This item is held in Loughborough University’s Institutional Repository (https://dspace.lboro.ac.uk/) and was harvested from the British Library’s EThOS service (http://www.ethos.bl.uk/). It is made available under the following Creative Commons Licence conditions. For the full text of this licence, please go to: http://creativecommons.org/licenses/by-nc-nd/2.5/ A STUDY OF CYCLIC VARIATION IN GAS VELOCITY AND THE TURBULENCE STRUCTURE IN SPARK IGNITION ENGINES by N. S. M. SAIANIA A Doctoral Thesis Submitted in Partial Fulfilment of the Requirements for the Award of Doctor of Philosophy of Loughborough University -Qf-Technology November 1974 I Supervisor: J. C. Dent, Ph. D., C. Eng. c by Nabil Salama Mohamed Salama (1) SUMMARY The thesis is concerned with the study of the characteristics of the turbulont flow field inside the combustion chambers of spark ignition engines. A comprehensive literature survey has been undertaken of the problem of cyclic variation in spark ignition engines, and the role of turbulence on flame propagation. The experimental methods used involve a detailed I application of hot wire anemometry, signal processing and computer techniques to the statistical analysis of the problem of cyclic variation in gas velocity and turbulence structure (intensity, scale, power spectrum and eddy diffusivity), at the spark plug location of motored spark ignition engines. Two engines have been used in the investigation, a Rolls-Royce V-SL and a Ford 2 litre V4. Extensive test programs were c arried out on both engines at a range of engine speeds and throttle settings, and a range of turbulence promoting devices have been investigated with regard to their suitability for promoting small scale turbulence during the ignition period. The variation of flow field characteristics with depth inside a wedge combustion chamber of the Rolls-Royce engine has been investigated. Cylinder-to-Cylinder variation in turbulence characteristics has also been investigated for the Rolls-Royce engine. . (ii) The spectral composition of turbulent eddies inside a wedge and a heron combustion chamber was invetstigated over a wide range of engine speeds. It was found that increasing engine speed resulted in increases of both the fluctuating velocity components and the high frequency content of the eddies. Both effects are believed to be responsible for increases in turbulent flame speed in engines with increases in engine speed. Comparisons between the results obtained in the present work and the reported data of other investigations on turbulence measurements in spark ignition engines and closed vessels, show close agreement. A direct correlation has been established between the characteristics of the turbulence field in bn-g-ilnes and other isotropic flow fields. In particular, a correlation is found to exist between the eddy diffusivity as obtained from the anemometer measurements in an engine and the eddy diffusivity data for highly turbulent pipe flow obtained by other workers. These findings establish a relatively straightforward method for obtaining quantitative information on turbulence characteristics from mean velocity measurements on an engine, which require simple equipment. A theoretical model of combustion variation has been developed, based on the assumption that cyclic variation originates during the growth period of the initial flame kernel. This process was related to variations in eddy diffusivities of the small scale turbulence for different (iii) cycles. The model equations are chocked by making use of the established correlation between eddy diffusivity and gas mean velocity and using the reported experimental data of other workers, which shows very good agreement between the predictions of the model and the measured values. / (lv) ACK NOW LEDGEMENTS The author wishes to express his thanks to: Dr. J. C. Dent for his guidance throughout the project. Mr. P. Clayton for manufacturing hardware. Messrs. K. Topley and G. Smith for photographic work. Mrs. J. Smith for typing the completed thesis. A great debt is also due to my wife for her encouragement during the period of study. Finally I would like to express my appreciat-ion'to Rolls- Royce Motors Limited for scholarship support during the course of this research. f Cv) NOTATION A Cross Sectional Area of a Hot Wire (M A Constant in the Heat Transfer Equation (3-2) A* Isotropic Area of Inlet Port (M 2 a Overheating Ratio of a Hot Wire B A Constant in the Heat Transfer Equations (3-1) find (3-2) C Correction Factor for the Effect of Finite Wire Length on Turbulence Measuremerlts C Heat Capacity of a Hot Wire WOK) w of Skin Friction Coefficient cp Specific Heat at Constant Pressure (JlKgOK) cv Specific Heat at Constant Volume (J/KgOK) D Cylinder Diameter (m) d Hot Wire Diameter (m) E Instantaneous Value of Bridge Voltage (volts) Mean Value of Bridge Voltage (volts) e Fluctuating Voltage Component (volts) F(VO Power Spectral Density Function (see) FM Power Spectral Density Function F(X) Fourier Transform of a Random Variable X F-l(x) Inverse Fourier Transform of a Random Variable X f Friction Factor gtr Transconductance of Hot Wire Circuit (ohms) h Heat Transfer Coefficient (W/M 2 OC) (vi) R9 Resistance of a Hot Wire at Gas Temperature (ohms) Ro Resistance of a Hot Wire at a Reference (ohms) Temperature RW Resistance of a Hot Wire at its Operating (ohms) Temperature ReD Reynolds Number (U. D/y) R eL Turbulence Reynolds Number (u' Lx/. ý Re Turbulence Reynolds Number (u', Ly/-ý ), Rt(-C) Auto-correlation Function (m2/sec2) Rj(z) Auto-correlation Coefficient RL(T) Lagrangian Correlation Coefficient Rxl(x) Longitudinal Correlation Coefficient Rý(y) Lateral Correlation Coefficient r Separation Distance Between two points (MM) in a Fluid Field Laminar Flame'Speed (m/sec) Turbulent Flame Speed (m/sec) SM Standard Deviation of the Variable x. Tg Gas Temperature (OK) TW Operating Temperature of a Hot Wire (OK) t Time I (see) U Instantaneous Value of the Turbulent Gas (m/sec) Velocity U Average Value of Gas Velocity (m/sec) u Fluctuating Velocity Component in Flow (m/sec) Direction v Fluctuating Velocity Component in Y Axis (m/sec) Direction w Rate of Energy Dissipation (Kg1m sec 3 w Fluctuating Velocity Component in Z axis (m/sec) Direction (vii) Instantaneous Value of the Bridge Current (A) I Mean Value of the Bridge Current (A) Int Turbulent Intensity H i Fluctuating Component of Bridge Current (A) K Slope of Hot Wire Calibration Curve (volts/m/sec) (K = dE) - ýi u Kg Thermal Conductivity of G as (W m20Cm KS Thermal Conductivity of Wire Material at (w/m2 OC/M) Gas Temperature KT Thermal Conductivity of Wire Material at (w/m2 oC/M) its Operating Temperature Lt Time Macro-Scale of Turbulence (see) LX Longitudinal Space Scale of Turbulence (mm) (Macro-scale) Ly Lateral Space Scale of Turbulence (mm) (Macro-scale) Lm, tm Prandtl Mixing Length (mm) Wire Length (m) 1* Von-Karman Characteristic Length (mm) Lt Lagrangian Time Scale of Turbulence (see) I LL Lagrangian Space Scale of Turbulence (mm) Nu Nusselt Number n Polytropic Index Frequency of Eddy Rotation (Hz) P Pressure (NIM 2 Pr Prandtl Number QC neat Loss by Conduction along the Hot Wire M Qe Heat Supplied to a Hot Wire W Convective Heat Transfer from the Hot Wire to the Surrounding Fluid M Re Cold Resistance of a Hot Wire (ohms) v (Viii) X Coordinate Axis in the Flow Direction Y Coordinate Axis Perpendicular to the Flow Direction z Coordinate Axis Perpendicular to the Flow Direction 0( Temperature Coefficient of Resistance Electrical Resistivity of Wire Material Ratio of Specific Heats Delay Time between the Signal at Two Different Instants of Time Shear Stress Xt Time Micro-Scale of Turbulence Longitudinal Micro-Scale of Turbulence Lateral Micro-Scale of Turbulence Gas Density Width of Laminar Flame Front Width of Turbulent Flame Front Gas Dynamic Viscosity Gas Kinematic Viscosity Coefficient of Eddy DiffusiVity m 9 Crank Angle r Kovasznay Criterion (r i Ax (MM) (mm) (mm) (/VC) (sec) (NIM 2) (sec) (MM) (mm) (Kg/m 3) (MM) (m) (Kg/m sec) (m 2 /sec) (m 2 /sec)' (degrees) (ix) Subscripts 9 Gas Conditions f Laminar Lin Linearized meas Measured micro Small-scale Turbulence Edaies (micro-sdale) macro Large-Scale Turbulence Eddies (macro-scale) t Turbulence, Time W Wire Operating Conditions, conditions at the walls Abbreviations ADC Analog-to-Digital Converter ATDC After Top Dead Centre BTDC Before Top Dead Centre TDC Top Dead Centre Ir Iridium MBT Maximum Brake Torque Pt Platinum (x) INDEX OF CONTENTS Page Nos. SMi 1,11ARY (i) - (iii) ACKNOWLEDGEMENTS (iv) NOTATION (v) - (ix) 1.0 INTRODUCTION 1 -8 1.1 General 1 -6 1.2 Object of the Investigation 7 -8 2.0 LITERATURE SURVEY 9 - 130 2.1 Relation between Cyclic Variation and 9 - 10 Engine Performance 2.2 Choice of Characteristic Parameters as a 10 - 19 Measure of Cyclic Variation 2.3 The Effect of Engine Operating Variables on 19 - 55 the Extent of Cyclic Variation 2.3.1 Ignition 25 - 31 2.3.2 Mixture Preparation 32 - 34 2.3.3 Exhaust Gas Dilution of the Charge 34 - 37 2.3.4 Compression Ratio 37 - 39 2.3.5 Throttling 39 - 42 2.3.6 Cylinder Water Jacket Temperature 42 and Oil Contamination of the Charge 2.3.7 Air/Fuel Ratio 42 50 2.3.8 Type of Fuel 50 52 2.3.9 General Characteristics of Cyclic 52 55 Variation 2.4 Effect of Gas Velocities and Turbulence on 55 102 the Combustion Process in S. I. Engines 2.5 Effect of Mixture Motion on Flame Speed 103 - 123 2.6 Possible Cause of Cyclic Variations 123 - 130 (xi) Page Nos. 3.0 HOT WIRE AhrEMOAIETER AND ITS CHARACTERISTICS FOR 131 - 196 TURBULENCE MEASUREMENTS 3.1 The Constant Temperature Hot Wire 132 - 133 Anemometer 3.2 Calibration of the Hot Wire Anemometer 133 - 144 3.2.1 Physical Properties of Hot Wire 140 - 142 Probes 3.2.2 Anemometer Drift 143 - 144 3.3 The Response of Constant Temperature Hot 144 - 152 Wire Anemometer To Turbulence ' 3.4 Statistical Analysis of Turbulence 152 - 170 3.4.1 Definitions of Correlations and- 152 - 161 Scales of Turbulence 3.4.2 The Spectrum of Isotropic 161 - 167 Turbulence 3.4.3 The Relationship between the Micro- 167 - 170 Scale and the Macro-Scale_. f. or Isotropic Turbulence 3.5 Effect of Large Turbulence Fluctuations on 170 - 175 the Response of a Hot Wiret 3.6 The Effect of Wire Length on Turbulence 175 - 181 Measurements 3.7 Turbulence Diffusion, Lagrangian Analysis 181 - 185 FIGURES (3-1) - (3-16) 186 - 196 4.0 DATA ACQUISITION AND PROCESSING SYSTEM 197 - 279 4.1 Data Collection 202 - 214 4.1.1 DISA 55M onstant Temperature 203 - 206 Anemometer System 4.1.2 Timing Mark 206 4.1.3 Measurements of Cylinder Gas 207 - 208 Temperature and Pressure 4.1.4 Signal Recording System 208 - 212 4.1.5 Probes and Traverse Mechanisms 213 - 214 (xii) Page Nos. 4.2 Data Preparation 214 - 224 4.2.1 Digitization of Mean Velocity and 214 - 216 Pressure Traces 4.2.2 Calibration of the Digitized Data 216 4.2.3 Calibration of Recorded Signals 217 - 218 4.2.4 Preparatlon of Turbulence Signals 218 - 224 a) Preparation for Multiple Records b) Data Preparation for Individual Records 4.3 Data Qualification 224 - 235 (Basic Assumptions about the Structure of the Turbulent Field) 4.3.1 Stationarity and Ergodicity of the 226 - 228 Data 4.3.2 Test for Stationarity 228 - 232 4.3.3 Isotropy and Homogenditi of 233 - 235 Turbulence 4.4 Data Analysis 235 - 247 4.4.1 Analysis of Gas Mean Velocities 235 - 237 4.4.2 Analysis of the Fluctuating 237 - 247, Velocity Components 1) Analysis of Multiple Data Records 2) Analysis of Individual Data Records 4.5 Programming of the Data Analysis Procedures 247 - 254 FIGURES (4-3a) - (4-29) 255 - 279 5.0 MOTORED ENGINE CONFIGURATION AND EXPERIMENTAL TEST 280 - 307 PROGRAM 5.1 Experimental Test Programmes and their 284 - 297 Objectives 5.1.1 Details of the Experimental Test 287 293' Programme carried out on the Rolls- Royce Engine (Xiii) Page Nos. 5.1.2 Details of tho Experimental Test 294 - 297 Program Carried out on the Ford Engine FIGURES (5-1) - (5-15) 298 - 307 6.0 DISCUSSION OF RESULTS 308 - 460 6.1 General Characteristics of Gas Velocities 308 - 324 inside the Combustion Chambers of Spark Ignition Engines 6.1.1 Effect of Hot Wire Direction on 310 - 311 the Measured Gas Velocities 6.1.2 Variation of Gas Velocities with 312 - 315 Depth inside the Combustion Chardber of a Rolls-Royce Engine 6.1.3 Investigation of the Flow Pattern 315 - 318 inside a Wedge Combustion Chamber 6.1.4 Variation of Gas Velocity 318 - 323 Characteristics with Engine Speed - 6.1.5 Investigation of GA's Velocity 323 - 324 Characteristics inside the Intake Manifold 6.2 Variation of Flow Field Chiracteristics with 325 330 Different Modifications of Intake System 6.3 Investigation of Turbulence Characteristics 330 - 355 inside the Combustion Chambers of Spark Ignition Engines 6.3.1 General Characteristics of Turbulence 331 - 335 Field in Engines 6.3.2 Variation of Turbulence Characteristics 336 - 340 with Engine Speed 6.3.3. Variation of Turbulence Characteristics 340 - 342 with throttling 6.3.4 Investigation of the Extent of Cyclic 343 - 345 Variation in Turbulence Characteristics 6.3'. 5 Effect of Different Intake 345 - 355 Modifications and Local Turbulence Promoter at Spark Plug on the Characteristics of the Turbulence Field (Xiv) Page Nos. 6.4 Investigation of Cylinder- to-Cylinder 356 - 357 Variations in Flow Field Characteristics G. 5 Effect of Combustion Chamber 358 - 361 Configuration on Turbulence Characteristics FIGURES (6-1) - (6-51) 362 - 460 7.0 CORRELATION BETWEEN THE CHARACTERISTICS OF TURBULENCE 461 - 494 FIELD INSIDE MIE CONT13USTION CMATBERS OF SPARK IGNITION AND OTHER FLOW FIELDS 7.1 Approximate Design Procedure for Predicting Turbulence Characteristics in Spark Ignition Engines FIGURES (7-1) - (7-14) 8.0 MODEL OF CYCLIC VARIATION 8.1 Experimental Verification of Cyclic Combustion Variation Model FIGURES (8-1) - (0-3) 9.0 CONCLUSIONS AND RECOIZIENDATIONS FOR FURTHER WORK 9.1 Conclusions 9.2 Recommendations for Further Work 10.0 REFERENCES AND APPENDICES REFERENCES APPENDICES PART I: Al New Analysis of Other Investigations. A2 Statistical Definitions A3 Physical Properties of Air A4 A Guide for the Sources of Different Equations Presented in Chapter 3. PART II: PROGRAWING OF 711E DATA PROCESSING SYSTEM 479 - 482 483 - 494 495 - 516 510 - 514 515 - 516 517 - 528 517 - 525 526 - 528 529 - 565 529 - 544 545 - 565 545 - 553 554 - 558 559 - 564 565 (XV) NOTE ON FIGURE ARRANGEMENTS The illustrations within this thesis are grouped at the end of the corresponding chapters, with the exception of the first two chapters. / 1. 1.0 INTRODUCTION 1.1 General The process of combustion in the cylinder of a spark ignition engine is initiated by a single intensely high temperature spark which gives rise to a nucleus of flame, and after the lapse of a certain time interval representing the delay period, this nucleus produces a stable advancing flame front, blue at first, but closely followed by the main heat releasing front, which generally has an orange colour. Examination of the combustion pressure diagrams of-any gasoline engine, operating under normal conditions, show that there is a large cycle to cycle variation in the rate at which the flame propagates across the combustion chamber in successive cylinder firing. This results in a variation in the rate of - -- a pressure rise (due to combustion), in the peak cylinder pressure, and in the work done by the gas on the p1ston. For maximum efficiency, reliability and acceptance of engines, it is necessary that their pressure development should be repeatable from one cycle to another. In spite of the fact that this combustion problem was noted in some of the earliest research on spark ignition engines (1), a firm understanding of its origin and means for its reduction have never been realised. Patterson (2) showed that fast burning mixtures produce less cyclic variations, Fig. (1-1) and consequently will produce less torque variation and will supply power to an automobile more smoothly. This could be accomplished by: enrichening the mixture to C) >I. Cd cn t) >0 cq $4 -A 04 :1 00 CD 0 -H -4 P4 $4 V) 4- 4- P, st 0 rs +31 0 ;40 Vk cl C) -a CD o V- ---f P. > -H vi V) -ri -ri P4 P4 00 V. 0 *r, 'ri 4J 4-3 -ri ori /9 tn T-i r-l 94 k -7---l- .. -9 a- I ;. j ri -- :3 cs cd bio ; -1 0 1H >> cd :ý 4-b CH V, 0 0. A cd > 4J 4-3 o dF vs 4-) -rq 44 C) cd 00 04 C) r4 %-4 4H e-Ift-nnstiva Almlosly w :ý00a (D 0%--l cli 00 84 ý- %. o " C) Cj C13 I 4 V4 0 -H 0 0 cl *as 44 C'l r: x to 0 -H CO) Ll -ri zI 4-) 0 a21a; Ai11 (D V) -H , vim lmgv"w boadnA3 re :30 +3 4-2 C3 0 -ri -^ 14 >V Cd. I CH CH > 14 00 $4, rn 4J 4 ý: C) 4-) 0 P4 P, -r4 cd r-4 Cd 0 C) U) 4-1 -r4 tP 4-l' 43 *: W"jj&d lboww C) ak: $4 0 cd 0 CH Ouj i J2 1 %-0 W4 3. best power mixture ratios (4,30,16), reducing exhaust residuals (4,13), installing shrouded valves (2) (to increase the charge turbulence), and multiple ignition of ihe charge (4). However, as a result of the present interest in the use of lean mixtures to reduce exhaust emissions, the method of reducing cyclic combustion variation by richening the mixture, as employed by most manufacturers will no longer be viable. At lean fuel air ratios, the effect of cyclic ýariation becomes severe (2,3,4,30), and one lean misfire will negate any emission reduction. , If it were possible to run an engine at weak mixtures and obtain each cycle equivalent to the best observed during normal weak mixture operation, then, according to Patterson (2), Soltau (4), Clarke (5) and Vichnievsky (6), gains of 10-20% in power and fuel economy might be possible, 3ý1g. (1-2), as well as important reductions in exhaust emissions. It will further reduce the octane number requirements and would permit a higher compression ratio, but without requiring higher octane fuel (7,8), Fig. (1-3). Previous investigations have attempted to explain qualitatively cycle to cycle variation-by a number of factors. Among the more important factors influencing this variation are: - i) Variations in the overall air/fuel ratio of the cylinder with successive cycles. 'ii) Non -homogeneous distribution of air and fuel through the cylinder, particularly in the vicinity of the spark plug. iii) Variations in the spark-timing, the type of spark, or the spark energy. 4. Ml C) it %- I\ I. - CL. ce- uj 8 0 0 . 1-1 tf) ul 0 A V 0 0 ho r. V4 0 0 r4 14 4-) Cd 0 4-b O-N cn V. co to . r4 %-A (D IH 0a 0 0 U) a) in 0-4 , _Z - 6 . rj P4 It la» ( < 0 b- C '/ ' ' r-i Co vý CL. w . c eN m :E C) C> cd x OXO 1ýII- CO cr) 94 . _Z 0 Co > %.. e . f-f CJ M- > 4j e% c: 0 10 ed 0 cu 4-1 u0 «H -ri 0 4-3 0V 0c 54 0 ci n tH -P Ei 4-4 V0 r4 0 C) %_o OlSd 38nSS38d NOISSM0103 *8803 5. iv) The temporal variation in the velocity ' gradients and turbulent mixture motion, again, particularly in the vicinity of the spark plug. All these factors may cause cyclic variation, but the effect of each is not the same. The last factor appears to be receiving the most interest, and is regarded as the major cause of combustion variation (2,9-13,15,17,23). There is a general agreeipent that cyclic variation originates in the early development of the initial flame kernel. During this period, the size of the flame kernel, is*very comparable with the small scale turbulence eddies. Consequently, the growth of such a kernel is greatly affected by the random 51*31- 4 nature of the turbulent field. When the, flame front approaches that of the large scale eddies, the flame prop4gates at a more or less constant speed and the effect of eddies will be averaged across the front. A detailed analysis6f this concept of cyclic variation will be discussed in detail in chapter 8. Several investigations tend to support this explanation due to the observed amelioration of dispersion in tests where turbulence intensity was increased either by: shrouding the inlet valve (2,15,16,17,20), modification of the inlet port (16,18), or reducing the inlet valve lift (19). However, the actual flow mechanism of these modifications have never been studied quantitavely. Although the effect of turbulence on increasing the flame propagation and reducing the flame travel time and consequently cyclic variation is well known, the constant impetus for better 6. breathing to provide increased full load output has resulted in engines with relatively large inlot ports and unshrouded valves. Fig. (1-4) shows a comparison between the compression pressures for three types of inlet valves; a plain valve, a valve with a 90 degree shroud and a valve with a 180 degree shroud. The effect of the shrouds on restricting the engine breathing at higher speeds is clearly evident. On the other hand, large inlet valves and inlet valve ports with good aerodynamic design cause small pressure drop in the cylinder and consequently low velocities and turbulence intensities at the low loads and speeds required for automotive applications. These usually result in longer flame travel times and probably high cyclic dispersion (9). Elucidation of the effect of turbulence on the Cyclic variation necessitates, therefore, a detailed study of the " -'ý- 0 turbulence intensities, scales and spectrum. So far as is I known, few attempts (21,22,24) have been made to measure directly the intensities of turbulence in a cylinder of a spark- ignition engine using hot wire anemometers. Moreover, no measurements of the scales of turbulence or the eddy diffusivity in engines have been reported. This provides the impetus to study such explicit factors in an attempt to determine the parameters which affect the flame propagation and consequently the cylinder pressure development (resulting from combustion) in a spark ignition engine, and which it would be desirable to control to reduce cyclic combustion variation. 7. 1.2 Object of the Investigation It has been concluded, by many investigators, that even with engine. operating variables under control, cyclic combustion variation still exist due to cyclic. variation in mixture motion and the random nature of the turbulent flow field inside the combustion chamber. The available knowledge about the characteristics of the turbulent gas motion inside the combustion chamber of S. I. engines are limited and most of the published investigations in this field are concerned with measurements of mean gas Velocities. However, part of the problem could be attributed to the complexity of the flow field after inlet valve closure and the difficulties of using hot wire anemometry in such a flow which undergoes very rapid changes of its characteristics. -,, -& Therefore, the main objective of the present investigation could be summarized in the following points: - I i) Development of a suitable technique for Studying the characteristics of turbulent flovi inside the combustion chamber of S. I. engines in terms of intensities, scales and spectrum functions. ii) Obtaining a detailed and reliable measurement of gas velocities inside the combustion chamber of actual commercial S. I. engines under variable operating conditions. iii) A study of the cyclic variations in gas velocities and turbulence as a possible cause for cycliO 013mbustion variations. 8. iv) An attempt to achieve better understanding of the flow mechanism and the associated turbulence characteristics of some devices which have been employed by other investigators and resulted in some improvement of cyclic combustion variation and to investigate the flow characteristics developed by some new ones. V) An attempt to establish some correlation between the turbulence characteristics inside the combustion chamber of S. I. engines and those predicted from pipe flow experimental data. Such an object, which if achieved, could reduce the amount of experimental work and make such a complex problem somewhat predictable. vi) The establishment of a model for -cyCI-16 combustion variation relating such phenomenon to the structure of the turbulent field inside the'combustion chamber of engines. / 9. 2.0 LITERATURE SURVEY 2.1 Relation between cyclic variation and engine performance Recently, most interest has been shown in lean mixture combustion as a means for reduced exhaust emissions, because of its low concentration of oxides of nitrogen as well as carbon monoxide in the exhaust gas (the lowest HC (exhaust hydrocarbons) contents are reached at fuel/air ratios 20-30% weak (60) ). Moreover, most modern spark-ignition engines attain their lowest fuel consumption at approximately 5-15% excess air. Generally, however, when the mixture is weakened to a considerable extent beyond the stoichiometric, problems are encountered due to poor combustion and occasional misfire which results in increased specific fuel consumption, rough engine operation and increased hydrocarbon emissions. Therefore, reduced cyclic variation results in a number of improvements in both engine performaAce and reduced exhaust emissions. In fact a correlation between the/irregularities of combustion process and the exhaust emissions has been always assumed (59,61). Tests on the effect of reducing cyclic variation by modifying ignition system design or increasing the charge turbulence tend to support the previous assumption (20,27,60), where it has been observed that factors which reduced cyclic combustion variation resulted in a corresponding reduction of exhaust emission level. Among these modifications of ignition system; are extended gap location, wider gap size, longer spark 4 10. duration, higher spark energy and smaller centre electrode diameter, Figs. (Z-1 - 2-3). On the other hand, controlled turbulence in the combustion chamber represents another means of reducing combustion variation and consequently exhaust emissions. This could be accomplished by fitting swirl generators in the inlet port (60), inserting guide vanes on the valve seat (20) or using shrouded valves (2,15). Fig. (2-4) shows the extension pf the lean limit, (defined as the largest air/fuel ratio for operation without misfire), by using an inlet valve fitted with six guide vanes inclined at 60 degrees to the mixture flow direction. Fig. (2-5 ) shows the resultant effect on engine performance when thi s valve was used in conjunction with an improved ignition systemand higher inlet air temperature. Also, increasing the small scale turbulence, which is generally observed to reduce cyclic combustion - ý- 0 variation, could result in a reduction of ui; burnt hydrocarbons, especially where the turbulence is generated within a general mixture motion tangential to the chamber wall (28). Fig. shows the effect of small scale turbulence on the unburnt hydrocarbons in a constant volume bomb wýere turbulence was generated by rapid opening and closing of a magnetic valve connecting the bomb to a variable Volume chamber filled with the same mixture at higher pressure. 2.2 Choice of Characteristic Parameters as a Measure of Cyclic Variation Investigators have employed various characteristic parameters for measuring the extent of cyclic variation in the cylinder pressure I, I -e UNY X) m IN44) IN UM 0 äu AN cc =I, 12 cc III 10 cc f! I "M -41 t-= W Op 6. .. II I' .00 .000 (3NYX31 IuI) SNO3Y3OUQAN p E £ p. - . 1. / r. 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One can summarize the most important ones as follows: - i) Maximum cylinder pressure# (Pmax)* ii) Maximum rate of pressure rise, (Pmax)- iii) Crank angle of occurrence Of kax or Pmax relative to TDC '. (Opmax ) and 0 Pmax respectively. iv) The time for the flame front to travel across the combustion chamber or across any specified path or the apparent flame propagation velocity as given by the distance of flame travel divided by flame-travel time. V) The time of pressure rise to a certain arbitrary value of the compression pressure measured from the time of ignition. vi) The indicated work per cycle (i. m. e. p). -ý--- vii) The mass burning rate. The maximum cylinder pressure (Pmax) arib the maximum rate of pressure change (Pmax) are very sensitive to cyclic variation and were employed as characteristic'paramete / rs in most of the studies on the cyclic combustion variations (2,10,12,13,32), because of the easiness in their measurements, Figs. (1-1)o (2-7 ). Moreover, Barton et al (10) have shown that there is a one to one correlation between Pmax and ýmax Fig. (2- 8 ), hence one or the other need be considered. The disadvantage of using only P or max Pmax is that it depends on the entire combustion process and does not provide specific information about the combustion process variation. 15. Soltau (4) and Burgett (27) have studied the problem in terms of the indicated mean effective pressure of each cycle, Fig. (2- 9). This reflects directly the effect of cyclic variation on engine brake torque variations. Peters and Borman (33) have used the mass burning rates (which could be estimated from the curves of mass burned fractions versus crank angles), as a parameter chardeterising the cyclic variation, since it is closely related to the rate of pressure change. Low peak pressure cycles have a much smaller burning rate initially after the spark than high pressureýcycles Figs. (2-10(a) and 2-10(b) ). Peters and Borman also noticed that the low peak pressure cycle continued to be lower than the high pressure cycle even after the combustion was well under way. - Many investigators have concentrated oný variation of flame front speed because of its close relatiohship to the possible causes of cyclic variation. Measurements of flame travel times between ionisation probes located in the combustion chamber or the reciprocals of these travel times as a representation of the flame speeds, were studied statistically (29-31), (34), (35), Fig. (2-11). However, as the flame front in an engine travels at a varying rate, it was difficult to elucidate the phenomenon systematically when the effects of operating conditions are taken into account. Harrow and Orman (30) have derived the flame arrival frequency by expressing the number of flames reaching ionisation gaps, (located atIS-6mm and 65 mm from the spark plug gap), as a percentage of the number of cycles. Two criteria were ob Sri .1rt; u 0 -. OTT we/isd onra unsn" 00 Uyl CL .4 W k ;4 0 CH V) 1: 1 54 0 ;4 0 0 34 4-3 0 Cd > CH -r4 0 C) >w +1 0 Cd k to al 0 A 0 to 19 0 44 lb r-4 m0 00 k0 P, C14 N 1ý -Jý 3Q Q k) Arnsvibd do 3jyu )fy3d vru Owwm MCMLVZ -P 17. a 000 00 \% 0 0 8 C9 -8 v to C%l VISd '3unss3ucj 0 0 w . 2w le 0 Z og -o rd Co -i Mi D H Cd 4 4--l -ri 4-1 M 4-3 cr) cs 0 U -H EO -r4 0) cl .0 ;4 co 4-1 . (D ýd r-I Cd 0 C) 0) k >1 p :j P. to Cd f-I cs P4 - > -r-I cl El 4- ri) m Cc g C3 0 14-1 (D Cd 14 -ri 4-) 0) x 4 at +) Cd 0 C14 P4 0 -ri -ri 4-b 4-1 Cd ci m P, 9 0) d0 > -ri ul I 4H Erl I 0 a) 4A C4 1 0 14 1 a01 r4 . r4 +3 . - "90 9H 0 00 0 4-1 4J cd 4-2 $4 44 W 0 00 0 +) . 1-1 (n cd ;4 -H $-I cri :30 > 14 C) 1 C-4, bo wl N &-. II Ar IF 1 C) rv 01 %a V cl a)s 18. 4 p4 4-1 . 044 ri J-- in -0 ra . ei xt .X C). «I-" U X- CZ m b Li) . c. I- e Cm cz e 2 .0 .2 4- e. t- te L-l ILI In III III IIII LA Nt CV) C14 C14 9-In co d -cs 6 C5 cs L51 va " -iz 6 03 m 9 WO Ia:: CL 0- w E !!. E-0W -: 3 :1N EP Iq L0 r- #014 . -A a I-C vIww I : F- "JO-1 0'.. 0'. -a '>- E cx 4% %% - Co 1% 1 to < Ift. qw... m 0 9t 9-- 11 -- -t -- 1-t --- -t ei? 000 le NA mi C$ (i (i ci 0 NOJIZVU. i 03NUnü SSVN a CH 0 4-3 C) -H -rf 0 4-) ., q Cd tH to 0 0 CD cel 0 r., 4-3 ca 4-) C3 g -ri a) > 0) k0z cl 10 IH 04 P4 'd cl k -A CIS cl Cd 0 CD Cd ji 4- CH 0 >b 0 +) -ri -A 4-) V Cd 00 -r-I Cd ;4 L) >> C11 P4 $4 +3 IL4 0 0 r-4 bo (1) C: ;4 ci :3 U) . 14 (a CD 0 0 4-1 Cd to ul cri 9; 0 -4 > 0 0 4-1, -4 -ri cd Cd 4-) 4 0 4-) Cd k 0 cH 4-1 0 0 A 0) H Cd 0 0 .. 0 ýO -F4 P4 19. employed on the distribution curve to represent combustion characteristics. Firstly, the time interval between the instant of spark and the point at which 50% of the flames have arrived was taken to describe the mean flame travel time (tb) and secondly, the time interval be . tween the 10% and 9076 point on the flame arrival curves was taken as describing the extent of cyclic dispersion, Figs. (3-12) and (2-13). I Other characteristic times were employed by different investigators. Barton et al (10) have used the time between ignition and the instant of maximum pressure or maximum rate of pressure rise (9 Pmax and 0j, max ), while Annand et al (9) have used the time between ignition ftnd the attainment of three times the compression pressure as characteristiý time Fig. (2-14). Winsor (23) used the time between ignition and the cessation of combustion as a characteristic burn time, where the cessation of combustion was selected to be the time I at which curves for the rate of pressure change with and without ignition intersects Fig. (2-15). 2.3 The Effect of Engine Operating Variables on the Extent of Cyclic Variation. _ The engine cycle pressure variation is a direct consequence of variations in the progress of the combustion process and the rate of energy releasedby combustion. The various operating characteristics which were discussed in the literature as affecting cycle to cycle variation in combustion rate and pressure are: - i) Ignition. (Number of sources, timing, energy and duration). v 20. C) 0 . ci 0 CD rf 2 ei 0 qr . r4 V G4 Cd P. P-4 > cs 0 k0 4 V-4 0 CH CH 0 0 V4 9 r: 0 11 0 4-1 -r4 -H 0 +4 +j 0 -r4 0 ;4 p0 ul d cd cr) " P. 0 ul r4 0 ce) cq bo cs E-4 U) 0 -ri C) I 4-) !:: F cs 4-) ol 0 LO 0 LO 0 III to f4 I .N C H ;4 cs v iT c: $4 cs u 0 10 ri Cl) cd o r4 0 C3 U) U 0) 0 jpW0k P. 0 :j0d k r-I 0000 0 .2 4n 13 Ir. -W - 1ý luO3J3d 3WV'ZA cl, 21. TWINGMAArKS 10M. S. SPACING- PI S Tbi IGNITION T PEAK OF VALVE TRAV EL TIM SETWE iv " E OPENING ;; 5 cPR EVENT TRACE 3X GGCMPRESSION PRESSURE TRACEE PRESSUPE AISE w cc 00 D V) V) w: 2 AC cc CL Lu 20 CC 0 12 Z Of 0- ZW ->: EO. 4 ui C3 wO-2 V) Ic Ln CC L- 0 WEAK I RiC H MIX'sURF STPENGTH RELATIVt TO CHDACALLY CCR9EC-r Fig (2-14). Effect of mixture strength on Pressure rise timeý and its standard deviation (9). 22. cc 00 000 Co *4» '1*34\'MI 3W113 NV3W 30 OA 9 .0C: to r; 4-3 :3 oý% CL. D 91-1 CO t-. < 0 %-0 1? 0 C H LO 0 0) V -r4 E-4 0 A E-4 6 0-1% tf% CM 10 0 -ri 4.3 4-1 el) P CM 0 -r-I cd 4-) rn -H r-i Z 00 > ci $4 4- ýQ C11 r-I :3 IH U) (d CH 0 00 tn - V0 V4 -r4 14 4-31 cs Cd :3 14 0 . 0-1 ýQ Cd (D ý4 0 V, in %-o E-4. > C-3 bD -rf P, asTa oannsaad jo aivd 23. ii) Mixture preparation. iii) Exhaust gas dilution of the charge. iv) Compression ratio. I V) Throttling. vi) Temperature. (Initial charge and engine coolant). vii) Oil contamination of the charge. viii) Air/fuel ratio. ix) Fuel composition. X) Mass of the charge per cycle. xi) Turbulence and mixture motion as a function of: efigine speed, intake charge motion, and combustion chamber design. In almost all investigations, the engine variables affect significantly the extent of cyclic variatiDV. This is not unexpected, as changes in air/fuel ratio, compression ratio, speed and inlet configuration should alter the combustion process specifically, flame speed and the effect of turbulence on flame speed. The average flame speed and the variation of flame speed are considered to be the most important causes of combustion variAtion. Any operating condition which is not repeated from one cycle to another influences the progress of the combustion process and causes cyclic variation. This will increase the longer the time taken for the flame to traverse the chamber and hence the slower the flame propagation, the greater is the cyclic dispersion (56), Fig. (2-17). -i qx0 <0 Z 1 5E 0 ýD Q0 V) - i3 0 f^ (i - -, , 0 cc - el E Z w cc w -0 cm rx w- cr +wD ce 0w w > !Z w %0 $W q t14 00+x CL 04 NOISMSIG IDVLNi3V34 ft 1% U E Wt x 0% Q CH 0 r: 0 ýI 4J ci .Z _H > 4-b ,Z Co cq 4.0 ba r. 00 -ri $Z 03 _H 14 to 0 0 to k cu 0 > j2 ýH 0 CY) Z: 0-% *%-4 0 ýQ bfl . f-I çx4 24. 25. Harrow et al (29,30) have shoAn that the relative dispersion in the flame travel time is almost proportional to the propagation time, Fig. (2-17). Similar results are reported by Winsor (23). This is also supported by the observation of Annmdet al (9) that the standard deviation of the pressure rise time, (as defined earlier), which was taken as an indication of the rate of combustion, decreases as the rise time itself decreases, Fig. (2-18). 2.3.1 Ignition There are several factors in the ignition system which could alter the ensuing combustion process in the cylinder head. These are: - i) The timing of the spark in relation to-the Piston motion. - ---- a ii) The type of the spark. iii) The energy content of the spark iv) The igniter position. V) The number of ignition sources. vi) The spark plug gap projection. vii) The spark plug gap size. viii) The physical configurations of the sparIcing Plug electrodes. ix) The size of the spark electrode. Most earlier investigations (2,4,32) of the cyclic pressure variation problem have concluded that its extent under normal operating conditions appears to be independerlt of the characteristics of the spark ignition system aild imProves when more than one sparking plug is used Figs. (2-19) anq (2-2C)). I. - -'re'sidi lln"Iv ,. Jq -IN, -jjs)dj linlosiv k, 4 'I. r 26. x x %.. 00 00 0 -p tn r. Id 0 9.4 0 ,Z 0 cl, U -rl P4 I R v t z jg t: 0 1ý 21. a -Z -Z >C. % -j 3inKnow b. 0 fa 0 V4 -r4 0 tio 1-4 cl %. 0 .! 4 0 9-, +1 Cd Pk r4 U) Cd 0 +) r: v cu > to ,Z 0') r-i cq %. 0 27. However, some recent research studies (20,27) have shown that some improvement in the cyclic combustion variation could be obtained, especially with lean mixtures, by proper'design of the spark plug and ignition systems, Figs. (2-21 - 2-27). These modifications could be summarized in the following points: - i) Increasing the gap penetration into the combustion chamber reduces cyclic variation due to the increased heat release from the flame kernel before contact wili the cylinder walls, thereby reducing wall quenching Pig. (2-28). Moreover, this introduces favourable conditions for the flame kernel growth due to the increased temperature of the electrodes and consequently the reduction of their quenching effect on the kernel. ii) Increased gap size and spark duration increases the probability of igniting lean non-homo. geaeous mixture by exposing a larger volume of the mixture to the ignition source. It iii) Increased spark energy, may overcome the quenching effect of spark plug electrodes particularly for narrow gap widths or when the spark timing is so advanced that the mixture pressure and temperature are low. It is also required when the mixture velocity and turbulence levels are high Fig, (2-29). For the former case, -the heated volume is increased due to the mass motion during the spark discharge, thus the energy is distributed over a larger mixture volume. For the latter case, the rate of heat dissipation is increased by the higher turbulence intensities and the corresponding increase in the eddies diffusivity. EO-0- 0- C: ) Ln gi La Z c> -0 c (3 0Z F- CL < C) o-c 0--0-0-0 0 (D Co cm -x IINII NV31 r. X s4 28. p c: 0 n 9 4 4J gz V (n r: 0 .p ni r-f rý 0 ti $-4 0 to . Z 4.3 -% (L) 0 0 0 CH ýH N f4 LO cli C-1 cl, to _H p4 -00 (D I. 0kr. C%j 4-3 0 %. o 0 -ri F 1 (D 4-) 4-) V0 E - f0 q rCd cq Pý (D Cd r-f - b. 0 to (D rý g -H IS "4 tr) -0 -- --I ti) r. p Cý 0 >* $4 bo Cd $4 " cs 0 In 14 r ý - 0- - -- - (: ) " < t -- Cd Cd E--4 -4 01 , 0 LO -P $4 .0 0 IH IW 04 CD 00 CD -7 Fa pq %-. 0 C4 to :3 r-q E CL 2f 'r 2 - LU ct: . _: i ca Wt I ýA d, . 4. .0 (El J. NOUTIVIASCI Cia'"lalivIL"ll Mol. " -- C: ) [la 0 C). vi 0 0 04 0 29. -4 !4 4A P 0 > 00 cli -H 0> 4-3 V -0 a ca (1) 0 !. A 0 $4 k 0 04 . rf 4-) C3 cs to bo 0 E- 10 Ic cl _V He 0 rz . %j +i C) 0 ez C) CH t- 0-n CH cq 0 ri f4 %.., ei bl) %-0 C%l 1 N to . ti ,. Z p 0 cq 94 0 r= u -ri 0 $-, 4-1 0 E) -ri C. ) 4-) 0, () -Z P. :b P, cq tß 34 to 0 +i 44 4 %-. ,Z C13 to . rj P4 co Lo I EN 11 NV31 1; C! 14 wl le C3, n 0.5 qv co :1 ($01-10 WOUVIA313 CHWONVIS Xkiom w92 CD (SlInCil NOUVIA30 OtjVC&VLS - 11, joM 4. deý LE - I- ht. I c3 EI . d, f V, 4.4 CL b- .0, *, *Z %%% cs . 1% C. a a .-- cc -a a I- a' 0 -ri +1 Cq 0 %. o (D 0 U) 0 F3 -r4 120 44 C) (I cd - bo -H r4 U > r-i 0 C13 "-I > +3 ýd Cd ul Q4 LO 14 rd V P4 U) 0 0 v H P-4 Cd 0 Cd ri Cd CH 0 4-1 0 Ad 0 $4 CH 0 Cd 44 04 1 04 %.. 0 bo -r-I Ik4 30. 0 ul -H . jj, ul 0 Cd 0 L. 0 :3 0 P4 0a cs > $4 t-I -0 Cd -ri Cd P4 ul U) (D ,a Cd 0 14 o Cl) 0 (1) LO V r-4 Q 0V Id r. ýq Cd +1 C: t- 0 o) cli ., j . 4-) CH C: $4 0 00 :% -1 .0 4-) 0 as 0 0 -ri 0 k0 Cd 0 cd CII P4 k > %-., U) P4 (slinorl Noumia ouvo%-. is uuom cli 1 A 31. lie us CZ 64- -A P. - I-- ILJ C2 96 cc -K 46 die C2 cr C, z C3 % 0 . r4 +3 a cl P4 0 p P4 CH 0 0 r: 0 .H 41 0 %4 0 4-3 CH IH co c1l, bo -H P4 0 vs 0 (n Qo C S 4A Cd 4-3 Cd &4 0 > :3 . a) qJ a *ý) Cd 0 p P4 14 ca U) c Cd ca CA: W :1 (D r-f a Ei o-4 0 14 r-I Cd r. Cd r. P. oo - P. -, -1 $4 os 4-3 -P to 0 cs 0 o 0 cs > P4 Its cli cl, MUM I P4 32. 2.3.2 Mixture Preparation Satisfactory combustion in a S. I. engine requires a proper mixing of fuel and air. Therefore, variations in the uniformity of the mixture could lead to corresponding combustion variation. Soltau (4) noted that a premixed charge obtained with a gaseous fuel such as butane or methane does not show less peak pressure fluctuations than a liquid fuel mixture which is either carburetted or sprayed in the manifold; but if the fuel is injected directly into the combustion chamber the, stabili-ty of the cycle worsens. However, the latter situation could be improved by placing the injector near to the inlet valve (60). In fact, the fuel and air mixing process depends more on air turbulence than on the actual time interval during the cycle, and at high speed, although the available time is reduced, the increased turbulence gives much improvedlmixing. Hansel (13) has reported a reduction in cyclic variation when propane was used rather than gasolinje under the same test conditions and attributed such effect to the perfect mixing of propane and air. The values of (A'-%P/P) max was reduced from 0.34 to 0.23 for the two cases respectively. The effect of fuel composition on this experiment is also included in this reduction. Patterson (2) has found that improved mixing decreases cyclic variation slightly. It also increases the average burning rate with lean mixtures, Fig. (2-30). He noticed that cylinder-to- cylinder pressure rate differences are strongly related to fuel distribution. However, the large rate differences remaining when 6- hh- 0 _____ _____ I'. _____ _____ _____ _____ ____ ___ ___ ___ ___ ___ I.. _; _ ___ -4-\__ _"-Ij4 o_ ___ __ Jt. r __- - -.. ) I / $ to- ____ ._ ___ - ---- -- ___ co 4b, I CCl'4 4* M33134 NOILY'. IYA 31VV UnSS334 I . IH5131A AS V/j 4M 'n Lp 40 \-. - -i ý 21 ,0 z- 0 Z91 0 !6 d OC 0.1 CL. in :R r% In 01117s 3ýNT%vmnoi U) 33. x0 P. 4 -p p4 C) .H -1-, 9 0 >0 to cu > V cu 0 to 0 C) Ei x x CH 0 0 P. r-4 CH 0 «H ý4 4-b cq . rf p4 :ß ti X %.,. - > S-4 b- U) -ri ,Z m cq 34. fuel distribution and preparation are carefully controlled, led him to conclude that the other factors such as differences in mixture motion between the cylinders are equally important, Fig. (2-31). Barton et al (10) have noticed that any improvement in air/fuel mixture uniformity obtained by using a mixing tank instead of a direct induction method was completely masked by a very large change in flame speed variation, and, although the average flame speed increased, the f lame speed variations also increased by almost 3: 1. This contradicts the notion that increases in average flame speed reduces the variations in flame speed. They attributed such contradiction to large differences in the intake process between the two systems. These differences must affect substantially the variations in mixture motion which is thought to be the primary cause of combustion variation. 2.3.3 Exhaust Gas Dilution of the Charge 1- The effect of exhaust gas dilution on cyclic dispersion was studied by purging the cylinder o-f residualsbetween firing cycles. Firing the engine every second on' every fourth cycle, the cycles in between scavenge the exhaust residuals. As the exhaust gas dilution decreases as the square of the number of cycles which do not fire, three idle cycles are sufficient to obtain a nearly perfect fresh gas charge. Tests carried out by Soltau (4) and Patterson (2) have indicated that when the engine is fully scavenged, combustion is much more rapid, but still not similar from cycle to cycle, pigs. (2-32), (2-33). Also, no effect was found when the engine back pressure was raised to increase the exhaust gas residual. 0 C C V a S 2 p. 32 ar20A. 292v a 5 g 'a I I- C I a a a a 'Otivv wwwv 0 o 35. 0 000 . -s -r4 (1) 0 4J a) H Cd H CTS 0k ii :3> 4J ýu P-4 a -ri CD ;q CH 4J cn (1) Cd 0 cli r-I PC 4-) 0 .. 0 U) > cl :1 -A Cd P-4 5 (L) CH tf) 0. a IJ 00, r. -H k ca 44 +ý o Cs -0 0 -ri 0 ýq k0 +31 CH cs 04 cd FA ;>-k C*4 Cl) cl bo -rf P4 r_ 0 00 .H 0 0 4J v-0 %. 10 -ri 10 to 0 r. 9: >00 0 -ri k -P CO P4 ;j1 j2 > ri p rl 4-3 -ri 0 0) . ri (D r-f (» CH E) Co cl-j :im %-f bo -ri P4 i i i , - I - 'Ooqnu 1174 tomiNd ;4 U 1 36 0 +j . cl 1 :4 .00 ul -H ci U) U) El rj 0 cd C) r4 P-4 !44 r-i cs 4J 4- cis 4- ýi th > (D 0 0 r-4 .0 +-) +1 4-3 44 ýd 0 0 Z ýo 4-) 0) ýa ca r-4 >0 0 V-4 0.0 L4 r-I W --p to 0 U rj C) -, R 5 000 +) Cd (D u -rq 4 4-) Cd Cd W dc >0 4-) C9 CH r: 0 to w 0 Z tL LO a) (1) u 0 0 0 r. 0 4.0% Cd :3 r-f -1: %m N 10 a) a 0 Lo 9: V) C4 z C -c (D -ri H 4 ps > -ri 0 4b 14 W0 0 u rd z 0 4-) LO r. -0a, in Cd k 0-0 Cd ri cl P cq 0 +) 0) 4 44 cr) C-1 a P4 u ul LAI I, Sh o0000 0 . cr) I uluou: d/ (UTUI xv ra Cq cl- d) (D 2 : . 10 : 0, r 2ai r - .r rk pq 0 4-) Cd N r. 0 l cq ý :s %-, 4J U) Cd Cd -ri to k 4-) > 2 Cd -H 0 ILI 4-3 Wica go im34u %MA3 oo »emwd ýli cq to 37. On the other hand, Karim (32) had carried out some tests whore addition of CO 2 or N2 to the engine air supply was made over a wide range of operating conditions. Ile found that increasing the concentration of the dilutents in the charge increases the maximum pressure variations and that CO 2 is relatively more effective in that respect than N2. These changes can be seen from Fig. (2-34) and are relatively small. Karim (32) also concluded that the probable kinetic role of some active species in the residuals, depending on their nature and concentrations, can, however, play an important role in 'seeding' the charge and influencing the combustion process. Hansel (13) carried out some experiments with propane as fuel (to eliminate any effect of non-uniform mixing between the fuel and air). The engine cylinder was purged of residual gas , -4 by interrupting the spark for 200 engine revolutions. The data was compared with another test at higher-*engine speed which has the same value of initial peak pressure under normal running. He reported a reduction in the cyclic variation measured by (P -p Vp from 0.23 under normal conditions to 0.1 for max min mean the purged case. 2.3.4 Compression Ratio The average flame speed increases by increasing the compression ratio and consequently the differences in peak pressure diminish, but the trend is very small and increases slightly as the air/fuel ratio changes from maximum power setting to weaker mixtures (4), (10). The steadier influence of the high compression ratio is thought to be due to the improved scavenging (and hence the - 38. 45 40 35 w u C4 LU a: -., 3 0 > 2 Cl UJ Ln w cc 5 cr 10 w CL 0 T $ I I I I I I *% CR 70 R15M'=9001 P . 9'. '10) C -R npm=, )()C)l S(p p r4. clx)lmax cR= 10: 1 RPM =2 00 01 4*c S(PMGX) 14p--mcx CR=9 I / RPM=1.200 13 **D .--- 10 Fig (2-35). 12 14' 16 is 2o AIR-FUEL RATIO Bifect of compression ratio on cyclic variations. . '2 2 30 2B 26 24 22 Gp - 20 IS 16 14- 12 39. smaller exhaust gras dilution) and to the higher gas temperature which promotes a more rapid flame propagation. rate,. Fig. (2-35). Barton et, al (10) showed that at 7: 1 compression ratio decreasing the air fuel ratio (17.73 - 14.5) decreased the variation in the maximum pressure, while at 9: 1 the variations increase slightly and at 10.5: 1 the variations in maximum pressure were greatly increased. The overall effect is that increasing compression ratio increases the combustion variations. The reasons for this were attributed to the combustion phasing and also the fact that flame speed variations are, increased when the flame speed increases. The latter effect could be attributed to density and temperature changes produced by increasing the I compression ratio which in turn augment the effect of phenomenon like 'flame generated turbulence'. Tests carried out by Curry (37) at maximum power air/fuel . 1. ratio, constant engine speed and spark timing corresponding to maximum brake torque (MBT), indicated a slight improvement in the cyclic variations for increases in the compression ratio from 8 to 10: 1 and results in a more repeatable initial phase of combustion Fig. (2-36) while slight adverse effects could be shown from Fig. (2-37) when increasing the compression ratio from 16 to 20. 