THE INFLUENCE OF WORKING FLUID CHARECTERISTIC PARAMETERS ON TURBINE PERFORMANCE FOR THE SMALL SCALE ORC SYSTEM

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1 Proceedings of the ASME 203 Fluids Engineering Division Summer Meeting FEDSM203 July 7-, 203, Incline Village, Nevada, USA FEDSM THE INFLUENCE OF WORKING FLUID CHARECTERISTIC PARAMETERS ON TURBINE PERFORMANCE FOR THE SMALL SCALE ORC SYSTEM Lei ZHANG, Weilin ZHUGE, Xinqian ZHENG, Yangjun ZHANG State Key Laboratory of Automotive Safety and Energy Tsinghua University, Beijing, 00084, China ABSTRACT The small scale Organic Rankine Cycle (ORC) using a turbine as expanders is considered as one of the most efficient ways to convert the waste heat energies of automobile engine into electrical energy, in the power range from several kw up to dozens of kw. In general, two important factors must be taken into account when designing the ORC turbine: the real gas effects of the organic fluid and the high expansion ratio presented in the machinery due to thermodynamic and efficiency factors. The characteristic parameters of R245fa have great difference compared with air. When designing an ORC turbine, the initial problem is the influence of the working fluid characteristic parameters on the turbine performance. Similarity analysis method is used to analyze this problem. When using the similarity theory to design two similar operating conditions, gas constant R and dynamic viscosity μ are easy to be taken into account as they have a dimension; specific heat ratio κ is hard to be taken into consideration. In this paper, a high expansion ratio ORC turbine is generated for a small scale ORC system working with the organic fluid R245fa, and the influence of κ on the turbine performance parameters analyzed. Firstly, the turbine geometry is designed in an iterative process using the commercial design tool Concepts-NREC Rital program, and the designed operating condition is determined. Secondly, the similarity criterion numbers are deduced with no consideration of the specific heat ratio κ, and the similar operating condition is calculated by the deduced similarity criterion numbers. The results achieved by the onedimensional design software Rital shows that the deviation of similarity criterion numbers is small, which indicates that the two operating conditions are similar. Then, to verify the conclusion above, the flow field simulation using one channel model is conducted based on the R245fa operating condition and air operating condition using the computational fluid dynamics (CFD) code NUMECA-FineTurbo. However, deviations of the similarity criterion numbers from the CFD results are more than twice to those from the one-dimensional results. The larger deviation may indicate that the influence of the specific heat ratio κ cannot be ignored. After that, the distributions of the total pressure, total temperature, the relative Ma number and entropy in the nozzle and rotor channel are compared. These results show that except the total temperature the distributions of the other three parameters are very similar. The similar distribution may indicate that the specific heat ratio κ has little influence on the efficiency and expansion ratio, but κ has greater influence on the temperature and output power. All of these conclusions are made according to the simulation results, the accuracy should be verified through the test results. NOMENCLATURE T c working fluid critical temperature K p c working fluid critical pressure kpa T temperature K p pressure kpa ɛ expansion ratio ƞ efficiency G m mass flow rate kg/s N rotational speed rpm n s specific speed ʋ speed ratio R gas constant J/(kg K) μ dynamic viscosity Pa s κ specific heat ratio ψ flow coefficient ϕ loading coefficient C absolute speed m/s U rotational speed m/s γ rotor radius ratio D geometry parameter m P output power kw C p specific heat at constant pressure J/(kg K) Subscripts total parameter turbine inlet parameter Corresponding author. yjzhang@tsinghua.edu.cn Copyright 203 by ASME

2 2 turbine outlet parameter ts total-static θ tangential direction m normal direction 4 rotor inlet 6 rotor outlet INTRODUCTION In recent years the automobile industry has made great progress in improving the engine efficiency. Current produced gasoline engines are working with top efficiency of 30%-36%, while diesel engines already achieve about 40%-47% []. Nevertheless, today s engine efficiency is already reaching its technical limit and will not be sufficient to meet future fuel economy targets without additional measures. In the internalcombustion engine, more than half of the fuel energy is lost in the form of heat. For example, modern diesel engine can achieve a maximum efficiency of approximate 45%, and at least 55% of the energy from the fuel is released via exhaust gas and engine coolant. Hence, waste heat recovery (WHR) is considered as the most useful method to improve the engine