 4 N * R 3 4-N 4 - h W I N Ln4 - 4 h d d d d d + d d F4.4 d & d m A d 4.4 d-4 4- 4 d 1 1 1 1 I 1 1 I 1 I I I 1 I t I 1 I 1 I I I UJU'UIUJIU!LLUJ LULL' L L W U.uI W U ! LULU L U L L ' I u LULU 6 h U ' l L b Q N 0'0' O'V 0 0 F t - 0 0 2 LIJP d V F m m O Q P - & C KiO e C W t P N G C & u-lQ 6 P - - l r n & r n s ~ ~ a e v 1-4 i f + r 3 p ~ 4 - N W c o F F r r r e r * e r n 0 4 - O N r~ e i dNNfi)CpPC r CUP +- * p- a CC N C C d a t - t 7 &I I I I I I I N I I C I * I V , I I i n I I I P - 0 ~ d 6 C 0 ~ 0 ' 0 ~ 0 ' ~ G C 0 6 ~ 0 0 Q I O C C C 6 O O C C C C C r C ~ C - l O d ~ ~ 1 U " G O ~ l W l l & + l U + I U I I U A ~ - + L L - - I U - I 1 I 1 I I I U . 0 I I CL I U O U ? U ' O I L O I U C U LilG I I C I L L O U U I W U ~ W U ~ L U ~ O U I U ~ O U I L T O C C ~ C U G C U I ~ , C + ~ O C U J U - O U C C ~ & ~ ~ a ~ o ~ ~ m m ~ ~ - - 4 o ~ m o ~ ~ ~ ~ ~ e ~ ~ 0 a ~ ~ . j r ~ 0 ~ O N ~ 9 6 @ 0 0 ~ O ~ b O b ~ C ~ ~ C L C I Q G ~ C G ~ ~ C O \ O C d m * d m t - & $ . l C ~ ~ O ~ ~ . G C T J . G Q - C C ~ C U ~ ~ \ C V F C W I ~ O y\ * N r n d * N . .nJLI \ . . . e r r . . . 0 . - . .O . 0 . 4 . . + * * 1 r 6 *CCO I r o t - N O * c l O P d C * N C 00-0 e 0 - 4 d Q d I * I 6 I 4 1 I m i T C d I v 1 ~ 6 6 9 b 9 ~ ~ C 5 9 C 9 ~ ~ 9 ~ C d \ C O ~ U O C T c C C F Q O Q G C d d m * ~ N L T , N ~ O O G O O ~ O C ~ C ~ C P ~ C ~ G ~ ~ C C U c C F C a ~ . . a ~ r n ~ p . e ~ . . e d . * ~ ~ r e . e e . e \ ~ . e e a * r - m I C T Q O N * O I ~ ' 0 4 - m c r - * c + ~ o d r c , o + r ~ c o c I I I I N I C C I I I d I I I I I I & 1 0 ~ ~ ~ ~ F ~ F ~ - P o ~ ~ c ~ J F c N ~ c ~ N ~ ~ o ~ ~ P ~ c ~ ~ c \ c ~ ~ c c c ~ ~ o I LLl LT a C * (r, * r- d I LL' * 4 N d r I I;' C CC 0 0 m d 0 W 0 0 C CT 3 e '-'..I I U C U > W C O W F ' C C c r C , C C ~ ' . L C C 0 cT,C 0 4 - r I C" . * a .c I C C C C C L C C U - C L L ' C / O N C C * . c C C P d C C * + C c w r c o f - 0 . . 0 . 0 0 . . & d . R ' * ..hF * h e .a e . * e e . . e 8 F' 1 rc r \ i n . ~ t ~ r c , m h 4 ‘ 4 ~ pl r . t ~ * . c o v r n r . r e O ~ c C O 0 O C O r((-lr(OLLLULLLU I I 1 L L O O G O L U U ~ L L 0 0 0 0 9 0 0 0 C 0 0 0 0 C 0 0 0 d l c @ * a r N l e eV. .-Id4 edmCCm Q .;t C O C ? O O O O O P " P * F F C n W t M ( n W l L U U W U W O O C C O O O C O O 0 0 0 C C 0 0 ~ 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 w ~ u l L l J w U ~ U UI C O C O O O O C C O C C G C G O O ~ 3 0 c 3 0 ~ 0 0 0 b Q O 0 0 0 O C O e * . r e * . e O C O O C O C C C CCaFd-&K)aN + C . 9 Q d G m 6 9 b & d C ~ + ~ d r ( + 6 ~ \ m m f + b V \ . - 1 h ' - J r - r * * L n m 9 L is ti ng B -5 . It er at iv e . TE M PR E O ut pu t Fo rm at f or N on L E qu if ib ri um Fl ow . NO N- EQ UI LIB RI UM F LO W M OD EL - TE M PR E EX PE Rl M EN TA L IN IT IA L TE M PE RA TU RE (O F) = 92 0. 0 IN IT IA L SL OP E (O F/F T) = 21 35 9. 9 FI N A L TE M PE RA TU RE (O F) = 13 50 .0 FI N A L PR ES SU RE : (L B/ FT ~) = 21 60 .0 M AS S FL UX (L B/ FT 2- SE C) = 0. 00 39 CH AR TH IC KN ES S (F T) = 0. 02 08 CH AR PO RO SI TY = 0. 50 PE RM EA BI LI TY C O EF FI CI EN TS AL PH A (F T- 2) 0. 50 E 09 BE TA (F T- 1) 0. 50 E 05 RU NG E-K UT TA ST EP S IZ E = SI M PS ON S RU LE ST EP S IZ E = NU M BE R OF GA S CO M PO NE NT S = 12 NO . CO M PO NE NT M OL E/M OL E GA S 1 H2 0. 34 97 2 CH 4 0. 43 66 3 C2 H6 0. 00 00 4 C2 H4 0. 00 00 5 C2 H2 0. 00 00 6 C6 H6 0. 00 00 NO N- EQ UI LI BR IU M FL OW M OD EL - TE M PR E EX PE RI M EN TA L CH AR D EP TH (F T) TE M PE RA TU RE (O F) PR ES SU RE (L BI FT ~ ) M AS S FL UX (L BI FT 2- SE C) GA S CO M PO NE NT TE M PE RA TU RE D RO P (O F) - - 93 0. 0 PR ES SU RE D RO P (L B/ FT 2) - - 1. 0 SU RF AC E HE AT F LU X (B TU IF T2 - S EC ) - - 0. 69 CO M PO SI TI ON ( MO LE IM OL E GA S) C . PHYSICAL AND THERMODYNAMIC PROPERTIES - This appendix con ta in s a s e r i e s of t a b l e s , f i g u r e s and c h a r t s r e l a t i n g p h y s i c a l and thermodynamic d a t a necessary f o r t h e c a l e u l a - t i o n s i n t h e TEMPRE system, I n a l l c a se s , t h e information presented r e p r e s e n t s abs t r ac t ed d a t a a p p l i c a b l e t o t h i s r e sea rch . References t o t h e o r i g i n a l and more complete sources of information a r e pro- vided. The fo l lowing o u t l i n e w i l l be h e l p f u l i n l o c a t i n g t h e p a r t i - c u l a r d a t a contained i n t h i s appendix. Table C - 1 . Empir ical Constants f o r Ca lcu l a t i ng t h e Heat Capaci ty of Elements t o 1000°K. Table C-2. Empir ical Constants f o r Ca lcu l a t i ng t h e Heat Capaci ty of Elements Above 1000°K, Table C-3. Empir ical Constants f o r Ca lcu l a t i ng t h e Heat Capacity and Free Energy o f Compounds t o 1000°K. Table C-4. Empir ical Constants f o r Ca lcu l a t i ng t h e Heat Capaci ty and Free Energy o f Compounds Above 1000°K. Table C-5. Lennard-Jones P o t e n t i a l s and Enthalpy o f Formation o f Compounds. Table C-6, Values of t h e C o l l i s i o n I n t e g r a l Used to Calcu la t e t h e Pure Component V i scos i t y and Thermal Conduet ivi ty . F igure C-1 . Gornell-Katz P lo t f o r a Low Densi ty Nylon- Phenol ic Resin Char. F igure C-2 Char Thermal Conduet ivi ty a s a Funct ion o f Temperature. T ab le C -2 . E m pi ri ca l C on st an ts f o r C al cu la ti ng th e H ea t C ap ac it y o f E le m en ts A bo ve 1 0 0 0 "~ E le m en t M ol ec ul ar 3. 04 36 9 0. 61 18 7 - 0. 07 40 - 0, 20 33 - 2. 23 86 7 0. 42 49 0 T ab le C -4 , E m pi ri ca l C on st an ts f or H ea t C ap ac it y a n d F re e E ne rg y C al cu la ti on A bo ve 1 00 0° K . 10 .9 50 5 - 40 .6 22 1 7. 13 70 - 4. 74 90 - 98 55 ,6 6 12 ,5 05 9 1, 43 08 18 .8 89 8 - 70 ,4 41 0 11 ,8 72 0 - 7 - 45 00 0. 00 14 .5 08 0 3. 50 23 11 ,5 92 1 - 44 ,7 45 2 7. 94 52 - 5. 32 35 44 54 .4 0 2. 46 67 5, 26 98 - 18 .4 02 6 3. 10 54 - 2, 00 04 25 63 7. 19 - 3. 14 48 4. 61 98 28 .8 09 6 - 11 2, 45 10 19 .5 76 3 - 12 ,5 81 0 0. 00 - 1. 16 78 - 3. 93 17 69 .3 81 8 - 52 1. 06 00 12 4, 96 70 20 9. 15 00 - 13 30 3. 80 0 41 .8 78 2 3. 19 23 - 12 .9 78 2 2, 41 47 - 1, 67 43 - 48 94 .4 00 - 0. 72 88 1, 55 25 - 6. 19 11 1, 13 50 - 0, 77 88 - 14 23 1. 83 0 6. 53 14 1. 85 60 - 7. 66 75 1. 51 04 - 1 .1 38 9 - 64 9. 67 0 - 7. 98 90 0. 61 19 - 73 .9 93 6 - 0. 20 33 0. 24 59 - 85 4. 91 0 - 1. 64 81 3. 03 17 - 8. 53 52 1. 17 91 - 0. 61 97 - 29 88 8, 99 4 6. 88 39 3. 44 36 - 12 .5 85 1 2, 16 92 - 1, 42 96 14 42 1. 80 4 2. 37 26 6. 49 29 - 22 .6 95 2 3, 73 94 - 2, 36 06 - 64 01 .9 62 9. 23 89 1. 59 76 - 6. 25 66 1. 13 16 - 0. 76 90 - 89 0. 17 5 6. 39 03 J I - 20 31 6. 6 - 23 50 0. 0 - 94 05 2. 0 - 26 41 6. 0 - 57 79 7. 9 - 11 04 0. 0 R ei d, R ob er t C. a n d Th om as K , Sh er w oo d, P ro pe rt ie s o f G as es a n d L iq ui ds , 2n d e d, , Ne w Y or k: M cG ra w -H ill , pp . 63 2- 63 3. (1 96 6) N ot e: T he a bo ve d at a a r e fo r H el iu m a n d N it ro ge n Fl ow T hr ou gh P or ou s C ha rs . 5 w/, x 10 (f t- 5 Ph en o 1 ic R es in C ha r. Ny lo n- Ph en ol ic R es in C ha rs (I Hi gh D en si ty 0 0 L o w D e n s it y Te mp er at ur e (O K ) D. SUMMARY OF EXPERIMENTAL & ANALYTICAL RESULTS - This appendix con ta ins a d e t a i l e d summary of t h e exper i - mental and a n a l y t i c a l r e s u l t s determined i n t h i s research . The Char Zone Thermal Environment Simulator e x i t gas composition d a t a l i s t e d i n Tables D-2 through D - 1 1 should be used i n conjunct ion wi th Table D - 1 , a complete summary of t h e experiment condi t ions wi th comments on t h e o v e r a l l behavior of t h e system f o r each c a s e s tud ied . The fo l lowing l i s t of Tables w i l l be h e l p f u l i n l o c a t i n g t h e s p e c i f i c information contained i n t h i s s e c t i o n . D - 1 Summary of Test Data f o r Simulated Pyro lys i s Gas Flow Through Porous Chars and Graphite i n t h e Char Zone Thermal Environment Simulator D-2 Flow of Simulated Pyro lys is Products Through Low Density Nylon-Phenol Resin Chars. Comparison of the Experimental Exi t Gas Composition (Mole Percent ) wi th t h e Frozen, Equilibrium and Non-Equilibrium Flow Models D-3 Flow of Simulated Pyro lys is Products Through Graphite Specimens. Comparison of t h e Exit Gas Composition (Mole Percent) wi th t h e Frozen Equil ibr ium and Non- Equil ibr ium Flow Models D-4 Flow of Simulated Pyro lys i s Products Through Graphite Specimens i n t h e Presence of Heterogeneous Ca ta lys t s Coated on t h e Specimen Surface D-5 Flow of Simulated Pyro lys is Products Through Graphi te Specimens i n t h e Presence of Homogeneous C a t a l y s t s Contained i n t h e I n l e t Stream D-6 A i r Oxidat ion of Porous Graphi te Specimens Between 1485" F and 2047°F D-74 I1 Summary of Radioact ive Tracer Analyses of t h e Various Exit Product Streams Leaving t h e Char Zone Thermal Environment Simulator M AS S FL UX 0. 