2.3.5 Throttling Throttling the charge will affect both the extent of pressure variations and the maximum pressure value, and hence will increase the variations Fig. (2-38). This is to be expected as the effect of increased dilutents and the-reducedlak4rtlivIg rate 40. I. ' 1*1 dCZ OJ tti 0 %-4 K.. o w e cli S33H930 VD't>lk! VdS *WOUA 3W1-t D2 10 CO 'n W m er-. 0 0 X -9- 0 w Z U) 0 to vi CL rt- cj 0 n* cr- U. N 0. z 6ý, o ý- 0 C3 c fr- o o 4LL-,,: < Cti CL 0 0 0 1 1 4-. 0 (I, ll 0 U. (1) LU C-, 2: e*% 00 S33U! D. (] VO YUVdS W. 0 UJ 3NI. I. I 00 v -H 4J cl (3 14 k -H O-N M t- Ef) V) 0 P. 4-3 0 cq - r-4 tO cq A Lr) 0 r-4 N +1 4i +3 -ri 14 ca El C's ý4 -r4 P. 0 ul 0 0 P r4 0 0 r-i 01 14 a Cd P4 0 ;4 to r-4 ý4 Cd 4-3 0 ri cl Cd CY) + cs 41 >0 0 c! ) 0 Cd P f-4 4J :3 0 >% o V0 I El 0 V4 4-3' 00 C. ) P4 0 ,Z CD cl, %.. o t; ., 4 P-4 41. in ir 0 Z w x CL 2 0 0 CL cq tr w fI. II jo 000 Iq Cld S338930 VO')iUVdS WO8zJ 3WIl - c-i : gil 1 0 :2 D-- r-. . Z c6 cr IS) 5: 1 C4 C'-- 0 fe tu S33H030 VO 4 )IH'VdS KIOU-A 3W1. L r-f Cd I ba IN, 0 4-) E-4 Cd 4-1 0 0 + CH H CH -rl cd CD Cl) 44 0 0 4-) 0 ts 4-3 Ul 0 4J .0 bo to 4J 00 a) 0 :j 10 P. 0 P4 :j (D 4-) Ef) Cd Cd 4-) >* A. 0H 4J H 'I -H ý; +, P 0 Cq r: Cd Cd -H f-I 14 0 cl 0 Cd -H 0 > 44 0 0 ;4 4-) a) 0 0 tz u ;4 0) 4-3 0 +3 to 4. ) Cd H I r-q 0 0 1 ci r-4 r: 0 -H (D I (1) Cd H > Cd 13 4-) :j cd 0 0 0 !d 0 ;4 0 P Cd 0 Ph " 0 4-3 0 cd 0 ;4 $4 0 $4 al -H 0) fA 0 U) 0 M k C: 0 a P4 0N 4-3 El r4 r-I 0 4-3 03 1 k 'rl :3 .0 1.4 Id 4J ho Cd a) m > (1) 0 > cl > t- bo 0 4-) 00 * -: 4 J. - q) 0 ,Z t- 42. will be the dominant factors, while a faster flame speed and reduced effects of dilutents contribute to the marked improvement in the cyclic variation observed with an increase in throttle opening. Peters and Borman (33) have shown that low load cycles have burning rates that were slower than the full load cycles Fig. (2-39) and consequently greater cyclic variations. They have attributed this to the presence of increased residual fraction left from the previous cycle and to reduced mixture motion in the combustion chamber because of the lower flow rates at low loads. 2.3.6 Cylinder Water Jacket Temperature and Oil Contamination of the Charge Soltau (4) has concluded that the lubricating oil in the combustion chamber and the heat effect of the cylinder head walls I do not contribute too much to the problem. However, Karim (32) has reported some reduction in the extent of cyclic dispersion when the cylinder water jacket temperature was increased. 2.3.7 Air/Fuel Ratio Soltau (4) reported a very great influence of the air/fuel ratio on the cycle-to-cycle variations. The most stable combustion occurs with air/fuel ratio in the region of 13: 1, which in fact corresponded to the region of maximum flame speed as reported by Taylor's work at M. I. T. It is lower than this value for low compression ratios and higher for higher ratios (taking a mean value of around 9: 1). As the air/fuel ratio range is traversed and 43. 0 to ci Co 0M tLi w 0 1 C%i 'er 0 3: ci cu Nn G2 Co 1 0 k ei 1 0 Lai (D e > to 1 00 Z - ri 4J 81 Ne%, Nlb < 0X 0 Cd % %.. b, ". 4,4 . qb 0% *-. ý zý --. . c3 Z to 'KZ 9-4 q4 bo r: cc li 0 toa 42 94 ul 4-f ul CH Jt c2 NOI-LZ%Ikfi 03Nune ssvw to . f. i 4-3 CH tH M V-4 0 4-) 0 cc 9 44 Q C%J ;4 i 4.3 -r P 91 o Cd >0 0 ký q-4 :3 ui 0 CII 2 C') ho El 0U ca in GO 4-) 14 4-) > a) 0) > U) Cd 00 $4 r-I :3 U) to 0 Eý4 4J N+ Lo +M ra co a 6T 660 a 6 1ý 1 co 1 C 4 ba P4 44. as the mixture becomes either richer or weaker, the deviation of peak pressure and i. m. e. p. from the mean increases, Fig. (2-9). It is mainly this phenomenon which prohibits the use of very weak mixtures. Near the limit of burnability, there is no sharp dividing line where it could be said that the mixture on one side burned and on the other did not burn. There is a very wide band where decreasingly efficient combustion can be maintained, as every cycle has a different burnable limit. Peters and Borman (33) have reported small effects of the air/fuel ratio in the range of between 19.2-and 14.1 with isobutylene as fuel on the mass burning rates with the stoichiometric mixture having higher burning rates rather than rich or lean mixtures, Fig. (2-40). The data of Miller, Uyehara and Mayers (38) using iso-octane as fuel show the same trends as the data of Peters and Borman Fig. (2-40), i. e. combustion with stoichiometric mi-ytures burn faster than rich or lean mixtures. However, they show a large influence of air/fuel ratio on mass burning rates Fig. (2-41). This discrepancy was 10 attributed to the variation of fuel type between the two tests. Harrow et al (29) have found that at any given engine speed the mean flame travel time reached a shallow minimum at approximately 12: 1 air/fuel ratio. On the rich side of the minimum, the mean time increases slowly to that corresponding to the richest mixture examined (about 9: 1 air/fuel ratio), while on the weak side of the minimum the flame travel time increased quite rapidly, until at the weak mixture limit some of the flames failed to reach the ionisation gap. Fig. (2-42) shows the mean flame travel time for benzene, iso- 0 IJ n3 ýE CL C) Iz I CC 0 (IC CL 4") 00a00 C3 000 a CU - (13u'url. q ssVI'll, 0 c'J a (2 us 0 to 0 tj %all) if 00 ,A tti 00 't 00 al Z 0< Aj cc 0 0 0- 45. 0) 14 . 1-i Cd CH 0 9.1 0 .H CH 10 42 vi vi Cd Ei 0Z W OD ci r2 +D %-0 00 C. ) ri ,Z r-i 0 NI qr 0 CH z P-4 to c- C*4 to lq- &0 w to 0w r: cs (D CC - C%l m cd w Cd ho 0 Ln C%J 04 LL 0) 0 cm K) d 0 W 0 J :3 cr) ;; r - V) ul cr) 0 0 0 4 14 0 %_0 z 0) <- > Cd 0 14 Cd - CO 7- 0p -ri k bo -, cs ul 4J 04 1 VA . 14 C) ce to CH 0 00 1 LO 0 ri H 41 0 i x 9 >b 4. b 4-4 cq +ä %. w cq fj ri 91 +b 1 lö 0 pkr. 0 t, 1 0 Xc Cd -ri 0 t- > 13 0- (13 cf) N bo -rl (D bio >1 4-1 :s .0 +3 0 ul Cd .a (n C13 -7i -Z--- - -P . 0 E-4 0 Ii ? 19 -. Im 0 .. *I \x IM r-I 4-) 44 > cq 0 (D 4-3 A Cý 0 LO 0 >1 0 Cd 0 ,a CH 00 Cd 10 to 0 r. E- :;: ý cl %-, Cd cli %-0 to 47. octane and di-isobutylene at various air fuel ratios and for engine speeds of 750 and 2500 r. p. m. The corresponding extents of cyclic variations for the same range of experimental results are shown in Fig. (2-43). The same trends were shown by Mori and Yamazaki (34) for the mean flame velocity and its standard deviation for iso-octane, reformed naphta and cracked naphta as fuels at 900 r. p. m. and 6: 1 compression ratio Fig. (ý-11). Barton et al (10) have conducted their tests with air/fuel ratios in the range of 17.73 to 13.5: 1 which are not rich enough to cause the flame speed to pass through its maximum value. Therefore, they have reported an increase in the flame speed as the air/fuel ratio was decreased which agreed with the previously mentioned data reported by Harrow et al, Fig. (2-35). The maximum pressure variation also decreased with decreased air fuel ratio in this investigation and the deviation of flame speed, (as measured by the angle of occurrence of maximum pressure Opmax) . 1. also decreased as the average flame speed increased. Thus increasing flame speed in their tests by decreasing the air/fuel ratio did not increase the deviations in flame speed but rather lowered these deviations. Again these results are in agreement with Harrow's (29) and Patterson's. (2) tests where faster burning fuels were used to increase the flame speed and reduce cyclic variation. Hansel (13) attempted to explain the general trend of cyclic variation to increase on both sides of the stoichiometric; mixture Fig. (ý2-44) by developing a semi-quantitative turbulent model based on the assumption of proportionality between variations 48. in mass burning rate (or peak pressures) and turbulent flame speed and consequently the effect of turbulence on flame speed. Assuming the effect of turbulence as an additional term to the laminar flame speed the following relation was obtained: 4--p rv uI p SL +u min Further assumptions that maximum variations in the turbulence intensity is invariant over the speed range of his tests (1180 - 2150 r. p. m. ) and that ýU' min -5: ý St led to-the foliowing relations: , ýýp "I p or (2-2) h, p tv A/F (for lean mixtures) P-3) p and AP rv 1/(A/F) (for rich mixtures) (2-4) p However, such a model predicted only 407o of the observed variations in (AP/P2 for lean mixtures and over-estimated Such aK variations for rich mixtures (by about 1507o in the reported example). In fact these discrepancies between the predictions of the model and experimental results are not unexpected in view of the severe assumptions used in developing the model. For example, ,, Or * I NOIIYIA3(3 CVVCINVIS I. LU z z t= C3,1 49. 0 . ri 1 4-3 .0 4j rý . X ti - > -f -1 0 0 !40 -ri ;4P. 4-3 0U (n 0 C) E-1 0 10 f-4 10 cý -4 11 U) .Z gz ý0 H r. 0 14 0 ri rz4 00 c: C. ) 0 ul p4 rZ %-0 Q -H ,Z cq %-11 to . rj r14 ca C2 C3 C3 I F- 0 Ln -W co r- EEE ... 4D . eq Ln 'a -' --I ý -i ir olul3nolHolois 4n ýi --" CO IT - 1. 'le 'lý ei 41 ri N c; C> CD c2 0 (3 d/dV '3>1nSS3gd 113(INIIA: ) XV3d Ni NOIIVIUVA VgliýIxya ui r. 0 . rj 4-) Cd -H 14 Cd 0 4 0 0. . rq cd ILI 0 -ri k. Cd Pý 4-1 ;q 00 r4 >3 CH 0 -ri 0 -, 4 1ý IQ, qQ14 cli %.. d La . r4 44 50. the assumption of a fixed variation in turbulence intensities irrespective of engine speed is not true, as will be seen from the discussion of the anemometer results of Matsuoka et al (15) section (2-4), as well as the results of the present investigation. Moreover, expressing the turbulent flame speed as the sum of the fluctuating velocity component and the laminar flame speed is only justified for the conditions of very weak turbulence, as will be discussed in section (2-5). Obviously such conditions never exist inside the combustion chamber of a S. I. engine, especially during the latter part of the. compression stroke. 2.3.8 Type of Fuel There is some connection between the type of fuel and cyclic variations in peak pressure and indicated'-m-ean effective pressure. The fuels with more rapid average combustion speed are less prone to produce cyclic variation. This is because less time is spent in burning phase and more on expansion phase. All hydrocarbon fuels exhibit the same kind of fluctuations, although their severity changes slightly with the chemical composition. Fuels which are rich in hydrogen exhibit very little variation as both their diffusion and flame speed are extremely rapid. Table (2-1) gives a comparison between flame speeds of some hydrocarbon flames. Harrow et al (29) have examined the effect of the type of fuel on cyclic dispersion in terms of the flame travel times for a fixed path across the combustion chamber. Using three types of fuels of different flame speeds, namely: iso-octane, di-isobutylene 51. and benzene, they have found that at each mixture strength iso-octane burned appreciably more slowly than th6 others. The extent of cyclic variations in flame travel times were larger for iso-octane than for either di-isobutylene or benzene, Fig. (2-43). The extent of dispersion depended markedly on mixture strength. Minimum dispersion was reached at about 12: 1 air/fuel ratio with all three fuels. The greatest dispersion occurred at weak mixtures. Advancing the spark timing reduced the extent of cyclic dispersion and reduced the differences between fuels. Tests carried out by Vichnivesky (6) ona CFR engine is in agreement with the previous conclusions, Fig. (2-45). Karim (32) carried out some experiments using a range of commercial petrols, which indicated that differences in the extent of cyclic dispersion from one fppl to another were very I small and being within the experimental error in determining 0 the values of maximum pressure deviation. Thus among the commercial petrols available, there is nothing to choose between-one and the other, and the choice will remain purely economic. 52. Table (2-1) Burning Velocities of some Hydrocarbon Flames (70) Compound Formula Burning Velocity (cm/sec) Ale thane (CH 4) 33.8 Ethane (C 2H 6) 40.1 Propane (C 3H8) 39.0 Butane (C4 11 10 37.9 Ethylene (C 2H4) 68.3 Benzene (C 6H6) 40.7- Acetylene (C 2H2) 131.0 Ileptane (C 7H 16 ) 38.6 Hexane (C 6H 14 ) 38.5 2-Alethylpentane (C H 18 ) 36.8 8 3-hiethylpentane (C 8H 18 ) 36.7 2,3-Dimethylpentane (C81118) 36.5 2.4-Dimethylpentane (C 8H 18 35.7 I-Pentene - (C 5H 12 42.6 2.3.9 General Characteristics of Cyclic Variation Summing up the conclusions of previous investigators, one could outline the general characteristics of cyclic variation as follows: i) Cyclic variations do not depend on events of any other cycle, but mainly on the intake, compression and combustion of each individual cycle. However, it-can be seen from typical cylic pressure records taken when large 53. cyclic variations are exhibited that a cycle with a very low maximum pressure will be generally followed by a few cycles with relatively low maximum pressure before the apparently true randomness of the'records is restored. ii) The dispersion is not due to variations in the spark timing or the type of spark. It improves slightly by using more than one spark plug, or modifying the ignition system so as to decrease the quenching of the flame kernel or increasing the energy given to the mixture 61 when spark timing is advanced. iii) Cyclic dispersion in combustion process occurs even with gaseous fuels and still persists when the quantity of fuel/air mixture delivered to the engine cylinder is the same on each cycle. iv) The extent of cyclic dispersion is less for fast burning I fuel such as benzene than for a slow burning fuel such as iso-octane. Factors which tend to increase the rate of flame travel in an engine, e. g. enriching the mixture to best power mixture ratios, reducing exhaust residual, installing shroud valves, and multiple ignition of the charge, tend also to reduce the extent of dispersion. Factors which slow down the flame in the engine tend to increase the dispersion. V) The variations of peak pressure, burning time and rates of pressure rise from cycle to cycle becomes greater as the mixture is made leaner, since mixture velocity has a great effect on the ignition and combustion characteristics of lean mixtures. 54. CYCLIC VARIATION IN PRESSURE DEVELOPMENT CYCLIC VARIA TION IN COMBUSTION PROCESS [TURBULENT FLAME SPEED IGNITION TURBULENCE .II MIXTURE H INTENS ITY , SCAIX PREPAPATION AIR/FUEL -RATIO TYPE OF FUEL I NLE T EXHAUST GAS RESIDUALS VALVES I NTAKE GEOMETRY MIXING MIXING AMOUNT a) LIFT PASSAGE OF ENGINE or or RESIDUALS OF b) SHAPE SHAPE COMBUSTION FRESH WITH RESIDUALS c) SHROUDS SPEED FRESH or CHA11BER CHARGE CHAR(; E VANES THROTTLING I COMPRESSION RATIO FIGURE (2-46) Relationship between engine operating variables which affect the mechanism of cyclic combustion variation in spark ignition engines. 55. vi) For rapid combustion and minimum heat loss, it is desired to have a high swirl velocity, especially at very lean mixture ratios. vii) For minimum variations in rates of. pressure rise, peak pressures and burning times, it is desired to minimise the variation in gas velocity or, if this cannot be done, to use the highest nominal swirl velocity and, avoid very lean mixtures, since variation in gas velocity and turbulence in the vicinity of the spark plut at the time of ignition appears to be the main cause of combustion variation. Fig. (2-46) shows the relationship between engine operating variables which affect the mechanism of cyclic combustion variation in S. I. engines. 2.4 Effect of Gas Velocities and Turbulence on the Combustion t. Process in S. I. Engines Investigations of the flow field inside the combustion chambers of S. I. engines are very limited in the literature and most of them have concentrated on mean gas velocity measurements. The study of the structure of the turbulent flow field, in terms-of intensities and scales, has received little attention, in spite of the fact that such ', knowledge is very fundamental for combustion studies in engines. This may be attributed to the difficulties in applying the conventional techniques used in the field of aerodynamics to the transient processes occurring during engine cycles. A review of the most important studies in this field will be discussed in this section. Lee (18) has studied the air movements in an experimental engine, which was basically a5 by 7 inch single cylinder engine with a glass cylinder and cylinder head to permit photography, Fig. (2-47%n) Different types of air flow were produced in motored tests by using shrouded intake valves and by altering the shape of the intake port in the cylinder head. The air motion was studied by use of high speed photography of feathers introduced into the main air stream which showed the following: i) For a plain intake valve air movements created in the engine cylinder during the intake stroke continued throughout the compression stroke at a slowly reducing velocity. By the time the piston had descended far enough on the expansion stroke mopt of the turbulence died out. During the last two strokes of the cycle, the air movements were mostly due to expansion and expulsion of the air by the piston. ii) The velocities of induced air currents were approximately proportional to the engine speed and about inversely proportional to the flow area at the intake valve. They were about the same whether the air flow was orderly or turbulent. 0 57. ci ý2- 4J 0 4J C: 0 0. (1) to Cd 4-3 %: 4 Ic co 0 :s to 0 r-i U) CH : -o- Ul 0 U) 4-3 0 -ri C) cd to CH " qT 0 %-4 0-% . o 8 l o " (\j "Jiv 0 Co to . ri P4 94 0 .0 Co r- 0 0 to ta 0 -p 0 rý ; -f 01 ce t- C-1 t3 / tZ .9 58. iii) The use of shrouded intake valves set to direct the incoming air tangentially caused the air to rotate rapidly about the cylinder axis. The maximum rate of rotation was reached at about 1100 crank angle after the beginning of the intake stroke and the rotation continued until the end of the exhaust stroke, Fig. (2-47b). iv) The use of a single plain intake valve with its manifold shaped to direct the incoming air tangentially resulted in a rotation of air accompanied by considerable turbulence and some vertical movements. In fact, apart from the inaccurate qualitative description of turbulence, particularly during the expansion stroke, (as will be discussed later), most of the conclusions of this very early investigation (1939) regarding the general flow pattern inside the engine, have been confirmed by the recent anemometer measurements of Winsor (23), James (24), as well as the present s tudy. Rothrock and Spencer (16) have studied the combustion process and its cyclic variation using the same engine and valve arrangements of Lee. The engine was fired only once by injecting and igniting a single charge of fuel. Table (2-2) lists the test conditions of these experiments. The burning times were determined from the high speed photographs of the combustion process while the cyclic reproducibility were examined from the pressure diagrams.. Table (2-3) gives a comparison between the burning times for different valve arrangements. The main conclusions of this study could be summarized in the following: 59. i) Excellent cyclic reproducibility was obtained by directing the air so that the swirl moved past the spark plug and was in a plane normal to the axis of the cylinder. ii) Doubling of the engine speed without increasing the linear velocity of the inlet-air caused an increase in the rate of combustion of the same magnitude as that caused by doubling the inlet-air velocity without increasing the engine speed, Table When the valves were shrouded so that the inlet-air velocity was doubled and were set to cause a directed air swirl,. the rate of burning was increased. iv) When the valves were shrouded so that the inlet-air velocity was doubled but were set so that there was no directed swirl, the rate of burning was not necessarily increased. It Examination of these conclusions reveals the importance of mixture motion and turbulence, especially the small scale eddies, in increasing the flame speed. The increased burning rate Cý accompanying an increase in engine speed is caused equally by increased turbulence intensities (higher intake velocities) and by decreased time-intervals. The latter factor reduces the effect of turbulence damping by yiscous action and results in hkgher turbulence intensities at the time of ignition. Moreover, the persistance of a directed mixture motion inside the cylinder for longer periods (in terms of crank angle degrees) on the compression stroke enhances the process of generating small eddies by friction forces on the cylinder head walls, together with the increased 60. Table (2-2) Test Conditions for the Investigation'of Rothrock and Spencer (16) Compression ratio Engine coolant temperature Fuel Air/fuel ratio SparR advance Fuel injection start 7 250OF C. F. R. S-1 reforence fuel - octane munber (100) without the addition of tetraethyl lead 90/100 iso-octane. 14: 1* 300 WIDC (± 10) 200 ATDC on intake stroke . 1. / IF Table (2-3) Comparison batween Burning Times for Different Valve Arrangements and Altered Inlet Passage Case Burning Time (Crank Angle deg) Burning Time (see) Plain valve 35 0.0117 H 32 0.01OG7 1 31.5 0.0105 E 29.5 .. 0.00983 D 29 0.00967. G 27.5 0.00917 A 27.5 0.00917 F 28.5 0.0095 Altered Inlet Passag 28.0 0.0095 . 00- G (D'. (D. 0 op 61. (6F F Table (2-4) Variation of Burning Times with Inlet-Air Velocity and Engine Speed Engine Speed Ntunber of Valves Burning Time (Crank Angle deg) Burning Time (sdc) 500 2 35 0.0117 500 1 25. 0.0083 1000 2 35- 0.0058 1000 1 25 0.0042 62. homogeneity of the mixture. This explanation is supported by the results of the present study, (as will be discussed later in detail) where comparison of the power spectral d6nsity curves for turbulence at any particular crank angle during the compression stroke shows an increase in the percentage of kinetic energy of small scale turbulent eddies at higher engine speeds. Similar arguments could be applied to the case of increased inlet-air velocities by shrouding the inlet valves or proper directing of inlet ports. Wenger (1939) (21) has conducted the first attempt of investigating gas motion inside the combustion chamber of a motored single cylinder engine, using hot wire anemometry. Fig. (2-48) shows the shape of combustion chamber and piston head used and the location of the measuring probe -A constant current anemometer system was used. The hot wiýe was made of tungsten material with 15 P in diameter and a length between 19 and 21 mm. Measurements were carried out at different points in the cylinder. Their distance from the cylinder wall was 20,40, 60,80,100 and 120 mm. Engine speed wasIvaried between 500 and 1800 r. p. m. at compression ratios of 4.8 and 5.2: 1 and different throttle openings. The main conclusions of this study could be summarised as follows: i) Gas velocities attain their maximum value during induction period and decay on the compression stroke. Further peaks occur during expansion and exhaust strokes. ii) Measurements at different points have shown practically the same range of scatter so that it was impossible to detect any functional relation between the behaviour of gas velocities and the distance from the wall, Fig. (2-49). 63. Fig (2-48) Installation of measuring probe in. the combustion chamber (21) 1 %% 4-) 0 Tnearl pis't neede crank Suct n compression e ansion exha st , les anr exhaust valve inlet valve exhaust valve inlet valve closure Closqre opening opening Fig (2-49) Air velocities versus crank angles for the six measuring points in Wenger's investigation (21). (500 RPM3, CR 4.8: 1) - Point 4 ......... Point 2 , ----Points : L, 3.., 5,6,. 64. Air velocities averaged over the whole chamber length increase with an increase in engine speed. However, this increase always remains below the increase in mean piston velocity. Gas velocities increase also with opening the throttle. The same trends were observed for gas velocities averaged over the whole cycle. With the exception of the general trends of variations in gas velocities during different strokes of the cycle with engine speed and throttle opening, the characteristics of the turbulent field inside the combustion chamber have not been. investiRated at all in this work. Moreover, the conclusion of random variation of gas velocities at different points in the combustion chamber has been proved by Semenov (22) and Molchanov (62). to be incorrect. In the latter two investigations, large velocitv_gvadients have been observed between neighbouring points in the combustion chamber and are believed to be the main source oft turbulence generation during the induction period. Nevertheless, this earlier work (1939), has ascertained (at that time) the suitability of hot wire anemometry for investigating the characteristics of flow fields inside engine cylinders where rapid variations of pressure and temperature take place. Molchanov (1953) (62) measured gas velocities and turbulent fluctuations in a cylindrical combustion chamber with a flat PistOri head, using a hot wire anemometer. The measuring sensor was a tull9sten wire of 19 P in diameter and 4.5 mm in length. The anemometer bridge used had a frequency response up to 2000 cycle/see. Measurelaents 65. were carried out at different locations in the combustion chamber as well as different orientations of the hot wire probe, which was introduced radially across a displacer ring at the top of the combustion chamber, Fig. (2-50). The compression ratio was varied during these measurements in a wide range (6 - 12: 1) at a constant engine speed of 900 r. p. m. and full throttle opening. The results of this investigation could be summarized as follows: The gas velocities increase rapidly at inlet valve opening and is followed by a continuous decay until inlet valve closure when it becomes approximately equal to piston speed at that moment, Fig. (2-51). Periodic oscillations were noticed during the decay period at all. the points of measurement which have been explained later by Sokolik (48) as causedby oscillations in the inlet pipe. The measurements showed that the flow field during induction does not have a contintious-distribution of velocities throughout the cylinder. During the compression stroke, a conceptional flow pattern was proposed which consisted of local vorticities resulting from the disruption of the orderly motion created during induction stroke. This was drawn from the observations of insignificant changes in the hot wire output when rotated through 3600 about its axis, Fig. (2-52). Moreover, a regularly repeated transition of local gas velocities from maximum to minimum for two adjacent positions of the N 0. HL U Q L! - I I I I II II 0) tn a t4 P Cd -N cl ;4 IL) bO CD > Cd > 4-b 0 0 4J 66. 0 k C9 0 CD 4-3 Cd 0 . r. 1 U) 14 0) (1) V0 0 -rq H 4-) a) C) > 0 -ri V-4 CH Ea +j cs bo to r. -H 0 S., :3 0v 0 -ri El) P4 0 to tD . 1) 0 p4 0 0 0 g 4-4 0 r: 0 -ri 4-3 cq $4 cj) a) %-, In VH 09 ri 0 Cd $-I r: bo C) cd -H . r4 0 .0 ., j Jý +3 cd 0 0 cl, to -ri N 67. wire was observed and interpreted by the presence of locally directed streams of different magnitudes at neighbouring points in the combustion chamber. iii) The flow velocities vary in different ways as a function of compression ratio (between 6- 12: 1), up to about 20 degrees before top dead centre. After this period., it appeared that they decreased slightly as the compression ratio increased. This led Molchanov to state that 'variations of compression ratio within wide limits has practically no effect on the velocities of ordered gas streams in the combustion chamber', Fig. (2-53). iv) Velocity traces without filtering the high frequency fluctuations showed an increase in the intensity of turbulent fluctuations towards the end of the compression stroke and towards the beginning of expansion, Fig. (2-54). The turbulent fluctuations are reported to be greAter than I the mean velocity in some cases. Once again, varying the compression ratio from 6 to 12 does not cause any sharp variations in turbulent motion of 'the gas. However, varying combustion chamber shape by inserting annular displacers resulted in a considerable increase in turbulence intensities. Although the response of the anemometer bridge used in this work covers the range of frequencies of turbulent eddies in an engine, as will be seen later, the very long wire used reduces its sensitivity to turbulent fluctuations and results in an under- estimation of actual intensities. This effect is very significant because of the very small size of eddies in S. I. engines as will be 68. U. rl %es 4 Z. Z. t" 9 ý, f .. .« ý 01 L LJ 0) T- r-4 -. 4.3 0 6 4. ) Z 0 4J 0 H -" -. -" a 0 Es 04 4-3 vi 0 tn M r-f .0 Cd > s i 4-D - r l 0) cn r-f 0 0 $3 H z- V4 C) 1" . I C: ý, 4-b cl $4 c) rl %_o -ri 0) +1 0 tn -ri 0 ., l . ri 0 C) C) 0 >0 ,Z ci %_o > to -ri F34 . ri %.. o r, ro 0 92 $-t cu 0 H Ei 0) 0 r3 Q 0 P ci 10 +1 Q) 9-4 p0 C14 U) 1 04 Ici 10 41 -a Cd 0 -N 4J Cd 3 4- cr cl %1 %0 1Z4 -p-i ' ul 91 00 r= 0 LIfL. -Al ;4 0 69. 0 .0 -H Ei 4J Cd 00 -, 4 4J to :: 1 ca .0 ri P0 00 4-1 0 0 Cd 0 C) , ;4 +) O-N V4 (D N El cq 0 %-f 4-3 0> 40 .00 4-4 4J C) 0H 0 (D M0 to 0 9: 0 tu . rj +3 4-) in U) U) 0 0 a) ul P4 1ý tr) U') cýI %. 0 4-) -H C) ." 00 r-4 -ri 0 > ! ý; a 0 'H .0 5 $4 Cd -H 4 Cd CH 00 'ri 4-3 0 +3 0 cli 'r. ) ci 0 0 +) 4-) in 00 -r4 0 +3 -H cd -P :30 cd 4-3 ;4 cs P-4 0 > to C*4 to -ri P-4 7o. discussed in a re-analysis of Semenov's work (22), (using the same anemometer system and combustion chamber shape under similar engine operating conditions). Moreover, the use of tungsten wire material was unsuitable for the previous investigation, especially at higher compression ratios (e. g. 12: 1) since this material is known to oxidise at about 3500C. This results in an increase in wire resistance and consequently reduces the output current of the anemometer which could lead to an under-estimation of gas velocities if the ambient calibration of the wires before test is used. The reported observation about magnitudes of fluctuating velocity components greater than the mean gas velocity could be only explained by an increase in the energy content of eddies in the high frequency range. Unfortunately the ban. ýýjdth of the filters used have not been reported to enable a definite explanation of this observation, particullarly in view of the measurements of the spectral distribution of turbulence in S. I. engines which have shown that most of the turbulent energy is concentrated in the low frequency range. (below 700 Hz) (22,24). It is generally recOgnised that the pioneer Nvork of Semenov (1958) (22) represents the most complete research on mixture motion in a S. I. engine. These experiments were carried out using a single cylinder CIFR engine with a variable compression ratio. The combustion chamber was flat and cylindrical as shown in Fig. (2-55). Semenov used a cOmPensation hot wire anemometer system (developed-by Chebyshev (66)). Its main principle is based upon reducing the hot wire curren tM under engine operating conditions 71. of pressure and temperature (P, T) to a corresponding value ) at some initial conditions (P ,T) as given by the 000 following relationship: i0= K(P, T). 1 (2-5) where the coefficient of reduction K(P, T) could. be obtained experimentally and introduced into the electronic cpMpensation circuit used. The measuring sensors of the anemometer system used in this work consisted of the following: a) a two wire sensor, in vhich a resistance thermometer wire 12 mm in length regulates the overheating current in the anemometer wire itself, which was 2.5 mm long-. (However a value of 4 mm is reported by Sokolik (48) in a discussion of this work). Both wires were 11 microns in diameter and of tungsten mateyial. b) An additional resistance thermometer which reduces the recorded current to the initial temperature conditions. The product of the voltage across the second resistance thermometer, corresponding to the instantaneous gas temperature times the signal from the hot wire anemometer circuit, gives the bridge voltage referred to the initial state of the charge, a quantity which determines directly the gas flow velocity. By chopping the continuous signal from the hot wire anemometer into pulses of 24 crank angle degrees in duration, (which was an arbitrary chosen period), the average gas velocities were measured and averaged over 20 to 40 successive cycles. Pulses of the fluctuating velocity component were separated from the continuous 72. velocity signals using band pass filters which consisted of 5 filters covering the following frequency ranges 850-1300, 1300-1950,1950-2900,2500-4250 and 4250-6200 cycies per second. This assembly was used also to obtain the spectral composition of the turbulent fluctuations. The root mean square values of the fluctuations were obtained over the same number of cycles, using a vacuum tube voltmeter. Further details about this measuring and recording system are given in reference (65). The main conclusions of Semenov's work could be summarized as follows: i) The gas velocity during induction periods varies considerably at various points across the combustion chamber which reflects the jet nature of the gas motion during this period and flatly contradicts Wenger's conclusions (21), according to which the gas flows into the, cylinder with the same veloqity over the whole cross section. This jet nature of the filling process leads to formation of velocity gradients in the cylinder which is believed to be the main source of generation of turbulence in the engine cylinder. ii) The average gas velocity during the induction increases almost linearly with engine speeds and decreases with throttling and increased distance from the centre of the combustion chamber. iii) The average gas velocity and the fluctuating velocity component decrease rapidly to a minimum during the first third of the comprestion stroke, after which they remain 73. almost constant for the remaining period of the compression stroke and finally drop smoothly near TDC, Fig. (2-56). However, a part of this observation could be attributed to the shape of the combustion chamber used (open cylindrical chamber) where no secondary flows are created during compression as will be the case for squish combustion chambers. iv) The average gas velocity at TDC compression, drops by about 20% with an increase in compression ratio from 4 to 9.5, increases with engine speed according to_the 2.1 approximate relation ý, -Jr. p. m. and increases by about 4% with an increase in throttle opening from 0.2 to 0.8 of its maximum value. The velocity gradients between various points in the combustion chamber are, markedly, reduced from the values attained during induction, (e. g. 20 see-' compared with 6000 see- I for the two cases I respectively). V) The spectrumdistributions of the turbulent fluctuations showed that most of the energy during the compression stroke lies in the frequency region below 500 Hz. The most serious concern with regard to Semenov's work are the adequacy of his calibration procedure and the suitability of the wire material used which is known to oxidise above 3500C, (the operating wire temperatures are not reported in any of the published literature about this work). The latter problem results in inaccuracies due to the changes of wire cold resistance and consequently the basic calibration used as reference conditions. 74. .I ci ". ". L - __ iii ______ ______ ______ _______ _______ - . t. u lu " ___ ___ ___ I I ___I J d , __ __ - __ __ __ __ __ __ I _ _ _ _ rF ti .0 fA cq cq u %0 Q 0 .. 4 4cz 9. > %-0 It4 r; l» ci : I- 9 0 2 it le C; It Cf) N 36 ba , r4 0 04 4-A cq cl %.. 0 1 9b ft 10 63 $3 -4 14 cl W 0 -lb 5.4 V fir tO . ri P4 Moreover, even Nvhen operating these wires at their maximum safe temperature results in a small temperature difference between the hot wire and the surrounding gas in the later period of the compression stroke, especially at the higher compression ratio used 9.5: 1. This decreases the accuracy of measurements during such a period. The macro-scale of turbulent eddies during induction were estimated to be of the order of 1.8 - 2.2 mm, but no estimation was given for the compression period. Also, tho micro-scales of turbulent eddies have not been estimated in the original work, but a re-analysis of the reported power spectrum curves, Figs. (2-57 and 2-58) resulted in values of micro-scales between 0.3 and 03-mm as shown in Table (2-5). The conclusions of Semenov's work should be taken with some reservation because of the limited range of engine speeds . 1. investigated (60o - 1200 r. p. m. ), and that only one shapet of combustion chamber was used. Table (2-s) Estimation of the Micro-Scale of Turbulence from the Spectrum Curves of Semenov Compression Ratio 5 F(n)n 2 dn U(m-/sec) mm x 4 . 672 x 10 7 1.439 0.6765 6 . 636 x 10 7 1.31 0.52 7 8 . 717 x 10 1.181 0.4425 7 9.5 . 835 x 10 1.084 0.376 75. 0 C.. *lU -/ ii, ___ ___ i' I I/u ____ ____ 1L - - :_ i j. - __ __ 't 0 E 10 11 e 0 2 j:: i %.. W %0 ab %0 91 ri 9 ! ý, ". r. .0 d u p4 0 92 9 to 4 C; 4 U to 94 u ti tt 92 ti ý70 o In, " 94 C 1-4 ' '. ri ri 0 Co rx. 76. , -Z to r-i %.. o 4-) 0 CH 0 to (1) ,Z cq %. 0 1 77. Matsuoka et al (15) have used a hot wire anemometer at the spark plug gap location, for measuring gas velocities in a motored CFR engine with flat and cylindrical combustion chamber. Three types of inlet valves were used, namely: a plain valve, a shrouded valve and a notched valve as shown in Fig. (2-59). The compression ratio was varied from 4 to 7 while the engine speed was varied from 500 to 1200 r. p. m. Measurements were made only at top dead centre under the assumption that this would adequately represent gas velocities during combustion. The same engine was fired every cycle and every third cycle to investigate the effect of exhaust residuals on the combustion cyclic variation. The combustion process was studied in terms of maximum*combustion pressure, the time from ignition to the attainment of maximum pressure, the maximum rate of change of pressure and flame arrival times to two ionisation probes located at 6mm and 76mm from the spark plug I gap. The conclusions of the air motion and combustion studies could be summarised in the following: I The flow direction at top dead centre on compression stroke is two dimensional and parallel to the top of the piston. ii) The flow velocity in the cylinder during the compression stroke reached a maximum slightly before top dead centre and then declined due to damping of the vortex motion. iii) For a shrouded inlet valve the average flow velocity was higher than the other inlet valves at all crank angles and the rate of decrease was smaller during the intake and compression stroke. 78. iv) The swirl flow created by the shrouded valve was not damped as much during the compression stroke as that created by the notched valve, which was especially designed to create turbulence. In the case of the shrouded inlet valve the value of the flow velocity 5 and its standard deviation S(U) were twice or more as large as in the case of the other two valves, but the coefficient of variation S(U)/U of the shrouded valve was less than half the value of the other two valves, Fig. '(2-60). vi) Increasing engine speed increases the standard deviation in flow velocity but does not greatly change the coefficient of variation. vii) Increasing compression ratio increases gas velocity and its standard deviation for the case of thd'-Ahrouded valve and has a negligible effect for the other two valves. . 1. viii) The flame arrival time to the first ionisation probe (located at 6 mm from the spark plug gap) was reduced with increased compression ratio and engine speed, but was not affected by changing the valve type, Fig. (2-61). The latter result was explained by the fact that this measured value represents the ignition delay, acceleration and flame arrival period and that flow velocity affects only the last term and could be masked by the experimental error. This explanation may be true with regard to the comparative order of magnitude of this small arrival timO and the experimental error, because of the well known effect of turbulence on. the growth of the initial flarne 3V1ISS3lid u199 001334 WW9L Goluld Z- W- ir_ WEIW Z XVU IVAIUNY 3wvlg IVAIbluy V, 4V1A x C3 w U. WN Q I-- 1 cm: iu. cr; 1 / a; -. 0, H3XIW-3ad-HLIA 3AIVA 03010H V3XIW-3Ud-RLtt4 3NIVA IVWVON 113XIW-33d-KLIM 3AlVA a3anomm H3XIW-34d- inomm 3AIVA (13anotms) ;ý "_2z? e eZ %0 le %"leg 1,4 qzi Zug U3XIW-3)JJ-HI114 3AIVA MHOION ulilw-au-mllm IA'IVA'IVWHON) 113XIW-3Vd-NIIM 3AIVA (13MOUHS) U3XIW-3Ud-. LnOHIIM 3AIVA 03anoUHS) S/W S/W I's US (X/Sys A113013A OIIVH HIV-SS33X3 . 1. Oliva J/V Cd ,a 0 Cd 0) 9 44 00 k bo . Cd 0 U) 00 W4 $4 4-2 Cd 14 Cd Cd 0 ;> P4 ý.. o bo V-1 rm, 0. e 0 0Z > LO r--1 (1) %-, 0 to p4 0 0 C%l ho 79. 80. CYCLIC MIXTURE VARIATION NON EXIST LPG CR 7 120ORPM THROTTLE FULL (OPENED SHROUDED VALVE MT IG-TIMING NOTCHED VALVE 34 NORMAL VALVE aoL- --4 . 26 2.2 /8 46 42 - 34- e jcL 30 - 26- a/ 003 006 cn 005 aO4 002 12 14 16 /B 20 22 A/F Fig (2-62) Variation. diagram: of maximum cylinder pressure. (%ax ) with air-fuel ratio for three types of inlet valves, (15)- 81. kernel (acceleration period). Nevertheless, the effect of valve type and its associated flow velocities were clearly reflected on the. flame arrival times to the second ionisation probe (located at 76 mm from the spark plug gap), where a good inverse correlation exists between gas velocities and flame arrival times. This discrepancy between the trends of flame arrival times at the two ionisation probes is also reported by Harrow et al (30), where no correlation could be established bet-seen flame arrival times at two ionisation probes located at 16.5 mm and 65 mm from the spark plug gap, of a Ricardo EG engine. However, in this work both ionisation probes showed similar trends of cyclic dispersion in flame arrival times at difforent fuel/air ratios. ix) Theeffects of valve type becomelvery noticeable when the engine was fired every cycle. In this case the pealc pressure and the maximum rate of / change of pressure were exceptionally large for tests with a shrouded valve as compared with the other two types of valves. The standard deviation and coefficient of variation of these two parameters have followed inverse trends, Fig. (2-62). These results are in agreement with Patterson's studies Figs. (2-63ý'a) and(2-63 b). In fact, the very low frequency response of the aneMOMOter system used in this study (250 Hz), means that the collected bridge voltage signals, as measured from oscilloscope traces, represent UA > * -*- - - X 0 - i X- - -0 C, 3 %n 0 -M ca C) cc WA 0 V ca /1 . Cb 0 to 2 !? rt 0- JLN32234 Notiviax, &% 3iY2s 3'xnss3vi 0 4 r* 0- su x MK gL 0 .0 he 0. - 0 9- . a (1 C1 1 C, t -J < < ý X wl > e- %n > : c )z dx 44 x Z Z 00 n lD3c'/'T, j ']Iva ainsnu as 0 .A fe 0 83. only the mean gas velocity variation during the cycle, rather than any turbulent fluctuations. Nevertheless, these general trends of mean gas velocity variation, especially the performance of the shrouded valve, are in agreement with the observations of Lee (18), as well as the anemometer measurements of the present investigation (as will be discussed later). The distinguished effect of the shrouded valve and its associated higher flow velocities and turbulence intensities on increasing the burning rate of the charge and reducing the cycliccombustion variation, could be explained by the same argument put in the earlier discussion of the work of Rothrock and Spencer (16). On the other hand the unexpected performance of the notched valve could be explained by its restriction to the inlet flow without any gain in directing. the-flow inside the combustion chamber. With this type of valve, one would expect some increase in inlet velocities, as well as the shedding of trailing vorticities from the edges of the notches, but these will be damped later on the compression stroke, probably at the same rate as in the case of a plain valve or even at higher rates. Similar observations have been reported by Patterson (2),, where an abrupt right angle change in flow direction near the intake port has increased the cyclic dispersion. Also a more pronounced increase in cyclic dispqrsion resulted when a shrouded intake valve was used that disrupted the flow to the combustion chamber. Barton et al (10,11) have investigated the air motion in a hemispherical combustion chamber of a CFR engine using a hot film anemometer. The sensor was located halfway between the piston crown and cylinder head wall with piston at TDC, Pig. (ý-64). 84. The angular position was such that the velocity through the intake valve opening was normal to the sensor length. Only mean gas velocities were measured in this investigation and their standard deviation calculated. Atypical velocity trace is shown in Fig. (2-63), which indicates the general trend of decay after inlet valve closure, and the cyclic variation in gas velocity. The values of gas velocities at the time of ignition at engine speeds varying between 600 and 1800 r. p. m. are reported to lie between 8.74 and 16.1 ft/sec, with standard deviations ranging between 43/10 and 487o of the mean value-. Cyclic variations in gas velocities during induction and compression stroke could not be correlated. However, the velocity magnitudes at the time of ignition were found to persist for approximately 10 to 15 crank angle degrees later. The authors assumed a statistical pattern of velocity regions with different levels inside thl combustion chamber. Regions of higher velocities at the spark plug gap at the time of ignition accelerate the growth of the inýtial flame kernel and consequently reduce the time required for its development into a stable flame front. This period was termed "the initial burn time" and was assumed to represent the time required to burn a fixed amount of the fuel between 2-5% of the total charge. Moreover, the variations in this initial burn time were assumed to be responsible for the subsequent cyclic variation in the cylinder pressure development during the cycle. t') w -J 0 T Ir! C2 s Eij U U I -e V c2 2 COIJ 0 85. > +1 +1 ri Z0 10 0 +3 01% ý4 () 0 ho a) z > -ri P, . 1-4 0 4- P4 0 r4 0 V) 0 0 CH a) 0) 0k H (n k 10 0) 10 0 C: > ý4 V cs 0 C) fm 0 00 -ri -F4 $4 4-1 Ul Cd ul >1 k Q 4-) CIS P -A C: 04 0 -! 4 0 E! 0 r. -H 0 rq Cd 14 0 P, U) >00 , C% 14 0" 4- A cs 0 Cd 11 0 0 4-3 U) C) . ý4 00, cl U) r-i o-% r-I 4-b 44 00 r. 4-f >% H tZ "0 C) %--I %-, o C%l ho -ri p4 1ý 0 V Cd 0 V-4 4J to 0 0 0 . 1-i 4-31 Cd 0 0 F-4 $4 0 P4 I- (2411/4) A1.100-11% 86. These assumptions were expressed in mathematical form as follows: dVr 0 (Vr = Vb (2-8) vi and dtb s (th) dU s (U) (2-9) where Vr is the ratio between the burned volume during the initial period Vb and the cylinder volume Vi* tb is the initial burn time, defined as the time required to burn the initial fixed percentage of fuel which governs cyclic variation. U is the gas velocity at the time of ignition. and S(t b S(U) are the standard deviations in the initial burn time and the gas velod. ity respectively. Using an expression for the rate of change of the burned volume as used in constant volume bomb tests, and assuming a hemispherical I burning flame front of radius rb gives the following expression: dVb ASE. f(U-) W dt or drb --sL, E. f (U) (2-ILI) dt I 87. where Ab is the flame front area. S is the laminar flame speed, which was L approximated from the experimental data of Dugger (67) and Garner (68). Tb Mu E is the expansion ratio = Tu -4 (2-12) which could be expressed in terms of mixture temperature at the time of ignition And air fuel ratio. T is the mixture temperature. hT is the molecular weight of the mixture. - f(U) is the increase in the laminar flame speed as a function of gas velocity. Substituting for SL, E into equation (2-11) and making use of the conditions given by equations (2-8) and*(2-9) led to the final expression of the proposed model for cyclic variation as given by: - F(O. V) S(t b C-g(u) s (U) (2-13) 1 where F(o. v) is a function of operating variables (e. g. gas temperature and pressure at the time of ignition and mixture air/fuel ratio), and g(U) is some unknown function of gas velocity which could be obtained by fitting experimental data. Using the measured variation in the crank angle for maximum pressure to represent the variations of initial burn time, a least square fit of the data gives the form of the function g(U) as: - g(u) U7] (2-14) 88. 2c IC 0- .w LL 0\1 --------- i - n2 0 A (ft/soc) Fig (2-66). Correlation of initial burn duration. and velocity variations (10). 