efficiency. Several technologies can be used to recover energy from the waste heat of a combustion engine in order to generate electricity. In general, the technologies consist of turbomachines, thermo-chemical reaction, thermo-acoustic effect, thermo-electric effect, Sterling and Rankine cycles [2]. When comparing these technologies for automobile applications, two key factors should be kept under consideration. One is the utilization of the waste heat temperature range, the other is the efficiency improvement of the engine. Of all the technologies, the organic rankine cycle (ORC) can meet both of the demands above. The ORC can utilize the low temperature source such as the coolant heat in the automobile, and what s more, the engine efficiency improved by the utilization of the ORC can reach approximate 5% on average, with top improvements up to 8% in the gasoline engine []. Hence, the ORC is considered as the most appropriate way of all the methods in the current conditions. Figure shows typical components in a practical ORC system. In Fig., the pressurized working fluid is heated in the preheater, the evaporator, and the superheater to the superheated state from the subcooled liquid state by the waste heat, then the superheated vapor enters the turbine where it expands to the condensation pressure, during which mechanical work is transmitted to the application device through the shaft of the turbine; the exhaust vapor out of the turbine is cooled in the condenser and becomes the saturated or subcooled liquid, then the condensate is pressurized by a pump, which completes the thermodynamic cycle.[3] In automobile applications, since the temperatures of waste heat and coolant heat from internal-combustion engines are of low or moderate level, the best efficiency and maximum power output are usually obtained by using an organic fluid instead of water as the working fluid. This is because a properly-selected organic fluid can minimize the temperature difference between the waste heat and the working fluid. The higher the temperature of the working-fluid before the turbine, the higher the efficiency of the WHR system, and thus, the more useful work the WHR system can produce [3]. Fig. the components of the Rankine cycle system[3] Working fluids usually used for ORC applications may be classified into three types according to the slope of the saturated vapor line in the temperature-entropy (T-s) diagram: wet, dry and isentropic fluids. Corresponding ORC for these three types of working fluids are illustrated in Fig.2, where CP is the critical point, L and V indicate liquid and vapor phases. In general, inorganic fluids (such as water, ammonia, CO2, etc.) are wet fluids. Most organic fluids are either dry fluids or isentropic fluids, except for some small-molecule fluids such as methane and ethane. Benzene, R3 and R245fa are examples of dry fluids, which have a positive slope for the saturated vapor line if the state is not very close to CP. For this type of fluids, the expansion process ends in the superheated vapor (dry) region. R, R2 and R34a are examples of isentropic fluids, for which the saturated vapor line is almost vertical in the T-s diagram in most of the temperature range, and thus in an isentropic expansion process, the working fluid basically remains as the saturated vapor. Fig.2 Fluid types:(a)wet fluid;(b)dry fluid;(c)isentropic fluid. R245fa is commonly adopted as the ORC working fluid, considering the operation conditions of the cycle and its environmentally friendly characteristics [4-6]. When a turbine for ORC system is designed, two important facts must be considered: the real gas effects of the organic fluid and the high 2 Copyright 203 by ASME

3 expansion ratio presented in the machinery due to thermodynamic and efficiency factors [5-0]. When describing a working fluid, the essential parameters are the gas constant R, the dynamic viscosity μ and the specific heat ratio κ. The characteristic parameters of R245fa have great difference compared with air. When designing an ORC turbine, the initial problem is the influence of the working fluid characteristic parameters on the turbine performance. Similarity analysis method is used to analyze this problem. When using the similarity theory to design two similar operating conditions, gas constant R and dynamic viscosity μ are easy to be taken into account as they have a dimension; specific heat ratio κ is hard to be taken into consideration. In this paper, an ORC turbine is generated for a small scale ORC system working with the organic fluid R245fa, and the influence of κ on the turbine performance parameters is analyzed. Firstly, the turbine geometry is designed in an iterative process using the commercial design tool Concepts- NREC Rital program. Then, the similarity criterion numbers are deduced with no consideration of κ, and the similar operating condition is calculated by the deduced similarity