Numerical modeling of the flow in an organic Rankine cycle small axial turbine with partial admission

U skladu s najnovijim aktivnostima u EU može se zaključiti da prethodno prihvaćene strateške odrednice EU energetske politike koje se očituju u smanjenju emisija stakleničkih plinova, iskorištavanju obnovljivih energetskih izvora i otpadne topline, poboljšanju energetske učinkovitostikako u industriji tako i u zgradarstvu, ne samo da se nastavljaju već i intenziviraju. Ključne aktivnosti su definirane u Energy Road Map 2050. Jedno je sigurno: EU legislativa jasno definira put razvoja energetskih postrojenja temeljenih na obnovljivim energetskim izvorima, posebice mikro/malih/srednjih snaga (1-10-5000 kW) za distribuiranu proizvodnju (eng. distribuited production) električne energije ali istovremeno i toplinske energije u kombi postrojenjima (eng. cogeneration power system). U tom kontekstu je značajno stimulirati proizvođače koji su istovremeno i potrošači energije (eng. prosumers), tj. milione malih investitora koji proizvode energiju za vlastite potrebe u svojim mikro i malim postrojenjima (eng. micro and small scale power system), prodavajući pri tome višak energije u centralnu mrežu. Sumirajući prethodna razmatranja može se zaključiti da distribuirana proizvodnja energije temeljena na obnovljivim energetskim izvorima (DES/RES), mikro mreže (eng. micro grids) te napredne mreže (eng. smart grid) s primjenom naprednih digitalnih tehnologija kao „digitalnog oblaka“ (eng. digital cloud) bit će ključni element energetske politike u EU u bliskoj budućnosti. To znači da hibridni sustavi koji integriraju solarnu i geotermalnu energiju, energiju biomase i vjetra, otpadnu toplinu, dizalice topline i skladištenje energije kod energetski plus zgrada, radeći u naprednim mrežama su izazov koji stoji pred nama. Pošto su solarna, geotermalna i energija iz biomase, te otpadna toplina pretežito nisko i srednjetemperaturni energetski izvori (do 350 °C) za proizvodnju mehaničke energije odn. električne energije a kod kogeneracijskih postrojenja i toplinske energije, u Rankineovom ciklusu vodu odn. vodenu paru kao radni fluid potrebno je zamijeniti s lakohlapljivim organskim fluidom pa imamo organski Rankineov ciklus (eng. Organic Rankine Cycle – ORC). Zbog niske temperaturne razine ORC ima relativno nisku termodinamičku iskoristivost pa je veoma bitna iskoristivost pojedinih komponenti, pumpe, isparivača, kondenzatora, a posebno je kritičan ekspander koji proizvodi mehanički rad. Kao ekspanderi se koriste turboekspanderi i volumni ekspanderi. Volumni ekspanderi su vijčani, pužni, spiralni, klipni i s rotirajućim krilcima, dok su turboekspanderi radijalna i aksijalna turbina. Treba napomenuti da se radijalne turbine znatno više koriste od aksijalnih. U ovoj doktorskoj disertaciji u središtu istraživanja je inovativna, aksijalna, višestupanjska turbina male snage (50 kW). Provodit će se numeričke simulacije strujanja na različitim geometrijama strujnog aparata turbine kako bi se utvrdio utjecaj geometrijskih parametara (parcijalnosti privoda, koraka i širine statorskih i rotorskih rešetki, itd.) na strujne karakteristike odn. unutarnju (izentropsku) iskoristivost turbine. Dobivene spoznaje rezultirat će preporukama za konstruiranje mikro i aksijalnih turbina malih snaga za primjenu u postrojenjima s ORC-om, čija će iskoristivost biti jednaka ili veća od radijalnih turbina. Imajući istovremeno u vidu nove tehnologije izrade (3D printanje) to će doprinijeti širem korištenju aksijalnih turbina.The energy crisis is a challenge for sustainable development. It is caused by the reduction in fossil fuel reserves and significant fluctuations in fuel prices, which are frequently caused by geopolitics and environmental issues (increasing global warming caused by greenhouse gases, air pollution caused by various pollutants, ozone layer damage, acid rains, etc.) because of the rapid consumption of fossil fuels. Low- and medium-temperature heat sources, such as renewables (solar, geothermal, biomass, and ocean thermal energy) as well as waste heat from various industrial plants and processes (such as petrochemical plants, gas turbines, and internal combustion engines (ICEs)), are widely available worldwide. The organic Rankine cycle (ORC) can play an important role in utilizing these heat resources, which is similar to a steam Rankine cycles but uses an organic fluid. The ORC working fluid is very important because it affects the efficiency, operating conditions, economic viability, and environmental efficiency of the entire system. Therefore, the selection of a