89. This form of g(U) has resulted in a correlation of 0.975 between the variables log F(o. v) S(t )IS(U) and log (U), Fig. (2-66). b Winsor (23) measured air velocities in a motored CFR engine with flat piston and head surfaces as shown in Fig. (2-67). The hot wire was oriented vertically, radially and tangentially at a location near the spark plug. Platinum and Iridium wires of 0.0002 inch diameter were used. The wire length varied between 0.05 and 0.096 inches. The vertical wire tended to measure higher velocities during the early part of the compression stroke. -Such observation was previously reported by Matsuoka et al (15) and is interpreted as the existence of rotary motion in the horizontal plane. The measured velocities show a definite trend of decay during the compression stroke. Moreover, similar velocities--were measured by the three wire orientations from 40 degrees DTDC to TDC, Pig. (2-68). This similarity was interpreted as- , is3tropy of turbulence during such a period. No significant effect of wire depth was observed on velocity measurements and this was interpreted as an indication of homogeneity in the turbulent field. Such conclusions may be justified if one regards the 'turbulent fluctua'tions' as a result of shear stresses on the walls of the combustion chamber and'the breakdown of eddies of different sizes- in the process of turbulence decay. A linear increase in mean velocity at TDC with engine speed was observed, which contradicts with the almost quadratic relation reported by Semenov (22). go. Neither the fluctuating velocity component, nor the scales of turbulence were measured in this investigation. However the. standard deviations in gas mean velocity were presented as a measure of the turbulence in the engine which included, the cyclic variation of mea n gas velocity and the actual'turbulent fluctuations as measured from the oscilloscope traces. This leads to more confusion for attempts'to investigate the effect of engine operating conditions (e. g. speed or throttle opening) on the turbulence characteristics in the engine. Comparison between the measured values of mean velocities by different wire lengths was used to give a crude measure of the eddy size and was believed to be of the order of 0.1 inch. The author proposed a model of cyclic combustion variation based on the concept that "the average flame sp! jeo is sensitive to local turbulent velocities only when the flame radius lies in a certain incremental range, dc, whioh is located at a finite but unknown distance from the spark electrodes, Fig. (2-69). All cyclic combustion variation is assumed to occur during this critical period". This is not strictly true as shown by Curry (37) and Harrow et al (30) where measurements of flame arrival times at different distances from the spark plug showed that their cyclic variations continue to increase along the path of the flame front, Figs. (2-13) and (2-36). Other than that assumption, the basic concept of the model is the same as Barton's model where cyclic variations in gas velocity are considered as the sole cause of cyclic combustion variation. The only exception in this case is that the turbulent flame speed was expressed as a linear function 91. Anýmcm, zter , *Probe Fig (2-67) Crozs-section of MR engine combustion chamber and cylinder head at TDC (23). A rN r- 9) _0 -- W ýg CL %. 0 30 - Vertfccl 0 >- wire v 0 -J20 W Rddlal > wire it z W V -fr :z lorTangýz*ntial wire 0' 1 I: C 1ýý 1 21ý 0 180 to 60 -40 20 TDCý CRAW-C ANGLE(DETrOC) Fig (2-08) Gas mean velocity in CFR engine during compression stroke. (1000 RTIM ard fully opened throttle), (P3). 1-4 U No to CS s. 0 0M 0 41 4. 4J Radius' (r) Fi, - 0-69) PIsIc lr, 8'lmpLio-, t of the model or cyclic variation dOvOloped by Winsor Q3). 92. of gas velocity as given by St= KU (2-15) where St is the turbulent flame speed K is a constant dependent on mixture conditions u- is the gas velocity Assuming that the critical distance is constant and using the condition of perfect correlation between the time period during which combustion variation occurs and gas velocity led to the following expression S(t S(t do. K. S(U) cbs2t (2-16) , S(tl, ) where S(t c )A and S(U) are the standard deviationS-In the critical period, the total burn time, and the gas velocity respectively. Using the relation between the mean and standard deviation of the flane speed and making use of equation (2-15) led to the expression for the proposed model as given by f S(t de s (U)/U --)2 b St i+ (s(u)7u (ý-17) Substituting for S(U)/5 from experimental results by a value of 0.41 and for St by tb /D, where D is the cylinder diameter and using also a linear relation between t and S(t ) gives a value for the critical bb distance of 0.42 inch. Tindal et al (25) measured gas velocities during the induction stroke in a Matchless twin cylinder engine with in phase cranks. 93. One of the pistons was used to provide a reciprocating drive operating a linkage for a hot wire anemometer probe in the test cylinder. pig. (Z-70) shows the engine and traverse mechanism of the probe. Measurements with stationary probes were employed at positions a, b and c as shown in Fig. (2-71). The hot wire was located j inch away from the combustion chamber wall. At position a, one of the wires was parallel to a line through the valve centres indicated by (0-0) and the other was in 4 the same horizontal plane but turned 90 degrees (010). The two measurements were made separately by one probe which was rotated I about its axis, as required. Fig. (2-720shows the results obtained with a stationary probe at position a, in the combustion chamber during induction, using a plane valve. The turbulent nature ofthe-Slow is well demonstrated, although the presence of a well defined jet is also evident in the region of the probe. Theluthors reported that the anemometer did not detect any inlet flow until about 25 degrees ATDC on induction stroke. They explained this as'the anemometer wire not being in the immediate jet formed at the valve opening- Fig. (2-72b) shows the velocity variation during the induction stroke and the resultant of the signals from the two perpendicular probes.. The decay of gas velocity after reaching the maximum, at about 105 degrees after inlet valve opening, is clear and continues up to inlet valve closure. Fig. (2-73) illustrates examples of traces obtained when a masked inlet valve was fitted, the hot wire being kept in position a with orientation (0-0) , In this case the flow over the whole cyclo is portrayed. 4 t -0 ý .4 Of.. ic W 0 ry %e to 9i 0 0 J., C 4-ý ul Id -0 w LO C: r: cq -H 0 r-I -ri C>. 4-3 -ri U) ri) 4-) 0 cd (n 04 Fi Q) 4-3 bO C) r. 4 CH -r4 4-3 0 4-31 cn 0 rl (d a) 0 V) 14 0 CD 0 to -ri 0 +) CS 4J r4 ;40 V) IL4 f4 0 Cd 0 El r-4 0) ;4 Cd r. Cd k ci r-I cq 0 4 cl 0 %. w 0 U) ni CH Ei 0 > bo ci rý 4 ce -p 00 r-I V) Cd 0 Cd 44 N 4ýo 6 b < cl mt c3 -1 2 b- .c . 2. - 3 '0' - u 2 19 x 0 3- U pf :Z 0- CL *c 46 k rlo. - tic -ro N I /; 4) 0> +1 -ri 4-3 0 1 -"0" o do . - / ' ro o c% a§22qn En 14 Q) :j V0 cd CH So 4-3 k a) IH > 00 9 10 0 a) ., q bi) 4J cd Cd ;4 0 93 > G C3 U) +) 14 LO cd C'I F-4 Cj Cd C. ) -H cq V) 4 %-, a) P4 H cd ba o ;4 -ri >,, 0 P4 V 1ý 4 C14 t- 1 04 biO -rl P4 ci I-. I- n 0 F! Lo (d A p4 0 ;4 > P-f C) Cd 0 ce > to p4 00 -ri F-f > e, - - ,Z ci %. f u -ri rx, 96. 1- CL - - --------------- 2 3ý ts 1) LO C-4 00 001 -rf -rf 0 44 +31 %-o 43 00 11 A -rf 0 4-) 1! 4 -ri U) V) (d 0 H P4 CH he $4 0 Cd "-I H 14 :3 to Cd Cd 4J Cd 0 q-t cd 0 0 Cd 0 +31 P CH -H 4-D 4-1 m 00 N +1 bD -r-I r, C) 0 -ri a 00 r-f 0 14 (D 4 P4 > Co %-o Cl) C14 bo -H P4 97. It can be seen on these traces how the signals are attenuated during compression. 7he negative signals on some traces are probably due to the very low operating temperature of the tungsten wire used (2000C) for the hot wire elements. Tindal et al reported, also, that the readings from the traversed anemometer were in general less regular than those obtained in the combustion chamber with the stationary probes, and the repeatability of the records was not quite as good. They explained this by the less orderly air motion lower down in the cylinder. The masked valve increased the air velocities by about 3076. As mentioned earlier, in the discussion of Semenov's -and Molchanov's work, the use of tungsten material is unsuitable for investigating gas Slow during the compression pqrjQd and this was the reason for limiting the reported results of Tindal et al to the induction period where succesdTul calibration could be assured. James (1972) (24) measured mean gas velocities and fluctuating velocity components in different band pass widths of frequencies using a hot wire anemometer. Two combustion chamber shapes were investigated, namely: a squish and a cylindrical as shown in Fig. (2-74). Different compression ratios were obtained by inserting spacers between the cylinder head and the cylinder block. The anemometer output signal below 200 Hz was used to represent the mean flow velocities by averaging over 22 cycles the instantaneous values recorded on UV paper at 10 degree' 98. intervals. The turbulence fluctuations at different band widths were obtained by subtracting instantaneous values of gas velocities from the mean value equation (2-18) and averaged over 12 cycles to give a mean value of u'. ul =u-9. (2-18) The band widths for these filters were: 90-180,180-360, 360-700,700-1500,1500-2800 and 2800-5800 cycles per second. The same technique was used by Semenov (22) with the exception that the later averaged turbulence fluctuations over a sample width of 24 degrees. Due to the difficulties in the recording procedure of James, no attempt was made to measure absolute intensities over the band pass ranges. Also, the scales of turbulence were not investigated. The'analysis was concentrated during the period between inlet valve closure and-40 degrees after TDC. A general tendency of decay in the mean velocity throughout the compression stroke was observed and was more pronounced at higher compression ratios and higher engine speeds. This was explained as a transfer of energy from the low frequency band width into the higher band pass ranges, where it is essentially dissipated into heat by the action of viscous friction. A linear increase of mean velocity with engine speed was observed in the latter period of compression stroke while a non-linear increase was observed in the earlier part after inlet valve Closure. A very marked increase in mean velocity at 30-400 ATDC On expansion was observed and were more pronounced at higher compression ratios, Fig. (2-75). No indication of squish velocities were measured at lower compression ratios (3.9 - 5.29) due to the larger Width of 99. "1 To "I Dull Czn*ro P L-1 View on pp Fig(2-74) Cross-section of the squish combustion chamber used in James's investigatioAv(24). 1300 - COMPression Ratio 6.1.9*1 C i R i G * ompress on at o . SB j 700 - 1500 Rev/Min 115 0 ReYM In u 600 - liOOReVMin V1, 500 - u '-+ 0 P 1 \ - -- -0.11 -41, C, 400 -- -V- ---V V LL 60ORev/Min --O_ -0- --01. % ý10 I 300 750 Rev/ M In N. 1 950 Rev/ Min 900 Rev/ Min Piston Position (Cronkangle Degrees) Fig(2-7.5) Variation of gas velocities with crank angles for a squish copbustion chamberJ23). IS II I _____ I b 100. spacers used (1.89 - 0.6 cm). However such squish appears at a higher compression ratio of 8.88: 1 when the spacer was removed and the squish height was that of the gasket width 0.15 cm. Regardless of the scatter in the data, the general trend of decay in the fluctuating velocity component during compression stroke was observed and most of the energy is contained below 700 Hz. However, no definite conclusion was obtained about the predominant frequency band pass range at any speed. Moreover, around TDC the distribution of energy in the most important region between 90 Hz and 700 Hz is not clear. James attempted to use his measured values-of fluciuating velocity component to predict the turbulent flame speed using the expressions developed by Shchelkin and Karlovitz. The first expression was tried with the maximmn values of U' in different bands of frequencies and even with a cLqxrection factor of 2.5 (as proposed by Semenov in his data), but no agreement was reached. Application of the second exprd'ssion with its modification for the effect of turbulence amplification by combustion improves the situation, but still a trial and error program was required to try the best fit for each frequency band and finally an arbitrary multiplication factor was employed in conjunction with only the highest cycle value of u' over the 12 cycles analysed. Such peak values were of the order of twice the average values given in Table (2-6). Further analysis of James' data was carried out using the same procedures of the present investigation., as will be discussed, in Chapter 4. The reported values of the fluctuating velocity component at different band pass widths were introduced with a program to a Hewlett Packard Fourier Analyser to yield the energy content of the fluctuating component and the mean value of u' for all the frequencies at different crank angles over the engine cycles (see Appendix Al). The results of such analysis are shown in Table (2-6) for the values of u' and the turbulence intensities u'/5 using the corresponding mean velocities at the same operating conditions. The very high values-of measured intensities (50 - 80%) of the mean values reflect very clearly the cyclic variation in the mean velocity that was superimposed on the actual fluctuating component in the lower frequency range. Such a cyclic variation in the mean velocity was reported by the author to be of the order of 50%. / 102. Table (2-6) Re-analysisof the Turbulence Measurements of James (24) 1. At TDC CR 1 r. p. m. ut (m/sec) U(m/sec) U, /U 100 %t x 10 (sec) (MM) 3.9 600 0.758 1.72 45- 1.695 0.282 3.9 930 1.293 2.24 57.75 1.535 0.3482 3.9 1200 1.88 2.76 68.0 1.272 0.352 3.9 1450 2.43 3.16 77.0 1.28 0.405 5.29 700 1.13 2.02 56.0 1.6 0.323 950 1.529 2.6 58.75 1.319 0.343 1200 1.985 3.12 63.7 1.2 0.38485 1450 2.885 3.66 81.5 1.13 0. -1035 8.88 900 2.63 3.79 69.4 1.75 0.66 1500 4.74 5.83 81.4 1.594 0.93 2. Measurements at C. R. = 5.29 r. p. m. u (U A) loo x0 secý -(MM) X- TDC 1.53 2.63 58.2 1.315 0.346 20BTD 950 1.588 2.754 57.7 - - 4OBTD 1.735 3.04 57.0 1.332 0.405 103. 2.5 Effect of Mixture Motion on Flame Speed It is well known that flame speed increases almost linearly with engine speed. This increase in flame speed is usually attributed to the increased turbulence of the charge caused by the higher inlet air velocities accompanying the higher engine speeds and the increased Reynolds numbers. Furthermore as the engine speed increases the compression period becomes shorter and the natural decay in turbulence will be less advanced at the time of combustion. The small scale turbulence is also increased at higher engine speeds, as will be discussed later, with a resultant effect of accelerating the propagation of the flame front. Such conclusions were first reported by Bochard, Taylor and Taylor (41) based on the inspectiod of flame photographs, Fig. (2-76). It is also confirmed by the measurements of iinuma (36), where both high speed flame photographs and ionisation gap measurements have shown the same trend of linear relationship between flame speed and engine speed, Fig. (2-77). Harrow and Orman (30) and Hodgetts (42) reported similar results for a Ricardo E6 engine and a Ford engine"respectively, Figs. (2-78) and (2-79).. The effect of turbulence on increasing the propagation speed could be ascertained also by combining the observations of Clarke's (5) (1912) and Semenov's(22) (1956) experiments on an engine cycle with closed inlet valves. In the former case ignition after two or three previous cycles during which the intake valve had remained closed resulted in a sharply retarded combustion, Fig. (2-80) which was still proceeding some 2000 after ignition. In the latter 104. experiment, Semenov (22) showed that the turbulent fluctuations almost disappear near TDC for a cycle with closed inlet valve and that the fluid energy (j (ý2 + ý, 2) ) consists, in this case, only 10% of the energy of a normal cycle, Fig. (2-81). This illustrates the significant effect of turbulence on accelerating the combustion process in an engine, in spite of the fact that Semenov's experiment was carried out with flat and cylindrical combustion chambers where no secondary flow is created during compression. Similar conclusions could be drawn from an experiment carried out by Bolt et al (3) in a constant volume bomb, where a complex flow pattern of mean swirl, small scale and large scale turbulence was created by a stirring fan. In this case an increase. in the pressure rise due to combustion by about 15 - 20% have been obtained by increasing the mixture velocity as shown in Pig. (2-82). A corresponding increase in the rate of. pressure rise has also I been observed due to the increased mixture motion, Fig. (2-83). Unfortunately the relationship between turbulence and flame speed is still disputed and most of the theories developed to explain such type of combustion have fundamental defects aLnd are contradictory in many cases. Such contradictions arise because of the lack of reliable methods for measuring the intensity, scale and spectrum of turbulence in combustion wave, in spite o: r the intensive efforts of many investigators. This leads to ELttempts of comparing and interpreting experimental data which may have been obtained under radically different flow conditions. oýZ 1 Ilb% %% r *wo @«mm 1 t-, i >c /X . 1. MR . %no I c'J 0 uDh3 . Cm 0 &r4 Z) - ci ck. c: %A . .3 0 P 0 Z; iz ab .9 . C. 4 . C) Cl- 0c 0b c5 > D 00, % e 1 : 0 . rJ 4-) Cl) . r4 --. 0 tf) 0 0 Cd cd C) 4-1 > cd 0 ., 4 0 4-3- r. rq 0 0 00 -ri 4-3 -ri 44 CZ ol ý, ) -H 0 -ri 0 IH rq 9: oq-4 00 r-% bo 105. 0 0 C> EI C> ri c> w ci CD c20 LO -Z X, 7 CN ". utw 4313013A 0-713 ,Z 106. . CD 4-3 m ce 0) u) Z tz c 0 4-3 :10 fil c 0 Ei 0 > U) cli U) +I $-4 ci r4 (1) 0 U) > --i 0 cq %. 0 to . rj P4 "I , "v- LO "m V2 8 C) M 09 Cý Ck. 0 a- C4 8-0 ci C) P. %r I -7 rX4 C3 (D Co Cl) C4 W- U) Ell cis 14 0 cn 0 .0ý .0 0 (D 0 Alb Cf) 14 P, Cd 0) > 10 0 W4 (D -rf 14 a) 4-) $4 P4 Cd Cd V) (n rl 00 (d N CH 0 4-) (n 0 +3 Cd CH 14 Cd Cd 14 0) k0:; 5 C) " %.., c1l, to P4 -0 vi 8; - _JO fy 1 ri - 0* %. 0 ý t7 w R2 aE, 3 :; y d Ai 2: 0. te w Wl W. 13 * 4x 0 K» 45 x3 C» a 30 10 Ir w 1. - 63bill «t3Ayv£ awvu wam «lv. %0,4402,4 II I. 0 bu a !2 12 6.4 I p. D 107. CH CIS 0 00 0 10 0. $-I ca 0 CD to > cl r. k cl 0 Ej C-3 rf 0 to 0 -rl LO 41 Lf") :j cli 0a > ý4 a) 0 :> cq to -ri P4 > CD Cli 0 e0 p4 r-i 0 r. k Ici - r3 CH 000 0 0. r. 4-3 000 42 a0 cu 1 r, r-4 0 0 vi -ri 4J ci ID Ir. ' 00 t- 1 cli P4 0 in 0 0 LIS U, 'quill JOADJJ UDOIAI h 4. U U .e tý ýil E d%N et l% w «iß e* qcb 108. 0 0 ýo 0 -ri 0 a) 0 cc (n -ri Cd cl %.. - +1 0 r. 4 $4 V4 04 Cd ,aý: S2, s x C: r: (D 0 0 "1 %-1 0-% U) 0) CV) ul Cd 0 >1 P. ps 0 E4 > 00 cd -rq 0 >% cq U) +a 0 N (n 10 ri -+J ý-oo a) ;. 4 0 00 4-31 4-) C: 0 > >. % (1) v- U U) 0 4-4 .0 0-% %.., 0 r-4 Cd C%l 0 ;40 0 CD -ri ta ý4 U) 0 +a cl U) r-I tis U) 4-) 0 V-4 :1 C: P ri U Cd -ri " .00 ý 0 En ILI 0-% 0 CH 0 r-A r. ) r-4 co I cq to .,. I 0 9-4 cj Cd P 4-3 0 rl 0) v Ix vs Cd 0 cl Cd P 4-3 bi) :5 cl 0 . 1-4 4 0 -P Cd 00 E) 0 %-d u . ri 94 .; 4 - eo r4 IP ri ei r4 r4 fy 2iZ, 8. _O e! 3. it >Z. di Z , -a A 0. - 10 ct 0 q, tli L. e 1. Ly 2 Co, tZ0 4L ox a 1" 10 Ct . OC co C, cE IE Im 4p ca N %D n -w el ra I Li :1 r4 "rl 0 >b iJ 0 cyl 0 0 ei +) IH IH 0 FA o IZ c-i Co cli %.. 0 bO "1-4 p4 to U) CH 0 4-) CV) -rl %-o 0 0 0 > 44 0 bo r: 0 $4 4-31 1ý fn CC) I, cq P4 109. 110. Turbulence fields are known to consist of a wide spectrum of eddies of differing sizes. However it is common to distinguish between small scale eddies in which the ratio of eddy size to flame thickness is small and large scale eddies in which this ratio is great. Such distinction is obviously an artificial one ýor the reference length can only be the flame thickness and the more intense the turbulence the thicker this is. The first class of eddies (small scale) are usually considered of less importance in accelerating the flame speed from its laminar value*, and their role is to cause slight increase by virtue of increasing the diffusivity of gas from its molecular value to some value which is proportional to the scale of turbulence and its intensity. In other words, the flame surface remains even, but the intensity of the transfer process increases. Such effect was formulated by Damkohler (43) as follows;, . ý-* If S S (for small scale turbulence) t L where St and S are the turbulent and laminar flame speeds respectively, is the eddy diffusivity and Y is the kinematic viscosity. Using the general principle of combustion theory, Schchelkin (52) also obtained the following relationship for the turbulent flame propagation velocity in the presence of small scale turbulence: (2-1.9) * However, the effect of small scale turbulence on the initiation of the flame kernel in engines is very important and greatly controls the entire combustion process. ill . st at st 01-M (for small scale turbulence) (2-19a) where a t, cý L are the turbulent and laminar thermal diffusivity' respectively. In this case the ratio St does not go to zero for SL 41( = 0, as follows from the previous relation of Damkohler. It t follows that a continuous and smooth transition must exist from turbulent to laminar flame propagation. Zelldovich and Frank-Kamentskii (53) also discussed the problem of turbulent combustion and proposed the following relationship for the case of small scale turbulence St = (2-20) where P is a constant depending on the rate-of. phemical reaction. On the other hand the effect of large scale turbulence has It been the subject of many theories and is usually considered to be of much more importance than the microscale. These theories could be put into two main groups according to the, model of flame turbulence interaction on which they are based - The first group accepts a surface model and the second, a three dimensional model of combustion. A brief summary of the basis of each theory, and the corresponding proposed expression for the turbulent flame speed, will be discussed in the following. a) Surface Model (wrinkled and fragmented flame front models) Such a model assumes that turbulence chiefly affects flame speed by wrinkling the flame front, thereby increasing its area, at each part of the front. Nevertheless it propagates at its laminar 112. velocity. The turbulent burning velocity can, in this case, be defined in terms of the relative increase in the combustion surface. stAt sLA( Such a model was first proposed by Damkohler who considered the calculation of this area increase impossible in the case of complete fragmentation, while for slight wrinkling the surface may be represented by series of adjacent laminar cones with vertexes oriented differently, Fig. (2-84). The surfaces of these cones are, approximately, proportional to the fluctuating velocity component. Therefore: and AtU, At st ut sX or st IV uI . 1. / - (2-21) (2-22) (2-23) expressing the fluctuating velocity components in terms Of the eddy diffusivity and considering the Lagrangian scale of turbulence as constant for the particular test conditions considered, we can write the following relation: ul Et JLL. and StvF, t (2-24) 113. Defining a turbulence Reynolds number Re L.. ut and assuming V a constant value for 'ý) we get st ,v Re. (2-25) The experimental data of Damkohler for mixtures of propane-butane with oxygen in Bunsen burners were fitted by a linear relation of the form sta+b Re (2-26) Shchelkin in his development of Damkohler model assumed the height of the elementary cones to be equal to the'distance through which an element of the flame front is carried, by a fluctuation out of the common flame front (h = u"ot) where (t) denotes the life time of an eddy, t= LX/Sj, where Lk is the scale of turbulence. The base of the cones was also assumed to be represented by the scale of turbulence Lx- The increase in combustion surface could be, therefore, I-epresented by the ratio between the lateral surface area of the cone and the area of its base. This led to the following expressign: StI+ (2 u' 2 (2-27) SLS which, for strong turbulence u'7; ý-S t gives tv ul (2-28) However, Sokolik (48) has shown that the determination of the cone height by (h = U' t) is justified only for very weak turbulence and it is inconsistent therefore to apply conditions for very strong 114. turbulence to equation (2-27). He discussed also the case of a fragmented turbulent zone whare each eddy is assumed to burn up from its surface at the laminar velocity SC Each elementary volume with a surface area of is fragmented by fluctuations when it entersthe combustion front. Expressing the distance travelled by any elementary volume during the combustion period by L=tbU, LX/S t )U, (2-29) .3 and assuming that the time required to burn the volume Lx is considerably greater than the life time of an eddy. The number of sections of elementary volumes passed over the distance L during the period tb is LA x= u'/SL; which is accompanied by the formation of a new flame surface with an area L2 at each section. The effect of large scale turbulence on the flame, in this case as well, is simply an increase in tIT6*combustion surface by a factor Lt = u'/SL and once again ST fv u'- sL It. Karlovitz (45) defines the turbulent burning velocity as the mean velocity over the path of diffusive transport of the eddy during the period of its combustion 'which could be expressed by the following relationship: \F7 SS+x (2-30) tLt rý=2- where x is the average displacement of an element of the front under the influence of turbulence fluctuation and t is the average time during which an element of the combustion flow remains associated with an eddy. Taking into account the theory of Ao 115. turbulent diffusion the following relationship is obtained: st exp For strong turbulence equation (2-31) reduces to stt -=I+ F2 ju-, (Ut >>S (2-32) stsI and for weak turbulence equation (2-31) reduces to stu + (S sLst IL According to Karlovitz, the values of St calculated from u' using such an expression as equation (ý-31) aref_ive to ten times smaller than the measured values. He explained the difference by a supplementary turbulence created by thd*fluctuating flame itself (attributable to the expansion of hot gases). Such supplementary turbulence is expressed by the following relation for the case of isotropic. turbulence Ulf JU (2-34) SL 3 -Tb- where Y and are the densities of the unburnt and burnt charge Ub respectively. Another approach to the problem of turbulence amplification by flames is developed by Mizutani (50) where the kinetic energy of the turbulence is assumed to increase because of the rapid acceleration and its effect on increasing the kinetic energy of the gas, Fig. (2-85). 116. irr hI se I 0T An elementary flame conet formed by turbulent fluctuation. & a Fig (2-84) The effect of large scale turbulence on a flame. -ý ý- ------------- "I le ooo . 0o St 0o 00 . -I loll . 00, U= Approach gas velocity. Ub= Actual accelerated gas velocity. Ub'= Accelerated gas velocity for an infinite plane it combustion. Ub= Accelerated gas velocity for a condition of unchangeable flow direction in the combustion wave. Fig (2-85) Amplification of turbulence level by a flame and turbulent flame speed, (according to Mizutani (50)). It'.. I 117. Such increment in the turbulence level is assumed to depend on the turbulence in the approach flow. This condition is expressed by the following relationship: ut f2 UT 12 Ul 2 Ot p --+k()-(. a E) 2212 where klp c< are constants, U, 1 is the intensity of turbulence andA E is the increase in kinetic energy of the gas. Using the Karlovitz expression equation (2-31) and substituting for A E, the following expression is obtained: ul f2U, 2 ut stm (*L (-)= (- )+K -S sLs(2L 0 E(L 2 u (m + n) /2 x Sb (2-36) where K, L , rv and n are constants determilted from experimental data which gives the following value for the case of confined flames in a combustion chamber: I K2Lmn 3.6 0.44 2.67 0.75 for 807o reacted portion of the mixture One of the main contradictions in the Karlovitz model is the determination of the cone height by the diffusion length (X2 u'. t which naturally leads to the conclusion that St ý'- u' for very weak turbulence which contradicts the theory predictions for very strong turbulence as mentioned before. 118. Scurlock and Grover (46) proposed a wrinkled f lame surface model where the height of the cones was represented by a diffusion length, defined in terms of both the Eulerian and Lagrangian correlations (R t and Rx )* as follows: vo d2 U- 2RR dt (2-37) dttx The relative increase in the combustion surface and consequently the burning velocity was expressed in this case in terms of the laminar flame speed (S the Eulerian scale of turbulence L and x the duration of the effect of turbulent flow (t) on the flame as follows: stuIt -= (1 +C (2-38) sL x 2u' b) Three -Dimens iona 1 Models of Combustion Many objections have been put forward against the surface model of combustion (51,63,64) because of the absence of a complete description of the diffusive nature of turbulent flow in such a model. Moreover, experimental data of turbulent flaines do not show enough folds of laminar fronts to satisf y the observed large increase in the burning velocity. This led many investigations to reject the idea of wrinkled flame front. Summerfield (63) has elaborated an expression for the turbulent flame speed by replacing the molecular conductivity in Von Karman's derivation of the laminar flame speed by the corresponding turbulent dimension ( E, --F Cp). This led to the * Definitions of correlations are given in Chapter 3. 119. following expression: (2-39) Tt where St and ýL are the turbulent and laminar flame front thicknesses respectively. Sokolik (48) also considered that the role of turbulence is to augment the diffusion between the unburnt gases and the gases already partially or completely burnt. Dividing the flame front into a number of micro-volumes whose composition, - temperature and degree of advancement of the reaction, change under the influence of turbulent diffusion. This led to the derivation of the following expression for the turbulent flame speed: uL. -- 0 St t -2L-3. (2-40) ti ti where ti is an auto-ignition delay period "L'i is the Lagrangian time scale t LL is the Lagrangian length scale It is interesting to notice that Sokolik'seKpression (2-40) fOk the turbulent flame speed is independent of the laminar burning velocity. More recently (1972) Van-tiggelen (51), also rejected the model of wrinkled laminar front because of the experimental evidence that only half the apparent volume of the turbulent flame could be statistically filled with wrinkles. He suggested an expressiOrl, which was verified by experimental data for an opposed jet burIlGr as follows: st (2-41) 120. Kovasznay (57) developed a criterion to define the conditions which give either a wrinkled laminar. flame or a distributed zone. The ratio of velocity gradients in the turbulent apprQach flow u'/-,,, to a gradient within the flame SL/S. is equal to r-,, the criterion. The Kovasznay criterion states that a continuous, wrinkled laminar reaction zone is present for small values of rj whereas large values Of r. signify the onset of a disrupted or distributed reaction zone which has various degrees of reaction. Povenilli and Fuhs (14) interpreted Kovasznay's criteria in a different way, by considering VSL as a characteristic flame time or chemical time. Likewise, - 1/u' may be considered a characteristic turbulence time or the time required to distort the flame front. Hence: t (chemical)/t (turbulence) (2-42) For values of r less than unity, the flame consumes the reactants faster than the turbulence c. 1h distort. the reaction zone, thereby yielding wrinkled flames. When r exceeds unity, the consumption of the reactants is not sufficiently fast to prevent the turbulence from disintegrating the flame front. c) Spectral Theories of Turbulent Combustion Since states of purely large scale and small scale turbulence do not exist attempts have been made to develop expressions which account for both effects at the same time. Among these is the proposed formulation of Povinelli and Fuhs (14) where both 121. reaction zone wrinkling and increased transport affect the turbulent propagation velocity. The two effects are accounted for by introducing a "weighting function" based on'partitioning the spectrum curve into small and large scale regions as follows: stAt no St A P(n) dn + F(n) dn (2-43) to no where n0 is the frequency of partition which maybe obtained rom no =S t/S t At The first term is expressed by the effect of large scale turbulence on flame speed as given by Karlovitz's expression (2-33). It is also worth noting that the second term is derived from Summerfield's expression (2-39) with the EýpýRýoximation of S/S )=1 and modifying the numerator to be the sum of laminar t and turbulent diffusivities, most investigators ( (45), (52), (55) agree on expressions of the fonn (2-19). De Soete and Van-tigglen (58) have discussed a similar approach to the problem where the effect of small scale turbulence was expressed by equation (2-18) as follows: For small scale turbulence (micro-scale eddies) st (2-18) The effect of micro-scale eddies could be introduced by defining a micro-eddy diffusivity as follows: F- = VI I micro micro micro (2-44) where X is a Lagrangian scale of small scale turbulence and Micro 122. Ve is the root mean square value of the turbulent micro fluctuations contained in the small scale eddies as given by: v2vF (n) dn (2-45) micro total ij, --2 where v total is the total kinetic energy of the turbulent field. Also defining the eddy diffusivity of the whole spectrum of eddies in the field by F- = vi, Z (2-46) total total ý total where L total is a representative Lagrangian (diffusion) scale of the whole turbulent field. Thus, we can write: micro total 1ýnicro CrF _(n M-47) 'Ltotal The effect of macro-scale eddies could b.? introduced by a corresponding increase in the flame front area as given by: tt (2-48) t micro t where St is the mean flame speed of the turbulent field$ and At, At are the real wrinkled surface area and the average or apparent surface area respectively. This increase in the flame front area is mainly caused by the macro-scale eddies and could be expressed from the %arlovitz expression (2-3ý'D as follows: 123. At -=I+F (v' 17jlf(n) din) =1 +F(vI (2-49) AI total 0 macro Combining equations (2-48) and (2-18) gives the expression for the mean flame propagation in terms of both effect of small and large scale eddies as follows: st emicro 1+F (V' (2-50) s11 macro Iy 2.6 Possible Cause of Cyclic Variations It is now generally accepted that, apart from small improvements resulting from mixture homogeneity and combustion chamber configuration changes, the primary causes for cyclic combustion variations are attributed to fluid motion considerations, particularly with respect to-conditions at the spark plug gap and during the early combustion development. Ricardo (39) has stated "that the observed variations take place for the most part in the initial delay period and are, no doubt, due to variations in the composition of that minute part of the mixture forming the initial nucleus of flame". Soltau (4) has reported that the principal variable is the delay period between the occurrence of the spark and the formation of a stable reaction front travelling at constant speed. The third stage of combustion which starts behind the premixed blue flame reaction zone and during which most of the heat is released, was also noticed tp vary cyclically. Slow reaction resulted always after a long delay period while a rapid initial flame resulted in a better third stage combustion than a much slower one. This led 124. him to conclude that cyclic variations in combustion processes resulted from variations in the delay period and if this delay period could be made constant, then providing a mixture which burnt at a consistent rate will solve the problem and stabilised pressure traces could be obtained. Also, Peters (33) and Troutman (40) have observed from calculated burning rates that the lower initial burning rate yields lower maximum pressures. The same observations have been reported by Miller, Uyehara and Mayers (38) where two individual consecutive cycles were analysed. The spark was experimentally observed to occur at the same crank angle, the calculated charge weights had indicated no difference in the weight of charged inducted, the rates of heat release were almost identical and the only marked differences were noticed during the early part of the combustion process. After 10% of the mass was consumed little difference existed in the rate at which the fuel/air charge burned, Figs. (2-86) (2-97). This led them to conclude that the propagation of the combustion process just after ignition by the spark appears to be the controlling factor in cyclic variation and that to minimise such variation some means must be found to control the initiation of burning and the rate at which the chemical reaction I proceeds during the first 107o of the combustion period. Curry (37) performed a 3-dimensional study of flame propagation in a Waukesha CFR spark ignition engine. Using ionisation gaps he reported a small variation in the flame travel times at an ignition gap located at 3/16 inch from the centre electrode Fig. (2-36), while a much greater variation was noticed at a second ionisation gap located at less than one inch from the spark plug- Approximately 45% of the total variation in the time required to 0 40 -N zz D D D cr 00 ti C) Z.. 0< ri cc . 0 00000 SSVII INTD83J ---f U . -- -. - --s. L t I I I. - Ix I sm I N - , .. I -I II N I Ih x. 2 2 i -. l.. 1.! e1.. 1.1 -0, 0 0 14 -ri 0 4-) ILI 0 bo o V. cs Ir. 0 *rl 4-3 cl Cd $4 k U0 P4 U) 0 :3 U) 4J $4 0 0 cs > 4-1 M ýu r. 00 10 cn m9 cri bo cs cd 4-) 4-) 9: cn 0 '(D tj 00 >, C') t- C-4 bo 00 a) C) . a --% .H0 00 93 CI) 0 0 ce -P Pd 0 0 r-) 14 to 0 r. c4 -p 14 0 p4 Ei p4 e) 00 4-b -rf 4j ;4 ni cd 0 c ,l rd ;1 > k to P, c) ,Z CD Co cli -0 to -ri I P4 125. 126. complete combustion had occurred by the time the flame had reached this second point. This led him to conclude that the. ignition process and the subsequent initial propagation of the flame kernel was repeatable from cycle to cycle and that the sizeable variati ons in the time for complete combustion and in the time of maximum pressure signal, which could reach a value of 25% of the average time, occurred beyond the point of ignition in the early development of the flame front. However, one has to notice that this reported data was obtained under reldtively ideal conditions of a single cylinder engine at maximum power fuel/air ratio and maximum brake torque (MBT) spark timing. However, Robinson (37) in his discussion of Curry's work has not excluded the probability that such small variations in flame speed at the spark gap could have a pronounced effect on flame speed later in the cycle. He mentioned that measurements Of flame rate at ionisation gaps located j In from the spark gap during normal combustion have indicated that slow rates of flame propagation at these gaps resulted in corTespondingly slow total combustion time for a particular cycle. Conversely, fast initia3. combustion time results in fast total combustion time. He corIcluded that, in general, the primary cause of cyclic-combustion variatitm originated at the spark gap. Harrow and Orman (30) have noticed a similar general featUre of cyclic variations of flame arrival times at two ionization 'Prc-)'ýes located at 16.5 mm and 65 mm from the centre electrode, pig. (2-12). Furthermore, they noticed no correlations bet%veen the devia tion D: E flame arrival times at the two probes. The extent of *cycl: LO v'o--X': Iation 127. was noticed to decrease after the formation of deposits in the combustion chamber. They have shown by a process of elimination that the only cause for such reduction could be an increase in the turbulence intensity. Furthermore, they have noticed that such effects were more marked at the first probe than at the second which one can attribute, in view of the previous discussiop, to the effect of small scale turbulence generated by-the increased surface roughness due to deposits formed on the early development of the initial flame kernel when its size is comparable with the size of small scale turbulence e-ddies. Patterson (2) stated that the combustion rate variations are the result of mixture velocity variations that exist within the cylinder near the spark at ignition. Similar conclusions were reached by Barton et al (10) where correlation was obtained between variations of mean velocity at the spark plug and variation of the initial burn time. In a basic investigation of the effect of mixture motion on the developing flame kernel, Cole (12) utilised high speed Schlieren photography to observe the combustion process in a constant volume bomb with central ignition. He used a stoichiometric propane/air mixture at one atmosphere -pressure and directed in a small jet of mixture into the region of the spark gap. 7his distorted the development of flame kernel and increased the area of the flame front by an amount dependent on the jet velocity. The increase in flame front area was correlated with the Ate of pressure change dP/dt with greater jet velocities, Fig. (2-88). Similar observations are reported when the mixture velocities are increased by means of swirl generators fitted in the inlet ports 128. cn co W) W C: C) CL) E cu (D6 -iR I \ U . - aIC: . 413 cl Ln Ln (a to lro a c: LE 0 C3 E : E5 %C> if% !R tr% CD Lfl% C) I; zr C'*Ii Z)Seaj: )Ul WOO JOd rý CL) Ln C) - .. zr E; u 4-) CL) ri 0 0 C-) >b 4-3 -H C) 01, 0 C%j 0 4-3 CH 1ý - co 0: ) I CD cl, VN CD LA CIZD 129. (60) or on the valve seat (20), Figs (2-89) and (2-90). Therefore, it has been concluded, from the foregoing discussion, that the most significant variables affecting cyclic variation are the mixture motion and the effect of small scale, eddies on the growth of the initial flame kernel. I S. -, / eH 0 Li I 00 01 Co -0 CH 0 0-- :1 Ei -gt +I cu 9-1 00 0 ri 1-IN ci CH 0 C: ) in ri Ln CH PA Hlookis - mm A0 NOI1V83d0 '31V8 31iI: ASIN AO SS3NHIOOýiS- 130. 00 tH bo :j (n '4-f 1-4 r4 P4 /I Ll ý ? --- a -ri 0) p 4-b 0 09 -A Ld 0 -d -1 Z- - 0-4 0' W0 .0 P4 -P lop c! ) cc 0 co $4 -r4 Cd 00 :j 4-) v . - Of D (D . J* 0 LL 0 $-1 13 0 (, III cr 'o &ý ,Cd $4 N 0 C. 4 0 00t; " -H to 0 ; r, 4-b a C) C) C) 0) z to) 4-1 000 Cl CH 0 C4 0 09 8 -7. p C) ul cr-) 30190 4S(J/6 'NOTIdVirSNO3 'ONINII MVdS i3n-4 DL41: )3dS cn co "" . f-I 132. a measure of the flow velocity. The DC component of such unbalance voltage is a measure of the mean flow velocity while the AC component. provides a picture of the fluctuations in the flow. Examination of the response of constant current anemometer to turbulence fluctuations (79) shows that its sensitivity is a function of the wire temperature (Tw), the mean flow velocity (5), and the frequency of the veldcity fluctuations (n). It decreases for large values of the frequency and a compensating amplifier must be used to correct the errors due to the thermal inertia of the wire. The time constant of this compensating circuit must be equal to the time constant of the wire. The latter is a function of the mean flow velocity and the compensating network should, therefore, be readjusted when the mean flow velocity changes. Moreover, the constant current anemometer could not be used in a field of high velocity fluctuations'because of the risk of burnipg out the wire at high rates of current flow. Therefore such a technique cannot be used in an engine because of the wide variations in the gas velocities and consequently the heat transfer rate from the wire during the cycle. 3.1 The Constant Temperature Hot Wire Anemometer This method employs a feedback amplifier to supply current to the hot wire in order to keep the wire resistance, and accordingly its temperature, constant as far as possible. In principle the constant temperature anemometer consists of a Wheatstone bridge and a servo amplifier, Fig. (3-3). The active bridge arm consists of the probe and one of the two top resistances. 133. The passive bridge am contains the other top resistance, the comparison resistor and a compensating network to minimise the influences of inductance and capacitance of the probe cable. When the bridge is in balance, no voltage differences exist between the end points of the horizontal bridge diagonal. Any change in the flow acting on the probe will affect the temperature of the sensor, causing it to grow cooler or hotter as the case may be. The resultant resistance change brings about a voltage difference at the horizontal diagonal which is fed to the input of the servo amplifier. The output voltage of the servo amplifier is applied to the bridge input (bridge top) under such phase relations that the original temperature will be restored by increasing or reducing the bridge operating voltage. The higher the gain of the servo sysýýcýR, the more rapidly the amplifier responds, the lower error voltage will be required at the horizontal bridge diagdnal in order to compensate for a temperature change in the sensor. This is of great importance because it is the method employed in attempting to overcome the thermal. inertia of the probe. 3.2 Calibration of the Hot Wire Anemometer Accurate measurement of gas velocities and turbulence in a fluid field depends to a great extent on the accuracy and generality of the expressions used to describe the heat transfer mechanism from the hot wire anemometer used. Such requirement is of paramount importance in engine investigations where the Wires are usually operated under conditions of varying pressures and temperatures which are different from the calibration conditions. R- The work of many investigators of heat transfer from long cylinders, with flow perpendicular to the axis., was reviewed in 1932 by Ulsamer (72), in 1954 by McAdams (73) and more recently in 1972 by Andrews et al (74). McAdams showed that most of the available data of various investigators are very close to those of Hilpert (75) which cover a very large number of diameters from 0.0079 to 5.9 inches as shown in Fig. (3-4). All these data are correlated by an equation of the form n Nu = 33 Re where Nu is the Ilusselt number and Re is the Reynolds number. The exponent (n) increases and the factor (B) decreases as the Reynolds number increases. However a more general expression for the heat transfer from a cylinder to a gas or liquid perp2ndicular to the cylinder t axis, as expressed by many investigators, could be written as Nu =A+B Re (3-2) where A, B and n are constants over a specified range of Reynolds number. The constant A in equation (3-2) is intended to represent a combination of the conductive heat loss of the wire supports with buoyancy effects as a component of the total heat loss. This constant has an initial value of the order of 0.3 and is set equal to zero for Re) 44 in Collis and Williams' investigation (76) and for Re> looo in McAdam's investigation (73). Davis and Fisher (77) have criticised the existence of such a constant and show that the effect of buoyancy in the analysis of forced convection from heated wires could be ignored, when the wires 134. 0 135. are sufficiently small. No other explanation was found for the origin of the constant A and was, therefore, attributed to the error introduced by extrapolating the measurements of electric power over a limited range of velocity to zero velocity. An error that resulted in an over-estimation of the power loss at zero velocity and could be as high as-eight times the true value, As shown in Fig. (3-5). Different calibration procedures were used in the published investigations on measurements of gas velocity-in engines. A review of the important ones will be discussed briefly below. Semenov (22) overcame the problem of variations in fluid properties during the engine cycle by redur-Ing the current flowing through the anemometer bridge circuit at the temperature and pressure conditions of gas flow in -the engine (I) to the bridge current that flows at ambient conditions (10). The flow velocity, U, was then evaluated from the. calibration curve U=f (I) obtained at ambient conditions as follows Io =K (p, T). I (3-3) The coefficient of reduction K (p, T) is determined from*the equation of the heat balance of the wire as given by 12 Rw = h. A (Tw -T 9) (3-4) where A is the lateral surface area of the wire, h is the heat transfer coefficient, Tw and Tg are the wire and gas temperatures respectivelY. Using a relationship between Nusselt and ReYnolds iI numbers in the form yn Nu =B Ro (3-5) Substitution for the heat transfer coefficient from equation (3-4) the coefficient of reduction K(p, T) was given by Yo)m/2 M/2 KO) K(p, T) (3-6) J? g Kg ý00 Making use of the polytropic relation and expressing the gas density in the cylinder in terms of a filling coefficient the following expression for K(p, T) resulted 1 m/2 K m/2 K(p, T) -- (Tg) w- I( 0) ( Y-R) (3-7) v. To K9 PO k1 where f is the fluid density T is the fluid temperature K is the fluid thermal conductivity 1P is the fluid viscosity n, is the polytropic index of compression J3, m are constants and the subscripts o and g refer to conditions at ambient and gas conditions respectively. 