03 5- 0. 08 7 T ab le D -1 . Su m m ar y o f T es t D at a (C on tin ue d) Sa m pl es o f e x it g as c o ll ec te d . La m p bu rn ou t, in su la ti o n m e lt ed . J I I I I I I T ab le D -1 , Su m m ar y o f T es t D at a (C on tin ue d) . * E st im at ed F ro m P re .v io us E xp er im en ts , T ab le D -1 . Su m m ar y o f T es t D at a (C on tin ue d) RE M AR KS m a te ri al b al an ce c a lc u la te d . Ta bl e D- 1, Su mm ar y o f Te st D a ta (C on ti nu ed ). M A SS F LU X T ab le D -1 . Su m m ar y o f T es t D at a (C on tin ue d) RE M AR KS ta g e) . A ir c o o la nt f lo w e ff ec ts L iq ui d fe ed s ys te m t e s te d w it h C u T ab le D -1 . Su m m ar y o f T es t D at a (C on tin ue d) M an om et er bl ew d ur in g r u n 84 . R ad io ac ti ve p he no l fe d to s ys te m . P o ss ib le l ea k i n e x it g as l in e, C M + ' Eq ui li br iu m a n d No n- Eq ui li br iu m Fl ow M od el s. EX PE RI ME NT AL EX PE RI ME NT AL RU N NU M BE R M AS S FL UX EX PE RI M EN TA L X PE RI M EN TA L M AS S FL UX FR ON T TE M P BA CK TE M P FR ON T TE kl P EX PE RI M EN TA L EX PE RI M EN TA L EX PE RI M EN TA L T ab le D -3 . Fl ow o f S im ul at ed P y ro ly si s P ro du ct s T hr ou gh G ra ph it e Sp ec im en s (C on tin ue d) . T ab le D -4 . Fl ow o f S im ul at ed P y ro ly si s P ro du ct s T hr ou gh G ra ph it e Sp ec im en s in t h e P re se nc e o f H et er og en eo us C at al y st s C oa te d o n th e Sp ec im en S ur fa ce . T ab le D -4 . Fl ow o f P y ro ly si s P ro du ct s T hr ou gh G ra ph it e in t h e P re se nc e o f H et er og en eo us C at al ys ts (C on tin ue d) . M AS S FL UX EX PE RI M EN TA L EX PE RI M EN TA L Ta bl e D- 6. Ai r Ox id at io n o f Po ro us G ra ph it e Sp ec im en s Be tw ee n 14 85 OF a n d 20 47 °F . AI R MA SS F LU X FR ON T TE MP (N o An al ys is M ad e - Ai r Co nt am in at io n Af te r Ru n Te rm in at ed ) Ta bl e D- 7. S m a r y o f Ra di oa ct iv e Tr ac er A na ly se s o f th e Va ri ou s Ex it P ro du ct S tr ea ms Ex pe ri me nt X XV II I (C 14 l ab el ed p he no l) Ra di oa ct iv it y Fe d to th e Sy st em ( To ta l) , c pm - - 18 ,9 00 ,0 00 Ra di oa ct iv it y in G as S am pl es ( 6 Sa mp le s) , c pm - - Ra di oa ct iv it y o f th e Li qu id P ha se , c pm - - 16 ,0 00 ,0 00 Ra di oa ct iv it y o f th e Ca rb on D ep os it , c pm Ra di oa ct iv it y o f th e Ve nt Ga s (b y di ff er en ce ) m e Ra di oa ct iv it y % Ra di oa ct iv it y 1 0. 02 15 2 0. 08 41 3 0. 10 59 4 0. 07 37 5 0. 10 71 6 0. 12 26 7 0. 71 15 60 .3 1. 32 64 10 0. 0 Ta bl e D- 8. Su mm ar y o f Ra di oa ct iv e Tr ac er A na ly se s o f th e Va ri ou s Ex it P ro du ct S tr ea ms Fr om t he C ha r Zo ne T he rm al E nv ir on me nt S im ul at or . Ra di oa ct iv it y Fe d in to t he S ys te m (T ot al ), c pm Ra di oa ct iv it y in G as S am pl es (5 Sa mp le s) , c pm Ra di oa ct iv it y o f th e Li qu id P ha se , c pm Ra di oa ct iv it y a s Ca rb on D ep os it , c pm Ra di oa ct iv it y in V en t Ga s (b y di ff er en ce ), c pm Di lu ti on F ac to r (T ot al R ad io ac ti vi ty /G as A ct iv it y) 1 0. 02 15 2 0. 08 41 3 0. 10 59 4 0. 17 37 17 .7 5 0. 10 71 10 .8 6 0. 12 26 7 0. 36 63 37 .7 0. 98 12 10 0. 0 Fr om th e Ch ar Z on e Th er ma l En vi ro nm en t Si mu la to r. e m (T ot al ), c pm Ti me Ra di oa ct iv it y % Ra di oa ct iv it y Ra di oa ct iv it y % R 1 0. 01 45 2 0. 04 14 3 0. 03 31 4 0. 05 55 5 0. 05 65 6 0. 04 84 10 .0 7 0. 05 65 11 .7 8 0. 17 59 36 .5 0. 48 18 10 0. 0 Ra di oa ct iv it y in L iq ui d Ph as e, c pm - - - - 1 0. 01 11 0. 9 2 0. 03 73 3. 1 3 0. 07 92 6. 7 4 0. 07 83 6. 5 5 0. 08 53 7. 2 6 0. 10 15 7 0. 08 22 6. 9 8 0. 74 20 60 .1 1. 18 69 10 0. 0 7k Sa mp le S pi ll ed . Ta bl e D- 11 . Su mm ar y o f Ra di oa ct iv e Tr ac er A na ly se s o f th e Ex it Pr od uc t St re am s Fr om th e Ch ar Z on e Th er ma l En vi ro nm en t Si mu la to r. 1 0. 03 74 3. 0 2 0. 07 36 5. 9 3 0. 15 26 12 .3 4 0. 15 50 12 .6 23 05 .2 * 11 .6 5 0. 14 90 12 .0 6 0. 14 80 11 .9 7 0. 52 11 42 .2 1. 23 67 10 0. 0 >k Sa mp le S pi ll ed . V1 0 lu E. INTEGRITY OF THE ANALYTICAL METHODS - The accuracy and i n t e g r i t y of the ana ly t i ca l methods used i n t h i s research were determined by ca lcu la t ing the standard devia- t i o n from a mean value a t a 95% confidence l i m i t . This technique was used f o r analyses by chromatographic and l iqu id s c i n t i l l a t i o n spectrometric methods on r e p l i c a t e samples. From these measure- ments an average was ca lcula ted by equation (E-1). 2 From these averages the variance, s of any measured value, x x ' i ' from t h e average value, %, can be ca lcula ted . The standard devia t ion was ca lcula ted by applying the t t e s t a t the 95% confidence l i m i t f o r the s t a t ed degrees of freedom (N - 1 ) . 2 112; Therefore, t h e measured q u a n t i t i e s were expected t o be f f (8,) Obviously, t h e lower t h e range about 2 t h e more accu ra t e t h e method f o r determining x i ' For t h e cases where a n a l y t i c a l measurement of va lues va r i ed over a wide range, a weighted va r i ance based on t h e number of degrees of freedom i n each subgroup was ca l cu la t ed . The s tandard dev ia t ion was ca l cu la t ed a s be fo re (equat ion E-3). The fol lowing pages present t y p i c a l d a t a and r e s u l t s of t h i s method f o r deterrniniag t h e i n t e g r i t y of t h e a n a l y t i c a l procedures used. Determination of t h e Accuracy of t h e Gas Chromatographic Analyses The gaseous po r t ion of t h e e x i t stream from t h e Char Zone Thermal Environment Simulator was sampled i n one hundred cubic cent imeter con ta ine r s and analysed by gas chromatography. The p a r t i c u l a r gases contained i n t h e samples were methane, carbon monoxide, carbon d ioxide , e thylene , ace ty lene and n i t rogen i n vary ing q u a n t i t i e s . I n order t o determine t h e accuracy of t h e a n a l y t i c a l method, t h e d a t a i n Table E-1 were obtained. The va r i ance i n each subgroup was ca l cu la t ed i n Table E-2 and t h e s tandard d e v i a t i o n a t 95% f o r each gas spec ies i n t h e system and t h e o v e r a l l o r n e t s tandard dev ia t ion were ca l cu la t ed i n Table E-3. The range f o r t hese ana lyses was + 0.97% ( n e t ) . Table E-1, Measured Compositions of t h e Gas Species i n t h e Feed Stream Stream I d e n t i f i c a t i o n Feed Mix 1 Feed Mix 2 Feed Mix 3 Feed Mix 4 t o t h e Char Zone Thermal Environment Simulator N2 12.0 12.8 14.0 Cx 38.8 5t 12.93 N - 1 2 15.8 16.1 16.0 16.0 Cx 63.9 2 15.97 N- 1 3 14.0 14.0 13.6 14.0 13.7 14.6 14.6 13.5 13.95 Cx 125.95 2 13.99 N- 1 8 - - -- Cx - - co 4 .5 4.9 3.6 13.0 4.33 2 8.6 8.7 8 .1 8.4 33.8 8.45 3 4.95 5.0 4.95 4.9 5.0 5 ,9 4.6 4.5 5.5 45.30 5.03 8 7.5 7.5 15.0 x , :.5 N- 1 %) H2 35.8 37.7 36.8 110.3 36.77 2 36.5 37.5 36.5 110.5 36.83 2 35.0 35.0 35.0 33.9 35.0 35.2 35,O 34.1 278.2 34.78 7 66.3 66.25 132.55 66.275 1 Composition, CH4 42.0 40.7 40.9 123.6 41.20 2 33.0 34.0 33.5 34.0 134.5 33.83 3 45.0 43.9 45.0 45.0 45.2 44.1 43.5 311.7 44,52 6 12.8 12.8 25.6 12.8 1 x (Mole i C02 5.7 6.3 5 .3 17.3 5.43 2 6.8 6.78 6.75 20.33 6.78 2 3.0 2.6 2.5 3,O 2.6 3.0 3.0 2.4 2.7 3 ,O 1 , 27.3 2.73 9 1.9 1 .8 3 , 7 1.85 1 Table E-2. Calcula t ion of t h e Variances f o r Each of t h e Square of t h e Differences (R - xi) I d e n t i f i c a t i o n Feed Mix 3 C 0.0474 s2 0.0158 X 0.0001 0.0001 0.1552 0.0001 0.0864 0.3672 0.2440 0.2100 0.0700 0.0002 0.0010 0.0002 0.0176 0.0010 0.7516 0.2840 ' 0.6874 0.2291 0.2304 0.3844 0.2304 0.2304 0.4624 0.1764 1.0404 0m 0.0007 0.0707 0.0179 0.0547 0.0707 0.0179 0.0707 0.0707 0.6700 0.3350 0.0484 0.0484 0.0484 0.7784 0.0484 0.1764 0.0484 Ov er al l G as C om po si ti on R a n ge Combined Accuracy -- of t h e Sampling and Analyt ical Methods f o r t h e Gas Phase -- The accuracy of t h e sampling p lus a n a l y t i c a l technique was