criterion numbers. Finally, the flow field simulation was conducted based on the R245fa and air operating conditions and the performance parameters of the two operating conditions are compared to find out the influence of κ on these parameters. TURBINE DESIGN PROCEDURE The preliminary design of a turbine can be completed by the following several steps of parameters inputting and calculations: fluid properties selected operating conditions input design parameters defined nozzle and rotor preliminary geometry parameters calculation Firstly, the working fluid must be selected, which is quite a crucial step for the ORC turbine design due to the organic fluid special properties. In this case, organic fluid R245fa is selected as the working fluid in the turbine. Figure below shows its T-s diagram. The critical temperature T c is 427.6K, and the critical pressure P c is 3.65 MPa []. It is a typical dry fluid. Fig3. R245fa T-s diagram (the blue line is the liquid saturation line, the red line is the vapor saturation line) Secondly, the operation conditions of the turbine should be determined. In this step, the inlet total temperature and the rotational speed should be chosen. Three of the four following parameters also should be chosen: inlet total pressure, exit static pressure, mass flow rate and stage power. In this case, the boiling water is used as the heat source, so the inlet total temperature is limited to 364K, and the mass flow rate is given as 0.4kg. As the inlet total temperature T is assumed at 364K, and then the inlet total pressure p is estimated about 0.9MPa based on the R245fa thermodynamic property. In addition to this, the total-static expansion ratio is designed as 3.0. The main reason to set the value to 3.0 is to make sure that the flow is not supersonic because of the uncomfortable noise and low efficiency. Hence, the exit static pressure is determined as 0.3MPa. When deciding the rotational speed, two factors must be taken into consideration:.the rotational speed of the high speed generator can reach; 2.the specific speed of the operation condition should be in high efficiency region. These two factors restrict each other. If a high rotational speed is chosen to make sure the specific speed is in high efficiency region, this rotational speed may exceed in the speed limit of the generator. The rotational speed is set to 50000rpm to make a balance between the specific speed and the speed limit of the generator. The turbine specific speed is about 0.4 in this operation condition. In the end, the operation condition is determined as following: the inlet total temperature is 364K, the rotational speed is 50000rpm, the inlet total pressure is 0.9MPa, and the exit static pressure is 0.3MPa. Thirdly, the design parameters should be defined. Two methods: the method based on the flow and loading coefficient and the method based on the specific speed and speed ratio, are used for the preliminary design. The experiment parameters, such as the flow coefficient, the loading coefficient, the specific speed and speed ratio, used by the two method are recommended in a specific range based on large amount of turbine experiment performance data. In this case, the first method is used for the preliminary design. The flow coefficient ψ and loading coefficient ϕ can be expressed as: C U 4 6 () 4 C U 4 Where γ=r 6/r 4 is the rotor radius ratio, U 4 is the rotational speed in m/s, C θ4 and C θ6 are the tangential speed of rotor inlet and outlet absolute speed in m/s. C m 6 (2) U 4 Where C m6 is the rotor outlet normal speed in m/s. In this method, the recommended value of the flow coefficient is 0.2 to 0.3, and the value of the loading coefficient is 0.9 to.0. [2] The value of the flow coefficient is set to 0.25, and the value of the loading coefficient is set to In the final step, before the nozzle and rotor preliminary geometry parameters are calculated, several preliminary geometry should be defined, including the nozzle vane number, 3 Copyright 203 by ASME

4 rotor blade number, radius ratio of nozzle inlet and nozzle exit, rotor exit deviation angle, etc. Finishing these settings, the volute, nozzle and rotor preliminary geometry parameters are calculated in an iterative process to meet the design goals. The picture of turbine geometry is shown below (see Figure4). And the detail information about the turbine geometry is shown in Table Fig.4 the ORC turbine geometry in 3D Table the geometry of the designed turbine Volute Throat radius 53 mm Throat area mm 2 Nozzle Inlet radius 40 mm Exit radius 33 mm Blade height 2.2 mm Inlet blade angle 67 Exit blade angle 77 Number of blades 5 Rotor Inlet radius 32 mm Inlet blade angle 0 Exit tip radius 9 mm Exit hub radius 2.2 mm Exit blade angle -60 Number of blades The performance of the turbine working in this operation condition with R245fa is shown in Table2, which is calculated with Concepts-NREC design tool Rital. Table 2 the