136. Barton et al (11) calibrated their sensors using a heat transfer law as in equhtion (3-2). 1. The values of the constants A, B and n were obtained experimentally. Matsuoka et al (15) used a similar expression for their calibration of gas velocities at TDC. The values of the constants A, B in the latter case were obtained by taking the ratio of gas properties at TDC and at ambient conditions, while the exponent n was taken as 0.5, as proposed by King (78). 137. Winsor (23) operated his hot wires at two different temperatures and used King's expression for the heat transfer from the wires. Ile derived a relationship between the pressure- velocity product*and the differencein the dissipated power from the wire at the two temperatures as given by: H2 2 LC+C (P 1j) (3-8) R It RL12 where E is the bridge voltage, R is the operating resistance, P is the pressure afid U is the gas velocity. The subscripts H and L refer to the high and low operating temperatures respectively. The values of the constants C and C were 1.1 2 obtained experimentally. i'diies (24) used a heat transfer expression developed by Collis and Williams (76) and accounts for end losses from the wires by an expression derived by Davis and Fisher (77). The radiation losses were also considered. However, their effects are-almost negligible (77,79). A calibration procedure based on analytical methods, which was experimentally checked, was presented by Davis and Fisher (77) in 1961.. This procedure has been successfully used by Dent et al I (92,93) in engine investigations and was employed in the present work. In this case, a comprehensive heat balance for the wire leads to an implicit equation in a single unknown variable (K which could be obtained by successive iterations. This equation is given by: 12 Rw 2 Ks Rg tanh(41 K11 t/2) R-R wg -1 Klj=o AKTt (T w ---T 9KT KJL Rw (3-9) 138. 12ýa ck rr dh where K K- A2 KA (3-10) Ww d is the wire diameter t is the wire length A is the wire cross sectional area. 'K are the thermal conductivities of wire material T s at the operating temperature and supports temperature respectively T T are, tN) wire and gas temperatures respectively w 9 RR are the wire resistances at the operating - w9 temperature and gas temperature respectively 9 is the electrical resistivity of the wire at gas temperature 0ý is the coefficient of temperature for wire material I is the electric current and h is the heat transfer coeffýpient. Davis and Fisher (77) showed that the heat transfer coefficient could be related to the mass/flow past the wire by the following relation h CK vwU (3-11) Tr K9 where is the fluid density C is the-specific heat at constant volume v K K is the thermal conductivities of the gas at the w g wire operating temperature and gas temperature respectively U is the fluid velocity and Cf is the skin friction coefficient which is given by: 139. ef = 2.6 Re- /3 0 Re -< 40 (3-12a) -1 /2 cf = 1.4 Re [40 Re"< 1000 (3-12b) where Re is the Reynolds number based on flow conditions approaching the wire and the wire diameter. ' The lower range of Reynolds number (Re< 40) covers most of the practical range of hot wire anemometers. Substituting equation (3-12a) into equation (3-11) gives the. following relation hd 2.6 Kw rry or NU =-2.6 rr -C cpp9d. U K 9 ýg 13 Pr. R. (3-13) (3-14) where Nu is the Nusselt number, Pr is Prandtl number, Pg is the dynamic viscosity of the fluid at its temperature, Cp is A the specific heat of gas at constant pressure and T is the ratio between specific heats at constant volume and constant pressure, The variation of gas properties with temperature is required for such a calibration procedure. This was obtained from a polynomial curve fit of the published data in the literature (95-100), as will be discussed in appendix A3. 131. 3. HOT WIRE ANEMOMETER AND ITS CHARACTERISTICS FOR TURBULENCE MEASUREMENTS The hot wire anemometer has been the most satisfactory instrument for measuring turbulence and turbulent. fluciuations. This is because its small size introduces a very small disturbance of the flow field and its low thermal inertia makes a reasonably high frequency response practical. Fig. (3-1) shows an example for the frequency characteristics oý a constant temperature hot wire anemometer as a function of flow velocity. A hot wire anemometer consists of a fine electrically heated wire stretched across the ends of two prongs. The-wire is cooled by the flowing fluid, causing the temperature to drop and consequently the electrical resistance of the wire to diminish. There are two basic methods of operating hot wire anemometers which are the 'constant current' and the 'constant terop-eraturel. In the first method the electrical current is kept constant and the fluid speed is determined from the chandbs in electrical resistance, while in the second method the wire is maintained at a constant temperature and the fluid speed is determined from the measured value of the electric current. In either method, the hot wire consists of one am of a Wheatstone bridge circuit. The constant current anemometer uses a i3robe powered by a constant current from a power source having high internal resistance so that the current through it will be independent of any resistance change in the bridge. Fig. (3-2) shows a practical set up of a constant current bridge. The probe resistance changes 0 are the result of flow changes acting on the probe. The consequent voltage difference across the horizontal bridge diagonal is a 140. 3.2.1 Physical Properties of Hot Wire Probes Calibration of hot wire probes requires an'accurate knowledge of the physical properties of the hot wires. This includes wire length, wire diameter, electrical resistivity, thermal conductivity of the wire material and the temperature coefficient of resistance of wire material. The physical properties of wire material can be obtained from the published data or measurements of individual wires. The first method requires that the wire dimensions should be known with sufficient accuracy. The temperature coefficient of resistance for the wire material (C<) used in the present work (pt - 20% Ir) was obtained by heating a sample of wire material in an electric oven for a long period of about two hours for annealing before measurements of its resistanc&71's' carried out during heating up and cooling down processes. Plotting of I (RH/RC - 1) against (TH - TC) yields the value of (c<) as given by: Cý, =(RH /R C)-1 (3-15) T il - Tc where R is the wire resistance and T is the wire temperature. The subscripts H and C refer to the hot and cold conditions of the wire respectively. A typical example for the graphs obtained for a 10 micron diameter wire of pt - 2076 Ir material is shown in Fig. The value of Oý-is obtained from a least square fit of the data, appendix B13. The wire length was measured using a travelling microscope and uncertainties of the order of fO. 02 mm is likely 141. to exist. This could result in an error in calculating the wire cold resistance of about -0 . 07 ohms for a wire having the following nominal values of Rc =7 ohms, and length of 2 mm. If such a wire is operated at a resistance of 10 ohms (Tw = 5200C), the error in the calculated wire operating temperature would be of the order of t2OOC (or t3.85% of the nominal value of wire operating temperature). Such-an error would result in an error in the estimated heat transfer coefficient and a more pronounced effect on the estimated gas velocity because the velocity is proportional to the third power of the heat transfer coefficient. Moreover, because the probes have several junctions of dissimilar material, a temperature difference is developed when a small electric current (about 2 mA) is passed through the wire to measure its cold resistance and hence a small power dissipation will exist in the probe assembly, owing to these temperature gradients. This results in an over-estimation of the measured cold resistance and consequently in the predicted wire temperature. Davis and Fisher (77) showed that although these small power dissipations will be negligible at current densities sufficient to heat the wire appreciably during its Operation, it could lead to an over-estimation of the measured cold resistance at very low levels of dissipation. For example, a wire of 6.5 ohms cold resistance achibits the following measured resistaLrices: 7.6 ohms at 6.5 PW power dissipation 7.75 11 ' at 2P IV power dissipation 142. A much better estimation of the probe cold resistance could be achieved by operating the hot wire at a constant air velocity while reducing its operating resistance until no change is observed in the output voltage. This is usually a very small value which could be attributed to an extraneous noise in the system. Repeating the same experiment at another air velocity, which could be the case of zero flow and plotting th6 difference in the output voltage between any two cases, shows a levelling of the curve after a certain value of operating resistance. Such a value could be used as a better approximation to the exact value of the probe cold resistance and represents the conditions where the heating up of the wire by the flowing current has been just equal to the power dissipation at the various dissimilar material junctions of the probe. Fig. (3-7) shows typical graphs of the difference in the output voltage of the hot wire anemometer between two I cases of air velocities and the zero flow conditions. Therefore a reasonable calibration procedure could be achieved if the measured cold resistance is changed slightly to yield an agreement between the experimental and theoretical calibration curve. An iteration program (94) is used for such a purpose and the amount of change in the cold resistance has always been within the tolerance of measurements as stated before. The correct value of cold resistance should, therefore, ensure coincidence with all curves produced for the same wire a at different operating conditions. Figs. (3-8) and (3-9) show a set of experimental calibration curves together with the theoretical prediction of the iterated cold resistance where an excellent agreement could be easily observed. 143. 3.2.2 Anemometer Drift It has been noticed that some wires change-their characteristics during engine tests, especially after long periods of engine running at higher speeds. This is observed as slight changes in the wire cold resistance in most cases which results in a shifting of the calibration curve, while in a few cases the cold resistance remains very close to its original value but shifting of the calibration 01 curve still occurs. These changes could be due to: contamination of wires with oil or dust particles inside the combustion chamber, oxidation of wire, erosion of wire surface or any other unknown factors. Every care was taken to run the wires below their oxidation temperature, which was about 7000C., tageFther with running the engine with a heavy oil but the trends were unpredictable. As such changes in the wire characteristics could not I be tolerated in the present investigation, a very careful checking procedure on the wire characteristics was employed before and after tests. Wires which did not maintain their characteristics were replaced and their results excluded. The checking procedure could be summarised as follows. Every new wire was operated for about one hour before starting its original calibration process in the wind tunnel. This anneals the wire and usually its cold resistance drops slightly but remains constant after that. A first calibration is then carried out. The wire was introduced into the engine and run for about 144. j hour and when it cooled down, its resistance was checked and the test was carried out if consistent values of-cold resistance was maintained before and after the engine run. A second calibration procedure was always carried out after each test to make sure that the calibration curve was maintained. All the reported data in the present work corresponds to wires which have proven repeatability in their calibrations. 3.3 The Response of Constant Temperature Hot Wire Anemometer to Turbulence As shown in (3-2) the heat transfer relation between the wire and the surrounding gas could be expressed by equation (3-14) - hd 2.6 113 (, Peg) (3-14) Kw rl rFg K9 . 1. This relation could be rearranged in the following form 2.6 Pr (Lg ) 113 u 113 (3-14a) ITT d 2/3 #9 The f irst group of variables on the right hand side of equation (3-14a) is a constant value for a certain wire diameter and for air as a working fluid. For a given operating wire temperature Kw is constant and equation (3-14a) could be simplified to the following form hC1(fg) 113 U 113 (3-14b) P9 where c 2.6 Pr Kw (3-16) n -f p 145. Using the equilibrium relation between the heat generated in the wire (Q e) and the heat loss by convection, one can write h= Qe 12 Rw a' R (3-17) , red e (T,, . I-s de (Rw - Rg) where Cl< is the coefficient of temperature for wire material and Ro is the wire resistance at a reference temperature. Substituting for (h) from equation (3-14b) into equation (3-17) we get where 12 Rw g 1/3 1/3 (Rw Rc2u (3-18) 9g c C, ` ildt - (3-19) 2R0 Now defining the instantaneous turbulent velocity (U) as the sum of an average value (U) and a fluctuating component (dU) as given by IJ =U+ dU (dUSO (3-20) Furthermore defining the turbulence intensity (Int) as the ratio between the fluctuations to the mean value, one can write dU Int u or Fu (Int) u dU dE I (3-21) dE u 2 - 17 KU (3-22) 146. where and e U2 N, rý2 are the root mean square values of the fluctuating components in gas velocity and bridge voltage respectively. K is the slope of the calibration curve. (E vs U) at appropriate gas conditions. and E is the bridge voltage at gas conditions. An expression for the slope of the calibration curve (K) could be derived from equation (3-18) after rearrangement of terms as follows: E2 c2gu (3-18a) R (R. - R ww9 or E9 [C2 Rw. (R w-R9 ýg (3-18b) Differentiating equation (3-18b) we geý ?g 116 1'' K= dE =*EC2 Rw (Rw - RAI (- ) 5/6 (3-23) dU 6 pg U Multiplying both sides of equation (3-23) by U we get CR (R - Rg)]l g) I IT U 1/6 KU 2ww (3-24) 6g Combining equations (3-18b) and (3-24) gives KU (3-25) Substituting for XTJ into equation (3-22) gives a simple expression N for the turbulence intensity in terms of the root mean square value of the fluctuating voltage component and the mean value of the bridge voltage at the appropriate gas conditions as given by: 147. Int 6e uE (3-26) Another approach to the problem could be carkied out using the definitions of temporal values of variables as the summation of a mean component and a fluctuating component as given by U=+U, (3-27a) I=+i, (3-27b) E=+ e' (T-27c) where u, Vand e'are the root mean square values of the fluctuating components of gas velocity, current and bridge voltage-respectively. From the thermal equilibrium conditions, the heat transferred per unit time to the surrounding fluid must be equal to the heat generated per unit time by the electric current through the wire. Therefore: 12 Rw = fy dIh (Tw - (3-28) Now substituting for h from equation (3-14) we get, after some rearranging of terms, 12 Rw =d 1/3 e Kw (Rw - Rg) 2.6 Pr) ( _4 113U 113 Oý no y pg (3-29) or 12 Rw = C4 (Rw -R 9) Pg)1/3 u 113 (3-29a) Fg- 148. where C4=2.6 Pr Kw I dl/3 -ra no (3-30) Expanding U in a power series and neglecting second order terms, knowing that the electric resistance of the wire is constant and equal to Rw, and substituting for I from equation (3-27b), we get 12 Rw +2i R-W =C 1/3 1/3 fgV3 -V3 Ul (3-31) 4 (Rw -R) (-f-G) 5+C Rg) (-) U. - 9 Y9 4 /Jg 3U whence j2 jjw 113 C4 (Rw -- R9 (Lg) (3-32) pg and g 113 u 2Vi fiw C (Rw -R)U (3-33) 49 ýv g 3U Equation (3-33) could be written in the form c4 (Rw -R 9) g)113 IU (3-33a) 1 iiw yg 6U The consequent fluctuating voltage component e' could be given by e10 RW c4 IRW - Rg) 9; /3 ý 113 u (3-34) P9 - 6 or S. ut (3-35) / where S is the sensitivity of the constant temper4ture'hot wire anemometer S=2.6 Pr kw ed 113 (Rw -R 9) (3-36) ri Ro 61 5213 The turbulence intensity (Int) could be obtained, therefore, by substituting for 5 from equation (3-32) into equation (3-34) which gives once again u2 u6 72 6 e" Int (3-22a) uuEE where i fiw is the mean value of the bridge voltage corresponding to the gas velocity 5 at the appropriate gas conditions. The aboveanalysis has assumed a perfect equilibrium between the heat developed by the electric current and the heat transferred to the flowing gas. This. is possible only if the thermal inertia of the wire is infinitely small. Due to the 149. finite thermal inertia of the wire, however, a time delay exists between the rapid fluctuations of gas, velocity and the corresponding temperature fluctuations of the wire. Therefore, in order to study the dynamic behaviour of the wire a term representing this thermal inertia of the wire should be introduced into equation (3-29). Moreover the slight variations in wire resistance should be considered. This could be written in a similar form to equation (3-27) as follows: Rw=Rw+rw (3-37) 150. Also equation (3-29) is modified into the following form: 12 (R -R)(gg) 113 U 1/3 +C'd Tw Rw "" C4 w9 Ys w -dr- where C is the heat capacity of the wire w 2 C =c d (3-39) ww IV 4 cw is the specific heat of wire material per unit mass is the density of wire material w Substituting equations (3-27a), (3-27b) and (3-37) into equation (3-38), calculating and neglecting quadratic terms in the small fluctuations il, r and ul we obtain- W ý- I (3-38) f2 Yg 113 113 +2Vc (r) U+R U'l + CwdTw w4gwg= I Itr 3TJ dt Introducing the relationship between the compensating electronic current V and the change in wire resistance rw as given by iII r' -9 tr (3-41) where g tr is the transdonductance of the electronic circuit. Equation (3-35) could be written in the form: di + c< Ro (C4 ( ý9) 113 U 113 _ 12 +2 12 ýw gtr dt Ew- pg _ C4 gtr 1 Ro (lýV - ng) fg )113 ü113 U, -Z- =0 cw F9- 3U (3-40) (3-42) 151. Using equation (3-32) we can write C4 fg ) 113 U 1/3 12 =R9 12 (3-43) log Rw-R9 Substituting equation (3-43) into equation (3-42) gives di' + CK R9+24- gt i9 -0tR o gtr 3 R, U'- =O (3-44) dt cw IR w-R9 cw Hence the time constant for the constant temperatiire hot wire anemometer ( Z, ) is given by CT c Zc T -2 w (3-45) cA R01 [Rg/(R w- Rg)] +2 fi w gtrl Examination of equation (3-45) shows that the frequency response of the constant temperature anemometer system could be improved by operating the wires at higher operating temperatures and by increasing the transconductance of the electronic circuit. The latter effect could not be easily achieved because of the appearance of high frequency oscillations in the bridge system (due to the feedback technique employed in the circuit). Nevertheless, such a feedback has increased the frequency response of the anemometer system by a factor of several hundred compared with constant current operations. Anderson (115) has performed similar analysis for estimating the performance of the 152. system and shown that the anemometer's upper frequency limit is increased, due to feedback, by a factor g as given by g=2aRw 9tr where a is the overheating ratio a= (Rw - Rg)/Rg) (3-46) 3.4 Statistical Analysis of Turbulence 3.4.1 Definitions of Correlations and Scales of-Turbulence Taylor (84-86) introduced new notions in the study of turbulence problems which are the correlation functions or the coefficients of correlation between two fluctuating quantities in turbulent flow. These correlAtions-could be either between velocity components at two points in the flow field, or between the values of a veloc! "ty component in a given direction at a fixed point in the flow field at two different instants (t) and (t +-(). The latter type of correlation which is usually called the 'auto-correlation function' was employed in the present investigation because it is easy to measure with a single hot wire anemometer and because it gives most of the required information about the turbulence structure (intensity, scale and power spectrum), if the conditions of isotropy and homogeneity are satisfied, as will be discussed later. The auto-correlation function-is defined by R (v )= 'im u(t) -u (t +Z )dt or Rt(r)=uMu (t +, c ) (3-47) (3-48) 153. Such a function describes, therefore, the general dependence of the values of the data at one time (t + Z) on the values at another time (t). Fig. (3-10a) gives an illustration of the definition of the auto-correlation function while Fig. (3-10b) shows a typical shape of this function. We can also define an auto-correlation coefficient by R' (T) R tt ul (t) .u (t + 7 (3-49) where the time average of U2 is taken with respect to undelayed signals. The most important properties of the-auto-correlation function could be summarised as follows R= lim 1 -i u (t) u (tý = (3-50) and correspondingly (0) = 1.0 (3-51) Therefore, the auto-correlation function reduces to the mean square value at zero time delay (r ). 154. Also Rt lim uM-u (t - -C ) dt T-. Poc put t' =t -'c gives Rt lim T -cc so 1 Rt( -C ) Thus, the auto-correlation function (and correspondingly the auto-correlation coefficient) is a symmetrical funýtion of -r (3-52) Hinze (79) showed that the shapE! of the auto-correlation coefficient curve in the neighbourhood of t=0 could be expressed in terms of the velocity derivatives with respect to time as follows: t2 gL]t = t4, ý4 R! t t=0+. .. -53) R' M++ (3 t T! at ,-0t4 2 R' Mt+ -b u (3-54) 2 zt It =041 U2 12 It =0 t2u zt 155. Now we can define a time such that t u a2 ýt 2 u2 I ; ý-t I=-1, (3-55) t0 L-Tt. 2 jt0 I- is called the micro-time scale and is regarded as a t measure of the most rapid changes in the fluctuations of u(t). For small values of t equation (3-54) may be written as IMt2 t2 Yt Another integral time scale could be defined as cr- Lt= R'(t) dt It (3-56) (3-57) This integral scale (or macro-scale)L t could be considered as a rough measure of the longest connection in the turbulent behaviour of U(t). Taylor also defined correlation coefficients between the fluctuating velocity components at two different points in spacei Fig. (3-11). The longitudinal correlation coefficient Rx between the values of u at two points A and B separated by a distance x measured in the direction of the x axis is given by: Il' UA UB x (3-58) AB 156. Also, the lateral correlation coefficient R' between values y of u at two points A and B separated by a distance y measured in theY-direction is given by R' (Y) u A. UB y Nfu FUB Similar to the auto-correlation (time-correlation), the (3-59) longitudinal and lateral correlations are symmetrical functions of x and y respectively. The general shapes of these correlations are shown in Fig. (3-12). Both correlation coefficients decrease from a maximum value of unity to zero as the separation distance varies from zero to infinity. The decrease of either may be a monotonous or an ospl-llating function. The shapes of these correlation coefficients-in the neighbourhood of zero separation distances could be expressed as follows: 2 R' y y 21 and -IR Ty T2ý y4 y 244 +X _RX 2! -b x2 11x=0b x4 x=0 (3-60' (3-61) 157. or u u24 bx 4u2Z2 ]X =O x0 and y21 -d uy41[ ju ] u2- «Dy (-Yu2Zy2y =o For small distances we can define the length micro-scales as follows and Therefore: ýx R' y2 y ýy . 1. S..., - ' 2 -2 u Ru ýx X2 0 2u 2X0 2Ru2 -6 y 2 ýy 2u 2y '), yy=0y=0 (3-62) (3-63) (3-64) (3-65) (3-66) (3-67) 158. These micro-scales are considered as a measure of the average dimensions of the smallest eddies in the flow field which are responsible for the dissipation of energy, or more correctly as the dimensions of eddies which At the same intensity produce the same dissipation as the turbulence considered. We can also define the macro (or integral) scales of turbulence as follows: L R' dx (3-68) x Of x and cc L R' dy yfu (3-69) These lengths could be considered as measures of the longest connection or correlation distance between the velocities at two points in the flow field. For isotropic flow a relationship exists between the two types of correlation which has been verified experimentally by Von Karman and Howarth (101). Such a relation is given by ID R; ( r) R' (r) + -t = R; ( r) (3-70) x2 zr Substitution of equation (3-60) and (3-61. ) into equation (3-IrO) gives the following relation: Ry2 62 R (3-71) r2- r=c) t. 2ý 159. Using equation (3-71) we obtain the following relationship Cx between the longitudinal and lateral micro-scales andl) xy as given by: 4T 2 (3-72) Also integrating equation (3-70) from zero to infinity with the condition, Lim r Ry =0 gives r-o. oz L2L (3-73) As mentioned earlier, if the turbulent f ield is homogeneous in its average structure, one can expect some xeTdtionship between the. time correlationýand the space correlations. Also, I similar relations could exist between the time. -scales as given by equations (3-55) and (3-57) and the length scales as given by equations (3-66) and (3-68). The relations could be obtained using Taylor's hypothesis for a turbulent flow with a mean velocity 5 in the x-direction where 5 )ý/' u which could be expressed as follows: and (3-74) ID t 160. Lin (109) showed that, for isotropic turbulence and large Reynolds number, an estimate of the accuracy of Taylor's hypothesis could be made from (d u/dt) 2_ u2 52 (Z UPD X) 2 U- 2 In fact, the turbulence intensities inside the combustion chamber of an engine reached much higher values than those observed in pipe flow, in spite of the low values of mean flow velocities for the former case. For example, the magnitudes of turbulence intensities in pipe flow are, usually, less than 20% except in a small region very close to the wall where much higher values are observQd,. depending (3-75) on the surface conditions (104 - 108), while engine measurements give intensities as high as 40% (22). 'however, a check on the validity of Taylor's hypothesis for engine investigations could be made by applying such a condition (3-74) to equation (3-75) and calculating the corresponding values of turbulent intensities. This gives an estimation of intensities of the order of 44.77o which is higher than the-measured values in engine investigations in some cases, as will be seen later. The physical interpretation of equation (3-74) is that if U)ý u, the fluctuations at a fixed point in the field may be imagined to be caused by the whole turbulent field passing that point with a constant velocity U. The oscillogram of the velocity 161. fluctuations at that point will then be nearly identical with the instantaneous distribution of the velocity. u along the x-axis through that point. Therefore: R' (x) = RI (-c) (3-76) x (3-77) and ULt (3-78) This explains clearly the reasons, as mentioned earlier, for the selection of the auto-correlation function and auto- correlation coefficient for studying the characteristics of the turbulent field in the present investigation. 3.4.2 The Spectrum of Isotropic Turbulence Considering turbulence to be made up of eddies of different size, the total kinetic energy of the turbulent field 'o be distributed among the eddies. The may be considered '41, spectrum of turbulence, gives the distribution of kinetic energy over the various frequencies occurring in the field. At any point in isotropic turbulence the mean energy of the eddies is proportional to U' 2. Taylor defined the one dimensional spectrum function F(n) to be the fraction (u2) of the total 72 ekiergy (u) which is due to frequencies between n and (n + dn). 162. 0 .W ý 2 u n+ dn I 2 u n F (n) dn (3-79) and P(n) dn (3-80) There are direct relations between the power spectrum function and the auto-correlation function and correspondingly between the power spectrum function and both the micro-scales and macro-scales of turbulence. These relations could be explained if we imagine the whole field to have a translation with uniform velocity U in the X-direction. Then at a stationary point, 'the largest eddies will cause fluctuations of low frequencies, whereas the smallest eddies will cause fluctuations of high frequencies. Therefore, if the turbulence contaixxs only large eddies, the spectrum function will exist mainly in the region of low frequencies; if there are only ýhall eddies P(n) will exist mainly in the region of high frequencies. Hence one may expect when the auto-correlation curve decreases rapidly to zero, the spectrum will have high values in the region of high frequencies and vice versa. Generally, the auto-correlation and power spectrum functions are Fourier transforms of each other as given by the following relations: OC R; (t) =j P(n) ei 2rTnt dn (3-81a) 0 or (using the condition of symmetry of ly(t) cc R; M F(n) Cos 2 fT nt dn (3-81b) t0f 163. Similarly P(n) =4 R' (t) e-i 2 IT nt dt and cc P(n) 4 R' (t) Cos 2 TT nt dt (3-82a) (3-82b) Using equations (3-55), (3-57), (3-66), (3-68), (3-81b) and (3-82b) we can write the following relationship between the longitudinal correlation and power spectrum function on one side and the micro-scales and macro-scales of turbulence on the other side as follows: 00 Rý (X) SF (n) Cos 2 Tr nx dn (3-83) U, F (n) 4 CG R' (x) Cos 2TTn x dx (3-84) x L R' (t) 1 lim P(n) (3-85) tTn-. 0 Lu lim F(n) (3-86) x4n0 1 /02 Rý 2 00 2 222 TT JF(n) n dn (3-87) ý-t tt=0a 164. and 2 F (n) n2 dn Iýx 2x21x=0 2C All the above mentioned relations are concerned with the one- dimensional energy spectrum. w - ýBecause of the three- dimensional character of turbulence , the energy spectrum must also have a three-dimensional character. What is actually measured by means of a hot wire anemometer ýs, strictly speaking, a one-dimensional cut of the spatial - spectrum. However, for an isotropic flow field, relationships exist between the one-dimensional spectrum functions in different coordinate directions (79). Hinze (79) made use of the work of Kolmogroff, Von Karman, Lin, Batchelor and Townsend to analyse the spectrum curve and develop a mechanism of the tuAulence structure. The analysis is carried out in teims of the-wave number (K) instead of the frequency n and an enerqy spectrum function F(K) instead of F(n) as given by: K= TI n u (3-88) (3-89) F(K) F(n) 2 Tr 00 J F(K) =1 (3-90) (3-91) 165. It is sufficient here to summarise briefly the main ideas of that mechanism. The spectrum curve is divided into different regions according to the size of the eddies and their role in the dynamic behaviour of the turbulence structure as shown in Fig. (3-13). The larger eddies are assumed to produce smaller and smaller eddies through inertial interaction, thereby transferring energy to smaller eddies. At the same time viscosity effects and with them dissipation, becomes more important for the smaller eddies. In the fully developed state it is not the largest eddies that wil. 1 have the maximum kinetic energy, but the eddies in the higher wave number range. The range of the energy spectrum where the eddies make the main contribittion to the total kinetic energy of turbulence is called tho-Idnergy containing eddies. In this range the energy spectrum shows its maximum, which could be associated with a wave number Ke- On the other hand, dissipation by viscous effects increases as the size of the eddy decreases, up to a maximum for a certain size of the smallest eddies, where another wave number Kd could be defined. The value Of Kd corresponds roughly to the maximum in the (IC2 F(K), K) curve (see equation (3-87). Comparing the relative rate of decay of the total kinetic energy of turbulence (du, 2/dt)/u'2 with the frequencies of various eddies (u' K. ) on the spectrum curve, three main regions could be distinguished. The region of the largest eddies where the frequency (u' K) is very small compared with K the rate of decay; 166. the region of the smallest eddies where the frequency ( Uý Kd is very large compared with the rate of decay and in between a region where the frequencies (uý K) are of the same order as" the relative rate of change of the total turbulence. The latter region consists, obviously, of the energy containing eddies, since these eddies make the main contribution to the total energy of turbulence. In the higher wave numbers, the decay process may be considered as a relatively slow process compared with motion of the eddies. Such a range may be considered, therefore; as nearly steady and the rates of change of the-mean value may be regarded as negligible. The eddies corresponding to these higher wave numbers are excited by the transfer of energy by inertia forces from the larger eddies. It may ý? Eissumed that, in rpontrast. with the largest eddies they are independent of the external conditions producing the forces-i-that generate the initial largest eddies. This led Kolmogoroff (89) to make the following hypothesis: "At sufficiently high Reynolds numbers there is a range of high wave numbers where the turbulence is statistical in equilibrium and uniquely determined by the parameters (W 3d u'2 ) andY , where W is the rate of energy 2dt dissipation and is the kinejýatic viscosity. This equilibrium range is termed 'universal' because the turbulence in this range is independent of external conditions". 167. Kolmogoroff characterised this region by a length scale and velocity scale as defined by 3 For the length scale I= (-19; ý ) (3-92) For the velocity scale V= (VVj) %/4 (3-93) The Reynolds number for this region equals unity and the wave number Kd could be considered of the same order as 1/'fL . Similarly in the region of the energy containing eddies we can define (Ke) as of the order of 1/L. where L. is the average size of the energy containing eddies.. - Kolmogoroff also defined a sub-range in the region of large Reynolds numbers, but where the dissipation is very far below the region of maximum dissipation so that it could be neglected compared with the flux of energy transferred by inertial effects. In such a sub-range the effect of 1) would then vanish and the turbulence could belharacterised by (W) only. 3.4.3 The Relationship between the Micro-Scale and the Macro-Scale for Isotropic Turbulence This relation could be established by equating the rate of decay of the kinetic energy as given by Jq to the rate of dissipation in a flow of viscous fluid as given by: U2V2W2 w2+2y+2 ID v2 (-, 5- -u + ZI wvv2zuw2 x 'ay ( 'D y+ 'Dz )+( :ýz+x)I (3-94) 168. where u, v and w are the fluctuating velocity components in the x, y and z directions respectively and 22 v+w Introducing the condition of isotropy, Taylor (84) simplified equation (3-94) to the following expression W=6u )2 +6( -zu)2 +6 ('ý-v - 2-u x -0 Y 'DX 'D y or I 7.5 (Du) Ty Substituting for 'X from equation (3-67) into (3-95) we get y W=-7.5 u2 = 15 JJ U2/ 2 -i y In fully developed turbulent flbw, the Reynolds stresses are proportional to the square of the turbulence (3-95) (3-96) fluctuations. Therefore, the work done against these stresses, which in the absence of external forces must come from the kinetic energy of the system is proportional to f U3 /L, where L is a linear dimension defining the scale of the system which may be taken as L.. Equating the two expressions for the dissipation we ge A Lx (3-97) 169. Where A is a numerical constant of the order of unity. Defining two Reynolds numbers based on Ay and Lx as given by Reuy (3-98a) v and Re I? LX (3-98b) v Equation (3-97) could be written as L xA Re (3-99) xy 15 and 2 Re,, A- ReX (3-100) 15 Robertson (102) has reported experimental values for the ratio between Lx and "Y at the-centre of a conduit where the condition of isotropy is approached and showed a definite tendency for the scale ratio to increase with Reynolds number (Rex) and approaches the expression predicted by equation (3-99) at Re > 80. Similar results have been reported by Sato and Yamato (103) for turbulence measurements behind a grid. In the latter case a curve fit of the experimental data was given by the following equation: 170. 1.23 0.0228 Re X+1.06 (Re, ýp 30) y Fig (3-14) shows a comparison between thQ experimental data of Robertson (102), the prediction of the isotropic theory and the empirical relation (3-101). The measurements of Laufer (107) in channel flow are also plotted. 3.5 Effect of Large Turbulence Fluctuations on the Response of a Hot Wire In the previous analysis (3-3) for the rýsponse of the hot-wire to turbulence fluctuations, the relative. intensities were considered to be small (of the order of 107o) so that a linear relation is obtained between the voltage fluctuations and the velocity fluctuations. - As.. will be seen later, the measured turbulence intensities in the combustion chamber are appreciably higher and one may expect a distortion of the linearised hot wire response. The same problem usually exists in inves'tigations of turbulence in pipe flow very near to the walls and in free jets and have been appreciated by many investigators. Therefore, second and higher order terms in the expansion of U 1/3 in equation (3-31) cannot be neglected and the same argument is applied for the use of the slope of the calibration curve to get dU/dE. It is also no longer permissible to consider only the turbulence components in the same direction as the mean velocity, (3-101) I U, We must take into account the other turbulence components also. 171. Thus if 5 is defined as the true mean velocity (which is assumed to be perpendicular to the wire), U, v and w as the instantaneous components of the fluctuation velocity and U meas as the effective velocity which causes the cooling of the wire, then FU-m-e as (u + U) 2+v2+w2 Corrsin (91) showed that the relationship between the actual mean velocity 5-and the measured value U;, ý,, s may be obtained by 5. u+2u+ (11) 2+ (-Y) 2+ (E) meas uuuu or by letting 222 v+w C4 U1+2u+ cK (U) meas u, u (3-102) (3-103) (3-104) (3-105) and expanding the radical out to terms in (11)4 U U{i+ ca) 2 (C(- 1) 3-1 (0ý 2- 5o( +54 meas 2U2U8U (3-106) 172. since u This expansion converges only for 2u Thus it may be seen that what affects the cogling of the wire is a mixture of the three turbulence components u, v and w. The principal difficulty with such a theoretical n correction is that the-valuesof are unknown for the U integer n-/2 . Therefore, the expansion cannot be computed to any desired accuracy. If all powers of u/U higher than the second are omitted and 0( is assumed equal to 2, then from equation (3-106) we get -ýý I u meas u2 (3-107) 1+2 (-ff Hinze (79) obtained similar relations for the case of a two-dimensional flow as follows: 22332 4-5 (1 , -a uIv+1u+... -Umeas 28 D'7 +4 F2 T6- ýT -ý H5=v (3-108) 173. which reduces to the following expression after taking the time average u2 v2 1 u3 3u2 u f5 3L -3 meas 8U+Z Uý-7 + u3 or u2v2 U3 3u V2 meas 4j -2 + -U2 +U34U3 1 U2 1v 2_ 2252 (3-109) If the departure from isotropy is small, so that L egative, that is, the actual U2 the correction is n velocity is smaller than the measured value. Substituting for the measured velQcity from equation (3-108) intq-the heat transfer equation (3-28) and using King's expression for heat transfer from the wire, Hinze (79) showed after lengthy algebraic calculations the relationship between the actual turbulence intensities and the values calculated on the assumption of the linearized theory as follows: ý2 2 2 lin 2) act (u, V) (3-110) 174. where c(l +2 CK ry(ul V) (ul V) +4 qu lin R 12 R (3-111) (3-112) g and (u, V) =* I+ 2cq u3u V"ý 5+ 12 + 12 c;, % 12u4 2 U U2 u2 16 - U2 U2 v4, I+8 CIC + 12 2 7+ 6N, u2V2 u2 452 U-2 42 -U2 16 U2 + .1 (v 2)2 1+4 C4 1v2 (3-113) 452 -2 4 rj 2 u Equation (3-110) shows that what actually_js measured 1. is not the turbulence component u alone, but a mixture of u with the other component v. In order to estimate the order of magnitude of the error made by applying the linearised theory even if the turbulence intensities are not small, we can calculate the value of ey(u, v) according to equation (3-111). Hinze (79) showed that for an isotropic flow if the fluctuating velocity components u and v have normal Gaussian distributions and are normally correlated, then U2 v2 U4 v4=3U, 4 u3 v3=0 u2v 2 UP2 V92 = U, 4 (u I= F=U2 ) (3-114a) (3-114b) (3-114c) (3-114d) 175. Substituting into equation (3-111) gives 19 ýU, 2 8u2 Another approach to the problem of correcting hot wire readings at high levels of turbulence, is to simulate such conditions by vibrating the wire sinusoidally in the flow direction of a relatively low turbulence air stream. The correction factor obtained by applying this procedure-is 11 much smaller than expected in a one-dimensional randomly fluctuating motion. Fig. (3-15) shows an experimental example of this approach (91). Thus for a turbulence intensity as high as 25%, the linearised theory would give higher values with a maximum error of the order of 15%. Such an error is piermissible in turbulence measurements and we can conclude that the use of the linearised theory is still within the accuracy of the measurements itself. 3.6 The Effect of Wire Length on Turbulence Measurements Because of the non-uniform velocity distribution of the turbulent flow, very short wires are required for true 'point' measurements. On the other hand, more uniform temperature distribution along the wire requires high values of length to diameter ratio, and since the minimum wire diameter is usually governed by strength considerations, hot wires of relatively longer 176. lengths than the scales of turbulence are usually used. This necessitates the establishment of some relationship between the measured turbulence parameters and their actual values, as could be sensed by very short wires. If the length of the wire is very small in comparison with the scale of turbulence and if the variation of the I fluctuating velocity component (u') along the wire could be neglected, the value of the mean square of the voltage across the wire could be written as 2Ku where K is a constant depending on the wire characteristics and on the operating conditions. When the length of the wire is not neglected (compared with the scale of turbulence), the variation of -u along the wire cannot be ignored. The measured value of the square of the voltage could be expressed by the fol/lowing relationship e2= K2 ( je ud s) 2 (3-117) meas CN Frenkiel (81) and Skramstad (82) have deduced by two different methods, the same expression of the measured mean square value of the voltage with a wire of non-negligible length e as a function of the true value of u2 and of the transverse. correlation R, as follows: y 177. e22 K2 u2 e R; d meas 0 Defining a correction factor C as follows meas Then I= (s) ds When 4/Ly is large, eq'uation (3-118) coul d be written as 22 K2 ý2eL meas y LY(l)] (3-118) (3-119) (3-120), (3-121) where L is the first moment of the transverse correlation YM curve YM 0rsR; (s) ds / (3-122) It appears, therefore, that when (tlLy) is large, the longitudinal energy of the turbulence measured in the flow is a linear function of the wire length and decreases with increasing The correction factor C in this case is given by: 12[LyL YM L Yýl (3-123) ce Ly ze 178. where Ly(., )/L y2 depends on the shape of the correlation curve When t. /Ly increases indefinitely, it is found at the limit lim 0 (3-124) t/Ly ---). coc. and lim e2 ( meas 0 (3-125) I/L y ---Jýoc K20 The longitudinal turbulent energy measured by a wire whose length is very large in comparison with the traverse scale of turbulence will approach zero even if the real energy is not negligible. For homogeneous and isotropic turbulence one can make use of the relationship between the longitudinal and transverse correlations to express the correction factor C in terms of either of them as follows: Id Rx' R; Rx' (r) +. rd (3-70) Substituting for Ry from equation (3-70) into equation (3-120) we get 1-1 je Rx' (s) ds (3-126) 179. Making use of equations(3-73). &(3-126) we can write for large Q/Ly) that e222 meas K. 2eLx=2Ký2eLy (3-127) or I- LX 2 Ly- (3-128) ce-e When the length of the wire is of the same order of I magnttude as the scale of turbulence (Ly), the correction factor (C ) depends on the shape of the correlation curve (81). For a correlation function of exponential fom as given by R (y) -YlLy -ý- v 1" The correction factor, in this case is giyen by 2_ !L_ exp (_ It Ly Y2 [1 1 T f2 Ly (3-129) (3-130) Expanding the exponential function in a Taylor series, equation (3-130) could be reduced to the following expression: 1 C/L - 3 (3-131) 180. Also, for the case of a correlation function represented by a Gaussian error function Rý exp y2 (3-132) 4Ly The correction factor for this case is given as follows: Ly - 11 4 *I Ly 2 e2 12 2 erf ( 2 )_ E y- IT ) 1 - exp - 4 -L-Y2 (3-133) h rn12 /L y w ere -Y erf - e dy (3-134) 2L Tr y 0 Similar corrections for the measured scales of turbulence could be established as follows: K LX and K y Ly (3-135) Lxm LY eas meas For a correlatio n function given by R' (y) = exp (- y/Ly) (3-136) y it is found that K2( LY) 2 rr -2+J (3-137) ye2LyLy Ly ] where IT12- i(a) +2 exp (- a Coseep ) d/-? (3-138) a Cosec p 181. While for an isotropic turbulence with a longitudinal correlation function given by and R; (x) = exp (- U) 4L2 x 1 and LL xxx meas 8 exp Tr e2 TG ý2 KyLy erf IT t Ly :iLy Corrections of the order of 30% for the effect of wire (3-139) (3-140) (3-141) length on the turbulence measurements have been carried out in the present investigation assuming that the auto-correlation coefficient could be approximated by an expon6nV3: al function similar to equation (3-129) as proposed by Dryden et al (82) and Hinze (79). 3.7 Turbulence Diffusion, Lagrangian Analysis Diffusion of heat and mass is one of the major processes controlling the combustion process in engines. This is greatly itensified by the turbulent nature of the flow inside the combustion chamber. Taylor (1920) (86) was the first to show that turbulent motion is capable of diffusing properties through the interior of the f luid in much the same way that molecular agitation gives rise to molecular diffusion. The main difference between the two lori 182. types is that in molecular diffusion, the medium consists of discrete particles, while in turbulent diffusion ýhe medium is continuous. The essential feature of purely turbulent diffusion is that the fluid particles retain their initial properties throughout the history of the motion, but the spatial distribution of the particles changes. Therefore, it is possible to follow a particle of the fluid while it moves in. the turbulent field and to find the degree of correlation between the velocity of this particle at time t-and the velocity v (t + C) of the same particle at a later time (t +. IC) Fig. - (3-16). A Lagrangian coefficient of correlation could be defined, therefore, by the following relationship I Rý(Z) (t) (t 1 (3-142) where the averaging process is carried oqt over a large number 'of particle motions. This Lagrangian correlation coeff; cient has properties similar to those of the previously treated Eulerian correlations, namely: Rý (0) = 1.0, RL (t)'s symmetrical with respect to V because of the homogeneity of the field, and will decrease to zero for large values of 'C. The displacement of a particle initially at the origin of the coordinate axes, could be obtained after an interval of time- t by the following relationship t j (t) dt (3-143) 0 183. Because of the random nature of the motion, we can write y (3-144) and t2 2=[Sv (t) dt (3-145) 0 making use of the definition of the Lagrangian cokrelation coefficient, the mean displacement of the fluid particles exrresw L3 could be, the following relation of Kampe de Feriet t y2=2 v2 S RI dZ: (3-146) L 0 For very small values of t, where 'ýLM=I, the integration of equation (3-146) reduces tp / (3-147) and the diffusion proceeds proportionally with time. While for long periods of time we can define a Lagrangian time scale jIt by (t) dt (3-147) 184. and equation (3-146) becomes cc y22v2Ltt-2 V2 jt RL' Mdt (3-148) 0 For a very long interval of time t, the second term on the right hand side of equation (3-148) will become very small with respect to the first term, so it may be neglected. Hence: y22 V2 ill tt (3-149) Defining coefficient of eddy diffusivity E by 2 y V2 v (3-150) 2t Lt where L,. is a Lagrangian space scale (scale of eddy diffusion) e given by Lt Many investigators (110-114) have attempted to establish some empirical relationship between the Lagrangian and Eulerian correlations and consequently between the macro-scale of turbulence I, Unfortunately such a .. and the scale of eddy diffusion LL- correlation has not been established yet. In fact, the scatter of the data in each investigation and the contradicting trends, if any exist, between different investigators, make it impossible to obtain a definite conclusion about the form of such a 185. e relationship. However, one can say that both Lx and LL are roughly of the same order of magnitude. A detailed discussion of this point will be given in Chapter 7. -ý. v It I 186. Relative Amplitude Phase Lag (dB) (Degrees) i j i l F .1 . -Issm - t L ",N o A l- ! -- I k H - 1 1.0 140 -, ro MO . ob . ob -40 . Frequency (RHZ) Fig (3-I)Example for the frequency characteristics of a constant temperature hot wire anemometer, (121) , ý, a . 