suitable working fluid has been the objective of many investigations. After 40 years of development, the ORC has proven to be a reliable and adaptable technology in many applications for renewable energy source conversion and waste heat utilization. The key component of the ORC is the expander, which is available in different types: volumetric (piston, scroll, and screw) and turboexpanders (axial and radial inflow and outflow turbines). Axial turbines are not receiving much attention as an option for expanders in small ORCs. Hence, this study focuses on the design of an innovative small-scale, multistage, axial turbine in an ORBC (Organic Rankine Bottoming Cycle) for ICE (Internal Combustion Engine) waste heat utilization, which is competitive with volumetric expanders in terms of efficiency. The high rotational speed of axial turbines, which is their most criticized characteristic, is overcome by using partial admission. The main aim of this research is to develop an innovative small axial action–reaction multistage turbine with partial admission intended for an ORC. It is known from the turbine theory that the rotational speed has a positive effect on the expansion ratio and a negative effect on the height of blades, that is, the mean diameter. Therefore, in most cases, small turbines have high speeds and small mean diameters, which limit their application in ORCs. If the design of the flow part with partial admission is adopted, a satisfactory blade height can be achieved, and the mean diameter can be increased to reduce the rotational speed. In this way, the limiting factor for small turbine application in ORCs is eliminated. CFD analysis is used to investigate the characteristics of the organic fluid flow in the small organic turbine, with the aim of increasing the efficiency of energy conversion. Methods The main aim of this dissertation is to develop an innovative small axial action–reaction multistage turbine with partial admission intended for an ORC, which is comparable in terms of efficiency to existing volumetric expanders. The design process consists of the following steps. Mean diameter 2D preliminary design (PD). The PD has many repetitive calculations to find the relevant geometric characteristics of the nozzle and moving blade cascades, as well as the aero and thermodynamic performances of all turbine stages. This process is known as mean diameter 2D modeling, which is based on flow analysis of the turbine mean diameter and neglects flow property variations in the spanwise direction. The calculation equations and procedure, that is, the mathematical model for this approach, was developed using the Microsoft Excel® software as an in-house 2D code with the input parameters. The Microsoft Excel® software was connected to the REFPROP® database to determine the thermodynamic properties at characteristic points of the turbine stages. Subsequently, the geometric and gas dynamic characteristics of the newly designed axial, action–reaction, multistage turbine with partial admission were determined. Blade geometry generation. Nonstandard profiles were used to design the nozzle and moving blades of single-turbine stages. These profiles were obtained using the original software developed by the University of Zagreb, Faculty of Mechanical Engineering and Naval Architecture. Based on the obtained geometric parameters, the aerodynamically ideal profiles of all nozzle and moving blades were designed using the previously mentioned original software. It is an analytical method of profile design automated by the Matlab® code. The contours of the concave and convex sides of the blade profiles are polynomials of the fifth degree. Modeling and meshing of the nozzle and moving blade cascades. The aim of this step is to create and mesh the stator and rotor cascades from 2D models based on the previous step. The tool for this is the ANSYS Gambit® module, which is used for discretization, that is, dividing the passage, inlet, and outlet fluid domains into a suitable number of elements. Based on the nonstandard designed profiles, the 3D nozzle and moving blade cascades were modeled. The first stator cascade inlet and last rotor cascade outlet were modeled as pressure inlet and pressure outlet, respectively. The hubs, cases, and blades were modeled as walls, while the inlets and outlets of other cascades were set as interfaces. The internal cascade volume was set as a fluid. 