turbine performance in design point Performance parameter Mass flow rate 0.397kg/s Total-static efficiency 73.4% Output power 6.65kW U/C0 0.8 Specific speed SIMILARITY ANALYSIS Deducing the similarity criterion In this application, we assume that the flow in the turbine is adiabatic, steady, viscous and compressible. Dimensional analysis method is used to deduce the similarity criterion. All the independent variable which can influence the turbine performance and the main performance parameters are listed below: Mechanical characteristic parameters: the geometry parameter D and the rotational speed n; Working fluid characteristic parameters: the gas constant R, dynamic viscosity μ and specific heat ratio κ; Flow condition parameters: inlet and outlet total pressure p and p 2, inlet and outlet total temperature T and T 2, the mass flow rate G m; Turbine performance parameters: isentropic efficiency ƞ and output power P; In all these twelve parameters, the geometry parameter D can be ignored as the turbine is the same in the two working fluid calculation conditions. In this case, there exits four basic dimensions: M, L, t, T. Hence, four of all the parameters should be chosen as basic parameters, and seven similarity numbers should be deduced. The four chosen basic parameters are gas constant R, dynamic viscosity μ, the inlet pressure p and temperature T. As the specific heat ratio κ and isentropic efficiency ƞ are dimensionless parameters, the similarity number needs to be deduced are only five. Then the calculated results of the five similarity numbers based on the dimensional analysis method are listed below: Solving dimensional equation about n: n (3) p Solving dimensional equation about p 2 : 2 p p 2 (4) Solving dimensional equation about T 2 : 3 T T 2 (5) Solving dimensional equation about G m : 4 G p m (6) 2 RT Solving dimensional equation about P : 5 Pp (7) 2 T R T R In these five similarity numbers, π andπ 4 consist of the parameters of single valued conditions, so they are the qualitative criteria. According to the similarity theory, if the 4 Copyright 203 by ASME

5 qualitative criteria are the same, the other criteria can also be the same. However, the influence of the specific heat ratio κ cannot be taken into consideration because it is dimensionless. In this case, the deviation between κ of air and that of R245fa is more than 5%. This deviation of κ may lead to a result that even the qualitative criteria are the same, the other criteria may be significantly different. A rough estimate about the influence will be done in the following. The rough estimate using the software Rital According to the deducing results above and the design operation condition using R245fa as working fluid in the former part, the similar operation condition using air as working fluid is calculated. In order to make the two operating conditions similar, the qualitative criteriaπ andπ 4 must be the same. In these two qualitative criteria, dynamic viscosity μ is setting as the inlet dynamic viscosity. Once the dynamic viscosity μ, the inlet total pressure p and temperature T are given, the rotational speed n and the mass flow rate G m can be achieved. For air, the deviations of its properties change little in large range of pressure and temperature, so an approximate value of μ can be given in advance. The other two parameters are independent. Hence, in theory infinite operating conditions can meet the demand. In this paper, the similar operating condition is determined in two following steps:.the inlet total temperature is set to the same as the R245fa operating condition; 2.then give different inlet total pressure, calculate the speed n based on the same π, and then input the p and n into the software Rital to achieve the mass flow rate G m, choose the operating condition of which π 4 is the same as the R245fa condition. The calculation results of the operating condition is shown in Table3, and the comparison of the six similarity numbers in the two operating conditions is given in Table4. Table 3 the operating condition using air as working fluid property parameter Inlet total pressure 3000kPa Inlet total temperature 364K Outlet static pressure 000kPa outlet static temperature 288K The rotational speed 00000rpm Mass flow rate 0.766kg/s Total-static efficiency 72.2% Output power 54.53kW U/C Specific speed The results above shows that even if the deviation of the specific heat ratio κ is more than 5%, the two operating conditions can make a good similarity, especially in expansion ratio and isentropic efficiency. This result shows that κ has little influence on the similarity criteria in the similarity analysis. In the next part, the three-dimensional CFD simulation will be carried out to achieve more accurate results to verify the conclusion and make a deeper flow distribution analysis. Table 4 the comparison of the similarity numbers Similarity numbers R245fa Air Deviation π (given) 7.0e-8 7.0e-8 0 π % π % π 4 (given).65e+3.78e+3 7.9% π 5.23e+3.2e+3.6% Isentropic efficiency 73.4% 72.2%.6% NUMERICAL PROCEDURE The three-dimensional CFD simulation is carried out using the commercial CFD software FineTurbo. This software consists of the structured grid generation tools IGG and IGG/AutoGrid5, the three-dimensional Euler/Navier-Stokes solver EURANUS and the post processing tool CFView. One blade channel model One blade channel model is used in this flow field simulation case. The model consists of one nozzle vane channel and one rotor blade channel. The grid is generated in the tool IGG/AutoGrid5. In this tool, one parameter called the first cell width can be defined as the input parameter to generate the grids. This parameter is determined by the y + of the first cell close to the wall. In this case, the first wall y + is set to 0, and the calculation result of the first cell width is 0.003mm. Figure 5-7 show the blade-to-blade grid view and the blade-to-blade mesh topology configurations of the nozzle vane channel and rotor blade channel. Fig.5 one channel blade-to-blade grid view at midspan Fig. 6 the mesh topology configuration of nozzle channel 5 Copyright 203 by ASME

6 CFD RESULTS ANALYSIS Results convergence analysis Some calculated results are shown in Table7 and y + values near the wall are shown in Figure 8. Fig. 7 the mesh topology configuration of rotor channel Table 7 the convergence results of the two CFD case Variables R245fa model Air model Global residual 0e e inlet mass flow kg/s kg/s outlet mass flow kg/s s The grid size and quality generated by the tool IGG/AutoGrid5 is shown below. (See Table 5) Table 5 the grid size and quality of nozzle and rotor channel type Grid Size Mini. Orthogonality Max Aspect ratio nozzle rotor Max Expansion ratio Calculation configuration Fluid models In these two cases, the working fluids are air and R245fa. Air already exists in the working medium library, and R245fa is added into library. When adding this working fluid, the fluid type is set to real gas. The R245fa gas constant is set to 62J/(kg K), and the specific heat C p, the heat conduction K, dynamic viscosity μ consist of a group of data based on the Tabgen tool, which is a working fluid database software of FineTurbo. Boundary conditions In this CFD case, as there is no volute in the computational model, the nozzle inlet flow direction is determined in the inlet condition. The inlet condition is set to the type of mass flow imposed based on the velocity direction. The outlet condition is set to the static pressure imposed. The numerical values of the boundary conditions and initial condition are given according to the rough results from the software Rital. The values will not be discussed in details. Other main calculations to conclude the mathematical model are: modelling of turbulence and treatment of rotor-stator matching plane. All of these option parameters are shown below in Table 6. Table6 other CFD calculation configurations Parameter type Mathematical model Turbulent Navier-Stokes Equation Modelling of turbulence Spalart-Allmaras model Rotor-stator plane Conservative coupling by pitchwise row (b) Air Fig. 8 y+ value near the wall Table7 shows that both of the CFD case reach a good convergence result. Both of the global residuals are below the 0e-5, and deviation between inlet and outlet mass flow can be ignored. From the Figure 8, the y + values near the wall indicate that the calculation results are reasonable. The fine estimate about the similarity numbers by CFD Firstly, Table8 shows the property parameters of the turbine operation in these two cases; Table 9 shows the comparison of the similarity number in these two cases. In this CFD simulation, the volute is not taken into consideration, so the property parameters have significant deviation with the results of the one-dimensional calculation. Of all the six similarity criterion numbers, the deviations of π 3 (related to T) and π 5 (related to P) are large; the deviations of π 2 (related to p) and the isentropic efficiency are small. From the CFD simulation, it may indicate that the property κ of the working fluid has much influence on the similarity criteria related to T and P, but little on the isentropic efficiency and 6 Copyright 203 by ASME

7 expansion ratio. Then the flow field distribution characteristic will be compared in detail below to see the turbine performance between air and R245fa. Table 8 the property parameters in these two cases Property parameter R245fa Air Inlet total pressure 000kPa 3680kPa Inlet total temperature 349K 34K Outlet total pressure 330kPa 40kPa outlet total temperature 333K 242K Mass flow rate kg/s 0.766kg/s Output power 7.48kW 56.59kW Table 9 the similarity numbers in these two cases Similarity numbers R245fa Air Deviation π 6.28e e-8 9.4% π % π % π 4.87e e % π 5.63e+2.92e+2 7.8% Isentropic efficiency 8.0% 82.6% 2.0% The thermodynamic variables distribution on the flow field are shown below, Figure 9-2. (b) air Fig.0 total pressure distribution at midspan (b) air Fig.9 total temperature distribution at midspan (b) air Fig. relative Mach number distribution at midspan 7 Copyright 203 by ASME