1. I constant BRIDGE T op OP Amplifier Top (rat; q) Top (ratio) resistanci resistance Cor Wriso re . Cm DC generator 14 Output voltage ompensating network .S1, PROBE ms)arison sistance Fig (3-2) Simplified diagram for a constant current anemometer. 187. BRIDGE TOP S., -ý Top fratio) Top (ratio) amplifier resistanceýý resistance Error network irison resistance Bridge voltage Fig (3-3) Simplified diagram for a constant temperature anemometer. "l. 600 400 309 2CO 100 go 60 40 20 '10 6 4 cs 06 04 ONT w'Vennelyetol . I a KennelyondSon5om - I - - - - - . -- . 0 King, LV. .V A Hughes * Gibson - - z - - - - .+ Reiher I --- . 0 Poltz and Starr . - - . - I -- Y- V Vornehm - 11 .-. ' -- * Hilpert -- I. - - -- > Goukmon ef of 4H T x Smoll V Griffiths ondAwbery Coord mot les of A Berike recommended curve A-A ý&D, DOG 0.45 0.1 W4 to 1.83 to 5.1 too W 1000 q 56.5 10,000 - := = t 245 100,000 T r T ' t ffl 520 25qOOO t t 01 23468 to 2346 610 23468 102 7346 8103 ' 2.3 468 104 2346 8103 23 Re Fig (3-4) Data for heating and cooling air flowing normal to cylindersp corrected. for radiation to surroundings, (compiled by McAdamr. )(73)) 188. Cl cn cl cn C) T-4 en >< cz) cl C3 C'4 CC Cal . 0- C) to C:; C: ) C3 C) )% Lt 166 (/OC) CII IIIII 0.000 0.600 1.200 01' t3ca 2.400 3.0110 DT=(TP. -TC) (t) XIO-2 riL, ('ý-6) Evaluation of the temperature coefficient of resistance, -C. " t:; 4 0 0 to I 0-5 1.0 1.5 (veloci-Ity head, in. 1-1g)T Fig Typical hot wire calibration showing the error introduced by extrapolating measurements obtainýd over a limited range of velocity to estimate thb bridge voltage at zero velocity, (77). 18D. 2-0 1.5 1.0 : Z> J., 0 > .. 0.. 5 0.0 -. 1 i F- IIiI11 7.0 7.1 7.2 7.3 7.4 7.5 7.6 7.7 Rx (01'") Fig Exa=ple of operating the hot wire below its measured value 0j. cold resistance, showing the discrepancy between the measured and actual value of cold resistance. t3 to V) 94 %ý ni rl 11 F4 -ri 6 . 0 Co %0 (\j 1 4-» 0 94 0 ra r- 0 CO 4 ri 0 $4 6 0 i - 0 ci j2 ei Co 43 -r-i C. ) ri 10 r-4 ;4 .. .. .. .. .. f4 H 4j E-4 ri u2 fl. 93 i-4 ,. c) m t-1 (a r3 cl 0 4-3 " ci = m 413 41 4-b ýi 14.4 ffi p 0 12 0 9 wi 10 41 0 t4 G) r4 C 0 cs ti j4 ti Ei 9.4 94 cz 94 :Z -ri . 1:: 0 0 E= C) Q pt 0 G) C) Id Ic 0 p4 H x A E: -i r-i vi $4 ri 94 :: 0 0 0 0 -rf c) 0 UN tf\ t= % t. f4 -z - E4 9- " - 190. Ia / %S"I. 06 .0- \ jA .. t 01 Cal - C; C3 C5 ý4 >< C) : 4 W-4 C5 Li cs k t4 rf 0 tz C; C) co OOD .1 GOCO 00910 009 *0 "a I-DIX 3981-10A 3'9OIH8 V) co $4 %ý rl CA o 0 ". k, 0 co %D ul% - 0 0 4-3ý -ri 0 P4 . .. m 14 0 14 r-I C. )-cc a C3 ri C3 * 4J M .0 4-S 4.3. 4.1 , -1 4-4 CS 4-3 A-) U) CQ 84 t- 11 VA -ri a 0 (4 LQ 4-A <3 0 4 0 44 t4 CIS on co r-4 u cs +j -, j 4D ý4 $4 0 D P, 14 E- 10 "q 94 pq 0 X. .4 ca til ci 1 P4 0 E-4 E-4 IL> Cfl 191. E. I-V.. $4 4 rs $4 q. 1ý4 1--"IiI Ol Irl -ri 0Q -r4 00 Er% -4 U'% E cl 10 Cý 49% .. CO 4-3ý 0 cl $4 r4 4.4 fil 0 0 V4 0 t4 Cý u LU es - C% to ooo*rl - LeG'7, EEE; *I, . Goolz Lgg*l EEE'i coo*i- 192. 011% P 4J t; 0 -ri 4 0 o ILJ 4) 4-4 0 9 0 V-1 4-) V-1 4-t a) A %.. o 193. YY II ol IA A' X UN Y ku Fig (3-11) Definition of the longitudenal and lateral correlations-. " ý-- I r Fig (3-12) General shapes of correlation coefficients. 194. i. ), Dependent on condition of formation F(k) Independent of condition of formatiou , k e 'Wave numberv k Universal eRuilibrium range Largest eddies of L" permanent. characterl Ener&y- Inertial 11 Ia containing eddies 1. subranorel .1 ,, urbulonce,, (79). Fig (3-13) Spectrum distribution for isotropic_t . 1. . 100 80 "Ulea. 9 60 40 0 0 0 20 40 60 80 100 120 140 -160 (ul/u Irue % Fig (3-15) Test of hot wire response to high turbulence, (91). Air 195. 0 00, 1" .4 to CO 0 090+1 0\ Ok, Lie- I. %... 0 Z) D- :c 0 o(3 J c> Oz ,ý (i) tz, W l ý-40 -a--eN» ý» = Co E N . lib, IL; ) qlaw jw a 0 mom j2 «QW 0 P4 0 $4 4) 0 to 0 4-4 00 $4 0 0 ca 0 0 4-) ci 0 4J d ON to "I ý%4 196. V(O) Position of the particle at time t. Position of the particle at zero time -1- 4 1.0 R'(t) L 0.0 t 'p Fig. (3-16). Definitions of particle diffusion and Lagrangian correlation. 197. 4. PATA ACQUISITION AND PROCESSING SYSTEM The main operations in the Data Acquisition and Processing System used in the present investigation could I be simmarised as follow's: a) DATA COLLECTION This includes the timing mark, the output of the hot wire anemometer and the pressure trace. b) DATA RECORDING This is carried out using an FM (frequency modulation) tape recorder. C) DATA PREPARATION . The recorded signals undergo some operations before the final stage of data analysis. This includes: digitization of.,. the recorded signals and storing the output in appropriate format; calibration of the digitized signals and preparation of turbulence signals at some particular crank angle of interest in the engine cycle. d) DATA QUALIFICATION This process represents some tests on the validity of the basic assumptions about the characteristics of turbulence signals in the engine. 198. DATA ANALYSIS This could be divided into two main groups: 1. Analysis of mean gas velocities. This includes a statistical analysis of mean gas velocities at different crank angles in the engine cycle. The analysis is carried out over a number of cycles to give an estimation of the extent of cyclic variations in gas velocities in terms of standard deviation, coefficient of variation and range of variation, as will be discussed later, 2. Analysis of fluctuating velocity components. This process could be divided into two categories. - a) Analysis of relatively long data records to estimate the average characteristics of the turbulence field. b) Analysis of individual data records for consecutive engine cycles to estimate the extent of cyclic variations in the statistical parameters characterising the turbulent field. These variations will-be reflected as combustion variations during engine firing. The statistical parameters of the signals are evaluated in texms of mean values, standard deviations and Co6fficients of variation. 199. E-1 0 w F-4 W >4 1-4 z 0 1. E-4 Pr4 cr z 0 E-4 P. a z z 0 1. E-4 0 z z I Cd 4J . rl IJ 0 Cd :3 cr P-1 cs 0 9: 0 ., 4 U) 0 u0 0 H F4 cl P4 C. ) 4J 4-) Cd 0 CTJ :4 0 P4 0 to ýD cu E 4 ci 0 0 p4 L- - i CY 1. V (D G) . r4 Ici 0 -r-l. Vý ,i I 0 %-4 4J Ld 4-) cri M 1-4 ril >4 cl) C2) z Ea U 0 z E- CY U -ý4 -54 E-4 0 (D 0 0 1 200. 0ý a) Cd +) 0 > Cd Cd ý-4 1% r. 1ý4 bi) . r4 E-4 V 4-3 Cd a) :3 bD 4.3 cd 0 +1 00 cri :s r-4 W Cd 0) r-i 0 0) k > : Zý E-4 Cý r-4 (D -1-1 rj li P4 ul :j CH 0 as U rj Cd m VA 0 0 .4 CD k ;4 4-) :j (1) 0) 10 +) $-1 4-) 0 Cd -H (D 4- ;AB:: 14 ul a) 0 0 r). 4-) rt3 00 a) E-4 M ,w 14 CD . rj 4H -r-I r-4 P4 0 +) bo ul " 4-) -ri Ffll &4 Si -H E-4 LO 4-) 0 . rq 4 :jP. ej 14 ýl 0 4-3 Cd 0 r. 10 -r4 CD P-q E-4 $4 $4 4J 0 ca 4-) k Cd +) 0 ce. 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Cd 0 -rl C) 0 -r4 0 :>0 +j, ; ý; ,4 4J 0 Q) cl -P V) 1-4 r-I 1-1 0) 0 V-1 :3 C) r: -H 4. > .0 ft r-I a. k V4 Id Cd 0 ;4 H to C) 4-3 >b :j 00 ; -4 to C-) E-4 C. ) p P4 P, ; _9 0 4-3 1 +. - - r 0 %-.. i +2 , %-. - 1 4 %-0 C4 4- r: \ W to r4 P4 E-4 03 I. 914 -A EQ 0 .M C) ,1 .1 x 0 G (d 4-3 4-b " -Z c I 0 a +a cd 0 -rl r. cd E V. +3 (1) A :3 0 0 0 P4 0 CH ýzl to 0 0 a P4 r4 P4 0 0 r4 rd Cd -rf %-i Cd cs 0 E-1 4-1 E-4 -P 4-1 V 0 ., f cd cd cc ca En $4 ýd bn r-I H I I -P 0 $4 . 7-f 0 .0 o o 0 0 0 0 P4 ;4 (1) El 0 (13 k P4 CIS 0 0 o r4 cd to k o 1 bD 0 0 0 (1) C) 4-3 4-11 El 9 1 : , n ;j :5 ', . 0 . r 4 E-1 E-4 P4 pq P-4 $4 1 C3 Cd .! 4 Jý% -ýd V -P 0 C, j d Cd P4 0 %.. p Cd P4 9ý 4-1 4-3 0 0 = FZ4 Cl V tO 4-1 (1) Ea P4 F4 9 cd 0 U E-4 0 Cd ci r-i 0, %. 0 201. 0) $4 0 4-1 0 ri 0 cs P4 E-4 Cd >9 4-) 0 H 9.1 C%l 0 : P-g 4H a V) V4 En >8 9-4 Cd r. -K4 r-I cl 0 -ri 4-31 U), +3 C11 I A# r, 202. For both cases (a) and (b) the analysis includes: auto-correlation functions and auto-correlation coefficients; power spectral density functions; micro-scale and macro-scales of turbulence; intensities and eddy diffusivities. Fig. (4-1) shows a flow chart of the various steps for each operation, while Figs. (4-2a) and (4-2b) show flow charts of the hardware involved in each step and the input/ output of each individual operation. 4.1 Data Collection The required input data for investigating gas velocities and turbulence inside the combustion chamber of an engine could be summarised as follows. l. ' Gas mean velocities. 2. Fluctuating velocity components. 3. Instantaneous gas pressures. 4. Instantaneous gas temperatures. 5. A timing mark at a fixed time on the engine cycle. The first two quantities are obtained from the output of the constant temperature hot wire'anemometer bridge with the appropriate filtering conditions, which will be discussed later. The gas pressures and temperatures are obtained by using a pressure transducer and a resistance thermometer respectively, while the timing mark is obtained from a triggering circuit mounted on the crank shaft of the engine. Figs. (4-3), (a), (b), 203. (c) and (d) show an example of the simultaneously recorded signals for a Ford V4 engine. Detailed descriptions of each instrument are given below. 4.1.1 DISA 55M Constant Temperature Anemometer System The measurements of gas velopities and turbulence fluctuations are carried out, in the present investigation, using a DISA 55M constant temperature anemometer system. It consists of indivýdual units which could be arranged in any convenient combination to suit each stage of the Data Acquisition system employed. The main units of this system are: the 55 M05 power pack, the 55 MOI main anemometer. bridge unit, the 55D26 signal conditioner and the 55D31 digital voltmeter. The digital voltmeter is used for calibration purposes, either for the hot wire anemometer when exposed to constant flow velocities in the DISA wind tunnel, or for setting known voltages for calibrating the recorded signals on the tape recorder. Its range of measurement- varies in three steps from 0.000 to 99.99 volts with a maximum error of 0.1% of full scale range. A built in filter, switchable in seven steps, pyovides a choice of time constants between 0.1 and 100 seconds.. The power pack unit consists of a complementary part of the main anemometer bridge unit. It contains circuits to rectify and smooth out the AC line voltage, as well as voltage limiting and short circuit protection circuits. The stabiliser circuits are located in the main unit. It also contains a 204. I selector for obtaining either a high output voltage at low current or a lower output voltage at high current, The 55 L101 main unit contains, except for the power pack, all circuits required for operating the anemometer: amplifier, filter, decade resistance, square wave generator, protection circuits and other auxilliary circuits. Fig. (4-4) shows a simplified block diagram of this unit. Detailed descriptions of the DISA anemometer bridge circuit and its specification are given in reference (121). The main characteristics of this anemometer system could be summarised as follows: i) Compensation for lead resistance. is provided by a zero ohms potentiometer which is wired in series with the decade resistance. A. probe protection circuit is also provided which serves the purpose of insuring that neither faulty nor broken cables will cause -a high current to be fed through the probe that it will/burn out or be thermally overloaded. The square wave generator is used in the measurements of probe cold resistance and in balancing the bridge at high frequencies. The first operation is a simple balance of the bridge arms, where the appropriate value of the decade resistance gives the sensor cold resistance. The second use of the square wave generator in adjusting the bridge balance is based on simulating a sudden change in the velocity of the flow acting on 205. the probe by feeding a square wave signal into the bridge and monitoring the outPut. This method is shown by Davis and Fisher (77) to give an I under-estimation of the upper frequency limit of the wire as compared with subjecting the wire to 6 a velocity step in a shock tube. However, the errors introduced by employing the former method are not very serious. Exposing the probe to the maximum expected velocity during the measurements and ihjecting the square wave pulse, the output should show the shortest possible response without superimposed oscillation Fig. (4-5). This condition represents the optimum stability Of the bridge and servo-amplifier. If this condition is not satisfied adjustment of the gain and the filtel, -Vandwidth is required to obtain damped oscillation, Fig. (4-6). Cable compensation by varying an inductance and capacitance (L and Q) inserted in the bridge circuit results in the fine adjustment of the circuit. iv) The signal conditioner type 55 D26 was used, in the present work, as a band pass filter for obtaining the turbulence signal from the original anemometer output during engine measurements. The filter circuits of the signal conditioner comprises one low pass filter and one high pass filter both of which are switchable in steps of 1/3 octave. The low pass filter permits alteration of the upper frequency limit between 10 Hz 206. and I MHz; while the lower frequency limit can be varied between 0.1 Hz and 100 KHz by means of the high pass filter. 4.1.2 Timing Alark A timing mark at a fixed point on the engine cycle is required for triggering the Analog to Digital Converter (ADC) at the beginning of each cycle (TDC induction). This was obtained by generating a square pulse at this particular crank angle. In the early investigation on the. Rolls-: Royce engine, a triggering pulse was generated by closing a reed switch circuit by a magnet mounted on a rotating disc running at half the crank shaft speed. Later measurements on the Ford engine employed another triggering circuit where a photo-cell was used. The output of the timing marjr. circuit was always recorded on one of the tape recorder channels simultaneously with the measured signals. Fine adjustment of the TDC position was carried out by coinciding the generated trigger pulse and the peak of the pressure trace obtained from a cylinder having 3600 phase shift in-its firing order with respect to the reference cylinder. The use of a Tektronix storage oscilloscope facilitated such a process. This exact setting of the TDC for the reference cylinder was kept constant throughout the experiments for different cylinders and the firing order fed to the computer program to identify the actual beginning of the cycle for each individual cylinder signal. 207. 4.1.3 Measurements of Cylinder Gas Temperature and Pressure Calculations of gas velocities using the thermal equilibrium equation (3-9) requires evaluation of fluid properties at the appropriate crank angles, determined by the selected sampling rate on the ADC and the engine speed. These fluid properties are generally functions of gas temperature and pressure inside the engine cylinder. Resistancd thermometers are reasonably suitable for engine gas temperature measurements. Hassan (92) discussed the different sources of errors in such a method and concluded that its accuracy lies within 6% of the true values. Semenov (22) has shown that temperature fluctuations may ,, -, o affect the measured turbulence at TDC by"only about 2% and could beLneglected compared with other sources of errors. Fig. (4-7) shows the output signal from the resistance thermometer in the Ford engine for 17 consecutive cycles at a compression I ratio 8.9: 1 and an engine speed of 1000 r. p. m. In fact, no Y severe cyclic variations could be noticed on these results and a typical trace for the mean of a number of cycles could be used in the calculations of gas velocities. In addition I a considerable simplification in the processing of data could be introduced by using the measured gas temperature during induction and applying the polytropic relationship and the pressure trace for evaluating gas temperature at different crank angles during the engine cycle. The latter procedure was used in the present work. Fig. (4-8) shows a comparison 208. between the measured gas temperature and the computed values from the pressure trace. Cylinder pressure was measured using a Kistler transducer (Type 750S) with a factory calibrated sensitivity of 16. -57 picocoulombs per atmosphere. A Kistler electro- static charge amplifier (Model 50 01) was used to produce a voltage signal proportional to the pressure. Fig. (4-9a) shows a schematic diagram of the Kistler transducer while Fig. (4-9b) shows a typical pressure trace for the Rolls- Royce engine at 9: 1 compression ratio and an engine speed of 1000 r. p. m. 4.1.4 Signal Recording System Measurements of gas velocities-and'ruýbulence in the engine requires simultaneous recording of the following signals: a timing mark occurring at'a fixed time on the cycle; the gas pressure; the gas temperature (this is an arbitrary option as discussed in Section 4.1.3), and the output of the hot wire anemometers (mean signal and turbulence). Magnetic tape recorders represent the most convenient type of data storage systems because of their ability to store large quantities of data and to reproduce them in electrical form. Also, the bandwidth of frequencies for commercial recorders covers the highest frequencies expected in the turbulence signal (up to 10 KHz). In the early period of this investigation a Sangamo (nI) tape recorder Model 3500 was . Agop 209. available. This model has the facilities of 14 recording channels and, therefore, all the required signals were recorded simultaneously. Table (4-1) gives an abstract of the technical specification of this tape recorder. Later on, such recording facilities were not available and were replaced by a Racal Store 4 (FAI) tape recorder. The latter recorder has only four recording channels and, therefore, only the raw signal of the anemometer outPut was recorded during, the test. The turbulence signal was obtained by carrying out the filtering procedure at the time of processing and analysing of the data on the Hewlett Packard Fourier Analyser. Table (4-2) gives an abstract of some of the relevant specifications for the. Racal Store 4 tape recorder. _. 1 The basic principle of the frequency modulation (M) procedure is to make the*frequency ol a carrier signal analogous to th6 amplitude of the input data. With a sinusoidal input, the modulated signal, theoretically, ýooks like a sine wave which varies in frequency. Actually, the modulated signal looks like a square wave with varying width because FM signals are usually recorded at saturation. The errors introduced by the tape recording could be summarised as variations in the speed at which the tape passes over the record or reproduction heads. These are called time base errors and may be either static or dynamic in character. 210. Tije first type is caused by changes in the dimensions of the tape due to temperature, humidity and tension. For commercial tapes this static time base error is of the order of 0.1 to 0.25%. In addition inter-channel static time base errors are caused by manufacturing tolerances on the angle at which the tape passes the heads and the position of the heads (tolerance frbm stack to stack as well as from head to head) on a givEnstack and the azimuth alignment. These errors are generally of the order of 0.001 inch and are therefore a function, of tape speed. The dynamic type of time base error is flutter, which is the variation in tape velocity from the nominal. For the Racal type recorder the manufacturer's specification gives a value of 0.35% as the percentage of flutter at the highest tape speed of 60 in/sec. Therefore, one can concludelrom the above mentioned discussion that magnetic tape recording represents the most convenient recording facility forýthe data acquisition system and that the errors introduced by using such a procedure are quite negligible as compared with other sources of experimental errors. 21L. TABLE (4-1) Abstract of Some Relevant Specifications of the Sangamo 3500 Tape Recorder (119) Tape Speeds 60,30,15,7.5,3.75 and 13 ir)/sec Input Sensitivity 0.1 to 2.5 volts r. m. s. Nominal Input Level 1.4 volts peak Nominal Input Impedance 100 K ohms resistive Output Level (-: ý 40% deviation) 1.4 volts peak, into 1000 ohms with short circuit protection (SCP) I Output Current (± 40% 3 milliamperes peak with SCP. deviation) output Impedance Bandwidth Signal/Noise Ratio Harmon]: c 'Distortion Less than 50-ohms, unbalanced to ground with SCP DC to 20 KHz at 60 in/see. 46 dB at 60 in/see , <' 1.1.5% total at all speeds / 212. TABLE (4--: 2) Abstract of Some Relevant Specification of the Racal (Store 4) Tape Recorder (120) Tape Speeds 60,30,15,7.5 and 11/16 in/see Input Sensitivity Selected by Input Attenuators in the following rang2: (peaks fo r-full deviation) 20 voltp, ± 10 volts, 5 volts, ±2 volts, +1 volt, ± 0.5 volts, ± 0.2 volts and ± 0.1 volts) Output Level Continuously variable from 0 to +3 volts for full deviation Bandwidth DC to 20 KHz at 60 in/see Signal/Noise Ratio Harmonic Distortion I 48 dB at 60 in/see 1% at maximum modulation level / 213. 4.1.5 Probes and Traverse Mechanisms Measurements of gas velocities and turbulence characteristics were carried out in the present investigation at the spark plug location as well as at different locations in the combustion chamber. Fig. (4-10) shows a view of the cylinder head of the Ford engine where measurements were carried out at the spark plug location only, while Figs. (4-11a) and (4-11b) show two views of a cylinder head of the Rolls- Royce engine where measurements were carried out at the spark plug as well as at the different marked positions in-Fig. (4-11a). For the latter case, the probes were traversed inside a number of brass tubes (3/16 inch diameter) fixed in the wall of the combustion chamber and sealed at the water jacket of the cylinder head. The spark plug probe has two perpendicular sensing elements welded on the tips of steel needles, while only a single wire probe could be traversed inside the brass tubes. For both engines the facilifies of pr6be rotation about its own axis was required to enable detection of any consistent direction of gas flow during the different strokes of the engine cycle. Moreover, a traverse motion of the probe along its axis was required to enable investigations at different depths inside the combustion chamber. These facilities, together with the. requirements of adequate se aling and an easy way of insertion and withdrawal. without damaging the wires or removing the cylinder heads were satisfied by the construction of the traverse mechanisms shown in Figs. (4-12) and (4-13) for 10. = 214. the spark plug and the different locations inside the combustion chamber respectively. The probes are usually fixed on rigid steel brackets and mounted on the cylinder heads during measurements. 4.2 Data Preparation 4.2.1 Digitization of Mean Velocity and Pressure Traces The recorded signal is usually reproduced at the same tape recording speed and is introduced tR the ADC of a Hewlett Packard Fourier Analyser Model 5451A. Such an ADC has fixed sampling rates varying from 10 /j sec/sample to sec/sample as shown in Table (4-3). Therefore, a decision on the appropriate sampling rate that Will reproduce the original signal accurately was selected on the basis of the required sample width along the engiae cycle (crank angle degrees) rather than on an'. actuai time basis. which'varibs with engihe, speed. This means that a sampling interval in terms of crank angle has to be maintained constant as far as possible for the whole engine speed range under investigation. It has been found that a samplo width between 2.5 and 4 degrees is quite sufficient for such purposes. Table (4-3) shows the variation of the number of samples per cycle and the sample size in crank angle degrees corresponding to each sampling rate setting on the ADC for various engine speeds. (0 r-I Co 4J f4-4 4-% cs Cfl 0 r-4 Cd r-f ca M 0 Cf) I -4 E-4 C, 4 r-i le ri m Co ; 1 c%) m CD CD CD r-f CI) CD rA 00 0 (D 00 . 0) 0 CL - 0 CY) le w 0 0 0 OD . -% Co Li) to 0 e t- 0 0 le Co (0 cli le Q 1 p4 FA Cf) cq (D to P, 0 CO2 (D- 0 cq 0 0 0 ( cq D Ln e-i u2 Lr) 4 "-1 CO (D 0 0 F-f le 00 cej rJ2 to m cq cq cq N Ni rn -ýL- 1 1 1 1 - 4-3 0 . rj 4-3 Cd a) P., 0 -H bo 14 (D P4 04 s Cd V) CH 0 (D 4 4-) (D ho r. CTJ cs N -H 0) (D H Cd .0 4-) Ul -H M 215. 'l, .- 216. The digitized data of recorded signals are usually obtained on paper tapes. Such tapes are produced in incompatible format with the input format to ICL computers. Therefore, an intermediate step is required for such a transfer process and is carried out by a FORTRAN program called DIGITIZATION AND CALIBRATION. A list of such a program together with the input-output formats are given in Appendix Bl. The output of this program could bý- stored on either magnetic tape or cards for further use by other data analysis programs. Such a program takes into abcount the scale factors introduced by the'ADC and the final stored information represents therefore the actual values of the recorded signals on the tape recorder. 4.2.2. Calibration of the Digitized Data The term calibration has two distinct meanings when appli'ed to the digitized data. First, of course, is the actual laboratory calibration made of the instrument. This includes calibration of the hot wire and pressure transducer and is discussed in the description of each instrument, Sections (3.2.1) and (4.1.3). The second use of the term calibration refers to the complete conversion process from digital counts to physical units and is thus an electrical-electronic calibration which accounts for any operation carried out on the signal before recording such as biasing some DC level or attenuating the whole signal level. 217. 4.2.3 Calibration of Recorded Signals The limitation on the input levels to s6me tape recorders together with the requirements of keeping the signal to noise ratio of recorded and reproduced signals as high as possible, necessitates some conditioning of the raw signals before recording. This conditioning process includes attenuation processes and in some cases biasing some DC level from the signal. A calibration process is, therefore, necessary to retain the recorded signals to their actual values at the output of the instruments. , This was carried out by introducing a number of known D. C. voltages to the electronic conditioning circuit and the tape recorder at the same points where the actual physical signals are normaliy' introduced in the actuaýl experiment. A simple conversion relation could be used, therefore, as given by E actual =E0+K (E recorded) 4-1 where E is the biased DC voltage 0 K is the attenuation factor E actual is the actual value of the measured signal E recorded is the recorded signals on the tape. 218. The biased DC voltage and attenuation factor in equation (4-1) could be obtained from the known values of the calibration signals and the corresponding digitized values from the ADC. A special case of equation (4-1) when attenuation processes only are carried out, the value of Eo equals zero. In the latter case, where no biasing processes are involved, such as the case of recording a filtered turbulence signal, another calibrationprocedure could be used when a number of AC signals of accurately known amplitudes could'take the place of the DC voltages mentioned earlier. These AC signals are introduced at the same output terminals of the instruments and recorded on the tapes. Attenuation factors could be calculated, therefore, by comparing the actual: --dnd digitized (recorded) amplitudes of the calibration signals. 4.2.4 Preparation of Turbulence Signals Preliminary analysis of turbuience signals for the Rolls-Royce engine, as well as all the published investigations on turbulence measurements in S. I. engines (22), (24) have shown that most of the fluid energy is contained in the frequency range below 6 KHz, especially during the compression stroke. on the other hand, the requirements of obtaining turbulence signals that represent only the fluctuations of flow velocity without any contributions of mean velocity signals, which are known to suffer large cyclic variations, necessitates the 219. application of a high pass filtering of the raw anemometer signal to get rid of the mean velocity trace Fig.. (4-3b). The limits of the minimum filtering frequency will increase at higher engine speeds because of the shortening of the time occupied by the whole engine cycle and correspondingly the increase of the frequency of the mean velocity trace itself. It is also known from sampling theory (114) that at least two samples per cycle are required to define a frequency component in the original data.. Hence, ' the highest frequency which can be defined by sampling the data at time intervals . At (seconds/sampýe) is 1/2 at cycles per second which is called the cut off frequency or the Nyquist frequency or folding frequency. n1 (4-2) max 24t Frequencies in the original data above n* (cps) will be max folded back into the frequency range from 0 to n max (cps), and be confused with data in this lower range Fig. (4-14). This problem is cailed "aliasing" and is inherent in all digital processing which is preceded by an analog to digital conversion. Its spectral effect is to fold back the spectrum about the Nyquist frequency n max as shown in Fig. (4-15). Thus a first requirement for digital analysis is to sample at a high enough rate so that all frequencies of interest are identified properly. 220. In practice, one will usually wish to maximise (4 t) so that computing time is minimised. Nevertheless, a selection of n max to be li or 2 times the maximum anticipated frequency in the signal is quite sufficient to overcome this problem. Another way for handling the aliasing problem is to low pass filter the analog signal before sampling. The cut off frequency of the filter is usually chosen to be slightly'less than the foldiný frequency. With these,, experiments in mind, a sampling rate of 50 P see per sample was employed in the digitization of the turbulence signal. This corresponds to a cut off frequency of 10 Mr,. Also, to eliminate any contribution of spurious noise picked up at any stage of the data collection, a low pass filter was used and set at a maximum-of.. IO, KHz. The DISA signal conditioner unit Type 55 D26 was used for this purpose. The tape recorder speed was selected to be 60 in/see which enables recording of frequencies up to 20 KHz and the signals were-reproduced at the same tape speed. The digitized data was stored in a data block of the .I Hewlett Packard Fourier Analyser for further spectral analysis. Such data blocks are of variable size with a maximum storage capacity of two blocks of 4096 samples. Other block sizes are n6- multiples of 2 starting from 2 (64). 221. The triggering of the ADC was actuated from the recorded triggering pulse (timing mark) which occurs at TDC on the induction stroke of the reference cylinder. For cylinders other than the reference one, the firing order was used to account for the shift of the fixed timing mark relative to actual TDC induction of each particular cylinder. a) Data Preparation for Muitiple Records A sampling procedure is employed in this technique which enables the construction of a continuous. data re7cord at a specified crank angle on the engine cycle from isolated samples extracted from consecutive cycles. These samples have a specified width (e. g. 100 of crank angles) and ' consists, therefore, of a number of digitiz ed samples as governed by the sampling rate of the ADC. We shall call the first one "cycle sample" to differenteLate between it and the fixed. sample intervals of the ADC. Each extracted cycle sample is joined to the previously assembled ones and the whole record is shifted by a certain time interval equal to the cycle sample to enable the addition of a new cycle sample and so on until the whole data block is filled and then spectrum analysis is carried out. The number of cycles analysed (assembled cycle samples) varies with the specified width of the cycle sample, the size of the data block selected for the Fourier Analyser, and according to the engine speed as shown in Table (4-4). 222. 4-1 0 r. 4-) ýu rl ,a Cd 0 P4 0 0 r-4 cQ cl -P Cd A 0 4H 0 11 Cd Cd 0 U) U) , -ZI 9 4H 0 .0 zo IH 0 C: 0 .H 4-3 Cd Cd CD 4-1 ., 4 0 . -d 0 -p (D ci F-4 r4 n Ei cd Co H 'F N EQ. (n 0 0 0 C9 >1 CD cr) C9 v C9 Cf) cq C-3 v co CH 0 a) 0 >1 r-4 F-4 Cd z Cf) v 00 q14 00 to v v 0 00 to r-4 r. 4 C9 cr) Cl) o rg 0 (D r 11 Nr In CD OD 1ý1 N cq cq 0 -, 14 (3 0 q co (D N C14 c qw Lf) (D 0 ;4 0 a) C*4 F A 11 N CD CD lqdq lcdq . ED N Cf) c P4 P4 0 v E! 0 Cd Cd W V3 -q 11 to Cf) 00 cq E- V) P-1 CD LO CV) cq cli H 44 4) 0H . 54 >b 0 0 Cl) 0 Cl) 0 00 to ce) cq CD 4 Cd P > bJD 4-) 00 W to LO z 4) H Cl) ce) NP "W t- a) b. 0 0 0 0 0 0 C; bo cis $4 ca C. )U) (1) a) r-4 r-4 ca 0 0 0 0 0 0 0 0 a) 0 0 0 0 0 co 0 9: 0 IV 0 fD cl) co 0 -H ": Jl cq cq b-O 14 (D co V 0 0 0 0 0 0 (1) 0 0 0 0 0 0 0 CD 0 C14 ki) 0 LO cq cq ba 223. The width of the cycle sample was chosen, in the 0 present work, to be 10 crank angle degrees, since the auto- correlation function was always found to decay to zero in this. period. A similar observation was reported by Barton (11) as well as a re-analysis of Barton's data by Winsor (23). However, a check on the suitability of such a sampling interval was carried out by analySing turbulence signals at some crank angles in the cycle for two different widths of cycle sample namely 10 and 20 degrees. The power spectrum function as well as the auto-correlation coefficients have shown almost identical values Figs. (4-16a) and (4-16b). A possibility of better utilisation of the computing time could be achieved by simultaneous analysis of the data at more than one crank angle. Typjpal examples of these programs are given in appendix B2. However, this results in a reduction of the number'bf cycles analysed at each crank -angle (length of data record) at lower engine speeds (e. g. below 1000 r. p. m. ) due to the reduction of the data block size. The Fourier Analyser, used in the present investigation, has a maximum storage capacity of two data blocks of. 4096 samples. The next step in the size of data blocks is 2048 samples which resulted in storing only half the number of cycles of the first case. Therefore, it is a matter of compromise between the length of the data record required, the specified crank angle width and the expense of computing time. Ali 224. b) Data Preparation for Individual Records The study of the problem of cyclic variations in the characteristic parameters of the turbulence field during the compression stroke and especially at the time of ignition necessitate analysing individual engine cycles rather than the averaging procedure employed before. However, for both cases the preparation procedure. of the turbulence data remains the same with the exception that after isolating and storing the signal., for a large number of cycles at the crank angle of interest a process of analysis is caýried out. This continuous record is analysed into its constitu6nt parts and individual cycles are stored separately in an intermediate storage facility (such as numeric magnetic tape or paper tape) . S..,. -. " After this stage a process of introducing only one cycle sample at a time to the Fourier Analyser after reducing the data block to an appropriate value prepares individual records for spectra? l analysis. / 4.3 Data Qualification (Basic assumptions about the structure of the turbulent f ield). In the preceding method of analysis of turbulence signals at any particular crank angle (with a record length b, ()), some assumptions were made about the characteristics of the signal. "00,41A 225. These assumptions are made to permit the application of conventional techniques of analysis used for similar random data or even for turbulence data under steady state conditions. It also helps to reduce the amount of experimental work involved in the investigation. Nevertheless, the validity of these assumptions could be tested by suitable techniques and is discussed below. 7he basic assumptions employed in this investigation can be summarised as follows: n i) Data records constructed from i'dividual records of consecutive engine cycles are stationary and ergodic and represent therefore the average characteristics Of the turbulence conditions. --. 0 ii) The turbulence field, especially during the It- compression stroke, is isotropic and homogeneous. iii) The turbulence energy of the flow is distributed over the whole frequency range from the lowest to the highest limits. Therefore, the appearance of peculiar periodic components at any particular frequency represents spurious signals and should be rejected. Adop 226'. 4.3.1 Stationarity and Ergodicity of the Data In the following analysis of turbulence signals at a particular crank angle along the engine cycle, some assumptions have to be made about the characteristics of the signal. The first assumption implies that the process is 'stationary' which means that the properties of the signal can be described at any instant in time by computing average values over the collection of data records (time histories of the signal observed over a finite time interval) which describes this random process Fig. (4-17). When a single time, history record is referred to as being stationary, it is generally meant that the properties computed over short time intervals do not vary significantly from one interval to the next. The word 'significantly' is used here toý. mean that observed variations are greater than would be expected due to normal statistical sampling variations. For example, if the mean square value or the auto-correlation function of a single sample record u (t) obtained from the Kth sample record of a random process K u(t) are obtained-by time averaging over a short interval T with a starting time t does not vary 'significantly' as the starting time tI varies, the sample record is said to be stationary. The same argument is applicable if the averaging processes are carried out over "ensemble" records at time tl, rather than on single sample records. For the first case we have: 227. 4 tj +T 2 u (tl, K) UK (t) dt ti and t +T R (tl, t, +Z: , K) t =1 T j UKM uK (t +Z) dt (4-4) t While, for the later one we have Z2 (t lim u -i (4-5) (t U N -#-oo N ý" i and UK(tl +Z: )] (4-6 l' tl +) =-- limN-r&-. ii 7-= 'l Eux(t1) The second assumption is that the process is vergodic' which means that the time averageýwalues of the statistical properties of the signals (e. g. mean square value, auto-correlation function..... etc) for any sample record are equal to the corresponding ensemble averaged values. This means that the expressions given in 9quation (4-3) and (4-5) are equal and similarly equations (4-4) and (4-6). Examination of the turbulence signal during an engine cycle, Fig. (4-3b) reveals that such a signal is basically a "non-stationary" process because of its transient nature, where the statistical characteristics are, continuously changing with time. A totally adequate methodology does not exist as yet for the analysis of such non-stationary data. However, because our major concern in investigation of physical phenomenon in S. I. 228. engines is concentrated on the characteristics of such phenomenon at particular times of interest, approximations to stationary processes could be assumed and experimentally checked. For example, a study of cyclic combustion variation concentrates only on the characteristics of the mixture at the time of ignition and during a shqrt period of time after that, compared with engine cycle. This represents the interval of time required for the development of the flame kernel into a steady flame front. Therefore, a logical approach to the problem is to apply a sampling procedure which extracts the signal under consideration during a small sample width of crank angles from individual cycles and to use these sample records to establish a stationary record of ensemble data. If such a continuous record satisfies the assumptions stated above, (stationarity and ergodicity) analysis by usual methods used for stationary data can be carried out. 4.3.2 Test for Stationarity It has been shown by Townsend that the probability density distribution of the fluctuating velocity component in an isotropic flow field follows approximately normal distribution. It is better to avoid any assumptions on the specific distribution function of the collected turbulence signal in the engine while running tests on its stationarity and confidence limits. This process could be carried out using what are called "distribution free" or non-parametric procedures. 229. One of the best known distribution free pr6cedures used for data evaluation techniques is the "run. test" (118). To conduct. a test on individual sample records to ascertain the stationarity of data, the following assumptions are needed. Firstly, it must be assumed that any given sample record will probably reflect the non-stationarity character of the signal. Secondly, it must be assumed thai any given sample record is very long compared to the lowest frequency component in the data. It is also convenient (but not necessary) to further assume that any non-stationarity of interest will be revealed by time trends in the mean square value of the data. The procedure for running this test could be summarised as follows: Individual records from each cycle are extracted 'from consecutive cycles, in.,. the same way used in Section 4.2.3. f The mean square value for each cycle sample is determined from the value of auto-correlation (Rt(O) ) at T=0 and these values are aligned in t time sequence, with the first cycle sample denoted by (1), the second by (2) and so on ..... . until the Nth cycle sampleas follows: 222 ul u2 U3 u or R1 (0) ,R2 (0) ,R3 (0) ... RN (0) 230. The cycle samples mean square values are then classified into one of two mutually exclusive categories. which may be identified simply by 0 plus (+) or minus This is carried out by comparing their values with a mean value u2 m '2 2 calculated over the N cycles, where u, -7 UM 22 or uu The sequence of plus and minus values might be as follows: 123456789 10 A run is defined as a sequence of identical signs that is followed and preceded by a different sign or no sign at all. In the previous example the number of runs is 11 in the sequence of N= 23 cycle -samples. Now, .' we hypothesised that the sequence of sample 22 7-2 mean square values (ul . U2 .... uN each independent sample values of a random variable with a mean square value 2 of u If the hypothesis is true, the variations in the m sequence of sample values will be random and display no trends, Hence the number of runs in the sequence relative to the median value, will be as expected for a sequence of independent random observations of the random variable u(t) as presented in standard tables of the MOCK ) percentage points for -the distribution function of runs, where cK is any desired level of significance. If the number of runs is significantly different 231. from the expected numbers in such tests, the hypothesis of stationarity would be rejected, otherwise, the hypothesis would be accepted. Applications of such a test on typical sets of data for the Rolls-Royce and the Ford engines have been carried out at different crank angles in the engine cycle. Table (4-5) shows the number of runs observed in the sequence of the root mean square value of the signal relative to the median. While Tablb (4-6) shows the standard values of the number of runs at various levels of significaýce A comparison between the experimental data and the standard values indicates that the hypothesis of stationarity is accepted at the different' significance levels. For example, at a significance level of 0.975, the numbee'61 runs should be between 22 and 39 and the experimental data are always between these two limits. Fig. (4-18) shows a typical graph of the fluctuating velocity component over 60 cycles for. a test on the Rolls-Royce engine. 232. TABLE (4-5) Application of the "Run Test" for Stationarity on Typical Engine Tests over 60 Consecutive Cycles Engine Engine Throttle Intake Crank Angle Number Type Speed Setting System (degrees) of Runs ROLLS- 1000 Fully Plain 320 25 ROYCE Opened Valve 340 28 (Intake 360 26 Vacuo 0.5 in Hg) Inlet 300 30 Valve 320 28 Fitted 3, $0 27 with 8 340 28 Vanes 350 33 360 27 FORD 1000 Intake Plain 30 Vacuo Valve 4 in Hg Inlet 350 33 Valve Fitted with 4 Vanes Intake Plain 34 VacL; o Valve 11.1 in Inlet 350 27 Hg Valve Fitted wi th 4 Vanes TABLE (4-6) Percentage Points of Run Distribution (118) Number of Individual Significance Level (C<) Data Records 0.99 0.975 0.95 0.05 0.025 0.01 60 21 22 24 37 39 40 233. 4.3.3 IsOtropy and Homogeneity of Turbulence A great simplification in the study of turbulence is introduced through the assumption of isotropy. This means that the mean value of any function of the fluctuating velocity components and their space derivatives is unaltered by any rotation or reflection of the axis of reference. This may be expressed by U2 = V2 where u, v, w are the instantaneous values of the fluctuating velocity components in the x, y, and z directions respectively. Isotropy also means that the fluctuA: 11; ns are (4-7) perfectly random with the result that there is no correlation between components of the fluctuation's in different directions, i. e. / UV = VW = UW =0 (4-8) The assumption of isotropy is not far from reality because of the experimental evidence that the fine structure of most actual nonisotropic turbulence flow is nearly istropic (local isotropy). This hypothesis was first introduced by Kolmogoroff (89) in 1901, as discussed in (3.4.2), where the motion of large eddies are assumed to produce smaller eddies, which in turn produces yet smaller eddies. The process continues If k 234. to the smallest eddies. From the standpoint of energy dissipation, it is postulated that the larger eddies lose their energy in forming smaller eddies and that in the process very little energy is dissipated as heat. The motion'of the smallest eddies is steady and almost all their energy is dissipated as heat because of the molecular viscosity of the fluid. Thus it is seen that the energy dissipated by the turbulent flow is dissipated mostly by smaller eddies. Kolmogoroff also states that, although large eddies of turbulent flow may be nonisotropic, the smaller eddies are isotropic, so most of the energy is thus dissipated in turbulence which is isotropic. Hence, many features of isotropic turbulence may apply to phenomena in actual turbulence that are determined malply by the fine scale structure, where local isotropy prevails. This assumption could be tested by analysing the turbulence signals collected from the hot wire anemometer at different orientations and under constant engine operating conditions as shown in Fig. (4-19). Homogeneity in turbulence means that the statistical characteristics of turbulence are invariant for any translation in the space occupied by the fluid. Batchelor (122) put the following argument for a grid produced turbulence* that "although the random motion dies away with distance from the grid, and to that extent is not statistically homogeneous, but the rate of decay is so small that the assumption -of A 10: 235. homogeneity of the turbulence is valid for most purposes. " Such a condition is more likely to exist in an engine cylinder, especially during the compression stroke. In fact, a proof of the validity of the isotropic assumption means that the field is homogeneous, otherwise certain directions would be preferred by a lack of homogeneity. 