determined by tak ing r e p l i c a t e samples of t h e e x i t gas stream from t h e Char Zone Thermal Environment Simulator. These samples were analysed f o r each gas spec ies (methane, hydrogen, carbon monoxide, carbon d ioxide , e thylene and ace ty lene) with t a b u l a t i o n of t h e average compositions, var iances and standard dev ia t ions i n Tables E-4 and E-5. Comparison of t h e o v e r a l l standard dev ia t ion f o r sampling p lus a n a l y t i c a l technique with t h e value f o r a n a l y t i c a l technique only , indica ted t h e reproducib le na tu re of t h e sampling system. These va lues a r e 0.97% f o r t h e a n a l y t i c a l s tandard devia- t i o n and 1.03% f o r t h e sampling p lus a n a l y t i c a l s tandard dev ia t ion . A l l of t h e d a t a i n Table E-4 were compiled f o r a simulated py ro lys i s gas composition described by Feed Mix 4 (or 5) i n Table 4-3. Accuracy of t h e Liquid Analysis for Phenol Aqueous Solu t ions The s tandard dev ia t ion of t h e l i q u i d ana lys i s over a range o f phenol compositions from 2 t o 70% (by weight) was f 0.71%. This compares well with t h e r e s u l t s reported i n ASTM B u l l e t i n D 2145 which was 2 0.5% f o r concent ra t ions near 85% (by weight ) . The var iance and standard dev ia t ion ca l cu la t ions f o r t h i s a n a l y s i s a r e presented i n Table E-6. dent if icat ion Samples 4 & 13 Cx 140.4 30.6 22.1 5.8 0.57 0.56 8 70.2 15.3 11.05 2.9 0.285 0.28 N-1 1 1 1 1 1 1 Experiment 65.2 15.4 10.2 8.4 0.7 0.12 m 65.7 15.2 9.6 8.7 0.7 0.16 - - Samples 5 & 7 Cx 130.9 30,6 19.8 17.1 1.4 0.28 8 65.45 15.3 9.9 8.55 0.7 0.14 N-1 1 1 1 1 1 1 Experiment 58.7 20.4 13.6 7.3 XXIII 57.7 20.2 14.6 7.6 56.9 21,5 14.1 7.6 Samples 10,4 and 11 Cx 173,3 62.1 42.3 22.5 2 57,77 20.7 14.1 7,5 N-1 2 2 2 2 Samples 15, 1 Identification * Table E-5. Calculation of the Net Variance, Standard Deviation for Each Group of Samples and the Overall Standard Deviation. N 2 igl (Ni-l) (sxIi N H2 6.092 CH4 4.146 CO 1.592 C02 1.210 C2H4 0.048 C2H2 0.043 Over - all - 512 Accuracy o f t h e Liquid S c i n t i l l a t i o n Counting Analyses The accuracy of the radioact ive analyses were determined i n the same way a s t h e gas chromatographic analyses. Replicate samples of t h e e f f l u e n t stream from the gas chromatograph were col lec ted as carbon dioxide a f t e r f i r s t passing through a combustion furnace. I n general t h e radioact ive l e v e l of the gas samples were very low be- cause of the l a rge d i l u t i o n f a c t o r associated with the Char Zone Thermal Environment Simulator. Typical values f o r samples col lec ted a t one minute i n t e r v a l s a r e presented i n Table E-7. The varying rad ioac t ive concentrat ions correspond t o the loca t ion where a de- composition product separated i n the gas chromatograph. By com- paring the chromatogram with a p l o t of the radioact ive concentra- t i o n s (vs. t ime), the i d e n t i f i c a t i o n of the important products of decomposition of a p a r t i c u l a r radioact ive labeled pyrolys is gas can be made. The standard devia t ion of the reported values a r e l i s t e d i n : Table E-8. Very good agreement was obtained with the value of t h e devia t ion estimated by equation (4-4). These values were f 1.03 cpm calcula ted by the usual procedure and f 0.90 cpm estimated f o r an average count of 2070 and an average radio- a c t i v e l e v e l of 40.9 cpm over the samples l i s t e d i n Table E-7. The standard devia t ion and percent e r r o r of the l iqu id and s o l i d samples were estimated by equation (4-4) f o r counting l e v e l s exceeding 10000. T ab le E -7 . M ea su re d R ad io ac ti vi ty o f G as S pe ci es i n t h e E ff lu en t St re am o f th e C ou nt s pe r M in ut e (cp m) E xp er im en t X X V II I 22 .7 0 19 .5 7 21 .0 8 97 .5 3 94 .3 2 31 .0 9 21 .2 1 28 .3 0 62 .5 0 21 .8 0 22 .8 1 19 .5 7 21 .0 4 97 .5 8 94 .3 3 31 .1 5 21 .6 0 29 .1 5 59 .0 5 21 .9 0 20 .8 0 21 .5 0 22 .2 0 95 .6 5 90 .5 0 30 .7 0 21 .2 4 28 .3 0 62 .5 0 21 .4 5 23 .6 0 20 .5 0 20 .2 5 96 .0 0 92 .1 0 31 .5 0 20 .9 0 27 .9 0 61 .5 0 23 .6 0 20 .7 5 20 .3 0 96 .0 5 92 .3 0 31 .4 0 20 .9 0 27 .9 0 61 .5 0 22 .4 1 20 .5 7 21 .1 7 96 .1 0 92 .3 5 31 .0 8 21 .2 5 28 .4 3 61 .0 4 21 .9 0 17 .6 5 18 .0 9 17 .3 0 19 .4 1 17 .9 4 17 .8 2 17 .5 9 17 .1 0 18 ,l O 17 .5 5 N et C ou nt 4. 76 2. 48 3. 87 76 .6 9 74 .4 1 13 .2 6 3. 66 11 .3 3 42 .9 4 o f th e Ef fl ue nt St re am f ro m th e Ga s Ch ro ma to gr ap h. 0. 16 00 1. 00 00 0. 01 69 2. 19 04 3. 92 04 0. 00 49 0. 00 01 0. 01 69 2. 13 16 0. 00 00 0. 15 21 0. 86 49 1. 06 09 0. 20 25 3. 42 25 0. 14 44 0. 12 25 0. 51 84 4. 04 01 0. 20 25 0. 29 16 0. 86 49 0. 96 04 0. 09 00 3. 24 00 0. 18 49 0. 16 00 0. 38 44 4. 24 36 0. 20 25 1. 41 61 0. 00 49 0. 84 64 1. 21 00 0. 06 25 0. 17 64 0. 12 25 0. 28 09 0. 31 36 0. 20 25 1. 41 61 0. 03 24 0. 75 69 0. 90 25 0. 00 25 0. 10 24 0. 12 25 0. 28 09 0. 21 16 0. 30 25 0. 70 40 0. 75 34 0. 72 99 1. 32 81 2. 90 58 0. 12 26 0. 10 58 0. 29 97 2. 61 44 0. 18 4 Ca lc ul at ed a s N ] x 10 0 fo r N (N um be r o f Co un ts ) = 20 70 . F. ISOTHERMAL FLOW ANALYSIS (1) - - There is a s i z e a b l e number of poss ib l e r e a c t i o n s t h a t can occur i n t he char l aye r a s was d iscussed i n Chapter 111. To a t tempt t o inc lude a l l of these r e a c t i o n s i n the s o l u t i o n of t he energy equat ion t o p r e d i c t the energy absorbed w i t h i n the char f o r non-equilibrium flow would be very d i f f i c u l t . Consequently i t was necessary t o devise a sc reening procedure t o e l imina te from cons ide ra t ion the r e a c t i o n s t h a t were n o t important i n t he temperature range of cu r r en t i n t e r e s t (500" F t o 3000°F). The fol lowing reasoning was app l i ed . The r a t e o f r e a c t i o n inc reases wi th temperature. For a p a r t i c u l a r r e a c t i o n , i f a s i g n i f i c a n t conversion of r e a c t a n t s t o products was obtained wi th the char a t a uniform and high temperature, then i t was assumed t h a t t he re could be a s i g n i f i c a n t conversion when the char was subjec ted t o a temperature g rad ien t between 500°F and 3000°F. Thus these r e a c t i o n s should be con- s i d e r e d i n any a n a l y s i s of the char zone. Conversely i f t he re wases sen t i a l l y no conversion a t a h igh temperature (3000°F) f o r the char a t t h i s uniform temperature, t h e r e would be no conversion f o r a temperature g rad ien t wi th 3000°F the maximum temperature. Thus these r e a c t i o n s were e l imina ted from cons idera t ion . Correspondingly i f t he re is complete conversion w i t h i n the char a t a low temperature, 515 t h e r e would be complete conversion f o r t h e case of a temperature g r a d i e n t . Thus t h i s kind of r e a c t i o n would a l s o be el iminated from t h e a n a l y s i s , although t h e products of such a r e a c t i o n may indeed be present a s important spec ie s i n the py ro lys i s products e n t e r i n g t h e char a t 500°F. To determine t h e important chemical r eac t ions i n t h e temper- a t u r e range from 500°F t o 3000°F, t h e conversion of an equal molal mixture of t h e r e a c t a n t s flowing i n t h e char was determined us ing t h e k i n e t i c d a t a reported i n r e fe rence (2) f o r each r e a c t i o n . The 2 mass f l u x r a t e s u s e d f o r t h e r e a c t a n t s were 0.01 and 0.05 l b / f t -sec and t h e char was 0.25 inches t h i c k with a poros i ty of 0.8. These r e s u l t s a r e presented i n Tables F-1 through F-4 f o r t h e temperature range considered a t 500°F i n t e r v a l s and a mass f l u x of 0.01 l b / f t L - sec. The lower mass f l u x r a t e gave a longer res idence time of t h e spec ie s i n t h e char l a y e r , and consequently a h igher conversion. However, i n comparing t h e conversions t h e r e was only a r e l a t i v e l y small decrease i n conversion due t o t h e f ive - fo ld inc rease i n t h e mass f l u x r a t e . I n Figure F-1 t h e conversion f o r two reac t ions a r e presented a s a funct ion of temperature. These a r e t h e thermal decomposition of e thylene and ace ty lene . It can be concluded by examining t h i s f i g u r e t h a t t h e r e would