3D CFD methodology. The limitation of the previously presented 2D mean diameter PD model of an innovative turbine is that it does not consider the flow inside the stator/rotor passages, which has an influence on providing efficient expansion through the passage. An accurate evaluation of the achievable small ORC turbine performance entails experimental data that are currently lacking and costly in terms of a prototype. Therefore, there is a need for a more advanced technique, such as 3D CFD analysis, to obtain more accurate predictions regarding the performance of a small ORC turbine. In this study, the simulations of steadystate 3D viscous, single-phase, compressible flow in both the nozzle and moving blade cascades of each stage in the entire volume (in the flow part) of the innovative axial turbine were performed using the ANSYS Fluent 16® solver. An element-based finite volume method was adopted to solve the 3D Reynolds-averaged Navier– Stokes equations with a k–ω based shear-stress transport (SST) turbulence model. The k–ω based SST turbulence model has the ability to capture the turbulence closure based on an automatic wall function treatment by identifying the nondimensional distance y + , which allows smooth shifting between the wall function formulation and low Reynolds number through computational grids without loss of accuracy. It produces a highly accurate prediction by the inclusion of transport effects in the flow separation prediction into the formulation of the turbulent viscosity (eddy viscosity). The SST model is a combination of the k–ω model (near the wall) and k–ε model (in the outer portion of the boundary layer ). A topology with a first-order upwind advection scheme was chosen because it is numerically stable. For all runs, the average value of y + was kept approximately at unity. If there is any information on the inlet turbulence, the medium turbulence intensity (intensity = 5%) is the recommended option. All CFD simulations were carried out with the convergence criteria in the range of 10−2 to 10−5 for all residual values and a time scale of 0.5/Ω. The solutions were obtained when the convergence criteria were satisfied. 3D CFD simulations of the nozzle and moving blade cascades. To achieve high isentropic efficiency of the turbine, the aerodynamic characteristics of the blade cascades were checked by numerical flow simulations. Then, based on the simulation results, they were improved by changing the geometries of the nozzle and moving blades. Modeling and meshing of the entire turbine flow volume. After improving the aerodynamic characteristics of the cascades, the partial admission (nozzle) and full (rotor) cascades connected with other dimensions of the turbine stages from the 2D PD were used to form the entire turbine flow volume. The nozzle cascades were all centered, with the Z axis being the centerline. The stator cascade interfaces are arcs, whereas the rotor cascade interfaces are annuluses. When ANSYS Fluent 16® connects them, the stator arc and equivalent arc portion of the rotor annulus are transformed into a single interface, while the rest of the annulus is converted into a wall. The entire flow volume (domain) was meshed using ANSYS Gambit®, and the simulation domain contained 12×106 cells. 3D CFD simulations of the entire turbine flow volume. Using the innovative turbine model, 3D CFD simulations were performed for the entire flow space (volume). The applied boundary conditions were the total temperature, total pressure, flow direction, and rotational speed as the inlet conditions. A rotational adiabatic wall was chosen for the blade, hub, and shroud surfaces. The static pressure was chosen as the output boundary condition. The results show that the quality of energy conversion based on the efficiencies of each cascade, each stage, and the entire turbine can be calculated. The simulations were computationally demanding in terms of RAM, CPU load, and hard drive space required for storing the ANSYS Fluent 16® case and data files. The comparison of 2D PD and 3D average differences of the Mach number, static temperature and pressure range from 2.2 to 13.1% for the stators and from 0.3 to 13.2% for the rotors. Generally, the 3D CFD simulation results agree well with the values obtained from the 2D PD. CFD verification. Regarding the output power and efficiency, owing to the lack of experimental data in small axial turbines working with organic fluids (high-density working fluids), the current 3D CFD simulation results were compared against 2D mean diameter PD results at the operational conditions, to assess the reliability of the PD model and provide an overall evaluation of the 3D CFD model. The maximum difference in terms of power is 6.8%, while that in terms of