4.4 Data Analysis The data analysis procedure, employed in the present investigation could be divided into twa main groups: i) Analysis of Gas Mean, Velocities. ii) Analysis of the Fluctuating Velocity Components. --. - v In each case the average characteristic parameters It of the signals are evaluated as well as the extent of their cyclic variations. / 4.4.1 Analysis of GasAtean Velocities The characteristics of the instantaneous turbulent gas velocities were examined statistically in terms of the following parameters: i) Mean values of gas velocities at different crank angles in the engine cycle, as defined by: NC u() u U, E)) (4-9) NC 236. where the subscriptso, :L refers to the particular crank angle in the cycle and the cycle number respectively, and NC is the total number of cycles analysed. ii) The standard deviation of instantaneous gas velocities at different crank angles in the engine cycle, as defined by NC 2 .z (U , E) s (u () 2f. . (i NC ), ue) (4-10) iii) The coefficient of variation, which represents the relative variation as given by s (Ue) CVR UE) (4-11) iv) The range of variation in' gas velocities at any particular crank angle, over the number of cycles analysed as given by Range of Variation = (U E) ) max - (u Ed min (4-12) v) The relative range of variation as defined by RRV =[ (U 0) max - (u 0) min I /UE) 237. Tests on the frequency distribution of the instantaneous gas velocities at any particular crank angle were carried out in terms of the coefficient of 'SKDVNESS' and 'KURTOSIS' as defined in AppendixAZ. 4.4.2 Analysis of the Fluctuating Velocity Components The average characteristics of the turbulence signals (fluctuating velocity components) were evaluated from relatively long data records, constructed-by the sampling procedure discussed in Section 4.2.3, While the extent of cyclic variations in the characteristics parameters of the signals were obtained by performing statistical analysis of individual data records for consqr-utive cycles. Analysis of Multiple Data Records As mentioned earlier, the original turbulence signal for a complete engine cycle is a non-stationary process. However, the sampling procedure at some particular crank angle and for a relatively short period of time provides a way of approximating the problem to a stationary one, at least during the small time intervals considered. Such approximation enables the application of statistical theory concepts for evaluating the characteristics of the turbulent field. Also, the use of relatively long records synthesised from a large number of cycles results in a good averaging process of the measured statistical parameters. 238. The procedure for analysing such data records could be summarised in the following steps: i) Transformation of data to zero mean value. ii) Calculation of auto-correlation function. iii) Normalisation of auto-correlation function. iv) Evaluation of the normalised power spectrum. v) Evaluation of the time micro-scales and time macro-scales of turbulence. vi) Running tests on the qualification of data. vii) Preparing the data for individual records analysis. ., -- 0 i) Transformation of data to zero mean value Although, the high, pass filtering of the anemometer signal removes any DC level in the data in addition to the low frequency signal representing the mean trace, the sampling process itself. could produce a fictitious DC level of the signal according to Ahe location of the particular crank angle considered, Fig. (4-20). In addition, some ADdshave an offset DC level which could be detected in a Fourier transform of the data. Therefore, to avoid any bias of the data according to its time sequence(or location in the engine cycle) a transformation of the sampled data to zero mean value is necessary. 239. This could be carried out in one of two ways, either by obtaining the mean values and shifting the whole trace to a new level of zero mean or by obtaining the Fourier transform of the signal, recognising the DC component (zero frequency) and removing it. Both processes were employed in these analyses. However, the second one is preferred because the Fourier transform represenis a step in the analysis for obtaining the 'raw' power spectrum or the auto-correlation function and therefore requires only one additional intermediate step of truncating the DC component. After transferring the data into a zero mean value the auto-correlation calculations follow. Figs, (4-21a) and (4-21b) show a typical engine synthesised turbulence trace (from 228 cycles) before and after the transform, ation to the zero mean levels, while Figs. (4-22a) and (4-22b) show their correspondingpormalised histograms, where the shift (bias) of the probability distributions are quite clear. Figs. (4-23a) and (4-23b) show also the Fourier transform of the signal, in polar coordinates, before and after truncating the DC component. ii) Auto-Correlation Function The auto-correlation function could be obtained by two methods. The first method is the standard approach of estimating the correlation function by direct computation of average products among the sample data values, equation 10 240. The second method is the roundabout approach of first computing a power spectrum by direct Fourier tralisform procedures and then computing the inverse Fourier transform of the power spectrum. a) Auto-correlation Estimates via Direct Computation uu (r Z, ) = (r= where T =T = M. t M max and B e is the maximum time displacement corresponding to m- fl5eý lags. hs the resolution band- width for the resulting power spectral density estimate. b) Auto-correlation Estimates via Fast Fourier wo Oc f F(n) Cos 2rrnrd n (4-14) (4-81b) lie 241. Conversely F(n) =4Rt (C) Cos 2r-rnz: dr (4-82b) 0 cc =2ý Rt (r) Cos 211nrdr (4-82c) _vc vc -J2 n nZ = 2, jRt (r) ed -c (4-82d) -VU The second method has proved to be from 5 to 100 times faster than the first depending on the maximum delay time ( 'r max desired. The available Hewlett Packard Fourke ,. r-; Analyser employs the second method and was, therefore, preferred in view of the time saving and the conveAience of obtaining the complete spectral analysis of the data at once. iii) Auto-Correlation Coefficient The auto-correlation coefficient is obtained by normalising the auto-correlation function using equation (3-49). IT ut. ut.,... ) dr, _ R t RtM (3-49) U2 242. iv) Scales of Turbulence The time micro-scale of turbulence ( It) is obtained by double differentiation of the auto-correlation coefficient applying equation (3-55). Rýt (V ,V= 32 (3-55) t2t=0 On the other hand an integration process of the auto- correlation coefficient curve gives the macro-time scale as given by Lt of Rt dt (3-57) For the latter case, the correlation curve was arbitrarily interrupted when it intersects the hoOizontal (time) axis. becauseýof its tendency to oscillate about such axis. Another approach to this problem of estimating (L ) could be carried t out by assuming some analytical expression to represent the auto-correlation coefficientcurve such as a decaying exponential function (as proposed by Dryden and Skramstad (82)) or a Gaussian error function (as proposed by Frankiel (81) and Hinze (79)). Solving either equation (4-15) or (4-16) will result in the approximate value of the time macro-scale. R0 (T) = e- r/Lt (exponential) (4-15) t , (-r) -vt2/4L t2 (Gaussian Error) (4-16) t Ar 243. Neither equation is applicable of course at the points very near to the vortex of the curve or for points after long time delays where the curve starts to oscillate about the time axis. However the latter problem also exists for the integration procedure as mentioned earlier. v) Nomalised Power Spectrum Function Finally, the normalised power spectrum function is obtained from the Fourier Transform of the auto- correlation coefficient curve as given by equations (3-82) In fact it is physically impossible to compute the integral of equation (3-82) exactly from real data because only a finite rather than an infinite, length of the sample correlation function is available. For example if the maximum value of -C is then the power spectrum takes 'the form TIM (n) 4 R" (T) Cos 2tnz: dT t 2 UTm ( -C )Rt .( V) Cos 2 ri n-c d-c (4-17) where L)rrn is a simple "box-car function" shown in Fig. (4-24) and defined by: u TM (T) =1 -Tm -: ý7' T '-: ý: Tm =Tm «IZ 244. The Fourier transform of U TM (T) is U, (-c) e-j 2rrn-c d -c -CID 2 Tm sin 2 Tr nz 2 tr n U TM (n) is called a. "window function" and is an even function of n as shown in Fig. (4-25). It is also known from the convolution theory that if signals are multiplied together in time, their spectra are convoluted with one another in frequency. Therefore the raw estimate of a true power spectral density function P(n) is the convolution of F(-n) with the window function U n): TM . t. F (n) FU (n Wd (4-20) 0fTm The net effect of this convolution when computing an estimate F (n) at frequency rý is to move the main peak of the window function to yj, , then to multiply the true P(n) by the translated window function and finally to integrate over all frequencies Fig. (4-26). Hence, the box-car weighting causes "leakage" by spreading the main lobe of the true power A spectral density function and by adding an infinite number of smaller side lobes because of the truncation Of TM . Half of these side lobes are negative, a most displeasing result, since average power is positive by definition. A07 245. A number of ideas have been suggested to alleviate this problem by modifying the box-car function in the time domain (or by an equivalent operation in frequency domain) and by so doing, broaden the principle lobe of the window function in the frequency domain. In fact, neither of these proposed windows could be employed in the present situation (turbulence analysis) where a wide spectrum of eddies of different frequencies exist, rather than a narrow spectrum centered at any particular frequency. Therefore, the rectangular window is applied, in the present work, on the auto-porrelation coefficient curve. The width of such a window was taken equal to the cycle sample width in the time-domain. The auto-correlation coefficient waA'always found tcx decrease- to zero and starts to oscillate within this period of time delay, as mentioned in (4.2.3). Fig. (4-27a) shows a typical auto-correlation coefficient curve for a maximum time delay ( 'C ) of about 30 times the original sample width, while Fig. (4-Z7, b) shows an expansion of the same curve for a maximum delay period of about 7.5 times the sample width. Although the auto-correlation function is the inverse of the power spectrum, so that the determination of either one is sufficient, a much more clear description of the frequency composition of the signal could be obtained from the power spectrum function. For example, the percentage of energy content within any frequency bandwidth could be directly 246. S obtained by integrating the area under the F (n) curve between the appropriate limits. Consequently, the same information about the mean square value of the signal could be obtained by integrating the whole area under the power spectrum curve (before normalisation). The value of the time microscale could be obtained also from the normalised curve using equation (3-87). Inspection of the power spectrum curve. reveals if any periodic signals are picked up during any process of data collection which will appear as a sharp peak centred at some particular frequency in the spectrum curve, Fig. (4-28a). Corruption of the signal by wide band. noise could be detected also as shown in Fig. (4-28b). Typical power spectrum curves for auto-ýcorrelatiorftfunctions represented by exponential curves and exponential cosines are, also shown in Figs. (4-28c) and (4-28d). These last two cases are very similar to the general shapes reported by other investigators for turbulence signals. Fig. (4-29) shows the schematic flow chart of the different steps in the preparation of the turbulence signals, at a particular crank angle, as well as its spectral analysis. 247. 2. Analysis of Individual Data Records The main objective of such a type of analysis is to investigate the extent of cyclic variations in the statistical parameters of the turbulence field inside the combustion chamber of the engine. The same technique for analysing multiple records is applied here with the exception that only one cycle at a time was used in the analysis. Further statistical analysis of the data in terms of their variance, standard deviation and coefficient of variation are carried out for the various measured parameters (mean square value, micro-scale, turbulence intensity and eddy diffusivity). Also, the analysis of these individual records enables running the test for the stationarity of multiple data records as discussed before. It provides also another check on the adequacy of the averaging processes involved in the multiple record analysis. 4.5 Programming of the Data Analysis Procedures The Data Acquisition and Processing System, described in the preceding sections, employs a number of programs at different steps of the investigation procedure. Such programs are written, either in a machine code (for steps carried out on the Hewlett Packard Fourier Analyser) or in FORTRAN language (for steps carried out on the ICL Digital Computer). 248. A review of the complete procedure will show the different steps where programming is required. This could be summarised systematically as follows: a) Calibration of the Hot Wire Anemometer. This step requires the use of a calibration program called (VEL CALB (94) ), which is fed from a set of experimental calibration curves at different operating temperatures and performs an iteration procedure to give the correct value- of the wire's cold resistance (RC). This accounts for the observed discrepancy betwben measured and actual values of (RC) due to the Peltier effects resulting from the dissimilar materials used ip.. the hot wire and the support prongs of the probe. b) Recording of the Data Signals using an FM Recorder. c) Digitization of the Signals using the ADC of the Hewlett Packard Fourier-Analyser. This step employs a straightfonvard instruction in machine code for introducing the reproduced signals to the ADC at the selected sampling rates and to produce the digitized output data on punched paper tapes. 249. d) Preparation of Turbulence Data. This step consists of the first part of the SPECTRAL ANALYSIS program which is written in machine code. It is carried out in the same procedure for the analysis of either individual data records or multiple data records as discussed earlier. its function is to isolate the turbulence signal at a particular crank angle during the engine cycle with a fixed sample width (4 The isolation procedure is continuously carried out during the replay of the data from the tape recorder and followed by a storing process in a data block of the Fourier Analyser. It ends when the number of extracted samples from consecutive cycles reaches the stated number in the program. e) Spectral Analysis. This step is carried out on the extracted data in step (d) for either individual data records or multiple data records. It is mainly concerned with the calculations of turbulence characteristics in terms of auto-correlation function, auto-correlation coefficient, micro-scale of. -turbulence and macro-scale of turbulence. A machine code program called SPECTRAL ANALYSIS is employed at this step. Different versions of this program are given in Appendix B2 for data analysis at a single and multiple crank angles in the engine cycle. . /d- 250. f) Formating, Scaling and Storing of Data. The incompatibility between the output format from the ADC and the input format to the ICL computer makes an intermediate step necessary. This employs a FORTRAN program called DIGITIZATION AND CALIBRATION which reads the paper tapes produced in step (c), accounts for the scale factors on the ADC and any conditioning operations carried out on the recorded signals and finally reproduces the calibrated digitized signals on punched cards with a suitable format for the ICL computer manipulation. A listing of this program is given in Appendix Bl. g) Calculations of Mean Gas Velocities. This step employs a FORTPAN program called VELOCITY PREDICTION which pprforms the following operations: i) Calculations of instantaneous gas velocities for a number of consecutive cycles at different crank angles as determined by the sampling rates on the ADC. The mean values of gas velocities, over the number of analysed cycles are also carried out. The output results are obtained on the line printer for any number of cycles. . 251. ii) Plotting of graphs showing the variations of gas velocities at different crank angles for individual engine cycles as well as the mean value over a number of cycles. 0 iii) Producing of the output results on punched cards for further statistical analysis of gas velocities. This step is made to meet the maximum storage capacity located by the ICL Computer for individual programs. A listing of this program is given in Appendix B3. h) Statistical Analysis of Gas Velocities. This step-employs FORTRAN program called STATISTICAL ANALYSIS, which 4s fed with the output data from step (g). It performs the following operations: i) Calculations of the various statistical f parameters of gas velocities at different crank angles in the engine cycle, e. g. mean value, standard deviation, the coefficient of variation, the range of variation and the relative range of variation. It will also carry out a test on the probability distribution of the samples (gas velocities) in terms of the values of thel5kewness and Kurtosis. ? rý 252. ii) Plotting of the different P4rameters., calculated in step (i), versus crank angle during the cycle. A listing of this program is given in Appendix B4. while a discussion of the definitions of various statistical parameters is given in Appendix A2. i) Turbulence Analysis. This step consists of a complementary part of the spectral analysis discussed in step (e). The output data from step (e) is therefore fed into a FORTRAN program called "TURBUIXNCE-ANALYSIS I" tog ., ether with the calibration of the,, hot wire anemometer and the digitised data obtained in step (c) to give the following turbulbance parameters: i) Turbulence Intensities (Int). ii) Fluctuating Velocity Components AA iii) Time Micro-scale of Turbulence t iv) Length Micro-scales of Turbulence (2 v) Time Macro-scale of Turbulence ( Lt ). vi) Length Macro-scales of Turbulence ( L,, L ). :y The calculated parameters at different crank angles in the engine cycle could also be plotted for any number of tests for comparison purposes. AOP'%' ')\ 253. A second program called "TURBULENCE ANALYSIS could also be used for plotting the autcx-correlation coefficient, the second derivative curve of the auto- correlation coefficient and the power spectrum function. These data are usually obtained in digital form (on paper tapes) from the Hewlett Packard Fourier Analyser. Listing of these programs are given in-Appendices B5 and Dr,. 0ý Cyclic Variations in Turbulence Parameters. The analysis of individual data records provides a way of estimating the extent of cyclic variations in turbulence parameters which affects the propagation of theflame front inside the combustion chamber. This step is carried out in the same procedure as for multiple data records# step(h) with the exception of' using individual'cycle data-, instead of the averaging process over the very large numbers of cycles. This also provides a check on the stationarity of the data at different confidence limits and at various crank angles during the engine cycle as discussed -in (4.3.2). The corresponding program for this step is called "TURBULENCE CYCLIC VARIATION" and is given in Appendix 117. Afr, r k) Correlation Between Turbulence Structure in Engines and in Pipe Flow. This process is carried out to investigate the possibility of using the semi-empirical theorieý§ developed for pipe flow characteristics in engine investigations. Its main function-is, therefore,, to compare the measured characteristics of the turbulence field inside the combustion chamber with the predictions of pipe flow data for the observed mean velocity at the spark plug. The analytical equations for such a process is discussed in Chapter 7 and the corresponding program (called CORREIATION) is given in Appendix B8. The output data of suth a program is usually obtained on the -line printer and the graph plotter. 254. . ddwml% AW74W ]255. >4 (D ho 0 bo q 10 Fig-(4-'3a) Instantaneous output signal of a hot wire anemometer % in a S. I. engine. Data representing three consecutive cycles for a test on the Ford V4 engine at 1000 RPM. 1 (D bo cl 4-) r-I 0 11 Pi. to 0 -H 4-) cd :j H N TIM-E-idC -*" QW. 10 uba. 3! 409.50 Fig (4-3b) Fluctuating voltage component of a hot wire anemometer in a S. I. enginer(Band pass filter. 250HZ-IOKHZ). Data correspond to the signal of fig (4-3a).. - 7 256. bo 0 4-) H 0 P4 4-) :3, 0 Fig (4-30 Output signal of a pressure'transducer for three consecutive-cycles. Data for the-same test conditions of fig (4*-3a)- 1" H C; bo Cd 4-) 1 H 0 P- 44 :1 P, 4-) !I 0 Fig (4-3d) Output signals of the timing mark and a resistance thermometer for three consecutive. cycles. Data for the same, test conditions of fig (4-3a) 257. Temperature - I Meter (2) Phaw i i Control OPERATE Circuit ", n t ve - RCS. MEAS. Detector ------- STD. BY I Square. *a. * Geýmtw Pro. w Prw Wnp. S. ", I Gain Control P. tase It P. tage it Filw Am probe F#Kback DC P. 1 Ou FUNCTION sývitch Protection Circuit Network ! Ad C., cu'l j. 55mos PIL94n Unit REMOTE 11 --4 ZFA0 1-7-S Power pock Fig (4-4) Simplified diagram of a constant temperature anemometer. 4 2. Ste ep riqc of ap- plied test voltage ---------- 2. Impulse response of the system is com- p2rable with a sud- .C den velocity decrease M . C1 0 3. Resulting output signal - Oscillations caused by Oscillations caused by poor bridge balance unsuitable amplif r bandwidth Fig. Response signal of a constant Fig (4-6) Adjustment of the temperature anemometer to frequency response of square wave impulse. a constant temperatur anemometer. C) 01 " --0 0 C, 4 9 Co 1 t' 0 0 t- . r: 4.3 E-4 pt 4 -4 U) 14 9) 4J . -f 0H bo M44cdg: s 0 es A : E2 07"a stlil * zu"a . . (; I,., F0.00.0 x (OZ, - 2, L).. OOUO-rO;; Ta ejnjvxedmaL ý5s. ,1 4 C3 V-1 44 4J co 0 V) 0 Cl. fj 1: 0 E >% 00 C ) r4 OU tri . t- 44 U `4 0, 0 el J-- 5.4 L'I *4 -0 4ý IN 0 C: C3 *a i C: cli i 0-4 ly-I (1) CP 4J J4 q> to 00V. i I Fa -- 0 $4 F.! .N s 00 0 rX4 CO - 4 vs Eý 4- V) Lrl cs (14 0 en 0 Cý 41 cs Q L41 cl 94 .3 r cn 4A C a. 0 84 U) 0 r-4 -H r. in 4-3 E! 0 0 vs 0 $4 Cd 0 ca $4 E, 4 0 r= 4.3 o 0) cl P3 U E-1 4 C4 Lj tf) N J-1 +1 vo (1) 44 0 - :3 -4 ý F; !ý IZ (a r-4 ; Lj oo0 ul CS 0 bo a) -41 9 40-. 4 o cd :3 4"= a0 41 E-4 rl cl C4 0 C: ý-4 N_ > 0.0 00 r-. bO 11 C: ý4 C ca 4) :j0 -rý 14 4J 14 ir C: 44 -" ý4 ir. 4 0 :3 11: 1 Ea (1) ul Ul 4j C: o -H 93 0 PM C., $4 ý4 L) :300 Cl ) cs 0 . rý. 43 4J C) 1-4 FE in =3 >* 00 QF 0 E4 E4 fs t- - . - a) co i 3 P4 MI, Cy 0x (OZ 11) G*uO'G;; Ta . E k 259. t CH 0k 01, En C3 U) Lo Cd (D 14 r -f 03 4-1 cd Q ý4 U) (D 0 4 Q) cu ý I -1 () v ILI , -- - . U3 4-b " ýi I - e j c2 c3 U) C3 H to f-4 ci 0 43 4-3 0 C) 4J C3 ý9r. 0 4-) ci 4- 0 Cd ca H Lu r-q 0 :3 C I Lij CH CH l C; 0 .1 1 tij , Cd ca i LU C3 100 to V) 0 oiz V) 0 C:; cr CL 4-) V- Cd z r-l , i, Cc C3 cr- P. bjO E-4 DOS I ON 0 1 plos T 1) 0,3 , 1) rl, in, sI u IDVU * a P4 Ix (W IN) i6, nc! R3t, 4,4 260. 46 lp lp Amok II Fig. (4-11a) A view of a Rolls-Royce cylinder head showing the different locations of velocity measurements inside the wedge chamber. w 4 a Fig. (4-10) A view of a cylinder head of the Ford engine showing the location of velocity measurements At the spark plug 261. ,. I ýQ, -Ps, 'fkm, -'al, -, ` Fig. (4-11b) A view of a Rolls-Royce cylinder head showing the different brass tubes used for probe traversing inside the combustion chamber. 414 Iý1, Fig. (4-13) A view showing a single wire probe-motinted on the traverse mechanism used for velocity measurements at different locations inside the wedge chamber. 'Arl Fig. (4-12) A view of the spark plug double wire probe and its traverse mechanism. 262. U(t) S a t UIU2U3U4U5U6 1, ". Fig. (4-14). Illustration of aliasing problem. FOO F(n) V-- n-n nmax max (a) True spectrum (b) Aliased spectrum Fig. (4-15). Aliased power spectrum due to folding.. 263. n A*, -, 'A 264. c3 q IFOUD V4 ENGINE Analysis at-200 BTDC Engine speed 2000 RPAT Intake Vaccum 183 mm Hg Xumber of analysed cycles 114 4J C; V4 4: 3 0 U 0 4-1 CV3 CS Q! - ,4 Cý, 0 Tite intefval for 20 crank angle or. - +) degrees_ 09.10 degrees -A n cl a. 0 -H +3 0 0 44 :3 -4 TI HE MSEC (a) Cycle sample 20 crank angle degrees 2. ZS 2.76 V TIHE HSZC (b) Cycle sample = 10 crank angle degreavf, Fig. (4- 16a) Comparions'between the auto-correlation coefficients for two different widt4s of cycle sample. 3.1s 265. v FORD V4 ENGINE Analysis at 200 BTI)C Engine speed = 2000 RPM M Intake vacuum =. 183 mm Hg. w Number of.. analysed cycle& lr4 14 'ý Cý 0* (D t- P4 t- U) 0 0 Tf 0 4) * Ln Ul 0 V-1 C3 PA Cý cis 0 %. o Z P4 C3 C3 2 . 50 SM FREQUENCY KHT (a)-Cycle sample = 20 crank angle degrees CD Nr $-, 4-3 C) U) U) 0 M C3 C: ) 0 %. o z rM4 : C3 IL 1.25 2.50 3.75 5.00 ENCY MZ FREQUE (b) Cycle sample = 10 crank angle degrees Fig. (4-16b) Comparison between the power spectrum functions for two different widths of cycle sample'. 266. u1(t) / 2(t) N(t) Time (t) Time q am Time Fig (4-17) Ensemble of sample records forming random process 267. 0 CD 00 CD 'i, CII ''o, -4ý4 C13 C-1 r-I 0 CD bD r. +) 0 (D 0 > P4 U 4-3 0 4- ,4 0m 4 0) 4H bjD 0 00 W 4J :> U) "4 0 .,. I 0 V) .0 00 P Cq Z 4-) bO 0 0 >-. 4 +) cd C: $4 A 004.3, 'H t) 4. ) 4-1 4) 0 (D +1 (D 41 r ho 00 $4 (D 0 4J q. 4 tH 4H 4-3 C: 0 P4 cd r. P4 x0 a) 04 C) Ei 0 r. 00 -: 4 U4 co bý . ri ýL4 U3 Ol m (D cr) 0 C; oes/m (, n) X: ýTOOTGA 2luTZj;, enjonja C) c; C) 8--f t. --: p >< cy tl: j >-O - t- C; C) -j r--l tjLj LIJ C) Cy tij W 03 cc: C) C7 a. oaa 268 Sao 1.600 2.1300 2.1800 *3.. Soo CIRNK RNGLE X1 ()-2 Fig. (4-1ýa) Variation of the Fluctuating Velocity Component with Crank Angle During the Cycle for Three Different orientations of a Hot Wire in a Combustion Chamber of a Rolls-Royce Engine. '(Compression ratio: 9: 1,1000 RPAI and fully opened throttle). 0 9: 3 L17 6 Ln C- ei .- a) 1-- :Z i--1 Wtf). L cv CC -. Do t-cl C) -T- IIIIII 01600 1.6013 MM 2.6 013 CRANK ANGLE X10-2 Fig. (4-19b) Variation of Turbulence Intensity (u/U)-100 with Crank Angle. Ao Wire Direction*: 60 degrees Wire Direction : 300 degrees Wire Direction : 330 degrees ujaT. a corresponas -Lo conaiTions or Fig. (4-19a) 269. u(t) 8 Ct) a) original Turbulence Signal 0 0 (t) b) X. 'solated Cycle Sample ( 9) at Crank Angle (0)*. Fig. (4-20). Illustration of the introduction of DC component by - the sampling process. 270. a c2- c2 c21 I t. FORD V4 ENGINE Analysis at 10 0 BTDC. Engine speed = 3500 RPM. Intake Vacuum =167.6 mmHg. Number of cycles analyzed=228. rs. iq 12'. 79 19.18 25'. 513 31'. 97 as. 36 44.76' 51'. 15 TIME MSEC Fig (4-21a) Original Eynthesised turbulence signal. p 4-) (D bkD cl 4J 1-4 0 to 9 Cd 0 4-) I (] 12179 Is". 18 31.97 30'. 3r, 44.76 51.1s TI ME MSEC Fig (4-21b) Synthesised turbulence signal*after transfering to a zero mean value. 10 271. 00 lid a! a N ca V P-# - 4) r-4 + r-1 %D cd P4 C-) 0 0 0 p 0 Cl- E--4 LA qýD 00 rQ " H to (D 0 (D ;S 0 W ;z 0 r-4 11 11 a r-i 0 H 0 H ca 4) - 0 F-4 10 :3 >1 >V P. 1-4 c I 4-31 4) ci Cd z cs 0 z - r. po rJ3 P4 cd 4-4 _. - W to ca > 0 0 V. -* VA -- Id 13 , td :> ca 94 (D I p Cd bo 4-1 F1 to 0 (1) 0 H : 2ý ho (3 bo cz to V 0 0 4-31 H 4-1 0 r-1 00 C\j a V2 tto 4--) - cm 0 ba 0 ba 0 bo Sý4 cis -H JL4 9 r4 a 0 0 ca-4 to 4-4 4-P 4-31 cs tto bD 94 . - :4 -j 0 4-3 -f-f to a) .0 . ---== I $4 -rq 0 (D A " 4-3 E I. z 4) f+4 0-4, A 10 C ) Q OX3 (IS A r-4 %-0 --a . %.. 0 - Cý N -H 0 10 cs +) Is 4J $4 Cd cs JE3 4-) 0 ; r4 0 cl C\j co* 0 zol 0 10*0 a- 31 00 solo -H ZRCOO x '02COOO x 9oauanooo jo Souanbaij aouejn3zo JO anbaij SOu I 272. 4-) al Q 4-) Q to 9 C; ri 0 to 10 TI (1) 0 co co W0 r4 P4 EQ F1 4) vi 41 A CD :s . : E: mN* to (10 pq ; 1_1 r-4 9 r-I 4J Cd 00 C- 0 AC) %D 0 9 E-4 Lf% r-I Eko 0 fQ PrN ca -f-I A 0 11 0) $ý4 13 W0 It H 00 ; _. r-I 11 C) 1-4 'El :3 bl-A (D CD 4J (D z0 . 00 1 ;4 Cd 4D 0 N 4> A W Pq W 4-4 to to> 0 4.0 to t %-1 > co o (D t4 C) 0 :S 0 N Pý 0W 4-3 0 M 3 t1i ff 0 C. ) 44 1 0 r: 11 : 1 P4 ,4wH ýr. , (a 4-4 tr) co 4. ) 4J $4 tto -H Cl Lq :30 0 cl P4 to W M- 2 P 4 (U)e ORL-410A 2uT_q-en4onjj bo 0 0 W 4-) N 4-4 Cý . Cd 93 bo q -H co LN :j Ln ci 4-3 0M 4-1 (1) Ea 9 90 W P14 $4 4-1 Lf) ho aRL-410A SuT4vnjonTd 273. F(n) ttc u UJC 0-, k- cm cc cr- c C: 3 c: ct) CD C)o rl% E-IL C3 0.000 H _ / TI Jt _ _ _ __ __ __ a a C", CDC u"Juu I. fluu Z. 7ou 3.600 4.500 5.400 G-300 7.200 CRRNK IINGLE (DEGREES) XI tit cn 0 41 I=ci- U- 90 LA- -- U-Cý - LLJ C) L) § 0.000 O. SOO LEGO 2.100 3.600 4.500 S-400 6.300 7.2.00 CARNK ANGLE (DEGREES) X10-2 Fig. (6-1) Statistical Analysis of Gas Mean Velocities at Different Crank Angles During the Cycle. Analysis for 10 Consecutive Cycles, Rolls-Royce V8 Engine, Plain Inlet Valve, 1000 RPAI and Fully opened Throttle. Probe at Spark Plug Location (Z = 17.78 mm), Wire Direction 3000, (See Fig. (5-3) for definitions). (c) Standard Deviations, S(U). (d) Qsýefficient of Variation (Sm/U). 100. 1 364 13 .6 r- in to CCC2 M LI) 94 cl 9: 1CL2 A 7.200 it. 800 2.700 3.600 1.500 ico 5.200 CRRNK RNGLE (CEGREES) XIO-2 C X -i ujý C3 cc .! Onrk 1. UUU C. I VIJ J. DwU 1. DUU ý. %UU 0. OLU CRRNK RNGLE (DEGREES) X10-2 Fig. (6-2) Statistical Analysis of Gas Mean Velocities at Different Crank Angles During the Cycle. Analysis for 10 Consecutive Cycles, Ford V4 Engine. Plain Inlet Valve, 1000 RR'. 1 and 102' mm Intakq, Vacuum. Probe at Spark Plug Wcation, 11orizontal Hot Wire at 3.8 mm from Cylinder Read Surface. (a) Mean Values (U). (b) Occurrence of Max. &. Alin. Gas Velocities. C9 Cý. C3 C2 C3, C3 Z 0- cw i2- ci 365. 4: 7 t. 4 2: c; / c2 m CL c2 CL e- 02 cl C? CH: n-- C2 C) Ll? cn c $A C., ti 6- X 0 0,3 tL. U- CIO 0.000 0.9013 1.600 2 700 9 sca 5.400 15.31ca 7.200 CRRNK ýNGLE (DE60GOBEES14' X1 E)-: z I Fig. (6-2) Statistical Analysis of Gas Mean Velocities at Different Crank Angles During the Cycle. Analysis for 10 Consecutive Cycles, Ford V4 Engine. Plain Inlet Valve, 1000 RRNI and 102mm Intake Vacuum. Probe at Spark Plug Location, Horizontal Hot Wire at 3.8 rim from Cylinder Head surface. '(c) Standard Deviations, S(U). (d) Coefficients of Variation (S(U)/U). 100. U. ULILI I. vUU 4. IUU a. Ouu l. JLAJ . ., J. I UU 0. JUU CHPINK RNGLE (DEGREES) XIO- 7.200 4 vfý it vr i MýL Vv- 0 3GG. C-3 ul tv Cl) I-, LY Cl -J,; - LLJ :: p 2ý cc Wo X7 0 I.., 0 0 I', C) , 1-11 X LLJ o; - z P-0 do I: cj cr- X cro v el 110 0 NG 5.70 0. r-RqNK R"ljGLE f OFIGREE IS) Wire direction 0p= 3300 (See Fig. (5-3) for Definition) Wire direction = Goo p Wire direction 0= 3300 p Wire direction o= Goo p 0 "C . 74 Fig. (6-3) Comparison Between the Measured Components of Gas Velocities -and the Occurrence of Maximum and Minimum Values for two Different Orientations of the Hot Wire. Other Test Conditions are the Same as those of Fig. (6-1). )J6 a 367. 0 0 I- I - CD GOS11 0 C9co I GDO"I I) t. C3 C3 in RX w ncr no _wuj 61 cl: CS J fS lz A , -i LAJ bj uj d V. 7. "N"L cju o3z"L 006,0 OF)910 DOC' 0 onn o 006'a OU 10 C" *0 - 09C wt 0 I-OIX 03SI14 NDIIUIA30 IIUU014UIS a-oix co(,, n/(n)G 'IAUA JQ'. IJ30) tz 10 W V) La W CC -Ae U C) V- z cc cc Cýu S C. C. S C. c )m o CD 9-ý ul L. j LLJ 0 a 8 0 0 60? 0 1000Y3 099*0 0WO eta 0 I-OIX : )j-731W NORUIAIG CLIUWULS Z-Olk OOL"flAIUS %UA qO'JiJO3 te m to 0 r. Cd 0 -rl U) +i r- ci 0 . r4 -H $wd 4.3 ci -ri > ýh4 0 0 C. ) 4. ) 41 U) CH 0 13 9), 04-3 0 > 0 KZ Mö 0 10 f. ' r. 0 cu CH li 0. 0 Co $m4 ce r: > 4) 00 in s4 0 %: CH 0 to :. tz 0 gl F-4 0 9) > bf çx4 /57.1 368. cr ; LLJ U) LAJ cc LLJ Il- c3 CJ 432 1.6013 Z. 7UU J. bULJ 1. Wu a. luu U.; Xju 1. zuu CRPNK RNGLE [DEGREES) XI to cr) Nr. -A JJ 4 01 c2 Z cr- >c cr- . r_ LO VI U. C; C2 W. I C; - 02 C; - C. 0 4. AAA 0. coo a. 501j 1. VUU 4.1UU j. bUU 1.5011 5.1 Uu b. JUU CARNK RNGLE (CEGREES) X10-2 Fig. (6-5) statistical Analysýýs of Gas MeAn Velocities at Different Crank Angles during the Cycle Analysis for 10 Consecutive Cycles# Ford V4 Engine, 102 mm Intake Vacuum, Probe at Spark Plug Location, Vertical 11ot wire at 3.8 mm from Cylinder Head Surface. (a) Mean Values (b) Occurrence of Max. & Min. Gas Velocities Idep"% 369. C2 C3 OC'4 u3c G) crc tljý L13 C3 cc ccc C3C cr-C o') 0.000 A 1 A1 e AAA C2 C. 2 0 cw 02 Cl LA- CD L) 6ý - C2 u. luu a. sua 1. ou CRRNK r FINGLE (DEGREES) -'ilO-2 200 2.100 3.600 CSOO S. im 6.300 7.20a Fig. CRRNK RNGLE I U-IREES) X 10-2 Statistical Analysis of Gas Alean Velocities at Different Crank Angles during the* Cycle Analysis for 10 Consecutive Cycles, Ford V4 Engine, 102 mm Intake Vacuum, Probe at Spark Plug Location, Vertical Hot Wire at 3.8 mm from Cylinder Head Surface. (c) 'Standard Deviations S(U). (d) Coefficients of Variation (S (U)Aj). 100. 370. Figs(6-6) and (6-7) Variation of Gas Mean Velocity Characteristics'with Depth Inside a Wedge Combustion Chamber. (Rolls-Royce Engine,. 9: 1 Compression Ratio ,, 1000 RPM and Fully Opened Throttle Conditions If 0000000 c%l e Co cq w c2 e r. (D r-f m cq cq u+0+X*1.4 > 371-. >b ce 42 K 13 cu x0 ) 0 :) 9-9 42 41 il te 0 921.1 u r. 00 U) U) r4 X Ei M 00 . to >4 .. 0. 0 c: 0. el (1) %-0 ic 00 to (ý C U) >c -p (D 00 4-4 0 el 41 >b Cd 0 8-- U) 01 (D gn U) :> 0> 92.1 id ce %. 0' 4 . cý U) 10 . 92 tu 00 to ri 9-4 4 , IH C) 0 p4 00 a) -, 4 -r4 4.1 41 0 4 10 4 Co r: J., > b-4 1-1 CD I CD t cli 0 00 cq le H 0-4 . p4 oas/u, 91. TZOTGA UUGIU s139 372. ei: e--1 8 E- 0-% -ri U) %_o b-4 94 0 44 80 . 14 0 :D el UN %. w 4j 0 r. -ri b. 4 ul g4 +b -% > cj IH m to %-o 41 Q %. 0, 121 IM 0 N. 1 Co 4-4 0 0 00 i-, . 4j 4 41 01 41 c; zi ýi IH JD li0 13 r: 00 0 0000 0 ij ru %, 0 0 -: r r bo 01 b3 r4 --: t co r-i r-1 ri tu i 1 c3 m0 e G) 0 H0 44 N E2 c3 0 + >< c; %. W 4 Icý 0 c; 4 UN _e t; "-I , ool *(n/(n)s uoTzl3Tj, BA jo zuaToTjxoo3 0 373. a) c , -4 1 t. T- r: Mi (D 00 U %. d 0 .. 0 0 0 v) 0 U) +a #-% 41 Q0 %. 0 J., U) 4- 0 0 0%.., > r. 0 00 0 0 -v-i Ei 6-b 0 ca u -ri 94 0 %. 10 LrN C\j 0-4 Oes/m JCI-TOOIGA uVall SUD )4. 0ý% 00< 00 D) :iU ti * 12. cr k- (+ 00 :10 :1 00 zr tr 0 0 0 C0 m r. 6-b 0 e+ 0 ri b-b 0 0 C0 ,0 14 0 0 0-% bi c:: ). -% %. 0 0, 0 N *a e, 0 :i 00 (D 91 W * YILC Coefficient of Variation (S(U)/U). 100 OD OSL *0 009,0 US$. "U fflý -u 05110 Z-OTX ý1130-13A NOIGICI - ý4sin-os 0 cli 0 in V4 Cý 0 C) CV) 6 in X cr) I 0-% cr) C: ) tii ei c2 %-d LIJ Lo "ýz " CE: cr- C: ) M ou 0 Ln Ln Cý 7 oj 000 *0 375. 0) I. e 14 10 C) 94 pl 0 Eý4 ri 0. rh r. . 0v +b 0 0 rý 0 0 U) -f-4 W C6 om 0 :: - C-) 00 %. d P4 -r-4 &4 0 w co 376. -. Z=0.5t' 3-5 0.0 0.1 0.2 0.3 0.4 0.5 Depth (inches) iFig. (6-9) Variation of Gas Mean VelOcity'at TDC with Depth Inside a Flat Disc Combustion Chamber. Data from Viinsor! s Investigation (23). 377. Fig. (6-10) Investigation of the Flow Pattern Inside a Wedge Combustion Chamber. (Rolls-Royce V8 Engine, Compression Ratio 9: 1, 700 RPM and Fully Opened Throttle). Probe Traverses Parallel to Cylinder Axis. (See Figs. (5-2) and (5-3) It 378. 4 a) Crank an&le 200 Crank an&lo (0) goo LEVEL: -Z 20 mm -200 b) 0. Sol' LEVEL: Z. 15 44 4 3k 04S LEVEL. Z 0.0 mm Fig. (6-10) scalc a/see 379. 1 1200 5 120(ý 5 d) 0w 160*" LEVEL: Zw 15 314-, '4 d) 1600 Zw 20 mm d) IGOO LEVEL: Zn0.0 04 Scale cVsec 380. u 01 u 00 ry co to C4 0 v0 Co (3) bD bO v0v to 0NMN 00 V. V. - LZ 0 C-A ci o C, 4CD ON V4 CY CD 0-4 ol 0 CD ba CD 0 381. 1 1 ,2 Z te P, o0 0 -I 6 382. Figs. (6-11) - Variation of Gas Mean Velocity with Engýne Speed. Ford V4 Engine. Analysis of Ten Consecutive Cycles with Probes at the Spark Plug Location. Z=3.8 mm: A Hot Wire Positioned at 3.8 mm from the Cylinder Head Surface Z=0.0 mm: A Hot Wire Positioned at the Level of the Cylinder Head Surfa6ý (Spark Plug Gap Location for this type of engine) I I 383. FORD V16INF INDUCTION VFRtQ-D CrAnk Angle (Degrees) HORIZONTAL vvIRE A 80 10. - IV 120 z 3-8 0 -W a 160 0 200 S. - X 240 0 > 6. - 6.0 1000,2000,3000. i. Exiclue Speed (RPM) rig (6-11a) FORD ENGINE 7. cra nk Angle COMPRESSTON P ERTOD 92 (Degrees) HORIZONTAL 'WIRE a 280 6. T 300 t712 A 320 v 0 340 5. - 360 + N. 4. 3-- a M dof oo, IOP de wo 1000. MO. 30CO. Engine Speed (Rpýj) Fie. (G-12b) Pt 25. F OPD -E*, %*Gr,; E TNDUCTrou PERIOD Crank Angle VERTICAL WIRE SDegrees) 3.8 mm ik 80 120 160 200 240 15 ILI IOr 0.0 1000.2CýO. ENGINE SPEED (RPV) Pic. (6-12a) I 3 3000- 384. 385. FORD ENGINE COYPRESSTON PERIOD 10. VERTICAL W. ':. E 9. ý Crank Angle 8. - 0 0 ýz (Degrger. ) 0 280 0 v 3000 A 3200 .4 It) 0 3400 + ý60 7-- 0 P. 6. - 4 4. - 3, 0.0 1000.2000. ENGINE SPEED (MI) FIC. (6-12b) 3000. 386. 12 10 0 0 4J 0 > c 0+- 0.0 FORD EXG I %T% . INDUCTION MRIOD IforizontAl Wire Zw0.0 m Crank Angle (do&roes) so . 120 1co - 200 240 2000 2000 Engine Speed (RMI) Fie.. (G-13a) '2000. 0.0 1000.2000. oo FORD FNC#'INF COMPRESSTON PERTOD 4.0- HORIECN'TAL '., 'IRE 0 Z=0.0 cm Crank Angle 3*9- (Degrees) 4J . 200 .4 43 0 - v 320 4 340 2.0- 4 350 E3 360 X 40 ol do .P le #0 dop dr de d, . 0, 0-0 r-r-Cine Zpecd (Rril) FIC. (6-12b) 387. Yo c of 493 1 6, Z- ' 0.0 9.0 - 8.0 - 7.0 - 6. o . 4.0 co 3,0 - . 2.0 - l; o 0.0 2ý 0. 0 1000. Engine Speed (M) 2000. FIC. (G-14a) FORD ENGINE CMPRESSIONT PERIOD VERTICAL WIRE Z=0.0 111M Crank Angle (Degrees) * 300 * 320 4' 340 A 350 is 360 .p0 41.10. IZ 4p dee// e>j . 41 ýe JO ., 141 , 40, Vertical Wire .Zm0.0 mm Crank Angle (degrees) 80 120 160 200 240 -I- 1ý00.2000. 129r, ine SPeed (RPv. ) PIC. (G-14b) 3000. 3000. so- FORD ENGINE 388. INDUCTION PERIOD Vertical Wire Z=3.8 mm 40- C rank angle 0 (degrees) V4 +b 80 30- cS v 120 > 160 I 08 200 240 VIE! 20 0 u 10 0 -j- 0.0 WjKxIItx 5pucu I. Itt-al; Fig. (6-15a) Horizontal wire Z=3. a mm 50 Crank angle 40- (degrees) A so r. 0 120 V4 4J 03 160 -r4 N 200 30 x . 240 0 00 1 4- 20 -, 4 co 0 10 ý 0 -t- ýI 0.0 1000 Engine speed (RPAI) 2000 3000 Fig. (6-15b) Fig. (6-15) Variation of the Coefficient of Variation in Gas Mean Velocity with Engine Speed During the Induction Period. Ford Engine, Probe at the Spark Plug Location. Hot Wires at 3.8 mm from Cylinder Head Surface. .1 3000 389. 30. - 20. IT- 0.0 a. 60*- -.. 0 r Crank Angle 0 ... (Degrees) 280 " 300 A 320 0* 340 4- + 360 40. - 0 4 0 3.0. - FORD NG74r, ccl-TRESSION MPTOD 1; 00.20 1 00.3 Co. Fig (6-16a) RORIZON"I'AL WIRE .Z =3.8 mm 201 0.0 ZCOO. 3C INGINE SPEED (R. r%) Pis (6-16b) Fig. (6-1G) variation of the Coefficient of Variation (S (U)A). 200 with Engine Speed. (Data corresponds to Ust conditions of FiCures (6-11b) and (6-12b). - 70- 60 Crank Angle .4 (Degrees) 41 Z, 280 >v 300 50-- 1') & 320 a 340 360 40-- 390. 8.0 7-0 Flat Disc Combustion Chamber C. R. uB. 5: 1 6.0 0 . 5.0 Comustion Chanber 43 4 C. R. u7.: l 0 0 Flat Disc > : Cobustion Chambor, C. P. *6.: l) 4.0 5 Squish Cocustion. 0 ICh&mber, C. R. -5.29: 1 . 3.0 A Winvor TDC Ser oivjýl) Tl: G v -en 0 Barton(ll) 360BTDC . 2.0 a James (24) TRC , 7rC 0- James (24) 20 0E 0 James (24) 4 O_I-ITLC 1.0 . 0.0 - 500. 3.000.1500 2000. ENGINE SPEED (PPI-11) Fig. (ý-17) Variation of Gas Alean Velocity with Engino Speed for Different Types of Combustion Chambers (Data ficut Published investiCatLons). 391. Figs. (6-18) --46-24) Investigation of Gas Velocity Characteristics Inside the Intake Manifolds of S. I. Engines. -W tj %C; 5 CP H c; AA J, v 392. 1.000 T. 7co 9.900 I. Sco 3.400 CFAM W4GLE IDEGAEES) XlLrt I J v_ C3 V., 2 0. oca 1. "It f. 7ca 3604 1. SLO S. Nu 1. too CFJV: K ANGLE MEGITIES) cr cl z 1 A 1- ______ ______ ______ ______ ______ 0 ____ T j\; - U. Q4j 9.3-0 1.6w C. IM I, M1. SAU L ILAI ?. too OPINK ANGLE (DIVIEES) xl(rt pig. (6-18) A Statistical Analysis of Gas Mean Velocities Inside ain Intake Manifold of a Ford V4 Engine at 3500 RPM alid 168 mm Intake Vacuum (see Fig. (5-5) for the dimensions of cross section). q ______ § bo ki L'i I Ica w ..,. 0 w Ft La V 94 d I I I sad . &W 1. Ivo s cuo I. W. .. -- CPAW ANGLC IDEGFIECS3 XIO't 0 S. AAR NV\l - -"600 1.500 2.700 3600 q. %go 1.409 CP. PtX ANCLE UGREES) 110'I -i ui 71.3 91 ICE: 4 'i 4 LL V! L& cc cl 9 t coo loo 2m V p ILMHN. T. rlrýVLC LutwILtZO JIM" Fig. (6-19) A Statistical Analysis of Gas Mean Velocities Inside an Intake Manifold of a Ford V4 Engine at 3500 RMM and 310 mm Intake Vacuum. 393. LAJ tr ta 91. - 0.009 0. Ico 9. &W Z. 100 3. s» 1 von Z 15.40K0 *. Sag 7. ZW mnN)c nNur (u)Eßnics) x10 (4 0 C -J 314 Zn a cc Z_ co I ýhi I A hCO 0 . 1" . 800 2.700 2.6w 4. soo - S. Wo C'S. 0 moo LKWNK 1414(At 81 -_ ______± I I' IjI i :iL. .: I Add Pý 703 600 4' wo if, 2DO CRANK ANGLE (07-CAMES) X10-1 rig. (6-20) A ýtatistical Analysis of Gas Mean Velocities Inside an Intake Manifold of a Ford V4 Engine at 2000 RMI and 183 mm Intake Vacuum. 394. 395. 100 80. 0 0 6 W4 0 0 V-4 0 > 40. cs V) 20. D. 0 FORD ENGINE Full Load. Par -t Load. v dOr ,E, 'J", ýU, dor dO' a. - -9- - . 00, 40. 0 .H 40 30. IH 4) %. 0 .H0 U %. 0 20 . 10. 0.0 0.0 1000.2000.3000.4000. ENGINE SPEED (RPIM) Fig. (6-21) A Summary of the Statistical Analyses of Maximma Induction Velocities Inside an Intake Manifold of, a Ford V4 Engine at Different Engine Speeds and Loading Conditions. a 1. 0.000 0.120 0.210 4.360 0.480 0. wo 0.720 CRANK RNGLE EDEGREES) XIO'3 ao u u iL 40 1 i 396. 'O. Coo 0.120 0.240 0.6O 0.490 $QQ Q7) CFAN( R1GtE DEGFtEES IIO- __ __ __ __ / __ C4 C5. C3 ý: 8 cc ý 0 0- Li t'k - ______ ______ - - -. ____ -- -- I PA -rA Or ýAIýI ýl vv V 61 3600 4 wa S. 400 4300 0.000 2- "0 1 CMA0 ANGLE WEGREES] X10-2 Fig. ' (6-22) A stitistical Analysis of Gas Mean Velocities Inside an Intake Manifold of a Rolls-Royce V8 Engine at 1500 RPM * and Fully Opened Throttle. (See Fig. (5-5) for the Dimensions pf Cross Section). J bd x cl: C-0 CAI 030 Crn« FWGGLE (OLGREES) XID*3 3 .111 ihý 11 1 I 000 0.120 0. z4o 0.360 0.49* 0.600 0.120 CRAMC FNGLE (DEGREES) X10-7 it 397. - W)w a. 11ko a-0- J-ý_ 2 19. wo 6.300 CRANK A46LE CC' EUIEES) X10- Fig. (6-23) A Statistical Analysis of Gas Mean Velocities Inside an Intake Manifold of a Rolls-Royce Engine at 1000 RPNI and Fully Opened Throttle. 398. 140 120, 100, 80. : 01 4-S -rf a 0 60. r 9: ci o- 4-0- cs LD 20. 0.0 s (U) /U 500. ', - - 1000.15CO. EINGINE SPEED (RPM) Vig. (6-24) A Summary of the Statistical Analyses of Wja%. imum Induction Velocities inside. an Intake Manifold of a Rolls-Royce V8 Engine at Fully Opened Throttle Condition and Different Engine Speeds 28. 24. 0 20. '1 16. V cs . r4 0 q-4 0 0 4. 0.0 399. Figs. (6-25) - (e-30) Statistical Analyses of Gas Mean Velocities Inside a Wedge Combustion Chamber of a Rolls-Royce V8 Engine at 1000 RPM and Fully Opened Throttle. Measurements at the Spark Plug Location (Z = 17.78 mm) and Hot Wire Direction of 300 Degrees. . 400. Ct ci 9.0 "t " __ __ I. Sr _ ___ ___ ___ ___ " b3 ci 22- ll!. 0 to 7-1 W, 43 C3 Cl 03 C: cca dzca 1.000 2.1-ca 3. (Ca Cma S. Ica 6400 7.100 SKLE mufus) xi CI-1 Fig. (6-25) A Statistical Analysis Of Gas Mean Velocities for a Test with a Masked Inlet Valve. 4 " . 11 III n 1. - - ' j : __ __ P-1 It CRRNK RNGLE tE) EGF-EES) XIO-" 4. 401. Cb- c 4f r el r_ -i LLJ Am, cl C! C, C C V C c C C! c c M ý'- c CLC r ). Cc c c c " "1. o= 0.1z(3 MM 0.360 0.463 IL= 0. IZCI C» u, MEES) XIG Wr%NK RNGLE (DEG -3 cx 0 bci ci ljjcl WC2 C) CC C2 t >C; Li 9 C3 m CCC3, C: jp ý- C! crý ve AV/ JW P, 0. sca 1. b5u Z. 74;; j 3. SM C= s. ioa 6.,: ca 1.200 CBPu%. < ANGLE MEMWES) X10-2 Fig. (6-26) A Statistical Analysis of Gas Mean Velocities for a Test with an Intake Manifold Fitted with Delta Wings. f is 402. w ci C, ei 0 ei cr w Dr. c >C cl 2' ý cr, xi E 0 - I -Koca 0.120 -- - 0.240 - 0. ZED . o. Cci . 0. izo L) Lac U)c =1 C2 C3 C3 CC cce 03 C CZRNK R NGLIL ED EU, 'iLL3J Xlo-' MOW 0.200 1.630 Z. Ica SAM 4.5W 5.100 6.300 7.200 CM%K. RNCLE (CEGFIEES) X10-2 Fig. (6-27) A Statistical Analysis of Gas Mean Velocities for a Test with an Inlet Valve Designed for Reduced Lif t. 4 t 403. ci ei b'Clj ti, cl 7- c ui a 0. CS; NK RNGLE IDEG8EES) XIO 6ý, 0. X: v 21. C) crc tlý C3 dn -or_ crc cl O, c c VI I V 4 .-o. rCO 0. SCO 1.800 2.7co 3.. X-0 U. Cra SADO 6. SGO - 7. NO MANK PNCLE (MGREES) XIO-z Fig. (6-28) A Statistical Analysis of Gas Alean Velocities for a Test with an Inlet Valve-Fitted with Four Vanes.. 404. C2 U ci f. cl do crc W A: c c C, c C2. I-C LAJ c c C3 7- CLC cc rl I NA a. . C. wa 0. IZG 0. zia - gAso 0.160 0. &OG a. 7ta CM. NK F: 4'JGLE tGEGPaS) XIO-3 C> CC C3 CC cr c3i 74 ý6 74GO 3. Ma Q: sca 1. VC0 Z. 7CO SACO I. Sm S. IGO 6.3013 ONZ RiCLE WEWEES) X1 Fig. (6-29) A Statistical Analysis of Gas Mean Velocities for a Test with an Inlet Valve Fitted with 8 Vanes. cz q ý 1\ý, 43 L) cr : 0 Lu" cc, X4 a C, - Of LY LLJC, C3 IAJ Q a cr Cc C3 A A C7 1 -RI 0. CGO 0.320 0M0 CP-; V. '< 9. NGLE t0 ! E'ýIRE ES III n- 3 I i. ___ ___ I ___ ___ 0.720 4 4 11 4 0. C03 0. tca 1. OCO T. 709 3. sca 1. Sm S. Ica S. 2CO 7.11. -3 CPRNK R. NCLE (DEGPEES) X10-2 Fig. (6-30) A Statistical Analysis of Gas Mean Velocities for a Test with an Inlet Valve Fitted with Six Vanes. 405. a 406. loci 90 so 70 co %I 40 30 20 10 0 Valve Valve Valve Slasted Valve for Manifold with wi th wi ih Valve Reduced with . 4 Vanes 6 Vanes 8 Vanes Lift Delta Wine. 5 rig. (G-31a) Comparison Between Maximum Induction Velocity for DIfferent Modifications of Intake Systen --I. " 407. Rolls-Royce Va Encino 1000 RP. 61 and Fally Opened Throttle 50 40 0 30 id 0 > ýt 20 N4 20 0 valve Valve Valve Masked Valve for Manifold with with with Valve Reduced with 4 Vanes 6 Vanes 8 Vanes Lift Delta WinGS Fig. (6-31b) Comparison Between the V&IUC3 of Coefficients of Variation of Maximum Induction Velocity for Different Modifications of Intako System 408. 24 22 20 is 14 12 0 0.4 10 10 es 6 4 U Valve Valve Valve Masked -Valve intake Manifold with N; Lth with Valve for with Dolta 4 Vanes 6 Vanes 8 Vanes Reduced Wines - Lift rig. (6-32a) Comparison Between Gas Mean Velocities During CompressiOn Period for Different Modifications of Intake System 409. 0 Id b. 0 .40 14 . .4 C, is 0 C: V r? 0 u 0 *4 0u 0 ý4 r to es .4s"4. 19 cc t, . C cl .. 4J 9: %4 " r 4.44 > .4 44 19 to 2V Z zi +6 c C4 3 LY %-Q 14 v *ý, ooi*(n/(n)s UOTINPIRA 10 %uQlOTJJQO3 410. 4 I Fig. (6-33) Analyses of Turbulence Signals During the Cycle for Three Different Orientations of the dot Wire Anemometer 9 (See. Fig (5-3) for Difinitions of Reference Axes). Measurements. at the Spark Plug Location (Z = 17-78 mm), Rolls-Royce V8 Engine, 1000 RPM and Fully Opened Throttle. CD ( C: 2 cy vý ,! D C-4 c2 0. -. CM F 5C2 8. -4 L)in C: 3 cy LLI LLI ri . r-C: 2 c7. - 411. POLLS-ROYCE ENGINE 1000 RPM and Fully_Opened Throttle Wire Direction* ý0= 60 0 I. SOCI 2. SLI13 2, Carl CRRNK RNGLE Fig (6-33a) LU 9: 2 twn c: 7 W, C; - ROLLS-ROYCE ENGINt 1000 RPM and Fully Opened Throttle Wire'Direction 9 60' +0 300 0 ---p CY LLJ cv LLJ C-7 C2 9: 5 Bali I S. saa -V IIII 513CI 1.600 2.50(3 2.600 . 3. sari CBRNK RNGLE Fig (6-33b) ., S. sv. f 2 SAM Cý C2 Cl >e. C2 LO 0-3 C) 1: 7 Cý CC C-) CO 0 C; D. 600 CBRNK RNGLE X10-2 Fig (6-33c) 0 ROLLS-ROYCE ENGINE 1000 RPM and Fully Opened Throttle C7 Wire Direction e =6 00 p 0= 300 0 =2: 2 + p 0 0= 330 p CC Li 0ý 0'3 I Cl C2 C: ) C2 13.600 1.600 1.800 2. Boa S. 300 CRRNK RNGLE X10-2 412. ROLLS-POYCE ENGINE 1000 RPM and Fully Opened Throttlo Wire Direction as 0p= 600 + op= 300 0 # Op= 330 9.800 3.6013 Fig (6-33d) 413. £0 cli 6 qr-- >-- Ln *lr 4: 5 OD cr; LLJ C2 U7 a3 9: ) C2 I CAM ROLLS-ROYCE ENGINE 1000 RPM and Fully Opened Throttle Wire Direction so 0p= 600 + op= 300 0 - . 46.1& 0-= 330 w- I eall 2.313a CRRNK RNGLE FiS (6-33e) 414. I Fig. (6-34) Power Spectrum Functions for Different Crank Angles During the Cycle. (Rolls-Royce V8 Engine, Compression Ratio = 9: 1, 1000 RM and Fully Opened Throttle. Measurements at the Spark Plug Location (Z= 17.78 mm) and a Wire Direction of 300 Degrees). 41S. a 0-% Cýj C; %. 0 X N =(D u CO C3 w 96- cc co C) z p 0 40 cs 0.000 1.000 Z. 000 3.000 4.000 5.000 FREQUENCIES HZ .: X10-3 Fig. (6-34a) Power Spectrum Function at a Crank Angle of 80 degrees. U' 0 V4 cm . X L-j cc: Lu N CL -q co'l CM uj rsi P. -_j (D CC 0 0 z 0 0-000 1.000 2-000 3-000 4.000 FREQUENCIES HZ X10-3 5.000 N Fig. (6-34b) Power SPeCtrum Function at a Crank Angle of. 12o degrees. 