be no conversion of ethylene wi th in t h e char f o r temperatures l e s s than 1000°F and no conversion of ace ty lene f o r temperatures l e s s than 2000°F. However t h e thermal c racking of e thy lene would be important f o r temperatures above 1000°F and f o r ace ty l ene above 2000°F. Pressure = 1 atm. Porosity = &8 Thickness = 0.25 in. Temperature, OF Figure F-1. Conversion of Pure Ethylene and Pure Acetylene at Isothermal Conditions (500°F-3000°F). To make the discussion quan t i t a t ive . the conversion of a r e a c t a n t is defined a s the r a t i o of the amount consumed by reac t ion t o the amount i n i t i a l l y present . To determine the conversion of a chemical r e a c t i o n of the form! a ma te r i a l balance is made on component j flowing through a volumetric s e c t i o n of the char having a cross sec t iona l a rea , A , and a width, A z , a s shown i n Figure F-2. I f N. i s the mo.lal f lux J of component j a t z , the ma te r i a l balance on component j fo r s teady flow i n the z d i r e c t i o n is: where R is the r a t e of formation of component j by chemical r eac t ion . j Rearranging the above equation and taking the l i m i t a s z approaches zero gives: The f r a c t i o n a l conversion X . of component j i s defined a s : 3 where Nj i s the molal f lux of component j en te r ing the char zone. 0 F i g u r e F-2. Schematic Diagram of t h e Char Layer. D i f f e r e n t i a t i n g the above equat ion wi th r e s p e c t t o z gives: The con t inun i ty equat ion i n terms of the volumetr ic flow r a t e , Q, of a gas e n t e r i n g the char is : Equation (F-3) u s ing equat ions (F-5) and (F-6) becomes: This equat ion can be i n t e g r a t e d from the back su r f ace of the char where X . and z a r e zero t o the f r o n t su r f ace where X j = XjL (z=L) J and the r e s u l t is : where St i s the average res idence time o r space time; i . e . , t he average time a molecule s t a y s w i t h i n the char . The r e a c t i o n r a t e , R j , f o r component A of r e a c t i o n (F-1) is: Equation (F-9) i s needed i n o rde r t o perform the ind ica t ed in t eg ra - t i o n i n equat ion (F-8). A t r i a l an e r r o r s o l u t i o n of the above in- t e g r a l equat ion is necessary t o determine the f i n a l conversion, 'j L, s i n c e the average r e s idence time, St , i s known f o r a given char depth and decomposition product mass f l u x . A computer program was w r i t t e n t o c a l c u l a t e the s o l u t i o n of equat ion (F-8) . The f i n a l conversion wasvaried i n the s o l u t i o n technique u n t i l t he c a l c u l a t e d va lue of St correspon&ed t o the known average res idence time. A to le rance l i m i t of f 0.1% of the known va lue wasspec i f i ed . A imp son's Rule i n t e g r a t i o n w a s u s e d t o eva lua t e the i n t e g r a l i n equat ion (F-8). A l i s t i n g of the Fo r t r an I V program i s presented i n L i s t i n g F-1. The r e s u l t s of the computations us ing t h i s program a r e pre- sen ted i n Tables F-1 through F-4. This inc ludes the conversion f o r each r e a c t i o n a s a func t ion of temperature from 500°F t o 3000°F i n i n t e r v a l s of 500°F. A s seen the re a r e a number of r e a c t i o n s which have a s i g n i f i c a n t conversion i n t h i s temperature range. Excluding any o t h e r l o g i c a l reasons which would e l imina te a p a r t i c u l a r r e a c t i o n from cons ide ra t ion i n the non-equilibrium flow a n a l y s i s , these r e a c t i o n s must be considered i f a r e a l i s t i c mathematical model is t o be formulated. L is ti n g F -1 . C om pu te r Pr og ra m f or C al cu la ti 9. g th e C on ve rs io n o f a R ea ct io n a t Is ot he rm al C on di ti on s. 10 00 01 C AL C U L4 TI O M O F TH F CO NV ER SI O N FC !R CH EM IC AL R EA C TI O N S 10 00 02 TH AT P OS SI BL Y OC CU R IN T H F D E C O M PO SI TI O N ZQ NF O f 10 00 03 C H AR R IN G A BL AT O RS , TH E R E SU LT S CO M PU TE D AR E F OR TH E 10 00 04 IS O TH ER M AL F LO W IN T H F CH AR Z ON F AT TE YP ER AT U Q ES 10 00 05 F R OV 50 0. 0- OF TO 3 00 0. 0- OF 10 00 06 10 0 0 0 7 E V A LU A Tl nN O F TH E E NF RG Y T R A N SF ER IN T HE CH AR Z ON E D U R IN G A B LA TI D N 10 00 08 10 00 09 10 00 10 D IM FN S IO Y Y ( 1 50 ) 9 EQ N! 1 50 ) 10 00 11 10 00 12 R FA D T H E E Q UA TI O N R l& R2 CR 3= Pl &P 2& P3 LO 00 13 CA LL FP TR A P (-3 ) LO 00 14 R E A 0 7 2 9 q( EQ N( I) tI =l ,l2 ) 10 00 15 F nR Y A T i 1 24 6) 10 0 01 6 10 00 19 R E A P TH E ST Q C YI O M ET 9I C C tlE FF IC IE N TS O F TH E R A T€ E Q UA TI O N LO 00 18 R E A Q7 30 ,R ll R2 ,R 3~ P1 tP 29 P3 10 00 19 10 00 70 R FA D FX PO NE NT S ON T H E C O M PR SI TI O N S OF TH E R A TE E Q U 4T IO N 10 00 21 R EA D 7 30 T Q 4r R 5? 56 ,P 4t P 5t P 6 LC ) 00 22 Fl 3R Y A T( 6F 4, 0) LO 00 23 10 0 0 2 4 R FA O T H F YO 1 Id GT n F TH E CO YP O NF NT S 10 0 0 2 5 R E A n 7 3 1 ~ F W S I ~ F W R 2 q F W R 3 ~ F W P l , F W P 2 ~ F W P 3 19 00 26 ~ o ~ 4 ~ ~ l 6 ~ 5 . o ) 10 0 0 2 7 10 00 28 R FA D T H F IU IT IA L C O M PO SI TI O N P F TH F R FA C Td YT S IN Y O iE F Q 4C TI O N 10 0 0 2 9 R F A n5 ~X P l, X Q ?r X Q 3, X P I 9X P 2? X "3 10 0 03 0 c O R Y A T (h F1 0. 01 10 00 31 10 0 0 3 2 R E A D T H E C n F F F I C I F N T S C ?F T Y E fn R W A Pn R E A C TI fi N R A TE CO NS TA YT 10 00 3' 3 1.l Rl JT S n F 4F AP E IN C U BI T, -C rY ?G N -~ nL E5 A ND SF C 10 00 34 f UN IT S OF AE F AR F IN K C 4L P FR GM -M OL E SE AD 73 3, AF ,S F, AF F 73 3 FO RM AT (F R. 09 2F 6. 0) C C R E A D T H F C OE FF IC IE NT S OF T H E R E V E R SE R E A CT IO N R A T E CO NS TA NT C UN IT S f3 F AP AR F IN C UB IC -C Mv GM -Y Ot FS AN D SE C C U N I T S n F 4F R A R E IN K CA C PE R GM -V OL E R E A ~ ~ ~ ~ ~ ~ A R Q S R ~ A F R C 8 2 8 P R I V T B 29 9~ EQ N( I) rI =l r1 21 87 9 F OR MA T( lH lp lZ A6 ) PP TN T 83 0 83 0 FO RM AT ( 1 X 93 SH IN IT IA L CQ MP OS I T lO N I Y OL E F R A CT IO N) ) P R I NT ~ ~ ~ ~ X R ~ ~ X R ~ T X R ~ ~ X P L ~ X P ~ ~ X P ~ C P R I NT 83 1 93 1 FO RM AT ( l HO v1 05 HF 1Y AL C OY PO SI TI ON (M OL E F R A CT IO N1 1 TE M P F R A GT IO WA L TP , TT ME (C C- SE C/ MO L 1 R E A CT IO N R A TF 1 P R I N T 83 11 93 1 1 Fq R Y A T( 1 H 9 1 05 H 9 1 P? 9 3 P 1 P 2 P 3 I (O F] CO NV FR SI OY CD M PU TF O SP FC IF lF n IY OL /C C- SE C 1 ) C f P 4S S F L UX O F l7 FC OM Pn SI TI fJ hl P Qn nl JC TS , Wv I N L R/ FT 2- SF C W= O. OL C c TN IT T AL V A I \ JE O F T F qP EQ AT UR F, T9 T S 5O Q- flF T= 50 0. C I N I T I A I \1 4 tl l~ n~ T H F P R ~ ~ S U R F T p , 1 5 1 .0 A TY S P = l , O . C G A S C ON ST AY T r Q r T N C A Ln P TF S/ G hY Yn t F- RK F = 1. 9? 7 C C CA LC IJ I E T I q N r3 F TH E A\ IF RA C, F Yn C W GT T1 F TY F G A SI FM A r F VT CR IN G TH F C PA R 70 N F FW RR =F W R L* XQ l E FW FZ % X R ?& FW q3 *X P 3 0 C u C V, a 0 W I C U LL Lb c, cn UJ k- I- LL -z I CY I- U- 3 c. cr A UA LL 0 .J cn cl u d J 0 C X 5 mr UJ c' I a C - u - 5 C U- u -. C ? ~ - - C 3 ZwSe G Z C - 3 * I- * 4 crj tn 4 4 u 3I- U II d o c U b c . U LL U. a 0 0 0 + C C k LLLLUU * * * * h i m d c v G C r Q Q x x x x II II II II a o a c c \ I m d C y K'ffCLa KLLUU C-U- w C3 2'2 Z U. a % H a L > G - , I w P U' v A Z Y r L L C b. C- u c - 1-3 c a u 4 to: e c 7 I U U t 4 - 2 4 C J X L Z \ I - - - . = - - - - - - U .J 4$ OK. - - u I I I I s r C k 0 vcl U O S C . I ( . * * * * S t z I t = - 4 Z Z . S L d C \ i ( r d f i f l Z.rI r c c C C O C a c r P o O n Cb- . d Z U ~ V ~ ~ ~ U L U U U U " V Q D - t V & 4 $ - - - - - - C Z I- W ~ U I C ~ C Y . V W W V W V ' KC3 c w c * C . N ~ C C C C C ~ . Q I - c k C C 3 d h u - 6 Q d Q C d 3 I U, U CC I1 \ I I (I l l li II I1 L: U. 11 &v, I I x a i h m d w v J C - XI-+ d \ 0 C I I t r C r Q ~ O Q a < I-LLU C U f Y C I U U G U U U U W c C. FO RW AR D R FA C TI O N R 4T E C O NS TA NT ? FK FY =A F= To K ** (-S F) *E YP ( (- A E ~* 10 ~0 oO )/ ~R fT ~K ~ 1 C R FV ER SF P F A C TI O N R A TF C O NS TA NT * R K c R K =A Q *T O K* *(- SR )*F XP ( (- 4E R* 10 00 00 f/ (R aT 8K ) 1 C C C A LC U LA TI O N O F R FA C TI O M R A TE V Q A tP F CO M PO NE NT A C R A H A S U N IT S D F G M YO LE S/ CI JR IC -C Y SF C R A = F K * I CQ l* *R 4) *t CR Z* *R 5~ *( CR 3* *R 6) -R K* ~C Pl ** P4 )* (C P2 ** P5 ~* 1 tC P3 ** P6 ) c C CA LC UL AT IQ N OF FU N C TI O N U NO FR IY T€ G 9A L- l/ Q A= Y( I I V ( I )= 1o O/ RA C C 1 XC A= XC A& HI C ST EP YC A TO GE NE RA TF 10 1 VA LU ES Cl F Y (1 ) C C 4L C IJ LA TI O N O F F IY A L C nM pf 35 IT If lN ( YO 1 F FR A C TI O N ) Y R l= FR Z /F T Y 92 =F R Z/ FT YR 3 =F R 3 /F T Y P l= F P l/ FT yP Z =E P ? /F T Y P 3= FD 3/ FT !