8 influence on the pressure expansion ratio and isentropic efficiency results. Hence, the similarity numbers need to be revised according to the specific heat ratio κ. However, as the simulation model is only one channel model with no consideration of the volute, the conclusion achieved above need to be verified by the simulation model with the volute. And it is better to verify the conclusion by the experiment data. (b) air Fig.2 entropy distribution at midspan The figures above show the total temperature, total pressure, relative Ma number and the entropy distribution in the flow field. Figure 9 shows the total temperature distribution at the middle of the blade-to-blade view. In the rotor channel, the two cases have different temperature distribution. The main difference is that the temperature drops slower for R245fa condition. Figure 0 shows that the total pressure distribution are almost the same in the two models. In the two cases, the total-total expansion ratio changes little, about 6%. Figure shows the relative Mach number distribution. Two cases have nearly the same relative Mach number distribution from the nozzle channel to the rotor channel. Figure 2 shows the entropy distribution. The value of the entropy in the R245fa case is about one fifth of that in the air case in average. What s more, in the pressure side, there is a much larger low entropy region in the R245fa case than that in the air case. However, the efficiency of the R245fa case is lower than that of the air case. The main reason is that the total output of power in the R245fa case is only about one seventh of that in the air case. To summarize the results above, in terms of total pressure, relative Mach number and the entropy, the two case calculation results show that the distribution of these three parameters are almost the same. The total temperature distributions are different from the middle of the rotor channel to the outlet. In general, when the similarity numbers are used as the judgment to confirm whether two operating conditions are similar or not, the expansion ratio and isentropic efficiency are similar, but the similarity numbers related to temperature and output power are not. This results show that the specific heat ratio κ has much influence on the temperature and output power results, and little CONCLUSIONS In this paper, a high expansion ratio ORC turbine is designed for a small scale ORC system working with the organic fluid R245fa, and the influence of κ on the turbine performance parameters are analyzed. The flow field CFD simulation is conducted based on the R245fa operating condition and the similar air operating condition. The CFD simulation results comparison between the R245fa operating condition and the similar air operating condition illustrate that, in terms of expansion ratio and isentropic efficiency, the calculation result deviation of the similar air operating conditions is usually less than 0% compared with the original R245fa condition. However, if the temperature or output power is calculated by the similar air operating condition, the results may have a deviation more than 20%. The flow field deviation directly effects the accuracy of the turbine performance variables. The deviation of the variables such as temperature is much larger, but those of the total pressure, relative Ma number and entropy are smaller. The results above illustrate that the specific heat ratio κ has much influence on the temperature and output power results, and little influence on the pressure expansion ratio and isentropic efficiency results. Hence, the similarity numbers related to temperature and output power need to be revised according to the specific heat ratio κ. However, as the simulation model is only one channel model with no consideration of the volute, the conclusion achieved above need to be verified by the simulation model with the volute. And it is better to verify the conclusion by the experiment data. ACKNOWLEDGMENTS The authors would like to thank the National Basic Research Program of China (20CB707204) for the support. REFERENCES []. Boretti, A. A. (202). "Energy Recovery in Passenger Cars." Journal of Energy Resources Technology 34(2): [2]. J. Ringler, M. S., V. Guyotot and W. Hübner (2009). "Rankine Cycle for Waste Heat Recovery of IC Engines." SAE Int. J. Engines 2(): [3]. Ho Teng, G. R. a. C. C. (2007). "Waste Heat Recovery of Heavy-Duty Diesel Engines by Organic Rankine Cycle Part II: Working Fluids for WHR-ORC." SAE international. [4]. Seok Hun Kang, D. H. C. (20). "DESIGN AND EXPERIMENTAL STUDY OF ORGANIC RANKINE CYCLE 8 Copyright 203 by ASME

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