416. 0) cr) cp a C" tu , (Lý or) ' 0.0co I: COO 2*= 9. coa Ccaa 5. = FBEGUENCIES NZ .. ', x 11)-3 Fig. (6-34c) Power Spectrum Function at a Crank Angle of 200 degrees. IZ %2 ri v! C>o X 0-% Zb cr: ZC cr_ c C) Z coo S. Oca 0.000 1.000 2. FREQUENCIES HZ Fig. (6-34d) Power Spectrum Function at a Crank Angle of 240 degrees. 417. C,, a 'r C: )X V4 tA -3 M LLJ CLvi 0 Lai tý4 _j CO crv- C: ) c34- 0.000 1. caj 2. CGO 3.001 4. s. cca MEQUENCIES H7 10-3 -Fig. (6-34e) Power Spectrum Function at a Crank Angle of 300 Degrees CO W. C', U! - C: )a V. 6 W. " CLQ V3,; tA. J r4 -i C- 0 Cý C? CO 2.0013 3. aaO 4. WO S. 000 0.000 1.000 FREQUENCIES HZ ")(10-3 X ig. (6-34f) Power Spectrum Function at a Crank Angle of 320 Degrees. 418. U, U, a c3c . -4 X. Cl= n Lot GO C3 LLJ N 9: 2 -1 1 0.000 1 coo 2: 000 3' Lcaa S. OW FBEUENCIES HZ - '. )(10-3 Fig. (6-34g) Power Spectrum Function at a Crank Angle of 340 degrees. Ln 91 C3 -1 A to CO Z" c CO c in LLJ r-j _j cr- 4, Ir- cr- ici 1. UL" &. Uulj ý. FRIEGUENCIES H7. -- . .. Fig. (6-34h) Power Spectrum Function at TDC. 000 419. 4. 3. 2. I. CRANK ANGLE (DEGREES) D tal 0% 50% Fig. (6-35) hlo,. Ximum Frequencies for Eddies Containing 10%, 50% and 90% of the Turbulent Energy. (Data from Fig. (6-34) ) 80 120 160 200 240 280 320 360 f X'Olu 3 /(U)3 A W C3 C: ) -9 c2 tA Ln 4J 420. ci C) 4J C: ) cn rcj .0X* U) W CD C: ) c-i C) +a CI-2 P4 bo 9 r. - 0 . f. 4 *ö X CD r-i 0 %-* . W -ri - . 4-3 0 > 4=) a) Ln 0 to M. 4 :i W 0 4-3 cd cs 0 14 p4 CD «-1 0 cd -ri C) Ai -ri C) ID %. 0 CD 421. Fig. (6-37) Effect of Engine Speed and the Use of a Masked Inlet Valve on the Turbulence Characteristics Inside a Wedge Combustion Chamber. (Rolls-Royce V8 Engine, Compression Ratio = 9: 10 1000 RPM and Fully Opened Throttle. Measurementsat the Spark Plug Location (Z= 17.78 mm) and a Wire Direction of 300 Degrees). . 1. 0 C> In C; C" cý LD ci cr_ tij c . r-C2 C: 2 - a-T- 0.800 C-7 4=2 LO 1; 1 - . ; 422. 1.800 Z. Jou CRRNK ANGLE Fis. (6-37a) ROLLS-POYCE ENGINE Fully Opened Throttle Falve.. Valve. 2ßOO 3.900 9.800 X102 e: )- I-. -- C%j >-C: ) C: ) CP C3 - C) C) : Zci - to cr: C: )C: ) C: ) c3l-ý 0.600 1000 RPM 1200 RPM Plain Valve. 1500 RPHI 1000 RPM Masked Valve. 1.600 2.300 2.600 QfiRNK ANGLE X10-2 Fig (6-37b) 3.3OCk 3.600 ROLLS-ROYCE ENGINE C) C: ) cri CD cri s- #-14 u U-i cn '-, 0 CO w LLJ C: 5 --i cr. C: ) CCC: ) LLI 5-- c2 cy Cl C: ) 9-1 C%j C2 C2 LD LLJ -i CE L) Cf) IQ 4:: )C: 7 ca m. - C-3 C3 C3 C: ) C2 POLLS-ROYCE ENGINE . Fully Opened_Throttle I 423. * 1200 RPM Plain Valvo 1500 RPM I 1000 RPM Hacked Valvo + 1000 VPM l i on 13 0 Ppm I 1.300 1.800 2.300 2.800 CRRNK RNGLE X10-2 Fig (6-37c) ROLLS-ROYCE ENGINE Fully Opened Throttle 1.300 1.800 2.300 2.800 2 CRRNK RNGLE )(10 Fig (6-37d) 1 3-100 3.300 3.800 3.800 424. 0 Ol >e_ C2 C9 0-00 r-4 CV C) __j C2 LLJ FOPD ENGINE. Engine Speed Intake Vacuum (RPM) (mm-Hg) 1000 102 2000 183 3500 168 / I. 1. OEM 2.300 2.600 CHRNK RNGLE xi t3-2 Fig (6-38e) . 3cn 8. ßOcI 429. 0 U) 00000 cq tD 00 Cq KI) 0 X to r-t H cq mm ti 0 r: 0 cu v11113 ul 9.1 %. 0 11 #ý% 0 A X = 4) 2E A %. 01 Co :ß CL 0% >t 0 "1 0: r. *0 c9 C) (1) N Vi in 61 175 cr c: a) meMw. p4 u 10 u --10 -- U P-4 .1 Ln 5 % %.; r . - (V p4 Nf .0 -ý: e7. t: 4 % a) 4 0 C) 0 u c: lz p: 0> sio olg . so b 3 9610*0 X Mei 4 C H0§9 in :3 0-4 ri mnaZoadS lemod PGSTTVUUON 0 r4 bo to >b to 0 :10 c4 Co 0-1 e% to U) C. C 0 to f--4 r. 0 03 0 00000 0 ti 94 cq CD Co N to Xi cq vi m ;111 9.4 %-0 ce UU c0 49 cs 0ü4>> 4 10 c00 P til ci b4 . 59 . 34 9) c3 ci r> to r. CIL 0 14.4 in W (x , to >t t) le 0 > 0 J2 0 0E *0 0 tr eg 4 Q 0 dr Co 0f 2fýý t to A4 Fa6 ----+- 0 ize tzl * zo. *0. (l_ZIIM) 7. L600'0 X (U)d urnaZoads jemod pasTIiamtoN 430. 0.4 (a)-DATA FOR COMPRESSION PERTOD 90.2 9- A&% Ob m*: FORD ENOTNE 4 1000 WIN 2000 IRM **3500 PPH ROLLS-POYCr MUM 1000 Rr. m 2200 IRIN 2500 DPH +0 00 0.0 0.0 2.0 4-0 6.0 8.0 10.12.16. GAS HEAN VELOCITY WSEC) 0.3 (b)-DATA FOR INDUCTION PERIOD I (S=e Tost Conditions as fig(&)) 0.2 0.1 0.0 000 4. -0 8.0 12.0 16.0 20.0 24.0 28,0 32.0 GAS MEAN VELOCITr (M VSEC) U-tj u 0.6 C< 0A 0.2 ý-)-DATA FOR TURBULENCE DECAY INSIDE A CLOSED VESSEL. ' ýt:, w Pre- rt taxat; on D= 100 M Zmsec Transi*ttiort 0 2msec A 5msec Relaxed 13 _; 4. d o. rdo . 0 -10 20 30 40 50 M. '70 GAS 11=1 VELOCITT (M/SEC) Fig (6-39) Variation of Time Micro-Scale with Gas Mean VeIoCIt7* 431. 4. ENG A 0 3. i. 2.0- cr 4) $4 90 % 90 1.01 50 50 ve, ' 10 % 0.0-1 80.120.160.200.240.280.0. 32 360. CRANK ANGLE (DEGREES) Fig. (6-40). filckximum Frequencies for Eddies Containing 10%, 50% and 90% of the Turbulence Energy at Two Different Engine Speeds. Test on a Heron Combustion Chamber. (Data from Fig. (6-38f)- FORD ENGINE FORD ENGINE c. 7- 0.6- ri 0.5 0.4- mt cs 0 0 0.2- . 0.1- , 0. i 1000 RPhl 2000 RPAI 3500 RPM ROLIS-ROYCE ENGINE . &. lr%rv% DM# 432. 0.0 12345678 Gas Mean Velocity (m/sec) Fig. (6-41; Variation of the hlicro-Scale of Turbulence with Gas Alean Velocity at Different Engine Speeds. «o C9 S I 433. P4 cn C14 +j 4) I in # C: C: 00 +b bk tlt to bq M: co -2 :3 c C4 ul 0v ;40 0 r- 0xaq 4) * 4J G) P4 r_ 0S -A 0 0 a El +& a OH Cd -8 M- >1 0 4J "4 4J 0 :3 4) V > z t-4 0 0-4 0 44 4-3 0 V-4 P r_ .0 4J 0 0%. 0 C: ; C 144 4J 04 to to CD eý oas/4j: paads eum'Ii zuolnqjnl 46 \7 434. Fig. (6-43) Effect of Throttling on the Turbulence Characteristics Inside a Heron Combustion Chamber of a rord V4 Engine. a) Engine Speed = 3500 RRNI, Horizontal Hot Wiro at 3.8 mm from Cylinder Head Surface, Inle-t Valve with Six Vanes. al - Intake Vacuum = 168 mm 119 a2 - Intake Vacuum = 310 mm lig b) Engine Speed = 1000 RM, Horizontal Hot Wire at the Level of Cylinder Hoad Surface, Plain Inlet Valve. bl - Intake Vacuum 102 mm, lig b2 - Intake Vacuum 282 mm Hg i 0 0 Ln r- ci 0-% L-) c2 LLJ c2 Ln -. P >-4 1--1 cjg t. n CD cu --jci - cr- LU 0 C: 2 r9c, C7 rI 1 1: 3 c2 . --01 >-«: 2 f- Ei e--. t CNJ 4:: 3 C: ) 1 0. i3a0 4. , 1.600 2.300 2.600 CRRNK RNGLE X10-2 Fig (6-43a) FORD ENGINE 1.800 MOO CHRNK PINGLE Fii; (6-43b) . 135- 3.300 Intale Vacuum Engine Speed (MM Hg) (RPM) + 168 3500 310 3506 102 1000 0-% * 202 1000 , 2.600 3. soci x10-2 3.000 S. 600 C2 C3 02 cý W-4 C) >c im c2 C: 2 1: 2- cr- 1 j C: 7 tr ýZ- im--f tý ih. 7 ge 2 tz) C: 2 .w leffl C: ) Cý e< wle c LSJ C2 Cc C-) -co I cl OW m IV, cl W C5 olsoo 43G. FORD ENO N Intake Vacuum Engine Speed (mm jig) (RPH) + 168 3500 310 3500 102 1000 282 1000 / r, RRNK RNGLE X10-2 Fig (6-43c) lluuu ?. zoo 2.600 CRRNK RNGLE X1 ()-2' Fig (6-43d) S. Soo 8.600 \ 1" 9.000 437. ci c2 In c3- CY La «q: c2 C: 7 LU F- :Z im--4 c2 V) a-i (r_ =c2 ). -ci c2 FORD ENGINE Intake Vacuum Engine Speed (mm 11g) (PPM) 168 3500 310 3500 102 1000 282 1000 I a, III 1.300 1.000 2.300 CBRNK RNGLE Fig'(6-43e) I16 2.800 3.300 9.600 X10-2 4) > Cd > P-4 > Cd > 29 fl. o c4 cq cq cq 0 OD 0 00 cq cq +b 4. ) +b 41 r: r. r. c: ca X < 0 Cr - sle 01, Soo (I-ZHX) LL600*0 x (UM mnaloodS JG&Od PasTivuLloN 0 44 in El Ic 0 U 0 kN 0 W c In 4-b 0 4a -M 0 41 P4 0: , -ý I .0X co I " $4 4-4 ul +* (4 L. 44 Ln CS C: tri 0 V4 14 0-4 $4 04 >b $4 0 4-b 0 ba to 0 r. a w0 C: $ cm 4 0 ON -r4 > b 4- cs 2 J! 0 co I ! %, tn *4 cr) 1 -0 438. 50 40 01% 0 30 ""I 4-1 Cd 44 20 0 43 Z lo 0 0 C. ) 0 50 40 %. o C: 30 0 cs $4 cs > 20 *4 0 4.31 10 0 0 u 0 Plain Valve with Valve 8 Vanes Intensitv of Turhulonno 439. BTDC BTDC TDC Fig. (6-44) Statistical Analysis of Cyclic Variation in Turbulenco Characteristic Parameters. Rolls-Royce Engino, 1000 RPM and Fully Opened Throttle. plain Valve with Valve 8 Vanos 440. 40 %. 0 9.1 30 ci tH ,0 20 10 0 Klif-rn-PI-nIn r%4' qhIll-liffIntirn 50 - Intensity. of Turbulenco r -i tz 40 0 ýl +31 r -i cs >. 30 0 a 20 0 10 0 Plain Valve Valve Valve with with 4 Vanes G Vanes Fig. (6-45) Statistical Analysis of Cyclic Variation in Turbulence Characteristic Paramotors (Ford Engino at 1000 RPM) and 100 BTDC. Intako Vacuum 282 mm 11C Intake Vacuum 102 Mm 119 coo UYJ LWWJ -1 ItIJS-OU: JIW 0 0 (13 0 0 CK) C%s X cc LU LU Q>- C%ju C3 441. 0 U ce T 09 00 c: 0) 0. -4 ,4mP. 4 U) c >, 9 0 p4 W. 4 e4 12 41 r. 92 Co 2= u2 -pf 9-4 § U U) >b «o to IH 0> er CK) p4 tu +, c2. Ei ca C) « ý 12 0 Ei > Co Co le 1 6 W4 44 fý 442. a 4) to ODST w ci 0 to 04 ci b 0 cn Lij . -j CD C3 a -1 o I In GOO'D (I 0 10 r. fit j2 43 k Pf zi v in %. 0 . V. 4 94 CS :> u u 0) >b 10 , 0 +ä Ei s4 cis 4) x0 < 01% j2 CD Co %.. o M 40 QOE *0 Guz 10 00110 Z-OIX % kIIGN31NI 30N3in86nJL 443. - 001 *2 00911 008 0 cOIX IIIAisni-4io iom ci 0 to V* ci ILJ to X CV) ci cc LLJ c2 Ivle cy Ci M Z a 2U C3 C) r. 0 el 0 Co 0 . mi 90 20 44 m4 Q>l 4. b W. 4 r4 tz v C 0 ý4 Ca . >b *0 0 M ci 0 %1.0 ýo . rq D4 444. Fig. (6-47) Effect of Intake System Modifications and the Use of a Local Turbulence Promoter at the Spark Plug on the Turbulence Characteristics in a Wedge Combustion Chamber. Analysis of 124 Cycles, Rolls-Royce V8 Engine, Compression Ratio = 9: 1,1000 RIM and Fully Opened Throttle. I 445. 0 C7 C2 04 WC: ) L) Ci CN LJJ zll=b C: 7 a C) r-2 to C; VIP LJ z LJLJ C) m -: )o ROLLS-POYCE ENGrNE 1000 RPM Valve for Reduced Lift: + Fully Opened Throttle. w 2511% Throttle Opening. Turbulence Promoter : m Fully Opened Throttle. f III. 61 1.6aa 2.3aa 2.600 s. sao Cf3RNK RNGLE )(I o-2 Fig (6-47a) ROLLS-ROYCE ENGTNE 1000 RPM Valve Xor Reduced Lift: + Fully Opened Throttle. w 25% Throttle Opening. Turbulence Promoter = Fully Opened Throttle I 3.800 2.600 CFIPNK FINGLE x W-2 Fig (6-47b) 3.300 BOC II CD C: 3 C: ) c2 c2 Ci - cm Co dz CD cl: Li CO 1 C: ) CD .4 Ci Z cl 0.800 0 C7 C) G) C%j cl %. j CO LAJ U) I C3 C C2 C) 9- CD 93 44G. ROLLS-ROYCE ENGINE 1000 RPM Valve for Reduced Lift + Fully Opened Throttle. ,x 25% Throttle Opening. Turbulence Promotor Fully Opened Throttle. f 1.300 1.800 2.300 2.800 3.300 `CRRNK RNGLE xiio-? - Fig (6-47c) ROLLS-ROYCE ENGINE 1000 ]RPM 3.600 Valve for Reduced Lift + Fully Opened Throttle. -* 25%! Throttle Openine. Turbulence Promoter Fully Opened Throttle. IIIIII . 600 1.800 2-soa 2.600 3.300 CRRNK RNGLE x 10-2 Fig (6-47d) 3. Sao CD C; C3 cl C: 3 M cri zc; LL. Jq C-. ) U) : zo: - WC2 C13 (). 600 c2 C: ) >< Co LJC3 LJJ 23 cr) LJO C: ) C3 cc 447. ROLLS-ROYCR ENGINE 1000 RPM Valve for Reduced Llýý + Fully Opened Throtr; Lp- w 25% Throttle Opening. T=bulence Promoter : . &A.. Fully Opened, Throttle. z cr- LLJ Cp ci 0.600 1.800 2.300 sacl 4. CFIRNK ANGLE Fig (6-47e) 0 44 2.800 MM JC)-2 3.800 ROLLS-POYCE ENGINE Fully 0]2ened Throttle 1000 RPH 0 Plain Valve. # Valve with 4 Vanes, + Valve with 6 Vanes. A Valve with 8 Vanes. Intake fitted with Delta Wings. . 1.3aa 1.800 Z. 300 mao ORNK RNGLE x 10-2 Fir (6-IL? f) 3: 300 3: 8GCt C) C3 C-1 cl:: p =45) 4-01" CE Cý c) Cýl co Boo 448. ROLLS-ROYCE ENGINE Fully Opened Throttle 1000 RPM 1.300 11800 2.300 2.80o 9. sao CRRNX RNGLE Xj 2 Fig (6--476) ROLLS-ROYCE ENGINE Fully Opened Throttle cli iOOO RPH r-4 Ln Ir 0 Plain Valve. 6 4 Valve with 4 Vanes. + Valve with 6 Vanes. Valve with 8 Vanes. Intake fitted with Delta Wings, 6--4 a) cr3 ze LLJ LLJ 0 ca cc -: 3 0.601) 1.300 1.800 2.800 2. Sao 9.300 CRRNK RNGLE X10-2 3.800 S. Boa 0 Plain Valve. 40 Valve with 4 Vanes. + Valve with 6 Vanes. A IF-1 -- --1 4- 1ý a Ira W% ^n 4=0 C) co C; 9-4 I C) C: j C3 C3 C3 U16 - C) LLJ C%j C13 Cý 0.800 C) c2 -qo cý c2 c> Cil LJLJ cn -o C: 0 C%i c3 cr CD Li C: )ROLLS-ROYCE ENGINE Fully Opened_Throttle 1000 RPM Plain Valve * Valve * Valvo to Intak, Delta 1.300 t. 1.600 2.300 2.800 CERNK RNGLE X10-2 Fig (6-471) I. ROLLS-ROYCE ENGINE Fully Opened Throttle 1000 RPM 449. Valve. with 4 Vanes. with 6 Vanes. with 8 Vanes. o fittod with Wings. 3. soa 3. BOO & Plain Valve. 0 Valve with 4 Vanes, + Valve with 6 Vanes. a Valve with 8 Vanes, in Intake fitted with Delta Wings. 1.300 1.800 2.300 2.800 3.300 CRfINK RNGLE XIO-2 Fig (6-47J) 3.800 450. Fig. (6-48) Effect of Intake System Modifications and a Local Turbulence Promoter on the Turbulence Charactoristics Inside a Heron Combustion Chamber. I Analysis of 124 CyclesfFord V4 Engine, Compression Ratio = 8.9: 1,1000 RPM. Measurements at tho Spark Plug Location, using a Horizontal Wire. a) Full Load Condition: Intake Vacpum of 102 mm 11g. b) Part Load Condition: Intake Vacuum of 282 mm 11g. I 0 451. Col. -IPRESSIOT PERIOD 2,0.1000IRPH, Intakc- Vacuum . 10.2 93: 3 Re Depth (MM) x Turbulence Promoter* 0 Valve with 4 Vanes- Z 3-8 a Valve with 6 Vanes. Plain Valve. 14 Plain. -Valve. Za . 0.0 0 o. 8 1 ol o. 6- 0.4 0.2. 0.01 '*20 3; 0 0 290 3CO 3lu 1 33 0 .0 CRAA'. "%* AVCLE (DEGPFZS) Fir -48a) 452. 0) %. 0 Iton zg_ in . 40- . 20 -4 rORD MITIE COMPRESSIO"T Pmrot) 1000 UPH Depth Irrtake Vacuum a 282 Cm 119) (mm) x Turbulence Pro*, ot: r Z_3.8 0 Valve with 4 VOno 1W Plain Valve. Plain Valve. Za0.0 'k20 %0 . 290.300 310 1 3.3 340 Crank Angle Degroog Flg. (6-48b) I 453. FORD rNGINR COMPII-ESSIon rFArOD IOOOIPPH 0.4- Intake'Vacuum 102 trim ITS Depth (M-A) Turbulence Pronot r. Valve with 4 V&nc: - 1 Z 236 Valve with 6 Vanes. 0.3. Plain Valve. a Plain Valve Z &0,0 %. 0 0 bý. V T 0 4 9:: -1 0.1- E4 0.0 Fie. (6-480) o. 6_ FORD ENGINF. COMPPESSIOT. PERIOD 1000 IRPH Dcpth Irdake Vacuum = 28i mn ITs) Z TurbulencO Prozoterl Valva with 4 Vanes. Zu3.3 V Plain Valve. 0.4. A Plain Valve. - Ea Oý. 0> 0.3- 4A 64 V 0.2. 0 0.1. 0.0 290 A00 310 320 330 It6o 340 350 CRA%K ANGLE (DEMEES) Fit. (6-48d) 454. 0.5 - 0.4 - 0.3 - 0.2 - to I 0 0.5 o. 4 cell 0.3-- 0 0.2- 0.1 rORD rNGTI? r. COMPRESSIM PERIOD 1000. PPH Irrtake Vacu= a 282 gm 119) Depth A Turbuloýcs Promoter. ) Valve with 4Vz "36 Plain Valve. j Plain Valve. Z BOX 3F Fig. (6-480; , FORD rrmrn COMPRWSMI P7RTOD Depth 100011MM (MC) Intake Vacuum 102 ITC ) A Turbulence Promoter 0 Valve with 4V n::: : Z t 0 Valve with 6V n W Plain Valve. A Plain Valve. Z WO. 0 0,0 -460 290. '200 310 320 %0 340 350 .0 33 CRANK ANGLE (DEGREES) Fit. (6-480 I 455. 20, - ROLLS-ROYCE CYLI%. DT! R ; TAD Plain Valve. 9.0- Valve with 4 Vanes. 31 Valve with 6 Vanes. * Valve with 8 Vanes. * Masked Valve. T. Valve for Reduced Lift. 8.0- FORD CYLINDER FEAD + Plain Valve* do Valve with 4 Vanes. + Valve with 6 Vanes. 7-0- 6.0 -4 I ' 0 4.0 E4 + + 3.0 -..,. ý +ý , A 2.0 1.0 0.0 9! 0 Id. 0 :L0 3-0 4.0 5.0 6. o 7.0 8-10 VALVE LIFT (cm) Fig. (6-49) A Comparison Between the Port Area (A*) for the Different Types of Inlet Valves Used in the Investigation. 45A). Fig. (6-50). A Study of the Cylinder- to-Cylinder Variation in the Turbulence Characteristics Inside a Wedge Combustion Chamber. Rolls-Royce V8 Engine, Compression Ratio a 9: 19 1000 RMI and Fully Opened Throttle. Probe at the Spark Plug Location (Z = 17.78 mm) and a Wire Direction of 300 Degrees.. I C: ) cl XCD CO %.. e 7- cr- LLJ ý-- £Z> c2 a, 1 0.800 0 t17 C%i C) C: j M co 7- ci LLJ LLJ C) c )U) -7- W-4 LLJ cz; cc 6aa ROLLS-ROYCE ENGINE 1000 RPM and Fully Opened Throttle Cylinder Wire DesiGnation Direction + 3A w 2A 4A 3000 2B 3A 3300 tee Fig (5-14) for Definitions. CRIINK RNGLE Fig (6-50a) 2" . 600 x 10-2 9.300 457. 9.8aa POLLS-ROYCE EVGINE 1000 RPM and Fully Opened Throttle Cylinder Wire Decignation Direction + 3A 2A 4A 300o 2B A 3A 3300 1.800 2.300 2.800 CRANK ANGLE x 10-2 Fig (6-50b) p S. Sao 3.600 C) C3 m C) e-4 U uj C3 C) cm cc u C: )C) CD 0-4 C3 C3 Cl 6-1 (). 800 c: i c2 fý C) r =C5, LLJ -i cl: U3 I C: )C: ) Cý CC r .. )46- C2 C) 10.600 458. ROLLS-ROYCE ENGINE 1000 RPM and Fully Opened Throttlo If DesiE; nation Direction 3A 2A 3000 4A 2B 3A 3 30P 1.300 t. i-sao 2.300 CRANK RNGLE Fig (6-50c) 4 1 2. ZOO ylo-2 I. 3.300 3.800 ROLLS-ROYCE ENGINE 1000 PPM and Fully Opened Throttle Cylider Wire Designation Direction 3A 2A 7 12 f%f%O III ]. Sao 1.600 2. SGO CRRNK FINGLE Fig (6-50d) 2.600 3.300 3.600 X10-2 ROLLS-ROYCE ENGINE Cý C2 W C; C: ) O-d C: l Xul lie T9 Cl Z a3 cr: --Do C3 . 3-rý 0.600 1000 RPM and Fully Opened Throttle 1.30a 1. t5uu zo; luu CBRNK RNGLE ic. vuu : 3. a uu X 10-2 45D. 3.800 4 Fig (6-50e) 4GO. c1d 0 (D V. cis >4 uo pq (A) Wedge (L) 00 Heron 01% 0 pq Ics (9) -H x 0 L) $4 41 Disc Combustion. Chamber Configurations. ______ ______ ______r ABC Combustion Chamber pe N U H 44 0 4H 4-4 -ri pq tQ (a)- Merit order of combustion chambers based on mean minimum hydrocarbon emissions together with corresponding mean specific fuel consumptions. . . 2 0 -ri P4 to U ;4 4 ps 0 P4 ABC Combustion Chamber (b)- Merit order of combustion chambers based on mean of peak nitric oxide together with mean specific fuel consumptions. Fig (6-51) Effect of Combustion Chamber Configuration on Exhaust Emissions (156). - 4GI. k 7. CORRELATION BEWEEN THE CHARACTERISTICS OF TUIIBULr., NT Fll., 'Ln INSIDE THE C011BUSTION CHAMBERS OF SPARK IGNITION ENGINrS AND OMIER FLOW FIELDS Because of the complexity of the turbulunt flow fiold, no rational theory which could enable the determination of its characteristics by calculations has boon established. Semi-empirical theories, however, have been developed into more or less complete theories. Those theories are mainly concerned with mean velocity distribution. On the other hand, the notions introduced by the statistical theory of turbulence enables measurements of some characteristic parameters of the turbulent field. This suggests that an attempt should be made to establish some correlations between the turbulence characteristics inside the combustion chambers of spark ignition engines as measured in the present investigation and the prpdictions of the conventional semi-empirical theories and the available experimental data for flow over a flat plate or inside constant cross-sectional pipes. Difficulties arise in such situations because of the main differences in the physical process of generating turbulence in either field. Inside the combustion chamber of an ongino a highly. turbulent condition exists with very small directional velocities (if any exist). Also, the flow conditions are time dependent during the engine cycle, while all the available information about turbulent fields have been obtained for fully developod steady state flow conditions. 402. There is also a need for assuming some characteristic length for the engine flow field, if comparisons have to be made in terms of Reynolds number or any other non-dimensional variables. Nevertheless, it is conventional in the fiold of heat transfer, to use some dimension of the experimental apparatus as a characteristic length. This suggests that the cylinder diameter could be employed in this situation, which avoids assuming any developing length based on conjectures about the flow pattern associated with the special geometries of the combustion chambers used in the investigation. Such a length has been-proposed by Spalding in a definition for Reynolds number in engines where engine speeds are used to give some characteristic gas velocity. Similar expressions were proposed by Siringnano (132) in his development of a combustion model using piston speed as a characteristic velocity. A Reynolds number for engine investigation is dofined, in the present work, as follows: 01 Re D (0) = U(E)). D where u(E)) and V(e) are the gas mean velocity and kinematic viscosity at the crank angle 0, respectively, and D the cylinder diameter. 4G3. Boussinesq (123) was the first to introduce the notion of a mixing coefficient (eddy viscosity) E At -in the expression of the turbulent shear stress T=d5 (7-2) tPuv %I dy The eddy viscosity is analogous to the molecular viscosity P, since the product of eddy viscosity and velocity gradient gives the turbulent shear stress. The total shear stress on the walls could be expressed therefore by: + Eat) dU (7-3) dy It is also convenient to define an eddy diffusivity EM (kinematic viscosity for turbulent flow) similar to the kinematic Viscosity v as: F- m= Al (7-4) s Therefore: (v+ (7-5) dy Different hypotheses have been assumed for the definitions of this eddy diffusivity, among them are the well known Prandtl mixing length hypothesis (124) and the Von Karman similarity hypothesis (80). 4G4. Prandtl tried to connect tho eddy diffusivity with the characteristics of turbulence. According to týO kinetic theory of gases, the kinematic viscosity is equal to the product of the root mean square velocity of the molecules and the mean free path; analogously, Prandtl assumed that the coefficient of eddy diffusivity is equal to the product of a mixing length and some suitable velocity. This condition could be expressed as follows: E-v' . (7-6) Assuming that the longitudinal fluctuating velocity component ul of a lump of particles is determined by the difference in mean velocity 5 between the plane considered and the plane from which the lump originates, thus dU (7-7) dy and consequently (7-8) dyI Since the sign of v' is determined by that of L, hence vL const. L2d (7-9) mmmI, dyI The constant of proportionality may be included conveniently in a new length e2= const. L2 7he expression for the eddy mm diffusivitY then reads: e=e2.1 51 (7-10) mmdy 4G5. Further assumptions about the mixing longth, boing proportional to the distance from the wall ( tM =K y) led to tho conventional logarithmic velocity distribution law which fits the experimental data very well. Von Karman (80) assumed that the turbulent transport processes are determined by local flow conditions. For dimensional reasons E_,, may be written as before as the product of a velocity and a length, for the velocity Von Karman used v'. This gives Em- This length f* is not identical with Prandtl mixing length. According to Von Karman, the value of t* must bo determined by quantities that have a local character, such as tho micro-scalo of turbulence Xy. and the local Reynolds number or Reynolds number of turbulence R% . Thus It f (u I 1-Y (7-12) v The simplest form is e cons no ). 2 or e* const. u' x Y/v (7-13) Various investigators have suggested expressions for the eddy diffusivity based on interpretations of experimental data. A summary of these OxPressions could be found in reforence (126). However, two or three separate algobraic equations wero usually proposed in each case for different regions in the turbulent f ield. 4GG. A single equation for the eddy diffusivity F- m has been proposed by Spalding (125) which provides continuity throughout the whole turbulent region and is given by: K[ KU+ _1_ KU+ _ KU+ 2 KU+ je qý, ) -( 31 )3 (7-14) where K=0.407, E= 10 U+ = U/U* u* is called the friction velocity and is a measure of the intensity of turbulent eddying and the transfer of momentum due to these fluctuations U* (7-1G) is the shear stress at the walls w The turbulent shear stress is usually expressed as the product of a friction factor and the dynamic head of the fluid. -C = .1i.,., y. u2 (7-17) w2x where Ux is the undLsturbed velocity for f low over af lat, plate and the bulk mean velocity for the case of pipe flow. Different expressions are proposed for the friction, factor as a function of a characteristic Reynolds number of the flow. A summary of these expressions for external flow over a flat plate and flow inside smOOth Pipes aregiven below: 4 G7. a) Flat Plate f 0.0585 (Re X) -0.2 Von Kaman (127) (7-18) f. 0.37/(log Ro x)-2.584 Schultz-Grunow (127) (7-19) f (2 log Rex _ 0. G5)-2.3 Prandtl -Schlichting(1 28)(7-20) f= 0.02G2 (RO x)- 1/7 Falknor (129) (7-21) f= 0.02296 (RO x) -0.139 Nikuradso (130) (7-22) where Re U. x (7-23) x The last two expressions (7-21) and (7-22) aro, especially recommended for flow at very high turbulbnt conditions (large values-of Rox) b) Pipe FlOw 0.04G ReD -0.2 (126,127) (7-24) 0.0014 + 0.125 Re D -0.32 Drew ot al (7-25) (127) 4.06 log(ReD if) -0.6 Von Kaman (7-26) (127) 1=4.0 log(Re rf) -0.4 Nikuradso (7-27) f -f D (127) where Re U. D (7-28) DV The expressions proposed by ralkner and Nikuradso, for flat platesagree reasonably well with'those for pipe flow at very high valýes of Reynolds number Figure (7-1). The e3eprossion for pipe flow (7-24) was, therefore, employed to give an estimate of friction factor and correspondingly the friction velocity. The. latter quantity was substituted in equation (7-14) for the eddy 4GS. diffusivity. Figures (7-2) - (7-4) show a comparison botwoon the values of eddy diffusivity using differont expiýossions for the friction factor at typical values of Reynolds number in an engine during the compression period. The second problemwhich arises in attempts to establish correlations between the flow inside the angino cylinder and that over a flat plate or inside the cross- sections of pipes is the-influence of temperature variations on the calculated fluid properties. All the flow friction laws (7-18) - (7-28) and the experimental data were obtained 'under constant fluid properties throughout the flow field, while in an engine both temperature and pressure are continuously varying during the engine cycle and their variations are very pronounced. The general effect of the variation of the transport properties with temperature is to change the velocity and temperature profiles, yielding differerit friction coefficients than would be obtained if properties were constant. For engineering applications it, has been found convenient to employ the constant property analytic solutions, or the experimental data obtained with small temperature difference and then to aPPly some kind of correction to account for property variation. Most of the variablo property results indicate that fairly simple corrections will generally suffice over a moderate range of temperature. Two schemes for corrections of constant property results are in common use. 7be first one assumes a #roference temperaturol which is a combination of the wall temperature and the free stream temperature and is used for evaluating all the fluid properties appearing in (Re, Pr, etc). The second schome is the 'property ratio' method, where all properties are ovaluatod at the free stream temperature, or the mixed mean tomperaturo and thon all of the variable property effects are lumped into a function of a ratio of some pertinent property evaluated at the surface temperature to that property evaluated at the free ptroam or mixed mean temperature. Kays (126) discussed the use of both schemes and showed that the first method leads to ambiguitios for intornal flow applications but could be employed for external flow over flat plates. The second scheme could be employed for both types of flow fields and the temperature dependent property offects can usually be adequately correlated by the following equations: Nu St (T, ) n Nucp - Stcp - Tra ). $ (7-29) and (TO) m (7-30) fc p TM where Nu, St are Nusselt and Stanton numbers, respectively, f is the friction factor and T is the absolute temperature. The subscripts o and m refer to the wall and the mixed mean conditions and Cp refers to the constant property solution.. Kays discussed the work of other investigators and suggested that for turbulent flow in tubes the values of the exponents n 469. and m for air between 100 to 3CX)OOF could be given by 470. . To __ F, 10.1 nn0 m (7-31) Application of the proposed corrections (7-31) for engine conditions over the range of compression ratios between 4: 1 to 20: 1 results in a variation of the friction factor by 3.6 to 8% of the constant property values. These correction values are within the range of experimental errors and could be, the refore, neglectod in calculations of eddy diffusivity using equation (7-14). On the other hand, the Taylor's theory of diffusion by continuous movements (86) provides another definition of the eddy diffusivity, as the product of the fluctuating velocity component v' and the Lagrangian integral scaleLL as dofined in Section (3-7). Em = VI L (3-150) = ve Rý( T) dT (3-151a) L where. R'(Z is the Lagrangian correlation coefficient. L Comparisons between equations (7-6),. (7-11) and (3-150) show that the Eulerian (Prandtl, or Von Kaman) mixing length equals the Lagrangian integral scale of turbulenco, i. o. IL = Lm =e* (7-32) our main concern was concentrated, therefore, in investigating the existence of a relation between the predictions 0.1 of the empirical expression of eddy diffusivity as proposed by 471. Spalding's equation (7-14) for pipe flow and the results of the preseot anemometer measurements in engines using equation (3-150). Such a relation, it it should exist, would provide a simplified technique for predicting the turbulanco charnotoristics in engines from measurements of mean gas velocities only. This would reduce, to a great extent, the amount of experimental work involved and the need for very sophisticated instruments and complicated data processing systems as discussed in Chapter 4. The main problem in such an attempt lies-in the fact that the Lagrangian correlation coefficients cannot be measured directly by existing instruments. However, the measurements of the Eulerian correlation coefficients could servo for such a purpose if some relation exists between both types of correlations. Experimental evidence has shown that, at least at large Reynolds numbers, the overall shapes of the Lagranglan correlation coefficients I and the longitudinal spatial (Eulerian) correlation coefficient R. (x) can be approximated by the following I exponential functions. e- R; (x) = e-X/LX (7-34) Thus these correlatIon coefficients have tho same functional form and one can assume, therefore, that the Lagrangian and Eulerian integral scales must be proportional. Such an assumption has been made by Mickelson (110) which could be writton as follows: -C t (7-35) 7L LX x 472. where p= Lx/J'L (7-3G) hfickelson has experimented with almost homogeneous isotropic turbulence in the central core of a turbulont air flow through a pipe 20 cm in diameter. The Reynolds 55 number ReD was varied between roughly 2x 10 and Gx 10 Nfickelson measured separately the longitudinal correlation coefficient R' and the Lagrangian Correl4tion coefficient from x the diffusion of helium downstream of a fixed injection point. He found that within experimental accuracy for equal- values of (x) and Rý (-t), x was proportional to T with a constant value R, of p. This proportionality constant increased with increases in the fluctuating velocity component u'. Its average value, in the range of u' considered was 0.6, Figure (7-5). 11inzo (70) discussed the unreliability of the determination of Lagrangian correlations for fluid particles from cliffusion of a tracer gas due to the unknown effect of molecular diffusion and concluded that to at the most, we may conclude from htickelson's experiments that the rough shapes of the Lagrangian and Eulerian correlation coefficients is the same". Uberoi and Corrsin (112) have also Investigated the relation between the Lagrangian and Eulorian scales of turbulence. The former scales were measured from the thermal diffusion behind a heated wire stretched perpendicular to (grid produced) isotropic flow in a wind tunnel. While the latter ones were deduced from similar measurements on grids having the same geometry. 7hough there was considerable scatter in the values of P -- as shown in Figure (7-6), its value increases roughly from 0.5 at 473. values of Re L- 10 to about 0.8 at values of no L= 100. Also, a regular decrease of. L L was observed with dbcroases in turbulence intensity (u'/U). Baldwin et al (111) have investigated the turbulont diffusion in pipe flow downstream of a line source of hoat, The authors used a similar method to blickelson's work with the exception that the factor of proportionality P was calculated at different separation distances of the correlation curve, Figure (7-7). *The Eulerian scale Lx was found to increase with mean flow velocity, while the Lagrangian scale was apparently constant for all flow rates studied. Mie nett result is that the ratio of Eulerian to Lagrangian integral scales increases from 3.5 to 6.5 as the mean velocity 5 varies from 72.6 to 160 ft/sec. Baldwin et al have cone'luded that the hypothesis. of similarity between the shapes of RI (x) and IIL is reasonable. However,. the two fold variation of the empirical factor(p) with mean velocity over the small range of their experiments certainly limits its utility'. Also, such similarity fails completely at large separation distances where R, (x) becomes X negative which suggests that nothing fundamental should be implied from this empirical comparison. Hay and Pasquil (114) have carried out similar studios in atmospheric diffusion which indicated a rapid variation of the Eulerian auto-correlation while the Lagrangian correlation showed tome persistence for longer time intervals. 7he proportionality factor was suggested, therefore, to be not less than about 10. 474. In spite of the scattered and even contradictory results in the published investigation for tho rolationship between the Lagrangian and Eulerian scalo of turbulanco, thoro is strong evidence that their ratio (IL/L x) is a function of the turbulence Reynolds numbers R OL 22 %; LX/V . This confirms the earlier assumption of Von Kaman (80) for the expression of the mixing length as a function of the turbulonce Roynolds number Re II=U, XyV. The relationship between both Reynolds numbers has been discussed earlior in Section (3.4.3). It is believed, therefore, that there is no point in applying any specific relation, deduced from other investigations, to check the existence of a correlation between the measured eddy diffusivities in the engine and the predictions from pipe flow empirical relations (as equation 7-14). Ifenco an attempt was made to establish a functional relationship between (L L /1, ý. ) and ReL from the measured data. ýn the present investigation which provides the minimum scatter in the data and to evaluate the coefficient of correlation between the measured values of eddy diffusivities and the predictions of equation (7-14). The simplest form of the relationship between the Lagrangian and Eulerian scales was proposed as Re (7-37) The value of the exponent n, has to satisfy the condition of providing the least square errors between the predicted and measured eddy dif Visivities in the engine, whore the latter was calculated by the following relation 475. I'L 6 rpeas = (u' Lx) moas (-,; ) (7-38) or &= (U' -L)- (a +b Ho n (7-3D) meas x meas L It is believed, also, that obtaining the values of a. b and n from the measured data eliminates the need ior applying any temperature. correction on the values of friction factor, used in equation (7-14). Such correction will be included in the coefficient b as well as the value of -the exponent n of R eL as governed by the variation of kinematic viscosity -ý) with gas temperature. A computer program (appendix no) was employed to search for the best value of n. as well as the determination of the values of a and b by a least square errors regression line between (, L /L ) and'(Ren). Figure (7-65 shows the variations of LxL the root mean square value of the errors and the coefficient of correlation with the exponent (n). Also, Figure (7-9) shows a plot of the experimental values versus (Re L 0.8 ) uhich gave the best correlation of 0.9722. Figure (7-10) shows a plot of equation (7-37) for the ratio of GLL/L. ) versus Re L using the values of a, b, n of the best correlation. Figure (7-11) too shows a comparison between the values of eddy diffusivities calculated from equation (7-39) and the predictions of pipe flow relation (7-14). These experimental data include tOsts on the Rolls-Royce and Ford engines for plain valves and modified intake systems$ as well as a now analysis of Semonov's work. 47G. Comparison between the measured values of tho macro-scale of turbulence using equation (3-GS) and the predictions'of pipe flow data under isotropic conditions has also shown very good correlation, Figure (7-12). The lattor values were obtained from the relationship botween tho ratio of the scales ly/L,,, and the turbulence, Roynolds number Ito as reported by Robertson ot al (102) and Sato ot al (103), Figure (3-101). Robertson (102) has suggested that the fluctuating velocity component (u') is proportional to some dharactoristic fluid velocity such as the friction velocity (U*). Thoroforo, in spite of the scatter in the data, which is a characteristic feature of all turbulence experimental investigations, some universal constant values could be established for the ratio U, ) for different types of flow. For example, a value of 1.7 U* is reported by Robertson for turbulent flow at 10% of boundary layer thickness or the pipe radius, Figure (7-13), where the pressure gradients in both types of flow, are very small. While for strong pressure gradients, such as turbulent flow in a diffuser boundary layer, this ratio is quite high (144)0 Figure (7-14). A similar attempt was carried out for turbulent flow in engines during the compression stroke where turbulence intensities are much higher than those of pipe flow or external boundary layers. A summary of the average values during compression periods for various types of combustion chambers is given in Table (7-1) which indicates that an average value of 5.89 could be established for such a flow field at the spark plug location. 477. Table (7-1) A Su=ary of the Average Ratio Between Fluctuating VelocitX Component and Friction Velocity for Dif foront Types of Combustion Chambers During Compression Poriod Engine Type Combustion Chamber Shape Test Conditions U9/u* 1. Cylinder : It, plain valve. 0 (1000 r. p. m. and fully opened E-4 throttle). Wire direction: 0= 600 4.23D .0 0 -- 3000 4.5GS CO rn 0= 3300 3.885 > 2. Intake System Modifications 0 L) a) (1000 r. p. m. and fully opened throttle). W i) Inlet valve fitted with 0 0 4 vanes 7.710 >4 ii) Inlet valve fitted with 0 6 vanes Ist Test 6.0392 14 2nd Test G. 5014 to rA iii) Inlet valve fitted with A 8 vanes 6.73G 1.4 W iv) Masked inlet valve 4. lG 0 V) Intake manifold fitted with delta wings 4.55 It b) (1000 r. p. m. and quarter throttle)' Inlet valve fitted with G vanes 4.731 3. Plain valve at 1000 r. p. m. a) Full load conditions 5.86 b) Part load conditions G. GG4 0 0 OD P. -I E-4 4. Intake System Modifications Inlet valve fitted with 6 z vanes, and full load 0 C conditions I O i) Engine speed = 1000 rpm 6.5215 ii) Engine speed a 2000 G. 3G4 0: ý!; L) Ili) Engine speed = 3500 7.10325 0 b) Inlet valve fitted with 4 vanes at 1000 r. p. m. i) Full load conditions 7.046 ii) Part load conditions 8.152 478. Table (7-1) Continued. Engine Type Combustion Chamber Shape Tost Conditions Us/U* 0 Semenov's Data at TDC U 0 (900 r. p. m. and 71% volumetrio 0 efficiency) ta 44 94 El Compression Ratio: 4: 1 5.843 0 CS 0 X: G: l G. 748 0 8: 1 7. G45 9.5: 1 9. G8 470. 7.1 Approximate Design Proceduro for Predicting Turbulonco Characteristics in Spark Irpnition Enginos It has been shown, in the preceding discussion, that the characteristics of the turbulent flow field In engines could be predicted using the pipe flow experimental data and a knowledge of the mean gas velocity at Mo crank anglas of interest. Figure (7-13) shows a proposed proceduro for obtaining the turbulence characteristics during the compression stroke which could be summarised as follows: a) Obtain the mean gas velocities at the crank angle of interest ( 0),, as well as the gas properties, T(O), P(O)ý. It b) Calculate a characteristic Reynolds number Ho(G). i. as given by equation (7-1). c) Calculate the friction factor f in the friction velocity u* and the non-dimensional velocity u+, equations (7-24). (7-17), (7-1G) and (7-15). d) Calculate the fluctuating velocity component by multiplying the friction velocity by the universal constant ratio of (u'/u*), obtained from Table (7-1). e) Calculate the coefficient of eddy diffusivity by equation (7-14). f) Obtain the Lagrangian scalo of turbulopce using equation (3-150). g) Obtain the Eulorian scalo of turbulonce (L x) using equation (7-37) by an iteration procedure. h) Obtain the microscalo of turbulonce ( ). ) using y the relationship b6tween the macro and microscales of turbulence for isotropic conditions, o. g. _ equation (3-101) or Figure (3 .1 I 480. 481. INPUT DATA 5(0), T(G), P(O), D Re(0) = Ü(O). D/ (0) f (9) nl (9) u* f /2 U+(0) = u* (0) U. (6) = K. U*(0) Int (0) - U-(0)7U(e) F- (0) - vu+(G), -ý(e)) LL (0) = F, (0). f UI(O) int (0) 1. nt G) Z (0) cem) f- (E» _Lx (0) a2+b1- u' (0), LX(O L. (e) b u'(E)) j. (e) 113 )l y (e) 2-V (0) y(O) ITERATION SU13ROUTINE L(e) Fig. (7-14) Flow Chart Showing the Analytical Procedure for Predicting Turbulence Characteristics in S. I. Engines 482. Table 7-2 Values of Constantsand 'Expo-nonts Used for the Prediction Procedure 0.04G b 28.582 n -0.2 a20.121386 b2=0.0228 n20 -0.8 a30.53 K-5.8935 n3n1.23 I p 483. KN N (U 0 e-i P-4 r. 1 r4 %-, %. ýf %.. o c6 ob A 02% C) #-% 10 4) r4 ce 93 el NC ci 1 p %.. - ý_.. %-0 tu HN m r- tv r4 9x c4 Pi 0 %_o %_o %.. - %D cm CM -t* 0 0 0 0 0 0 0 r-i CM m-% -t t4 0 u ca 93 0 %-4 Aj co 0 ul 1ý cr) 461 4P. 4 0 t- 0 otn $4 0 (0 X P4 tc X in LU r- CO CQ 4j Cl D $4 44 414 cn C: ) z CD >- In tii CC 93 0 N to cm QH t4 Cd pq n 0 t. ) -4 CEE *L L99'9 COIX UOU's EEC *S Y0138A NOIIOIUJ Lgg, v aI tn N 4 %. 0 LO ODDI 48-1, C-) UI 01% Ul% ON td*N 0 C> 0 0 11 76 td-% (U tu t% ri ri ef P-4 %-, %., %., g ,u 14 cy Co 4) :j 94 9.4 x :Z 1p -H cj 1 %. 0 :4 gl, i %». o %. 0 %.. 0 tu teN rt %_o 1 UN PZ p; gz %-0 %-0 %. 0 0 %D + CYN cu _T cu %0 %D r4 r*i r4 0 C) 0 ic; c; 11 ti 11 ri h-% :r 1- OSL *0 SU 10 Das/'w (a OH to 13 to 0 t 9: 63 V $4 V4 V4 11 0 (4 0 > C) 'in 1 q to m . 0 X %4 r4 (4 Lfl r4 cs LI. J. ej co M r4 #.. 4 cs 0 u -r4 cn :3 4J (Z) t-4 Cd 4J CJ C: ) Z Ci >- 0 cc 13 cs 4) Ic at 4.3 a 0 -r4 cri .0 41 u o C3 0 u o C; 050 *0 N I E- %_o bo -ri 485. 0' *0 0 0 c'J 0 a N 0 0 It' 01 P-, % ci CD a a3 3 . -4 0 (3 0 C3 in &ii -1 97, b _U UZIG %ju rj2j Das/zw - &0 x p) ýllAlsnj-ql(] 1003 oso ! 480. 9Z6 *0 uht -u bttb u Uut -u 5z14,0 Dase £0 1X (w-g) ýllAlsfliAlo n03 CD m cn CP) o 4 X 0 cr: C3 ca 6u cc U- z 0 cr) 1-4 cr) I-- '! u Ln @. -4 cr- U- N tu to osolo 41 ci 41 u ci -ab ci 4. ) ic 10 91 >b 0 41 C -4-4 > (13 .H fri v cz >, N., 0 r-i ci 92 > 0 el ci 9.4 Pt (0 >b > %»0 487. (2 9) %. 0 94 0 Ul) u 4) in 4-b 4H +1 -A u 0 4-b 0-4 C3 4J 4 j9 9.4 gn c; Co r. 0 j2 0-% 0 Z %w ". 1 0; 41 94 4A 0 C) 0 c: 0 In r4 r: 4- 0 to 0 u 0 c: Z 4) 9-4 P-4 tis Z >w ,Z Co t- to rj -TI xi ZI. T-IuuoTZjc>dwd lo ZutZsuo3 488. 0 tn 14.4 0 >I, 0 :ß +A 9) 9: C0 ý-% 03 *J m to f. 4 0 0 01 > %.. o @-4 r. ID c; > %.. 0 % 41 41 -0 0.4 c Ili r. ffli 93 N4 -A > r6 tz ri ri Al. «FleuoTZlodozcj jo ZUBZSUOD I 0 qbt. 0 w P. -4 0 CY 0 cli ". 4 P. 4 0 0 0 e14 I1 -1 10 00 00 0N rl Vx 'I ATILMOllaodOld jo luusu0c) OM% ti ". 4 9Aq N Co Co joi. z-i ojenb, -, uuc. -., jou: 1 91 1 _Z Co to %? t4 t- t- t- e- c; c; c; c; 489. 00 v 49 64 13 ul rs ti 0 - Co st i: zIt 0 0 -r 9 . 114 92. Co C4 W11 ct U07-41818jJ03 jo . 4uaTZTJjQ03 490. 2.5 Data for tho compression period (crrAnk uncles froia COO LiTI)C to TW) 2.0 AN 1.5 %. 0 a 0-1 Rolls-Royce Engine Data: (Fully opened throttle). - Plain valves (1000,1200 L 150( rpm) 1.0 - V4 - Valves with vanes - Intake Manifold fitted with M delta wings 0- 4F IL Ford Eng Full L 1000- Plain valves Part 35M Valves with vanes load rpm conditions Somenov's Data (22): _ k TDC, 900 rpm, 71% Volumotric efficiency. Compression ratios 0.5- 4,6,8,9.5. 0.0 0.0 1.0 2.0 3. o 4.0 5.0 G. 0 7.0 8.0 0-ý 102 n o L Fie- (7-9) Variation of the Ratio GLL/I-x)wIth Turbulence noymo'-Z's Number. 491. 9 ul lu 0 0 93 rin, fi C, If) cl 14 0 0 V a 0 an %4 0 c 0 .4 J2 $. 9ý 43 C; > cli 0 0 Go t- CD cl) N 04 x rl : DTUZS nnT-xO7E'-XI)/(7-r. 0jv3S mul-auva2u-1) 492. 00 -ri du -4 43 -ö 94 s4 r. cq 10 :3 ts 0 Cd 1-ý 14 oi p4 P. u (0 41 E) 4-b 9 iýh v r_ - i; -(i U) w > -"1.4 . 6-b (d Cd :N +a cp 04 14 01 > 4-1 r. Lo > 4J 4J ý4 > qj $4 0 14 00 ul 0 0 . 54 Cd u C 9: 0 > Cý 92 ý-4 -f >Q 4ý Cd ý4 4-A 1-4 94 _4 > cis r-4 0 r_ $4 Q r4 ýq 1-4 ci C: 0 13 14 cl C) . 06 H :3 > 1-4 -0 $4 ad > E. 2 H >% 0 P4 gi- 11 0 P41 H 0) 0 U) E-4 () TS V 0 to C-4 0 El r, V-4 CS > m cr) oa fft 4-A to 11. C3 %.. - Q > 'a -ri C) -(0 :2 vs LL- C: 0 LL- V4 In 0 1-4 1: 1 0 a M ta U: ) A CS LIJ 0 IL JF r cl: . E-4 t A :: ) 0 ;q +a cr- 0* 40.1 cn LLJ cs 136 148 0 4v rl X: E E-4 cr) a cs ci u +S 0 Cd 0 A co 0 r4 .- in 000*z L99*1 00011 L99 *0 EU 10 000 10 (zoas/tu) f. OT IIIAISnJJIO 031OI(]-'. Yd 493. L. UR It (r-) dr 1.6 Data for tho compression period (crank angles from 800 IrrDC to TDC) 0 01 1.4 W 41. Orl 04 9 .. 0 0 1.0 VI 0 * 00 0 00 V 0.8 :j0 oil 0 X /. rRoll a. 0. [ P1 , lai a _V: ýv al I I _Intcd 03 OR00116-40Yce Enrine Data-. (Fully opened throttle) 0.6- r I' !P -Plain Valves (1000,1200&1500 rpm) 11 E Valves with Vanes -wIntake 11anifold fitted 1000 rFz: k 0.4. - 04. wit! L pelta Wings. -I Ford RnSire-Vata- .0 -Plain Valves Full & Part -Valves with i- Load Condition 11000-3500 rpm. 0.2 Vanes. .0 0.0-/ 0.0 0 .20.4 MM1.0 1,2 1.4 1.6 Predicted Scale (L. ) fron Isotropic Flow Data (131) - -Ic (7-12) Comparison between the reasured values of the nacro- cala of turbulence in engines and the predictions fro2 the experimental data of isdtropic flow fields. 404. z3 Z. c LA %it > .x P V. L gN 4 0 tette. 461w1 1194v X u00q9 vvw A b«gl@9149 340S le 3.1e 102 3-te ht Ub us FIG. (7-13). Ratio Between Fluctuating Velocity Component and Friction Velocity for Rough and. Smooth Surfaces at 10% Wall Distance, (102). 130025000 8=3.0 114 RADIUS=4.76 10 ulta vs VIP . 00 . 4- LAUFER (PIPC-) 02 10 40 100 2-00 400 GOO 800 100c) yu /V FIG. (7-14)COMIPARISON OF TURBULENCE INITENSMES WITH PIPE RESULTS (144) 495. 8. MODEL OF CYCLIC COAMUSTION VARIATION It has been concluded from the litoraturý survoy that most of the cyclic variation originates during the early development of the flame kernel (10,13,23). it has also been stated explicitly by Barton et al (10) and Miller et al (38) that after a certain percentage of the charge is burnt, little difference exists in the rate of burning for different engine cycles. Such percontage was ostimated to be of the order of 2- 5% in the former investigation and 101% in the latter. Models of cyclic variation were constructed, therefore, to relate the observed variations in the cylinder pressure development or the flame speed to the corresponding .0 variations in the time required to burn such a quantity of tho mixture. Such variations are believed to be caused by velocity fluctuations at the spark plug gap at the time of ignition which consequently affects the flame speed and the burning time. Barton et al (10) attempted to establish from their experimental data, a form of a velocity dependent function which could represent the effect of gas Velocity on the flame speed and satisfies, at the same time, the assumptions of the proposed model. Their model could be expressed, therefore, as follows: dVb A, . E. S (2-10) dt bt or drb E. S dt t 496. and St =S f (U) where Vb # rb are the volume of burnt gas and the corresponding radius of tho flame front is the expansion ratio = Tb Alu/Tu Mb T is the mixture temperature hi is the molecular weight of the mixturo St is the laminar flame speed and f(U) is some unknown function of gas velocity which has to be established from experimental data .0 The subscripts b, u refer to burnt and unburnt conditions. Assuming tfiat a constant ratio of the rharge is burned during the initial period and that velocity variations and the initial burn time are correlated, the following oxprossion could be obtained. S(t F(O. V-) b) C. g (U s (U i) (2-13) where S(tb)x S(Ui) are the standard variation in the initial burn time and gas velocity, respectively. and F(O -V) is a function of the operating variables = 'P (A/P. T ill Pi. ) 407. The subscripts i refors to mixture conditions at t1lo timo of ignition. The form of the function g(U i) which satisfics tho assumptions of the model was obtained, thereforo, by loast square fit of log F(O V. ) S(tb) and log (U and is given by I So iTI 1.3 Ui (2-14) Winsor (23) has proposed a similar model, which assumes that the average flame speed is sensitive to local turbulent velocity, only when the flame radius lies in a certain incremental range (dc) which is located at a finite but unknown distance from the spark electrodes. The author attempted, in this case, to find the value of such a critical radius, again by relating variations in flame speed (. ýurn time) and gas volocity variations. Such a model could be described by the following relationship: d=S. t CtC and = K. U t (8-2) (2-15) where tC is a critical time period during which combustion variations occur. 