- r C A LT U LA TI G Y O F 5P A C F T I Y E F Q P TH E S P FC TF I E n CO NV EP Sf O N ? X CA F C JN TF G R A TT n\ ' I q P FR Fn R Y E 9 IJ SI N G 5 T Y P Sn YS 91 1L F ~ IJ ~ J II = ~ .O C; UY ?= 9 :(3 rl O ? T =2 91 0P 2 SU Pl =? .O *V (T )C SU MI 3 3 3 I= ?, 1 00 9 2 3 SU rJ I7 =? .9 *Y (I 1 C Sl JM ? r- IN TF G R 4L \IA Lt JF IS V IN T -U Y IT ? A 9F C1 J9 I C -C t4 SE C/ SY Y! IL FS t7 F A V I N T = I H 1/ 3~ 0) *l Yf 1) CS UM lC SU M2 &Y f1 01 ~) 10 SP AC F TT Y E C AL C U LA TF D 1 % V FT D -U N IT S AQ E C! jR IC -C M SE C/ G M M O LE $ 10 V FT O =X R l* V IN T 10 LO 10 C O M Pt JT AT IO N ST O PS IF S A TS L E S S T H A N L. OE -1 Q 10 IF (S A. GT . 1, O F- 10 )G fl TO 7 77 10 c,n TO 12 3 10 C O N TI N U E 10 D E TF R Y IN E T F TH E D IF FF R FN S E B FT W EE N TH F S P E C IF IE D A ND 10 C AL C U LA TE 0 SP AC E T IM E I S W TT H IY 0. 1. IF Y FS IN C R EA SE T H E 10 TF M PF PA TU R E B Y 50 0- O F 10 C 4L L SS W TC Ht l r JO B) 10 GO T O (1 11 1, 77 S) rJ OR 10 IF (A BS (S T- VF TO ) . L T *O el ) G O T O 1 2 3 10 10 Q FT FR YI M F TF VF TO IS G RE AT ER TH AN 5 T 1 0 IF (V FT O. GT .S T) GO TO 12 34 19 10 VF TD I S L E SS T H A N ST 10 LO IS V FT O N E G A TI V E 10 YF S- DE DU CF XC AF LO N n- C O N TI N U E 10 IF (V FT O. 1- T. 9. 3) G O T 0 1 3 2 1 1 0 1 0 TH E C AL Tr lL AT Tr 3M ST O PS TF TH E CO IV VF QS IO IV 17 G RE AT ER TH AN 9 9 - 9 9 PE R 10 IF IX C A Fe G Te O aq 99 9) Gq T O 3 2 1 10 10 TY E P P E V IQ U S V 4L U F OF VF TO I S R FC AL C U LA TF Q B Y IN C R E A S IN G LO X C 4 F R Y TH E Aw nU N T t7 F SA 10 TH E N C W 4Y G E 54 T I? 0. 5* S 4 10 XC AF =X CA FC SA LO SA =r ). 5* S4 LO G nT Q 7 22 7 10 O' a C C; * ZI Q * 0' I- .. - z Z:' w a n~ r > c u t - 4 i-4 LL. a arc u > m !- -4 - C 4 e u CLa ff > u L * (r l ,-I cn or, r 2 0 - U c W f i r C L C c % \ , c u C fx z &f LL! G z m cn I u II II d w C. ~ LU C \ U K M = a * 2 2. CT V) V) n 3 Q rn U E O a cp m J 3 u I- w a > U h V) C- iL * U, (Y - 2 0 - N t W UJ Z N X I I fl E rY 0 Q tY J O N 3 m Ir N a 0 a V C O 3 w N cl * * a 3 M N C o t , c W C N LL N ry X U _ I. n d LL cl C 4 l-4 4 r U * C X C J W d C ~ U ~ r Y ~ -4 C c C LLI C" 4 W u 3 c v / U ' C J u L c A W . C + m CC 0 a a Q U G - 3 . 3 - U - CyX cr? LYE L L - 7E V) 3 , J e 5 - 1 1 - 1 1 x u n c- r O\ Ui U. C - 4 - U-UOCU. U- - 4 h d 6 T C- D d U y I v d v - C T d * I X m * a u * C z Or -I *I Cr CY G Ct 4- - 4 " t3to UJ 4 u u o 3 m u ~ ~ e n ~ Z L fi ~ d i ~ Q e l - = c r d cc: - m U \ C r - a ' & c z e u c u a-rC e t o e?:Oo * o - o c - * c r c c - - olh b 4 !.LJ f- + O T C X d = N S C P X d T e X l f ' X x c . a ul. U d C CIA4 * Q h c l ~ d d d r l d d d N d d + d d W V ) U W V)O X 3 UJ C N v N - h - & ' c h - N - & - N - z t ~ a p ~ . u c 0- L L ~ Z . J I - ~ C N F - N ~ K ~ + & I - ~ c LL U U I V \ C II X c t ~ d t C + O C Q l = - 4 k - 0 t Q C C C > X Z M a U I l & +kt- Z Z ~ Z ~ Z Z Z T Z Z Z % T Z T 4 2 - W U C V, U Z - c u m u a ~ - a b - f f c b c t Y ~ - - C ' c t Y U J C ~ I Z I I U ~ U O U ~ Q O ~ C ~ C L Y C ~ Y C ~ C ~ ~ C ~ G W U - - I- --I- g m x w u u ~ a u a u a t ~ o ~ c c ~ u a u c u a u b ) D a d h F ' c d - p ~ C C d + + - , d d . - & N (L hi fv ru h' fi N f i i ~ 61 R~ 6' r\l C\ m 1 n VL' C U U U U U L'UU U G C P R IV T 7 7 19 7 7 1 9 FO RM AT ( 1 t4 09 45 H FX Dn PI FN TC r 7h l TH F Cf lY P. 3 F TH E R A TF E CJ IJ hT Ifl N) D R T Y T 37 16 2 7 1 6 F O P V A T( lH 39 74 Y R 4 9 5 P h p 4 P 5 f' f) D T lY T 2 21 79 R 4, Q 5, Q 6r P 4, P 57 Pf i ?2 17 F P FM A T( 1X 1S F4 .1 ) C P E A 3 IN N EW DA TA F r) Q T A LC 1I LA Tl Q YS Cl F FJ EX T EQ IJ AT In N G O T r) ll ll 7 4 Y rn D F Y 9 ISO TH ER M AL F LO W AN AL YS IS - IN PU T- OU TP UT D AT A C + C0 2 = 2C O IN IT IA L CO M PO SI TI ON (M OL E FR A CT IO N ) 0. 50 00 0. 50 00 0. 00 00 0. 00 00 0. 00 00 0. 00 00 FI N A L CO M PO SI TI ON (M OL E FR A CT IO N ) TE M P FR AC TI ON AL SP . T IM E (C C- SE CI M OL ) RE AC TI ON R AT E R 1 R2 R3 P1 P2 P3 (O F) CO NV ER SIO N CO M PU TE D SP EC IF IE B (M OL /CC - S EC ) M AS S FL UX (L B/ FT ~- SE C ) = 0. 01 00 S T OC HI OM ET RI C CO EF FI CI EN TS FW Rl FW R2 FW R3 FW Pl FW P2 FW P3 EX PO NE NT S ON T HE CO M P. OF TH E RA TE E QU AT IO N CH 4 = 1/ 2 C2 H2 + 3 /2 H 2 C2 H6 = (H 2> CH4 7 C2 H4 7 C) Cy c lo bu ta ne = t- bu ta no l = is ob ut en e + H 20 I 0 Is ob ut en e = Pr od uc ts C6 H6 = 1/ 2 C1 2H 10 + 1 12 H 2 REFERENCES 1. Pike, Ralph W . , G. C . Apr i l and E. G , d e l Val le , "Non-Equilibrium Flow and t h e Kine t i c s of Chemical Reactions i n t h e Char Zone," NASA-CR-66455 ( Ju ly 15 , 1967). 2 . P ike , Ralph W . , "Evaluat ion of t h e L i t e r a t u r e f o r Chemical Reactions and Reaction Rates f o r t h e Decomposition Products from Charring Ablators ," Langley Working Paper 181, NASA, Langley Research Center , Hampton, V i rg in i a (January 21, 1966). 3 . Happel, J. and L. Kramer, "Acetylene and Hydrogen from t h e Pyro lys i s of Methane," I n d u s t r i a l Engineering Chemistry, 59 ( I ) , 39 (January 1967). - METHODS FOR ESTIMATING PYROLYSIS PRODUCT COMPOSITIONS Three methods were used t o determine accu ra t e ly t h e t y p i c a l p y r o l y s i s product composition en te r ing t h e char zone. These were: (1) Analysis of t h e gases evolved dur ing t h e thermal degrada t ion of nylon-phenolic r e s i n s reported i n t h e l i t e r a t u r e ( 1 , 2, 3 , 4 , 5 ) . (2) Calcu la t ion of t h e hea t of py ro lys i s u s ing h e a t s of formation d a t a f o r t h e r e a c t a n t s and reported py ro lys i s products followed by a comparison wi th experimental ly determined h e a t s a£ p y r o l y s i s . (3) Q u a l i t a t i v e in spec t ion of t h e molecular s t r u c t v r e of t h e p l a s t i c m a t e r i a l s t o determine p o s s i b l e decomposition products based on t h e r e l a t i v e s t r e n g t h o r weakness of bond ene rg i e s . Each technique w i l l b e discussed i n t h e fol lowing s e c t i o n s . Products of Nylon-Phenolic Resin Thermal Degradation 3 Pyro lys i s Gas Chromatography The most d i r e c t method of determining the products of degrada- t i o n i s a n a l y s i s by py ro lys i s gas chromatography. This has been done by Sykes ( 2 , 7 ) i n which t h e hot degradat ion products were i n j e c t e d d i r e c t l y i n t o t h e gas chromatograph. However t h e r e i s a c e r t a i n amount of condensation of heavy molecular weight spec i e s which remain u n i d e n t i f i e d and a p o s s i b l e source of e r r o r . The method has , however, reduced t h e t o t a l amount of u n i d e n t i f i e d l i q u i d phase spec i e s from f i f t y percent obtained with t h e more convent iona l methods, t o seventeen percent (by weight). Also t h e kind and con- c e n t r a t i o n of t h e spec i e s a r e more p r e c i s e l y determined. These ana lyses form t h e b a s i s f o r q u a n t i t a t i v e l y s e l e c t i n g a p y r o l y s i s product c ~ m p o s i t i o n , The remaining methods a r e used t o make ad- justments t o t h e a n a l y t i c a l l y determined composition, e s p e c i a l l y wi th regard t o t he spec i e s which could l o g i c a l l y make up t h e u n i d e n t i f i e d po r t ion of t h e py ro lys i s product stream. A Comparison of t h e Experimental Calculated Heat of Py ro lys i s - Based on t h e Heats of Formation of t h e Ana ly t i ca l ly Determined Gases ----- The p y r o l y s i s products a r e obtained by t h e thermal degrada t ion o f v i r g i n p l a s t i c m a t e r i a l s such a s nylon, phenolic r e s i n and com- p o s i t e s o f t hese polymers. Phenolic Resin I Gaseous P l a s t i c s and Composites A ' Products + Char The hea t of r e a c t i o n i s t h e hea t of p y r o l y s i s , AH^^^, and i s c a l c u l a t e d knowing t h e h e a t s of formation of t h e products (char p l u s gases) and r e a c t a n t s (nylon and phenolic r e s i n ) , a long wi th s e n s i b l e en tha lpy c o r r e c t i o n s from t h e r e f e rence temperature o f 25OC. For nylon-phenolic r e s i n composites, the