isentropic efficiency is 9.8%. The calculated parameters are in good agreement and these results are consistent with those which were obtained by other researchers. Results To develop an innovative and efficient small-scale axial multistage turbine with partial admission, an in-house hybrid design methodology, in which 3D CFD analysis in combination with a 2D mean diameter PD code for the calculation of the basic expander geometry, was used. Real gas formulations of isopentane as the working fluid were obtained using the REFPROP® software. Subsequently, 3D steady-state simulations were performed with the next results: 1. The CFD analysis shows that discretization, that is, mesh quality, has a significant impact on the simulation results. Full stator and rotor cascades must be meshed because periodic boundary conditions cannot be used for flow simulation in a partial admission turbine. 2. The simulations are computationally demanding in terms of RAM, CPU load, and hard drive space required for storing the ANSYS Fluent case and data files. 3. Simulations in ANSYS Fluent 16® must be started with isopentane as an ideal fluid, and after it reaches satisfactory convergence, real gas EOS should be enabled. If the simulations are started with real gas EOS, they will crash. 4. The 3D CFD simulation results show good agreement with the 2D PD values with respect to the turbine isentropic efficiency (9.8%) and power output (6.8%). In addition, the values of pressure, static temperature, entropy, and Mach number (speed of sound) at the inlet and outlet of each turbine stage generally agree well with the 2D results. The exception is the Mach number, which show significant discrepancies, especially in rotor cascades owing to the appearance of large values of local Mach numbers. However, it confirms that 3D CFD simulations can capture better the flow physics than the 2D PD. 5. Although this is a subsonic turbine, supersonic flow occurs locally throughout the flow space. Therefore, additional losses due to supersonic flow are expected locally. In addition, entropy increases in areas that are not supplied with fresh steam, which is a result of windage and segment losses of energy in partial admission stages. 6. The pathlines of 3D CFD simulations indicate that the flow in the turbine is not axisymmetric but 3D. In addition, local vortices are present at the flow border areas. 7. The turbine exhibited an isentropic efficiency of 74.8%, power output of 60.35 kW, and ORC thermal efficiency of 11.18%. These results highlight the potential of using a multistage axial turbine to enhance the performance of a small-scale ORC system. Conclusion Waste heat recovery technologies are important for further minimizing fuel consumption and CO2 emissions of ICEs. In this dissertation, an ORC is integrated into a 537 kW natural gas engine to evaluate the possibility of generating electricity by recovering the engine exhaust heat (from exhaust gases and engine cooling water). ORC systems are currently regarded as among the most potent candidates for recovering engine exhaust energy and converting it to electricity. The critical aspects for maximizing the efficiency of ORC systems are the selection of the working fluid and expander design. The main goal of this dissertation is to develop an innovative and efficient small-scale axial multistage turbine with partial admission. To achieve this goal, an in-house hybrid design methodology, in which 3D CFD analysis in combination with a 2D mean diameter PD code for the calculation of the basic expander geometry, was used. The dissertation resulted in a new type of small axial multistage organic turbine with partial admission, which is competitive with existing volume expanders in terms of efficiency. A more detailed and extensive CFD study were conducted to determine the influence of the geometric parameters of turbine stages (pitch of cascades, width of cascades, etc.) on the turbine isentropic efficiency, which will be used to attempt to obtain further efficiency gains from the design. Scientific contribution The scientific contribution of the dissertation includes: 1) Development of a numerical model for the investigation of the influence of the geometrical parameters of the flow part on the flow characteristics in the organic turbines; 2) Methodology for design small organic turbines with recommendations for achieving high isentropic efficiency; 3) A new type of small axial action-reaction multistage turbine with partial admission, intended for ORC, which in terms of efficiency is competitive with existing volume expanders