498. Again, assuming constant valuo for such a radius and that variations in the burn time (dofined as the tin. 0 from ignition until combustion cessation) and tho initial burn time are related to velocity variations, the following rolations were obtained: ' S(t b S(t C) w dt c S(U) dU or S(t bdc S(U)/-u '9 -t 1+ S(U)/U- 2 where the subscripts b, c. t refor to total burn time, critical period (initial burn time) and turbulent conditions. Substiwting .6 numerical values, from the experimental data, the value of the critical radius was obtained as 0.4 inch. I Examination of both models reveals that their basic concepts are similar. Both have assumed a critical radius of the I flame kernel which has a constant value or a constant ratio of the total charge volume. Also, the effect of turbulence on flame speed was considered as a function of the gas mean velocity. Such a function was of unknown form in the first case and was assumed linear in the second one. Their basic hypothesis could be summarized, therefore, in the following: 1. Cyclic combustion variations are, mainly, duo to gas velocity variations and the affect of turbulence on the development of the initial flame kernel which is required to produce a steady state flame propagation. 499. 2. After a certain critical radius is reached, the flame front propagates at a constant speed and tho corresponding ratos of burning the charge will be repeatable from one cyclo to another. In fact, these conclusions explain that the offoot of turbulence is very critical during the early devolopment of the flame kernel, when its size is smaller than the size of the turbulence eddies. When the flame front thickness exceeds the size of the eddies, their effect will be confined to local disturbances on the flame front and the flame will propagate at a more or less constant speed. Tho offect of turbulence on this second stage will be averaged across the .4 whole front and consequently such a Stage will be statistically repeatable from one cycle to another. .t A model of cyclic variation can be doveloped. based on the assumption that smalf scale turbulence eddies are governing the propagation of the flame kernel until the size of such akernel reaches some critical value comparable to the large scale eddies. Such a critical value can be assumed either equal to the large scale eddies or of some multiple value of the small scale eddies. The case of a universal constant value can be also considered, based on the assumption of similar turbulence fields in the engine during the later part of the compression period when the turbulence is decaying. The effect of small scalo turbulonco on tho propagation speed is usually known to intensify the transport Process by Mo. virtue of altering the fluid diffusivity from its molecular value to tho turbulent one. Such a procoss can bo 'doscribad by the following exprossion of Shchelkin (47) St 'Emicro +9 (2-10a) where Y is the kinematic viscosity is the eddy diffusivity of micro-scalo micro turbulence (2-44) micro L(micro) V is the contribution of micro-scalo micro eddies to the fluctuating velocity component I is the Lagrangian scale of turbulence L Assuming that the spectrum curve (F(n) vorsus n) can I be divided into two regions of small scale and largo scale turbulence at a certain partitioning frequency n0 as follows no f F(n) dn and F(n) dn 0 no where n corresponds to the condition of transition as formulated 0 by Kovasznay (57) as follows r typical velocity gradient In approaching cold flow typical velocity gradient in laminar flame or I V (2-42a) lic tt 16 501. where r for disintegrated flame front by the action of small scalo eddies is the thickness of laminar flame and x is the micro-scale of turbulence we can write the following relations v P(n) dn (2-45a) micro total no and consequently micro E total 'LL micro Ij F(n) dn (2-47) no where total is the mean value of eddy. oiffusivity of the all turbulent eddies in the flow =Iq (2-4G) L total 'ittal L is the Lagranglan scale of turbulence which could be expressed in terns of the Eulerian scales Lx and Ix as follows: L L(micro) KIIx (8-3a) L L(total) K1Lx (8-3b) K is the ratio between tho Lagrangian and Eulerian corrolation functions. 502. Moreover the range of very high frequencies in the power spectrum curve of turbulent flow could be considered as stAtistically steady in its mean values and Indopondont of external conditions (universal range in Nolmogoroff hypothesis (89)). Therefore, we can use a moan valuo for tho oxprossion under the radloal (1'*'f F(n) dn t: constant) for any particular no engine speed, and equation (2-47) reducos to E. Kx (8-4) micro 2v 2 total LX It is also concluded by the present investigation that the total value of eddy diffusivity could be predicted from the proposed expressions for pipe flow undor appropriato conditions. A general expression for such eddy diffusivity which applies throughout the whole turbulent regions (laminar sublayer, buffer layer and the turbulent core), is proposed by Spalding (128) 1 as follows: E '2 E=V. K KU+ -1 ICU+ - (KU+) 2 (KU+ 3] (7-14) total mE 21 where U+ u/u* U* is the friction volocity u is the local gas velocity and the constants K and E have tho following values Ka0.407 and E= 10. 0 503. The ratio between the micro-scalo and maoro-scalos of turbulence in equation (8-4) could be obtained from the isotropic flow theory as discussed in Chapter 3 and is given by the following relation Lxu1 ijx -=K or Lx total 1=x4'j9 (8-5) Substituting for Lx from equation (8-5) into equation (8-4) )ýc gives -total-V (8-G) micro 22 K2 total 5 IF 'ý4 Knowing that the coefficient of eddy diffusivity is of the order of 200 times the kinematic viscosity during compression period in the ensin- cycle (as shown in Chapter 7) equation (2-19a) could be written as st (2-10) Substituting for Z from equation (8-G) into equation (2-19) micro gives stK F-total ) 0.25 St Gv KG )0.25 (8-7) 504. The rate of change of the burned volume could be expressed by a relation similar to that used foraconstant volume bomb (135), equation (2-10) dVbA, .S. E dt bt which could be reduced for the case of hemispherical shell flame front to drb E. st Integrating equation (2-11) and assuming that both St and E are constant. during the short time interval of flame kernel growth for any particular cycle, gives sVE. tb (8-8) where r is some critical radius of the flame kernel which b is required to produce a stable and steady flame propagation thereafter. Two assumptions could be made about the value of such a radius, either a constant value as assumed in the models of Barton et al, and Winsor or some multiple value of the (mean) micro-scale of turbulence. The latter one seems more significant because it introduces the physical process of transition from a flame kernel of a size smaller than the eddies existing in the field to a flame front which could average many eddies. 505. The definition of such a value is much more difficult because of the artificial distinction of the turbulenco Ziold into small and large scale turbulence while a wide spectrum of eddies of different sizes actually exists. Moreover, tho reference length of comparison can only be the flame thickness and the more intense the turbulence the thicker this is. The hypotheses used in the present model are the same as discussed earlier, where all combustion variations aro attributed to the fluctuations in the rate of growth of the initial flame kernel due to the nature of the fluctuations in eddy diffusivities which controls such a combustion process. We can-write, therefore, the following relation d tb S(S S(t b dS tt (8-9) where tb is the initial burn time St is the turbulent flame speed S(t b) and SO t are the standard deviations in tb and dt bSt respectively and dS t is a mean value of the derivative of burning time with respect to turbulent flame speed during the initial period of f lame kernel growth. Similiar expressions can be written for the relationship between the fluctuations in flame speed and the corresponding flUctuations in eddy diffusivities as follows: 50G. SO dSt ) t dýn S which can be reduced with the aid of equation (8-7) to K6s (EM) SO )=- t4 EO. 75 0.25 mv Substituting equation (8-11) into equation (8-9) gives ,x6(d tb ) at 0 s(%) S(t )=- 4 dS tE . 75 . 25 (8-10) (8-11) (8-12) If we assume that a minimum value of the critical radius is nearly constant, we may write the following relation then rb constant dr 0-b dt +abdS tbb IDS tt or (ýrb dt b) zs t iis-t -0 rb zt b Using equation (8-8) we get dt bbr dS t St t 507. Substituting oquation (8-15) into oquation (8-12) wo got S(t )= -K6 r. st SC bm 4s2Ev0.25 FE 0.75 t in or S(t K7 V 0.25 (8-1G) bs EJL*2,5 m Now let us consider the case of a minimum radius which is of some multiple ratio of the small scale eddies. This condition could be written as follows. K 8' 1 Equation (8- 8) can be written in the form . -S SrbE t Differentiating equation (8-8a) with re6pect to turbulent flame speed gives dt s drb r bt dS tb dS t2 st E The variation of the critical radius with flame speed can be obtained by differentiating equation (8-7) with respect to the critical radius as follows 508. dS Ks (d /dU) (dU/d r t6t0m0 dr b40.25 0.75 -)l) rn (8-20) Since the eddy diffusivity is a function of gas velocity and kinematic viscosity, the problem is reduced to establishing a relationship describing the variation of the critical radius with gas velocity in the engine. In this respect we can make use of the experimental data obtained in the present work and the availablo knowledge about varidtion of turbulent characteristics with operating variablos. The micro-scale of turbulence was found to havo a linear relationship with gas velocity. Therefore we can wri te - I. = x I where a is a constant value which decreases with engine speed. (8-21) Making use of equations (8-17) and (8-21) equation (8-20) can be simplified to the following form dS tKSC (d F- m /dU) dr 9 0.25 0.75 (8-22) b Lm where K9 4a K8 a constant value for any particular engine speed. .0 509. Substituting equation (8-22) into aquation (8-19) and making use of equation (8-7) we got dt b (a K8) (4 E m/(d en /dU) -U (8-23) dS tEq2( F-M/ 0.5 Substituting equation (8-23) into equation (8-12) yiolds the final model equation as follows S(t bK4E M/(d E M/dU) - Ul -v0.25 s (E2 0 1.25. st Lra where K lo K8 )/(4 KG) The variations in eddy diffusivity could be related to the corresponding variations in gas mean velocities a; follows: dE S( F-M) M. S (U+) (8-25) dU+ But Therefore Similarly dF-m vK2e Ku+ U+ _ U+2 (8-26) dU +E 'i K2 [ Ku+ s(8 )= ýL- 01-U- U+2 S(U+) (8-27) +) dU+ ). s (U dUs (U) (8-28) (8-24) 510. Consequently, equation (8-25) could bo writton in tho following form s(, E m)= f(U, V ). S(U) (8-29) Comparing the model equation (8-10) and (8-24) shows that the difference between the two expressions is tho introduction of the term K 10 (4F- /(d F- /dU) - U) for tho latter case. K7mm This term will have an almost constant value for any particular engine speed within a close range of ignition timing. 8.1 Experimental Verification of Cyclic Combustion Variations Alodel The proposed model of equations (8-1G) and (8-24) suggests that cyclic combustion variations are caused, mainly, by variations in the early propagation of the flame kernel. The model relates these variations to the random variation in the eddy diffusivity of the flow which are responsible for the transport process during this period. Therefore, if the resultant combustion variation (as reflected in variations of flame speed, cylinder peak pressure and peak rates of pressure changes) has originated during the propagation Of the flame kernel into a stable flame front of nearly constant speed, a high correlation must exist between measured values of standard deviations of flame speed and gas mean velocity as governed by the volocity functions of equations (8-16) and (8-24). 511. The model could be tested, therefore, using the experimental data of other investigators such as ihoso of Barton et al (10) or Winsor (23). Although Barton et al did not moasuro tho flamo speed directly, the angle of occurronce of oither the peak cylinder pressure or the peak rato of pressure change can be used to represent the flame travel times. Wo can thoroforo write S(t b)= SO Pmax) 720 120 rpm 0 or S(t b)= Similarly - SO Pmax) 6 rpm (seconds) (8-30) (8-31) S(t S("Nax) 6 rpm Substituting the numerical values for the different variables in equations (8-16) and (8-24) at different engine operating conditions should give consistent values of the ratio between the expressions on both sides of the equations, if the assumptions of the model are satisfied. The second set of experimental data which could be used for testing the hypotheses of the model is that of Winsor'j3 work where a certain characteristic time was measured from the time of ignition until the combustion cessation. The reported 512. measurements of gas velocities, in this work, corrosponds only to the TDC position with the oxception of a run at 1000 r. p. m. where gas velocities versus crank angles woro shown. However, estimation of the velocity traces at this engine speed suggasts that approximate estimation of gas velocities at tho othor two speeds (1200 and 1500 r. p. m. ) could be obtained using tho reported values at TDC and assuming the same rate of decay as that for the 1000 r. p. m. Also, the values of the Coefficient of variation ( S(U) ) at TDC could be assumed valid also at U- the time of ignition to give an estimation of the standard deviations in gas velocities at ignition. These two approximations are justified because of the close rango of speeds under consideration and the nbsonce of any secondary flow created during compression for the flat disC combustion chamber used in th2t work. It once again we can relate the variations in the critical burning time to the corresponding variations in the total burn time as defined earlier. Tlius S(t b)=S (tc) (8-32) The above mentioned approximations could be formulated as follows ui S-- b UTDC and S(U s (UTDC) Ui UTDC (8-33) 513. or s (U i)=b S(U TDC) (8-34) The model equations could be applied therefore on volocitios and their standard deviations at TDC. Application of the model equation (8-IG) to tho experimental data of Barton et al (10) and lVinsor (23) havo shown good agreement between the predictions of the model and the experimental results as shown in Figures (8-1) and (i-2). The deviations in the ratio between predicted and measured variations in flame speed were found to be 18% for Barton's data and 16.7% for lVinsor's data. I Unfortunately, turbulence measurements'mlero not carried out in either Barton's or Winsor's work to enable checking the validity of the second assumption about a critical radius which, is of multiple ratio of micro-scale eddies. h1oroover, the application of the approximate method presented in Section (7-1) for predicting turbulence characteristics from mean velocity, fluid properties and engine dimensions . will not be helpful in this situation. 7his is mainly because only few experiments were carried out in these investigations at each engine speed (one in most cases) which makes the process of estimating the variation of micro-scales with gas velocity unreliable. Nevertheless application of the model to a reasonable sample of Barton's data at a fixed engine speed of 900 r. p. m. where tho slope of U-vorsus IX could be included in the constants has shown an oxcollent result where the scatter of the ratio between the predicted and measured 514. variations in the burning time were found to be about 10% only, which is of the same order of magnitudes of experimental errors. However, the application of the model equation for a constant critical radius on the same set of data gives results of the same order of magnitude. This could be oxplainod by the fact that in this model the variation of flame speed with the critical radius are mainly a function of gas velocities at a fixed engine speed which are nearly constant within tho rango of ignition timing used in Barton's investigation. Figure (8-3) shows a plot of the variation of the factor (4Fm/(dF-,, /dU) - U) versus U which indicates an almost constant value for the particular engine speed considered. In fact exact comparisons of predictions of the model and experimental data should be carried out using variation in flame speeds (travel times between ionization gaps) rather than I variations in the angle of occurrence of maximum pressure (or rate of pressure change) as used in Barton's work or the burn time defined by Winsor. I 515. Co 40 r: 0 . 014 4-b 0 . e4 c9 > u . e4 0 0-4 c: 00 -0 4- c) ri 4J Oj *i V0 %. 0 C0 Co im 0 0 r. -x 00 es e r) -4-4 c el% Co 0.4 %. 0 t; . f. 1 44 M C; XI? M d O)s 00 CD cli : 2: > c; rr4 : HI to :D Lfi c4 cq 91 c; p4 4; CA- 0 Cl) (A 0) V (3; )s 0 r. 0 ri 41 43 r; f. 4 C) 0 . 04 Co U Co u 0 C) cq In: ti pf CY p4 0 to c 10 2 0 U m 0. -4 Co 1 u cio . pl %. 0 0 cr 0 0 0-% C Co :) c) ý. q IH %. # -0-( $. 4 0 cn 4a e4 cd > 03 Co %. 0 SIG. %" f (4 P-1 517. CONCLUSIONS AND RECOMI ENDAT IONS FOR FURIIIER V,, O" 9.1 Conclusions The present work was carried out on two typos of combustion chambers found in commercial spark ignition engines, namely: a wedge shape and a heron shape. Measurements of gas velocities and turbulence characteristics were carried out over a wider range of operating conditions than any published investigation in this field. The results obtained have shown that the genoraýl characteristics in gas velocities are similar for most shapes of combustion chambers used for spark ignition engines. However, the turbulence characteristics and-the levels of gas moan velocities during different strokes of the cyclo are mainly functions of the combustion chamber and intake system configurations. Measured gas volocithies at various locations inside the combustion chamber show a considerable cyclic variation in both their levels and tim. 0 of occurrence in the cycle, though the general shapes are very similar for different cycles. These variations could be as high as 40 - 50% of the mean values. The turbulence characteristics in engines are mainly affected by gas mean velocities during different strokes of the cycle. The fluctuating velocity components and the size of small-scale eddies follow similar trends to gas moan velocities. In particular, the size of small-scale eddies were found to increase linearly with gas mean velocity according to 518. a relation of the form: ýL = y where a is a constant value which docreasoa with engine 0 speed and depends also on combustion chamber and Intake system configuration. The time micro-scale of turbulence was found to'decrease with engine speed, indicating an increase in the high frequency content of turbulence oddies In tho combustion chamber. Increases in gas mean velocities with engine speed were found, therefore, to cause increases in both the fluctuating velocity components and the frequencies of eddy rotation. Consequently increases in flame speed with engine .0 speed could be attributed to the mutual offect of the two factors mentioned above. This findin. V is in close agreement with the experimental data of Lefbevre et al (49) for tile effect of turbulence on confined flames as given by the following relationship: st st1+0.43 u' + 0.04 (6-3) where the mean velocity term in oquation (6-3) could bo interpreted to represent the effect of higher moan velocity on increasing the frequencies of eddies ill the field. The wedge shape chamber shows that high frequency eddies are generated during the induction period, but decay later on during the compression stroke to slower eddios, while the horon 519. shape chamber shows a similar level of low frequency oddios during most of the cycle especially at low engine spoods. However the size of small-scale oddics in the wedge chamber are larger than the corresponding values for the horon shapo at comparable conditions. This moans that the horon shape may result in better performance with loan mixtures than the wedge shape providing that similar mixturo, homogeneities were used. - The use of Inlet valves fittod with guide vanes seems to provide a mutual effect of higher intake velocities at much higher rates of mixing that eventually result in smaller sizes of the small-scale oddios during compression. The performance of the masked valve clearly indicates that the directional velocities created during Intake period continue for a considerable time during compression. However, the frequencies of eddies during compression are not greatly affected and the reported improvements in the combustion process for engines fitted with masked inlet valves (Marvin and Bost (I)l Patterson (2), Caris at al (8), and Matsuoka et al (15) ) can only be explained by higher flame speeds resulting from the associated higher fluctuating velocity Components and improved mixture homogeneity. The creation of a strong jet inside the combustion chamber during the periods of inlet valve closure as the case of a valve used for reduced lift, is very helpful in enorgising the flow field during this period of very high damping rates. The improved engine performance at part load conditions in Stivander's tests (19) 520. with a throttled intake valve may be attributed to a similar flow condition rather than enhancing the small scalo turbulence. Also, the measured values of the largo acalo eddies inside the combustion chamber are very much smallor than the cylinder diameter 'as postulated by Stivendor. An intake manifold fitted with delta wings has produced a significant reduction of cyclic variation in gas volocitics, and contributed towards better homogeneity of the mixture. A study of the variation of flow field charact6ris tics with depth inside the combustion chamber has revoaled tho following points: i) A zone inside the middle of the combustion chamber seems to exist where flow properties are statistically steady anj cyclic variation in gas velocities are nearly constant during the whole compression period. ii) The minimum cyclic variation in gas volocities at any location occurs during the period of secondary flow created by compression (squish velocities). iii) The squish components were observed to develop along the wedge wall parallel to tho cylindor head surface (Rolls-Royce engine) rather than a simplo transfor of mass normal to cylinder axis as thought to bo tho case. The measured values of those componont3 are very much smaller than the prodictions of thoorotical models. One may explain this by tho fact that tho 521. squish velocities croatod during tho comprossLon period are transferrod into circul"Ing eddios inside the combustion chamber rathor than any hypothesised diroctional stroam volocitios. Summing up the previously mentioned findings about the flow field characteristics inside the combustion chambers and the effect of different intake modifications on theso characteristics, one can outline some possible sources of potential gains in engine performance by modification of tho combustion chamber and intake system configurations as follows: i) Proper directing of intake manifolds can produce strong swirl velocities which porpist during the compression period. These swirl valocitlea were shown, in the pro. -; bnt work, to produce higher levels of fluctuating velocity components and contributed towards better mixturo homogeneity. I Consequently faster flame speeds and minimum lovels of combustion variation could be achievod. Such swirl velocities will also reduce tho amount of unburnt hydrocarbons and the formation of deposits on the walls of the combustion chambor (28). ii) The insertion of swirl generators inside the intake manifolds or an valve seats are also very helpful inxeducing the combustion variation, for the above mentioned reasons in item (i) without sacrifices in engine breathing at higher engine speeds. 522. iii) Placing tho spark plug Cap inside the contra, of the charge during the compressioil poriod (by using long reach plugs) locates the flame kernel in a region of moro uniform flow properties which reduces the cyclic variation in its rato of growth and consequently reduces combustion variation and extends the 'loan limit' of engine operation. Other advantages are obtainable when applying this modification such as: creating more favourable temperature conditions for thý growth of the flame kernel by reducing its quenching by central electrodes and cylinder head surface (20), (27) and reducing flame travel distances which shorten the combustion period and reduced the octane requirement of the fuel (8). iv) Proper shaping of the cylinder head walls (in relation to squish area) to direct the squish velocities towards the spark plug l6c-ation is highly desirable for making use of this source of turbulent energy before its dissipation into decaying eddies inside the volume of the combustion chamber. This will result in accelerating the growth of the f lame kernel with all the consequent improvements in engine performance as mentioned earlier. This will also reduce the octane requirement of the fuel and make it possible to increase engine efficiency by Increasing the compression ratio while still using available fuels (8), Figure (9-1). 523. 10: 1 CR OCTANE REO-100 . 1- 11: 1 CR OCTANE REQ, 100 Fig. (9-1) Effect of better utilisation of squish velocities an mechanical octanon in a multi-cylindai engino (according to Diggs (8) . v) Igniting tho mixturb during the period of maximum squish velocitics can also reduco combustion variation and inprova engino performance. 0 The present turbulence measuit-ments in combustion chambers of spark ignition engines have made it possible to cheel; 'two proposed models for turbulent combustion in engines, namely the laminar model (43-50) and the three'dimensional Liodel (G3,64). Using some mean value of the fluctuating velocity component during the ignition period of the order of 0.5 m/soc, a mean value for the micro-scale of turbulence of 0.6 mm, a flame front thickness of 0.22 mm (42) and a laminar flamo speed of 1.3 m/sec (42) and applying ICovasznW'qCriterion (57). equation (2-42),, shovis that the wrinkled flame mechanism prevails for combustion in engines: r= 1- U, I (for wrinkled flame) (2-42) S, Xx 524. Comparing the magnitudes of ed4y diffusivitios during tho compression period with the corrosponding valuos of kinaMAtiC viscosities gives ratios of the order of 200. Consequently, the three dimensional model of combustion proposed by Summerfield (63), equation (2-39) can be rejected for combustion in spark ignition engines: sta se (2-3p) The ratio between turbulent and laminar flame speed in engines is usually reported of the order of 3 as statod by Harrow and Orman (30) and Phillips and Orman (42). The former investigation proposed a relationship of the following form: st -=I+0.002 (RP, 11) stI The same conclusion about the adequacy of wrinkled f lame model for turbulent combustion in engines was also reported by Do Sooto(2G). The extensive test programme undertaken, in the present work, has enabled the establishment of direct correlation between the flow field inside the combustion chambers of spark ignition engines and pipe flow fields. This resulted in developing an approximate procedure for predicting turbulence characteristics in engines from a knowledge of the gas mean velocities, which requires simple equipment. 525. The comprehonsivo litoraturo survoy undartaken hall shown that the propagation of flamos in spark ignition engines is greatly influonced by the rate of growth of tho initial flame kernel. 7his process is mainly govornod by the small-scale eddies which exist in the combustion chamber during the time of ignition. Variation in the rate of growth of such a kernel duo to variation in eddy diffusivitios of -the small-scale eddies between different cycles are beliovod to be the main cause of cyclic combustion variation. A theoretical model for cyclic combustion variation is davoloped based on the previously mentionod assumptions and making use of the established correlation between the flow fields in engines and pipe flow fields. The oxporimantal data of Barton (10) and Winsor (23) were used to chock 'the model and showed very good agreement between the measured and predicted values of the variations. Ad 520. 9.2 Ilocommendation for rurthor Work It is obvious from tho discussions of tho prosont. investigation, that an extension of the work is roquirod to study the variation of turbulonco charactoris tics Insido tho combustion chambers of S. I. engines with compression ratio. This problem represents a point of contradiction botwoon tho results of Molchanov (62), Somenov (22) and James (24), which have not been resolved yet. Some proliminary work on this problem has already started in tho Dopartment of Mechanical Engineering of Loughborough University. A Ricardo EG angino has been used in this investigation. Use of the Data Acquisition and Procossing System, which has been developed in the present work for wider studies of the turbulence characteristics produced by othqr shapes of combustion chambers than the ones considored here is also desirable. Future studies should be coAcentrated on some configurations that have shown improved engine performance with regard to the levels of exhaust emissions and smoothness of loan mixture operation. In this respect, the author would like to draw the attention to the studios of Dodd (15G) where low emissions were obtained with an annular chamber formed between a flat cylinder head and a bump on the piston. 7ho work of Tanuma at al (20) can also be consulted for these studies (seo Chapter G). On the other hand, modifications of the intake system by; proper shaping of inlet passage (1G), insertion of swirl generators inside the intake manifold (GO) or fitting guide vanos on valve seats, can be used to increase the chargo turbulenco and consequently reduce cYclic combustion variation. Somo firod tosts 527. are required for assisting the findings of tho prosont anemometer measurements on the offoct of those modifications in reducing the size of small scale turbulenco oddios. A detailed study of the flow -mochanism of croating squish velocity components inside the combustion chambers of ongines is also requirod. This sourco of croating secondary flow 'during the compression period represents ona of the most fruitful areas for potential gains in ongino performance, if carefully understood and utilised to hinder the decay process of the turbulence field during the combýstion period. The use of dynamic models for simulating combustion chambers configurations represents some possible oxperimontal set up. An extension of the studies of Tsugo and Kido (153, .1 154) on the mechanism of turbulence docay in closed vessols, is also required for better understanding of the charactoristics .1 of this particular flow field. Employing different methods of creating turbulence inside the vessels and investigating simulated combustion chamber shapes represents new areas for exploitation. These studies may extend the applications of the proposed design procedure (section 7.1) for predicting turbulence characteristics inside engine cylinders. A study of the combustion process inside the cylinders of spark ignition engines under carefully measured turbulence field characteristic parameters (intensities, scales and spectrum) can result in the development of turbulent combustion models for this type of problem. Ilia work of Sirignano (131,132) and Blizard and Keck (133) can be consulted in t1lis respect. This possibility is already under consideration by Dont and hL3 co-workors 528. for possible establishment of some correlations betwoon combustion parameters, turbulence charactoristics dnd mixturo conditions. This may lead to resolving some of the present contradictions in the known combustion models discussed in Section 2.5. For example, the phenomena of 'flame generated turbulence' which is still a matter of dispute between different investigators. The use of the concepts introduced by the spectral theory of turbulent combustion represents a more appropriate line., of approach for these studies. S *1 0 529. 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The Universal Equilibrium Spectra of Turbulent Volocity and Scalar Fields. Journal of Fluid Mechanics, Vol, 1G, 19G3. 149. GIBSON, M. M. Spectra of Turbulence in a Round Jot. Journal of Fluid Mechanics, Vol. 15,1963. 150. IANGE, K. Control of Exhaust Emissions f rom Internal Combustion Engines by Means of Engine Modification. MTZ, Vol. 34, No. 7, pp. 221-225, July 1973. h1IRA Translation No. 4/74, January 1974. 151. ELLE, B. J. An Investigation at Low Speed of the Flow Near the Apex of Thin Delta Wings with Sharp Leading Edges. A. R. C. R. & M. 3176, January 1958. 544. 152. IMIBOURNE, N. C. and DRYER, D. W. The Bursting of Leading Edgo Vorticas, Somo Obsorvations and Discussion of the Phenomenon. Aero. Resoarch Council R. L M. No. 3282, Londonj IDG2. 153. TSUGE, Morio, KIDO, Hiroyuki, YANAGIILARA,, Ifiromichi. Decay of Turbulence in a Closed Vessel. lst Report, Decay of Turbulence intensity. Bulletin of the J. S. M. E. Vol. 1G. No. 02, robruary 1073. 154. TSUGE, Morio and KIDOj 11iroyuki. Decay of Turbulence in a Closed Vessel. Bulletin of the J. S. M. E. Vol. 17, No. 107, May 1974. 155. TAYLOR, C. F. and TAYIDR, E. S. The Internal Combustion Engine. International Textbook Co., Scranton, 'Pennsylvania, 19G2. 156. DODD, A. E. Exhaust Emissions Studios using a Single Cylinder Engine. Paper C131/41, Air Pollution Control in Trinsport Engines Automobile Division and Combustion Engine Group, Conference Volume, Inst. htech. Eng. Symposium 1971. 157. SAIANIA, N. .0 Three-Dimensional Analysis of Gas Velocity Vector Inside a Cylinder of a S. I. Engine. -Internal Reports Dopartment. 9f 1jechanical Engineering, University of Technology, Loughborough, 1973. 545. APPENDIX Al NOV ANALYSIS OF OVER INVESTIGNTIONS The results of Semenov (22) and Jamos (2-1) wero analysed, using similar procedures to those pro3onted in Chapter 4. However modifications of tho general data processing procedures were necessary to suit tho form of reporied data in each investigation as follows: Al-1 Semenov's Data The power spectrum curves presentod by Somenov ware used to obtain the time micro-scale of turbulence as given by the following relationship: 2 Go 4 P(n) n2 cln Different turbulence characteristic parameters were obtained using the measured values Of gas mean velocities and fluctuating velocity components and making use of the relationship between micro-scales and macro-scales as discussed in Chapter 3. Corrections of the effect of finite wire length on turbulence measurements were also calculatod assuming an exponential form of tho correlation function as proposed by Semenov on his original data. However, the use of the predicted values of the scales of eddies rather than approximate values calculated from incan velocities and mean frequencies as given by equation (A2) results in much smaller values of the corrections as compared with Semenov's estimation. u x 2iTn (A2) 54G. For example the calculated corroctions using tho prodictod valuos of Lx vary between 1.36at lower compression ratios (CR = 4: 1) to 1. G04 at 9.5 compression ratio whilo a value of 2.5 was used by Semenov. A summary of these analysos is given in Table (Al). ý0 It f r. 0 44 cs co 44 0 W W 04-4 0 Ul -H 0-% %_o 2 im 19 C) C) "r4 -4 'Pl U "r4 $4 -4 0 -4 C- 0 E 8 a) I C) C) C) ri Co le Co Z 0 +b le Co ri -H ei gl 41 u f-4 Co c4 r- w Cb ßn 00 0-% 0 0 0 0 0 c; > 0 x N-4 X ý% e- ". i +b 44 u CD r) cla r) r- c4 vi c4 >0 %-4 in 0 c; c; c; *ö U) ý ti 2 "£ W %-0 1 Ci to c4 C-4 %W lý w! qý Ilý 0 0 0 0 9 9 1 50 0 C) 0 c; c; 94 Co CD C, 3 00 cl c; . 13 0 r) m Co Co Z Ile: li "i 1 : JE 0 0 .6 547p Irw 5480 Al-2 James' Data Since the original data in this caso worý roportod as variations of fluctuating velocity components with frequencics in six bandpamwidths, roprosontativo valuos of total mean square values of the fluctuating volocity components were obtained by integrating power spectrum curves. 'Mose lattor curves were calculated from the reported results using the following relations F (n) lim I IX (n) X* (n)] (A3) T t-. 06 u2 P(n) dn (A4) where X(n) and X*(n) are the Fourior transforms and its complex conjugato of thQ -fluctuatini; velocity components. .1 An interpolation FORMN program was used to calculato the values of u'(n) at specific froquencies corresponding to a I fixed sampling rate on the Hewlott Packard Fourior Analyser. In this case a data block of G4 points wero, used with vi maximum frequency of 5 KIIz which resulted in a frequency resolution of 156 IIz/sample. The time micro-scales of turbulonco wero obtainod by two different methods: 1. From normalisod power spectrum curves using equation (Al). 2. 'From the socond dorivatives of tho auto-corrolation coefficients. The latter values were obtained 540. continued. from an invorse rouriur transform of the normalLsed power spectrum curves. Figs. (Al) and (A2) show typical curves of those analyses while tho complete analysis is given in Table (2-0). Tho main concern about these analyses are tho limitod number of cycles used to Ovaluato avorago valuos of ul in the original work (12 CYcles) OsPecially with using instantanoous values at the particular crank angles of interest rather than a reasonable sample Width Of the signals. Also the largo cyclic variations in gas mean velocities were superimposed on the actual fluctuations in the lower range frequencies. A modification of the data processing procedure used by James will be discussed in the follpiring section which uses a combination of a fast ADC and a digital computer. 550. S. Ln Li, I'- CT, CV) CY) 5-f Ige nb in Z OW c4 -2 c3 tii re LIL 93 I 0 92 00 0 ti Pf 91 .. w. t3 -ri z94 ft t4 V 0" C. )v-4 41 to p L2 -P4 to %. 0 rv 4-b 4. to C3 6-3 0#4 0 to V4 ta Pýll 0-4 In ts ri di _H 41 ri p4 Cl% 2: 1 *0 8000 toll 0 0-- 991110x (U)a UOT. Izt-"n. 4 Qn. 1.43ods zolioj 551. 011 0-4 0 C3 m «2 to CD 0 C3 C3 Fig 0 0.7S I. SS ( IC I A typical example of the curves obtained in a now (Squish combustion chamb, 900 RPIII and TDC data. ) 2.35 3.1s TI ME MSEC auto-corrolation coefficient anal, Ysis Of James'-., data (22). or95.29: 1 cOmpression ratio, 552,, Al-3 Proposed Data Processing System for Evaluating Turbulonco Characteristic Parametors from Mean Velocitios Digitize instantaneous (original) hot wiro signals at a fast sampling rate ( At), o. g. So 14 aec/samplýe, Isolate a cycle sample of a fixed width (4 0) from each engine cycle at the particular crank angle of interest 0. iii) Calculate instantaneous values of gas velocities for different samples in the cycle sample. iv) Resolve the gas velocity signals for the cycle sample into a mean value Ui and fluctuating velocity components ui where the subscript (i) refors to the engine cycle under consideration. V) Obtain the root mean square value of the fluctuating ielocity component for the cyple number (i). vi) Repeat steps from (i) to (v) for a large number of cycles. 0 vii) Calculate the mean values of the fluctuating velocity components and gas mean velocities for the test under consideration by averaging values of individual cycles. Consequently calculate the turbulence intensity from ul Int(8) - (A5) u (9) NC u'(E» =7u; (0 (AG) NC A 553. where and NC ý (0) = iK 151 (0) (A7) NC (9) (AB) (AD) U is the instantaneous values of gas - i velocities for different samples in the cycle sample (i). (E» -U (9 N. t (Alo) iii viii) Obtain an average power spec*um curve by averaging individual power spectrum curves of each cycle. ix) Obtain the micro-scale of turbulence using equation (Al). X) Cyclic variations in gas mean velocities and turbulence characteristics pan be obtained by statistical gnalyqis of . the values for different cycles. 554. APPENDIX A2 STATISTICAL DEFINITIONS This appendix is concerned with dofining the various statistical terms used in the present investigation. - The arithmetic mean. The arithmetic mean or the mean of a sot of N numbers x 1,3c2 ..... xN is denoted by X and is dofined as xi The root mean square value (All) The root mean square of a set of numbers xl, x2... is defined by 2 =2 R. M. S. 4X 2 i=l xi F2 (A12) -4 NN 3. The range of variation The range of a set of numbers is the difference between the largest and smallest numbers in the set. Range of Variation = Xmax -x min (A13) The relative rangeof variation is defined as R. R. v. = (X max -x min)/R (A13a) 555. Sample Variance The variance of a set of data xjL# X2 "*"*** XN is defined as the square of the deviation of the data from their mean values as given by s2=e (xi - R) 2 (A14) 5. The standard deviation The standard deviation is defined as the root mean square of the deviations from the mean. Therefore N S(x12 N which could be simplified to the following relation 2 --2L - (R)2 SN-=I_ (R )2 (A15) 6. Coefficient of variation I (AI6) This is defined as a relative variation as given by v= x Skewness Skewness is the degree of symmetry or departure from symmetry of a distribution. If the frequency curve of a distribution has a longer 'tail' to the right of the central maximum than to the left, the distribution is said to be "skewed" to the right or to have positive skewness. If the reverse is true 55G. Skewness (continued) it is said to be skewed to the loft or to have 'negative skownoss'. This is defined by N ým 33 CS(X) = lmi (xi - ý) /S (X) (A17) N-2 For a normal distribution, the coefficient of skewness equals zero. Kurtosis Kurtosis is the degree of peakedness of a distribution, usually taken relative to a normal distribution. A distribution having a relatively high peak is called 'leptokurtic' while a flat topped distribution is called 'platykurtic". * The normal distribution which is not very peaked or very flat-topped is called Imesokurtic'. The coefficient of kurtosis is defined as 2ý 44 CKM = i=l (X - ý) IS (F. ) (A18) For a normal distribution the coefficient of kurtosis equals 3. 9. Best fitting curve This is a curve which approximates a given sot of data points with the minimum square deviations +D2 is a minimum Y N 357. Best fitting curve (continued) The least square line approximating the set of points (X 11 Yl) ...... (X N' YN) is given by a0+a1x (A19) where ao - (ry)(7 X2)- (EX)CEXY) (A20) HEX 2- zX 2 NT-XY (rx)(T-Y) (A21) NEX2 (ZX)2 10. Tests of hypolhesis and significanco (141) If on the supposition that a particular hypothesis is true we find that results observed in ýýrandom samplo differ markedly from those expected under the hypothesis an the basis of pure chance using sampling theory, we would say that the observed differences are 'SIGNIFICANT' and we would be inclined to reject the hypothesis. If we reject a hypothesis when it should be accepted, we say that a type I error has been made. If, on the other hand, we accept the hypothesis when it should be rejected, wo say a type II error has been made. 558. 11. Level of significance In testing a given hypothesis, the maximam probability with which we would be willing to risk a type I error is called the 'Level of significance'. This probability is ofton donotod by N. In practice a level of significance of 0.05 or(O. 01) is customary, which means that there are about 5(or 1) chances in 100 that we would reject the hypothesis when it should be accepted, i. e. we are'about 95% confident that we have made the right decision. .6 I 559. APPENDIX A3 PHYSICAL PROPERTIES OF AIR Ex=ination of the themal oquilibrium oquation for the hot wire, shows that accurate knowledge of gas properties are essential. 7hese properties are: tho thermal conductivity (k), the dynamic viscosity )g the specific heat at constant volume (Cv)t or the specific heat at constant pressure and the ratio between the specific heats at constant volume and constant pressure These fluid proportics are evaluated at the wire temperature and surrounding fluid temperature. Different expressions are proposed in tho literature for the variations of fluid properties with temperature and pressure. However for our practical situation where the maximum Mid pressure is of the order of 15 atms, the effect of pressure on fluid properties is negligible and, therefore, a least square polynomial fit of the published data from different references was employed to express the variation of fluid properties with temperature as follows: a) The specific heat at constant pressure The published data of Rogers and Mayhew (95) was used and a least square polynomial fit of the 8th order yields the values of various coefficients as shown in Table (A2) whore the equation is given by: 9 IT- T (A22) CPT = i=l 560. where ai (i = 1,2..... 9) are the polynomial coofficionts. TABLE (A2) Coefficients of the polynomial in oquation (A22 ao 0.1003G831G84 x 10 4 a1 0.4109764355 x 10-1 a2 0.109530395987 x 10- 3 a3 0.2115430395987 x 10- 3 a4 -0.74071031836 x 10-8- a5 0.116895608829 x 10- 10 a6 -0.102415350074 x 10-13 a7 0.483599303466 x lo- 17 1 -0.9G17976734G1 - x. 10-21 1 b) Thermal Conductivity Vargaftik (96) shows that the variation of thermal conductivity of diatomic and polyatomic gases at atmospheric pressure could be represented by the following expression (which agrees with the published data of Rogers and Mayhew (95) and Kutateladze(99)): p KT =K (T + 273) (A23) T+ 273 0 where KT is the thermal conductivity of the gas at tenperature, T. K0 is the thermal conductivity at a reference temperature = (0.02435 11/m 2 OC) 561. T is the gas temperature OC To is the reference temperature a (260c) p is the exponent of temperature dependance = 0.82 C) Dynamic Viscosity The viscosity of gas increases with increase in temperature. The rate of increase ý2 may increase, romain dT almost constant, or decrease as the temperature ýncreases. As a rough rule for compounds of the same typo, the higher the molecular weight, the greater the rate of increase of viscosity. Spiers (156) stated that at pressures in the neighbourhood of atmospheric, the viscosity of a gas is independent of pressure a Bromley and Wilke (97) showed that the viscosity of a _2 gas at any temperature T is related to the viscosity at reference temperature To by the relatiophip a* T po f T- where /V ýo T TO f is the dynamic viscosity at temperature T is the dynamic viscosity at a reference temperature T is the gas temperature (OKJ is the reference gas temperature (OK) Stofan Boltzman's constant (A24) constant characteristics of the chemical specics denotes the viscosity temperaturo function. 'lý 562. Due to the difficulty of obtaining Sý for some gasos, arT the ratio T may be estimated from er T=1.33 T (A25) Tr where Tr is the reduced temperature of tho gas. Valuos of the viscosity temperature function f(S T) are tabulated 15 by Reid and Sherwood (98) and are given in Table (A3). A least square fit of such a function in a polynomial of the 8th order was carried out, equation (A26), and the valuos of different coefficients are given in Table (A4). (crT T i-i (A2G) .I where a is the polynomial coefficient and T is the gas i. 1- temperature. Reid and Sherwood indicated that the use of the relationship (A24) is remarkably reliable over the temperature range 100 to 15000K. The reference value of the dynamic viscosity and temperature used are /0) = 0.00001717 Kg/m see at 20oC. 563. TABLE (A3. ) Values of the Viscosity Temporaturp Function (98) <$' T/iE f (loý T/e ) cr TZE :t (cr T/a ) 0.3 0.1969 3.1 1.7154 0.4 0.2540 3.2 1.7573 0.5 0.3134 3.3 1.7983 o. 6 0.3751 3.4 1.8383 0.7 0.4384 3.5 1.8789 o. 8 0-5025 3.6 1.9186 0.9 0.5666 3.7 1.9576 1.0 0.6302 3.8 1.9962 1.1 0.6928 3.9 2.0343 1.2 0.7544 4.0 2.0719 1.3 0.8151 4.1 2.1090 1.4 0.8744 4-2 2.1457 1.5 0.9325 4.3 2.1820 1.6 0.9894 4.4 2.2180 1.7 1.0453 4.5 2.2536 1.8 1.0995 4.6 2.2888 1.9 1.1529 4.7 2.3237 2.0 1.2048 4.8 2.3583 2.1 1.2558 4.9 2.3926 2,2 1.3057 5.0 2.4264 2.3 1.3547 6. o 2.751 2.4 1.4028 7.0 3.053 2.5 1.4501 8.0 . 0-337 2.6 1.4962 9.0 3.607 2-7 1.5417 10. 3.866 2.8 1.5861 20. 6.063 2.9 1.6298 30. 7.880 3.0 1.6728 40. 9.488 TABLE (A4) Coefficients of Dynamic Viscosity Function a0 0.011247287149 a1 0.6728087682 a2 -0 . 0487113925692 a 0.2735028893 x 10 3 a4 -0.8884856941 x 10 a o. 168231637794 x 10 5 a -0.18336035233 x 10-7 6 a 0.106525921085 x 10-9 7 10- 12 a8 -0.255293477119 x I 564. , 7- 565. APPENDIX A4 A GUIDE FOR 771E SOURCES OF DIFFERENT EQUATIONS PRESENTED IN CHAPTER 3 This Appendix is meant to be a precise guide for the reader who wants to follow the derivations of different equations presented in Chapter 3. Equation Number Reference Page (3-3) - (3-7) 22 126 - (3-8) 23 16 - 21 (3-9) - (3-14) 77 495, 501-502 (3-53) - (3-57) 79 40 (3-60) - (3-67) 79 35 - 36 (3-70) - (3-72) 79 150 - 153 (3-73) 81 10 (3-75) 109 302 - 303 (3-76) - '(3-78) 79 41 (3-81) - (3-88) 79 56 - 59 (3-94) - (3-97) 84 28 - 36 (3-99) - (3-100) 79 185 (3-102)- (3-107) 91 31 - 32 (3-108)- (3-115) 79 97 - 100 (3-118)- (3-141) 81 12 - 13 (3-146)- (3-151) 79 47 - 48 a Note: The classical papers on turbulence (e. g. 84 - 90) are compiled in reference (88).

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