temperature, Tr, where degradation s t a r t s i s approximately 250°C and the f i n a l tempera- t u r e a t t a ined by the products leaving, Tp, i s 1000°C. Mean molal hea t c a p a c i t i e s evaluated a t a weighted average temperature o f 700°C based on mass l o s s r a t e s from d i f f e r e n t i a l thermal analyses, and hea t s of formation a t 25OC a r e tabulated i n Table G - 1 . Values of the hea t s of pyrolys is of nylon, phenolic r e s i n and t h e i r compo- s i t e s were reported by Sykes ( 2 ) and Nelson (3) . Heats of forma- t i o n of t h e r eac tan t s a r e ca lcula ted from experimental heats of combustion d a t a presented i n Table G-2 and G-3, respect ive ly . De ta i l s of t h e experimental procedure and apparatus a r e contained i n t h e o r i g i n a l reference (1) . The combustion of nylon o r phenolic r e s i n forming carbon dioxide and water i s represented by t h e following expression: Nylon o r Phenolic Resin f O2 C02 + H20 The heat of formation of nylon (or phenolic r e s i n ) i s then simply: AHf Nylon = AHC - i=l C X ~ i 'bpi (G-4) Table G-1. Heats of Formation and Heat Capacities of Various Pyrolysis Products. (8) Dimethylphenol Trimethylphenol Hydrogen Me thane Carbon Monoxide Carbon Dioxide Water Ammonia Butylamine Acetone Methylamine Formaldehyde Ethylene Ethane Acetylene Butane But ene Cyclohexane Cyclopentane EthylBenzene Hydrogen Cyanide Methyl Cyclohexane Methyl Cyclopentane 0.0 -2013.8 -1697.1 -3850.2 -5780 ,O -1160.5 -384.1 -2214.7 -387.8 -1697.9 804.3 -1212 .O 3752.3 -923.2 9.7 -629.1 -475.0 120.3 2080.0 -676.8 -545.1 3.5 0.7 0.25 0.35 0.5 0.67 0.44 0,41 0.63 0.6 0.6 0.7 0.74 0.44 0.47 0.4 0.46 0.5 Pentane Propane Xylene Amorphous Carbon Note: * Estimated heat capacity by analogy with homolog(s). Mean heat capacity calculated over a temperature range from 250"-1000°.C , - 2 .O 16 .O 28 .O 44 .O 18.0 17 .O 73.1 42.1 31.1 30.0 28.0 30 .O 26 .O 58.1 56.1 84.2 70.1 106.2 27 .O 98.2 84.2 0.6, 0.6 9.3, 0.3 -871.2 -1012.2 76 ;3 390 .O 72.2 44.1 106.2 12 .O Basis: 1 gram of nylon (Molecular weight of monomer = 226) 1 pram nylon = 0.00442 gm moles 226 gr/gr mole 0,00442 x 12 = 0.053 0.00442 x 11 = 0.049 0.00442 x 2 = 0.009 AHf~02 = -94,052 ~al/gm mole (0.053) = -5004 cal/g = -57,800 cal/gm mole (0.049) = -2815 cal/g = + 8090 cal/gm mole (0.009) = 72 cal/g AHC = -7214 cal/gm (Experimental)- Reference (1) A H f~ = C&Hf - AHC prod = -7747 - (-7214) = -533 cal/gm (-959 B T U / ~ ~ ) Experimental Heat of Combustion Data. = 7n C02 + 3n H20 : 1 gram phenolic resin (Molecular weight of monomer = 106) 0.00943 gm moles 0.00943 x 7 = 0.0660 0.00943 x 3 = 0.0283 AHf~02 = -94,052 callgm mole (0.0660) = -6207 callgm AH^^^^ = -57,800 cal/gm mole (0.0283) = -1636 callgm = -7843 callgm = -7386 cal/gm (Experimental) - Reference (1) = -7843 - (-7386) = -457 callgm (-823 B T U / ~ ~ ) Therefore, f o r a known composition of t h e var ious spec ie s i n a nylon-phenolic r e s i n composite, t h e hea t of formation of t h e composite i s : = z AHfj Composite j=l ; j = nylon, phenolic r e s i n , e t c . Now a l l of t h e p e r t i n e n t da t a a r e a v a i l a b l e t o eva lua te t h e h e a t of p y r o l y s i s . I n doing so , a s e l ec t ed composition determined by some a n a l y t i c a l o r numerical method i s pos tu la ted t o be v a l i d . I f t h e ca l cu la t ed va lue of t h e hea t of py ro lys i s i s approximately equal ( t o + 10% of t h e des i red va lue , f o r example), t h e compo- s i t i o n i s judged a r ep resen ta t ive composition. I f , on t h e o the r hand, a mismatch i s obtained f o r t h e hea t of py ro lys i s va lue , t h e composition proposed a s a v a l i d s e t of va lues i s e i t h e r i n e r r o r o r incomplete. Correct ion of t h e mismatch i s made us ing any s i m i l a r l og ic t o t h a t l i s t e d below: (1) Inspec t t h e l i t e r a t u r e da ta over a wide range of condi t ions by seve ra l au thors , when a v a i l a b l e . ( 2 ) S e l e c t those py ro lys i s products which always appear i n t h e ana lyses . (3 ) I f var ious f r a c t i o n a l analyses a r e presented , weight each composition according t o t h e s i z e of each f r a c t i o n . For example i f gases a r e co l l ec t ed f o r f r a c t i o n s corresponding t o a t e n percent weight l o s s of i n i t i a l v i r g i n p l a s t i c , twenty percent weight l o s s and f i f t y percent weight l o s s , each f r a c t i o n a l composition should be weighted according t o t h e s i z e of sample (percent weight l o s s ) t o c a l c u l a t e an average composition, (4 ) Superimpose these r e s u l t s and cons t ruc t an o v e r a l l spec ie s l i s t i n g . (5) Average va lues of spec ies t h a t appear wi th in a reasonable range of va lues . ( 6 ) Use t h e spec ies t h a t appear i n ~ n l y one ana lys i s t o make minor adjustments t o t h e composition being co r rec t ed , (7 ) Continue t h e eva lua t ion u n t i l an energy-balance- ca l cu la t ed hea t of py ro lys i s matches t h e l i t e r a t u r e value. Now based on t h e b e s t poss ib l e l i t e r a t u r e composition, decide whether t h e c o r r e c t i o n s made t o ob ta in a match a r e l o g i c a l and reasonable. I f so , t h e procedure i s ended; i f n o t , r epea t t h e procedure with o t h e r more reasonable spec ie s . When no previous a n a l y t i c a l da t a a r e r e a d i l y a v a i l a b l e , an a n a l y s i s us ing the k i n e t i c theory approach i s suggested t o a r r i v e a t py ro lys i s products which a r e reasonable. A g rea t dea l of chemical engineering judgement i s necessary t o decide whether a s e t of proposed pyro lys i s gases a r e r e p r e s e n t a t i v e o r j u s t an a r b i t r a r y combination of some f i c t i t i o u s system. E i t h e r procedure r equ i re s a d e t a i l e d l i t e r a t u r e survey of a v a i l a b l e a n a l y t i c a l r e s u l t s and some background reparding t h e p a r t i c u l a r system under s tudy. Used i n connection with a n a l y t i c a l d a t a , i t becomes a powerful method f o r e s t a b l i s h i n g t h e c o r r e c t composition of t h e py ro lys i s products . Pyro lys is Product Composition & Rela t ive S t rength or Weakness of Bond Energies -- The thermal degradat ion of char forming a b l a t i v e ma te r i a l s i s a complex process , As a r e s u l t , l i t t l e q u a n t i t a t i v e d a t a i n d i c a t i n g t h e decomposition mechanism have been r epor t ed . The high r e s i s t i v i t y of t h e char l a y e r t o aerodynamic s t r e s s e s and high temperatures has been known f o r many yea r s . This a b i l i t y i s a t t r i b u t e d , i n p a r t , t o t h e h igh ly c ros s l inked na tu re of t h e aromatic polymers such a s phenolic r e s i n . The a l r eady s t rong C-C bonds a r e re inforced by resonance e f f e c t s r e s u l t i n g from t h e c ros s l inked s t r u c t u r e , Therefore, dur ing thermal degrada t ion , t h e s e C-C bonds remain i n t a c t , and, t h e weaker bonds (C-H, C-0, C-N, e t c . ) break producing t h e py ro lys i s gas pro- d u c t s . It i s t h e purpose of t h i s s e c t i o n t o i n d i c a t e t h e o r i g i n of l i k e l y p y r o l y s i s products based on t h e bond energ ies of t h e polymers. A q u a l i t a t i v e d i scuss ion f o r nylon and phenolic r e s i n and composites of t hese i s presented i n t h e fol lowing paragraphs. Decomposition of Phenolic Resin: Parker ( 6 ) ind ica ted a p o s s i b l e mechanism f o r t h e thermal degrada t ion of phenolic novalac r e s i n s , Emphasis was placed on t h e f i n a l char s t r u c t u r e , however, a g r e a t d e a l of i n f ~ r m a t i o n regarding the o r i g i n of some py ro lys i s products was a l s o r epo r t ed . Representing t h e phenolic novalac polymer a s shown below, OH H OH H OH (G-6) Parker pointed out the place where cleavage was most likely to be initiated was at the methylene bridge (-CH -) linkage, This re- 2 sulted in the formation of a variety of free radicals including those of phenol, the cresols and many shorter polymeric units of the novalac resin which undergo still further degradation. A schematic diagram of the proposed mechanism is reproduced in Figure G-1, In addition to the above mentioned products, water, hydrogen, carbon monoxide and methane are also shown to be formed. Decomposition of Nylon-66 (Hexamethylenediamine-Adipic - Acid): The nylon-66 polymer is formed by the polymerization of one monomer of adipic acid with one monomer of hexamethylenediamine in al- ternating steps. A Inspection of the bond energies between atoms of the CHON system listed in Table G - 4 , neglecting considerations of resonance and electronegativity effects that exist in the polymer, indicates that the most logical place for cleavage to occur is at the C-N bond. This essentially separates the polymer into shorter chain polymers and monomer'units. From this point cleavage of bonds within the monomer structure can occur forming such species as @OH-CH2-@OH-* + @ O H - C H r * DECARBONYLATION CHAR FORMATION Figure G-1. Mechanism of Phenolic Novalac Degradation to Char. Table G-4. Bond Energies Between Atoms in the CHON System ( 7 ) . Bond . H H H - C H - N H - 0 C - C C - N C - 0 N - N 0 - 0 C = C C = C . Bond Energies, Kcallgram 104 99 84 110 80 6 2 8 1 3 2 33 142 186 NH3, CO, C02, H20, Hz , CH4, C2H6, e t c . I n f a c t , repor ted expe r i - mental d a t a shows t h a t only about seven percent (by weight) o f nylon-66 i s degraded t o r e s idue (2 ,3 ) . The remaining n ine ty- t h r e e percent forms gaseous products . From t h i s a n a l y s i s , it i s ev ident t h a t t h e char s t r u c t u r e of a cha r r ing nylon-phenolic r e s i n composite i s p r imar i ly composed of t h e phenolic degrada- t i o n t o carbon, while a major po r t ion of t h e py ro lys i s gases a r e formed from t h e n y l ~ n - 6 6 . Decomposition of Nylon-Phenolic Resin Composites: Combining of t h e s e two polymers with subsequent thermal degradat ion would n e c e s s a r i l y r e s u l t i n a l l of t h e above mentioned products w i th r e l a t i v e q u a n t i t i e s based on t h e weight f r a c t i o n of each poly- mer i n t h e composite. A d e t a i l e d l i s t i n g of var ious p y r o l y s i s products i d e n t i f i e d by gas chromatographic and/or mass spec t ro - graphic ana lyses i s presented i n Table G-5. Many of t h e spec iep may only e x i s t i n small q u a n t i t i e s , however, t h e l a r g e number forms a ve ry good r e fe rence of t y p i c a l products which may b e . formed when nylon-phenolic r e s i n s undergo thermal decomposition. Comparison of, t h e Methods wi th Various Ana ly t i ca l ly Determined Pyro lys i s Product Compositions and Heats of Pyro lys is --- To i l l u s t r a t e t h e use of t h e above discussed methods, two works r e p o r t i n g py ro lys i s gas compositions and h e a t s of py ro lys i s va lues w i l l be compared. These a r e t h e ana lyses by Sykes and Nelson ( 2 , 3 ) and by Freidman ( 5 ) . Ph en ol ic R es in C om po si te s. Pe nt en e Me th an ol Pe nt an e Be nz en e Cy c l oh ex an e Di ae et yl en e Ca rb on M on ox id e He xa d i en e Vi ny la ce ty le ne Ca rb on D io xi de Ac ro le in To lu en e Is op ro pa no l Di me th yl B en ze ne 2- Pe nt en e- 4- yn e Di me th yl P he no l Is op en ta ne s He xa d ie ne n - Bu ta no l Me th yl P he no l Ph en yl A ce ty le ne Ac et on e Be nz al de hy de Me th yl P he ny l Ac et yl en e Cy cl op en te ne Fo rm al de hy de Me th yl S ty re ne Cy cl op en ta di en e Am mo ni a C9 A ro ma ti cs Cy cl op en ta no ne C1 0 Ar om at ic s Pe nt ad ie ne Hy dr og en C ya ni de Di me th yl S ty re ne I d e n t i f m of Pyro lys i s Products from t h e Thermal Decomposi t i~n of Phenolic Resin and Nylon-Phenolic Resin Composites: Sykes (2 ,7 ) - r epo r t ed t y p i c a l p y r o l y s i s gas compositions f o r e igh ty - th ree percent of t h e t o t a l decomposition products evolved during t h e thermal de- g rada t ion of nylon-phenolic r e s i n composites. His techniques in - cluded d i f f e r e n t i a l thermal a n a l y s i s , thermogravimetric a n a l y s i s and py ro lys i s gas chromatography of t h e hot gases evolved dur ing r a p i d hea t ing o f t h e composite ma te r i a l s . The remaining seventeen percent was repor ted a s an u n i d e n t i f i e d , dark t a r r y substance. The compositions from t h i s research a r e presented i n Tables G - 6 and G-7. Also shown a r e t h e comparisons of t h e hea t of p y r o l y s i s c a l c u l a t i o n s wi th t h e experimental va lues of Sykes ( 2 ) . A very good agreement i s obtained i n Table G-6 i n d i c a t i n g a high r e l i a b i l i t y i n t h e repor ted a n a l y s i s . The u n i d e n t i f i e d po r t ion of t h e py ro lys i s products was taken a s phenol f o r c a l c u l a t i n g the hea t of p y r o l y s i s . I n an e a r l i e r work, t h e r e s u l t s were somewhat poorer a s i nd ica t ed by t h e l a r g e r d i f f e r e n c e i n t h e ca l cu la t ed and experimental hea t of p y r o l y s i s va lues . This was probable caused by e i t h e r improper cur ing of t h e specimen r e s u l t i n g i n t h e h ighe r water conten t o r an i n a c c u r a t e a n a l y s i s o f t h e evolved py ro lys i s products . A s a t h i r d example t h e py ro lys i s products repor ted by Freidman (5) a r e compared in Table G - 8 . I n t h i s c a s e t h e composition was determined from near room temperature samples analysed by gas chromatography. The absence o f t h e h igher rnslecular weight spec i e s such a s phenol and t h e c r e s o l s i s ev iden t , This r e s u l t e d i n a much poorer comparison between t h e ca l cu la t ed and experimental h e a t of B as ed o n H ea ts o f F or m at io n o f th e R ep or te d P y ro ly si s G as C om po ne nt s (7 ). C ar bo n R es id ue (C al cu la te d) = 21 3 B T U /~ ~ P he no li c R es in Ba se d o n t he H ea ts o f Fo rm at io n o f Re po rt ed P yr ol ys is P ro du ct s (2 ). Av er ag e We ig ht Ca rb . Di ox id e Ca rb . Mo no xi de Un id en ti fi ed * Ca rb on R es id ue Re ac t a n t (C al cu la te d) = 11 0 B T U / ~ ~ (E xp er im en ta l) = - - 14 6 B T U / ~ ~ Ln Ln C C ar bo n D io xi de C ar bo n R es id ue (E xp er im en ta l) = 20 0- 50 0 P he no li c R es in pyrolysis as would be expected if important species were omitted from the composition. The inclusion of phenol and similar high molecular weight species which are liquids at room temperature where the particular samples were collected should be included. The quantity of each species added to correct the composition to a more representative value can only be det~rmined by investigating the literature for the specific conditions of the experiment and subsequent analysis. If no such information is available, com- parison with an analogous system (similar composite materials, for example) is a logical approach. Conc lusion As a result of these methods applied to several reported pyrolysis gas compositions in the literature (I), it was con- cluded that the composition in Table G-9 best represented the products evolved when nylon-phenolic resin thermally degrades, It is this composition that is used as the simulated pyrolysis product stream in this research. Table G-9. Most Representat ive Composition of t h e Pyro lys i s Products Evolved During t h e Thermal Degradation of Nylon-Phenolic Resins. Component Hydrogen *Water Methane *Ph eno 1 Carbon Monoxide *Dimethylphenol Carboq Dioxide *Toluene *Benzene * Liquids at room temperature. Pyrolys is Product Composition Mole % 33.4 48.9 6.7 4.7 3.7 1.2 1.1 0.2 0.1 100.0 Weight% 3.6 47.8 5.8 24.1 5.7 8.7 2.5 1.2 0.6 - 100.0 REFERENCES 1. A p r i l , Gary C . , E. G . d e l V a l l e , Simon Hacker and R. W. P i k e , "Comparison o f Methods f o r Determining t h e Composition o f P y r o l y s i s P roduc t s from t h e Degradat ion o f Nylon-Phenolic Res in A b l a t i v e Composites," NASA-RFL-9, Louis iana S t a t e U n i v e r s i t y , Baton Rouge, L o u i s i a n a (March 1969). 2. Sykes, G. F., "Decomposition C h a r a c t e r i s t i c s o f a Char Forming Phenol ic Polymer Used f o r A b l a t i v e Composites," NASA TN-D-3810 (February 1967) , 3 , Nelson, J. B . , "Determinat ion o f K i n e t i c Parameters o f S i x A b l a t i v e Polymers by Thermogravimetric Ana lys i s , " NASA TN- D-3919 ( A p r i l 1967) , 4 . Ladacki , M . , J , V. Hamilton and S. N. Conz, "Heat o f P y r o l y s i s of Res in i n S i l i c a - P h e n o l i c Abla to r , " AIAA J o u r n a l , 5 ( l o ) , 1798-1832 (1966). 5. Freidman, H. L. , " P y r o l y s i s o f P l a s t i c s i n a High Vacuum Arc Image Furnace," J o u r n a l of Applied Polymer Sc ience , 2, 1005 (1965) . 6 . P a r k e r , J . A. and E. L. Winkler, "The E f f e c t s o f Molecular S t r u c t u r e on t h e Thermochemical P r o p e r t i e s o f P h e n o l i c s and Re la ted Polymers," NASA TR-R-276 (1967) . 7. Sykes, G. F., Private Communication to R. W. Pike (March 14, 1968). 8. Perry, J. H,, Ed., Chemical ~naineers' Handbook , 3rd. Edition, McGraw-Hill Book Co., New York, 236-243 (1950). M I M I C SOLUTIONS OF THE FROZEN FLOW, VARIABLE H. - PROPERTIES ENERGY EQUATION The purpose o f ob t a in ing M I M I C s o l u t i o n s t o t h e f rozen f low, v a r i a b l e p r o p e r t i e s energy equa t ion was t o provide a method o f s tepwise checking t h e f o u r t h o rde r Runge-Kutta a n a l y s i s i n t h e TEMPRE System. M I M I C i s an a n a l o g - d i g i t a l s imula tor program which permi ts t h e i n t e g r a t i o n of func t ions wi th b u i l t - i n numerical i n t e g r a t i o n formulae. A f o u r t h o rde r Runge-Kutta technique i s used by M I M I C , and i s a d i r e c t method of comparing s o l u t i o n s o r p o r t i o n s of s o l u t i o n s i n each program. It essen- t i a l l y provided a r ap id means o f determining t h e c a p a b i l i t y of t h e TEMPRE System f o r c a l c u l a t i n g t h e c o r r e c t s o l u t i o n t o t h e d i f f e r e n t i a l energy equa t ion . M I M I C s o l u t i o n s were ca l cu l a t ed f o r two forms of t h e f rozen flow energy equa t ion . I n t h e f i r s t , t h e fol lowing form of t h e second o rde r d i f f e r e n t i a l equat ion was so lved . (H- I-) A second s o l u t i o n t o t h e energy equat ion a f t e r d i f f e r e n t i a t i n g t h e conduct ive hea t t r a n s f e r term, followed by rearrangement, was a l s o c a l c u l a t e d . This second equat ion was i d e n t i c a l t o t h e form used i n t h e TEMPRE System. The s o l u t i o n s t o t h e s e two equa t ions were obtained dke t o determine whether t h e c a l c u l a t i o n of t h e term, -dT > by i n t e r p o l a t i o n from a t a b l e of k ve r sus T d a t a was be ing performed e c o r r e c t l y . It a l s o proved t o be a very f a s t and easy technique f o r d e f i n i n g t h e incremental temperature necessary i n t h e i n t e r p o l a t i o n r o u t i n e . A comparison of t h e temperature d i s t r i b u t i o n s f o r t h e f rozen flow o f p y r o l y s i s products i n a one-quar te r inch t h i c k char between 500°F and 2000°F i s presented i n Table H - 1 , Very good agreement i s obtained f o r a s t e p s i z e o f one hundred u n i t s i n t h e f o u r t h o r d e r Runge-Kutta method (TEMPRE). The s l i g h t d i f f e r e n c e s i n t h e temperatures a r e a t t r i b u t e d t o round- o f f o r t r u n c a t i o n e r r o r s . Based on comparisons l i k e t h e s e , t h e numerical i n t e g r a t i o n method i n t h e TEMPRE System was proven t o g ive an accu ra t e s o l u t i o n t o t h e energy equa t ion . Copies of t h e MIMIC programs f o r s o l u t i o n o f each form of t h e d i f f e r e n t i a l energy equat ion a r e provided i n L i s t i n g s H - 1 and H-2 wi th t y p i c a l input and output d a t a . T em pe ra tu re ( O F ) D im en si on le ss C ha r D is ta nc e q I C (a ) M IM IC (b ) S ol ut io n S ol ut io n 50 0. 00 50 0. 00 62 6. 52 62 7. 11 82 1. 89 82 1. 95 11 05 .7 6 11 04 .9 0 14 92 .9 5 14 94 .8 9 G as C om po si ti on ( m ol e/ m ol e ga s) : CO = 0. 24 5, C0 2 = 0. 04 6, N2 = 0. 07 3, CH 4 = 0. 57 0, C6 H6 = 0. 06 8 (a ) s o lu ti on o f e qu at io n (H -1 ) Cn 0 \ rd Li st in g H -1 . MI MI C Pr og ra m. (a ) In pu t Da ta Li st in g H -7 . M IM IC P ro gr am f or S ol vi ng t he D if fe re nt ia l En er gy E qu at io n (H -2 ). Y I Y I C PR OG RA M F O R F9 0Z EN FL OW IN A BL AT OR CO N( LG rA XX vA XA 1 C O N I C T ~ D T M I N r D T M A X ) CO N( AK qB Kr A1 CO NS TA NT S IN H F A T CA PA CI TY F QU AT f O N - CP =A &R *T &C *T *T ED *T *T *T C O N ( A ~ T B ~ ~ C ~ ~ D ~ I CO f' J( A2 r6 2q C2 rn 2) CO N( A3 ~8 3v C3 rD 31 CO N( A4 rB bv C4 rD 4) CO N( AS rB 5r C5 rD 5) MO LE FR AC TI ON S FO P F I V E C OM PO NF NT S C O N (M Fl rM F2 rM F3 qY F4 rM F5 ) P A P A Y E T E R S PA R( T1 ~ D T S L ~ D T S H T D T I ~ T O ~ T O L I SE TS LO GI CA L V A R I A B L E S FW F S W (T IT RU €~ TR UE TF AL SF ~ FA F S ~ (T -L G- (A XX -~ ,) *L GA ~F ~L SE TT RU E~ TR UE ) FD F Sk (T -A XX *L GA ,F AL SE P T R U E T TR UE 1 FC FS W fT -L G -(A XA -1 . )* LG Ap FA LS E~ TK UE rT RU El FF F Sh (T -L G- (A XX -l .) *L GA -D TM IN ~F AL SE pT RU E~ T~ UE ) f E NO T( AN I) (F AI FF ) 1 F Y AY D( F A I F CT ND T( FW I 1 CO M D! JT ES IN IT I4 L C OY ST AN TS FW R S 9 45 4. 0/ (2 52 ,* 25 .4 +1 .8 ) FS d Cf i B R 3* (A 1* MF l& A2 *M ~2 &A 3* MF 3& A4 *p .lF 4C A5 *M F5 l G W CS P 3R *( Sl *Y Fl &R 2* MF Z& R3 *Y F3 &d G* YF 4b B5 *Y F5 ) F k C C P S B * (C ~ *Y F ~ & C ~ ~ ~ F Z & C ~ *M F ~ ~ C ~ *Y F ~ & C ~ *Y F ~ ~ iZ 4 CQ H 3B *( r)l *t: MF 1& D? *M F2 &D 3* MF 3& D4 *M F4 &3 5* YF 5~ FN T R I T I & 46 0. 0) /1 .8 FW T7 .7 3T T *( AY &R K* T3 )* 30 .4 8/ [2 52 *O *I eE !) F k TH Tr IC TC L F lrt T L T3 -T O L F - v, LG A L > C e C 1 SE T j C O N ST 4N TS F n G IT FR A T I ON PI IR PO SF S T E M P 0 01 TE MP 0 0 2 TE MP 0 03 T E M P 0 0 4 T E M P 0 05 T E M P 0 06 T E M P 0 0 7 T E M P 0 0 8 T E M P 0 09 T E M P 0 1 0 T E M P 0 18 T E M P 0 12 T E M P 0 13 T E Y P 0 1 4 T E M P 0 15 TE MP 01 6 T E M P 0 1 7 T E Y P 01 8 T E M P 01 9 T E M P 0 20 T E Y P 02 1 T E M P 0 2 2 T E M P 0 2 3 T E M P 0 2 4 T E M P 02 5 TE M P 02 6 T E M P 0 27 T F Y P 0 28 TF HP 02 9 T E M P 0 3 0 TE MP 0 3 1 T E M P 03 2 TE LJ lP 0 3 3 T E M P 03 4 LLi LU 4 cV u I- rn 3 - u7 3 L CL I- ni 0 3 - d C Y - 2 U- W LL - z \a - u * w Y =' U m 3 - - u 3 4. C - v, 2ul LL 3 aL Cn - * J i+ co J d Z cr C W W - D a C . - aC3 0, Y C - I - + - mZI ti c( C h , -I - -UJ - 3 G C .KIY Ij 4 + 2 N - rn u LLIV) * - CL r Q . - L W N O G + ~ 1 x 4 -I- 3.d C *--€I m h l b ? I * I- e m \ b e e CLC M a - O V \ C ~ V ) - I \ C C F ( * N C . Q O X J E - CLL * - r O t . V ) - + f \ U v I 4 t * W Q C. * * 4 * r OCJ1ILQ- U n i 3 C N c I-+- J I - I - 4 0 r . rC IV)m;ZO w - 0 4 6 - 4 X I - - I>C+ X *eV)I L C c J 4 L L . Q \ L L Q \ a d C - C fl I I L ! ! X * C L ' J 3 C b i o c c m L' a ? I v , m 0 * u * ~ Q W O ~ ~ M F * ~ ~ > . Q O U + ~ i t u b O x u~ d d c i ~ . + I ~ Q L X I ~ I - C ~ Q ( V ~ Y * ~ ~ Y O L ~ X O L a a -- - - U w - - - m u U a c l - ~ a 3 C ~ Y \ ~ I 4 -- a x 3 3 3 X S Z J 3 3 b W U U i $ * d d W ~ I - h X I - k - a + C X X O ~ ~ mrn - ~ W O + Q I - Q Q ~ Y * ~ ~ C Z I C ~ I Q U J L L A J & x A - I U ~ ~ - C + U ~ ~ L U C ~ & + - I O U Li st in g H- 2. MI MI C Pr og ra m. (a ) In pu t Da ta VITA Gary Charles Apr i l was born i n on . H e completed h i s secondary educat ion a t DeLaSalle High School of t h a t c i t y i n June of 1958. He then a t tended Louis iana S t a t e Univers i ty a t New Orleans dur ing t h e i n i t i a l two y e a r s of i t s opening and t r a n s f e r r e d t o t h e main campus a t Baton Rouge i n 1960. I n June o f 1962 he was awarded t h e Bachelor o f Science degree i n Chemical Engineering. Af t e r g radua t ion h e was employed wi th t h e Nylon In te rmedia tes Research and Development Group of t h e E. I. DuPont DeNemours Company a t Orange, Texas. Three and one h a l f yea r s l a t e r , he en ro l l ed i n t h e g radua t e school of Louis iana S t a t e Univers i ty whi le on an educa t iona l l e ave of absence. He rece ived t h e Master o f Science degree i n Chemical Engineering i n January of 1968 and i s p r e s e n t l y pursuing a Doctor o f Philosophy degree i n t h e same curr iculum. His immediate p lan upon graduat ion i s t o accep t a p o s i t i o n on t h e Chemical Engineering f a c u l t y a t t h e Un ive r s i t y of Alabama, Tuscaloosa, Alabama.

The Thermal Conduction Process in Carbonaceous Chars

Abstract

Extracted data

The Thermal Conduction Process in Carbonaceous Chars

Abstract

Extracted data

Related items

Related items