Flow field analysis of a turbo expander based on organic Rankine cycle for geothermal power system simulation

Over the years, people paid more attention to using renewable energy such as geothermal energy to decrease the dependency on fossil fuel energy. Organic Rankine cycle (ORC) can generate electricity by using low‐temperature heat sources, and geothermal energy is an ideal pollution‐free heat source that can provide continuous and stable energy. Meanwhile, the turbo expander, one of the essential components in ORC, has the advantages of high speed and single‐stage expansion ratio. In this work, we simulated and analyzed the flow field characteristics of the turbo expander under the assigned working conditions using CFX software. The results showed that the working fluid distributed uniformly in the volute, and there was no apparent whirlpool flow or secondary flow. The pressure near the leading edge of the impeller blade was sparse but became dense at the vicinity of the trailing edge. When the speed of the expander was 15000rad min−1 and the inlet pressure was 0.59 MPa, the isentropic efficiency reached the maximum value, and the change of the inlet temperature had little effect on the isentropic efficiency, which can be ignored in actual operation. The results guide in improving the practical application of geothermal energy.


| INTRODUCTION
Energy is the driving force and essential basis for human survival and economic development.With the rapid development of people's social economy and the improvement of people's material living standards, the demand for energy keeps increasing.At present, we hugely rely on nonrenewable energy sources, such as fossil fuels, which has limited reverses and the most harmful to our environment.So, we must pay attention to the exploitation of renewable energy.
Geothermal energy, 1,2 as a kind of renewable energy source, is not affected by temperature or weather change and has infinite reserves in the earth, and has been used as a heat source for more than a century.Commonly, geothermal energy is classified by temperature as low temperature (T < 90°C), medium temperature (90°C < T < 150°C), and high temperature (T > 150°C). 3Among them, low-temperature geothermal energy is the most widely distributed and is easy to be exploited.However, it is difficult to apply low-temperature geothermal energy continuously in large quantities due to its relatively low temperature.ORC systems can use different working fluids according to different grades of heat sources.The expander can operate at a lower temperature by using a low boiling point working fluid, which can absorb heat and evaporate.So it is considered as one of the active methods in generating electricity in the case of lowtemperature heat sources with ORC. 4 Turbo expander is an important part of the ORC power generation system.Because the thermal properties of the organic working fluid are different from that of water vapor, the organic working fluid expander has been studied by many scholars.To improve the efficiency of a turbo expander is still a hotspot for ORC technology to be applied to lowtemperature geothermal energy utilization.
Ahmadi et al. 5 performed a thermodynamic analysis of a geothermal energy-driven CO 2 power cycle where an optimal turbine inlet pressure exists, resulting in the highest combustion efficiency and lowest product cost rate.Ahmadi et al. 6 used a multiobjective optimization method combined with the NSGA-II algorithm to determine the optimal system performance from an economic and thermodynamic point of view.Ghazvini 7 studied hydrogen production technology based on geothermal energy.
Quoilin et al. 8 used R245fa, R123, n-butane, npentane, R1234yf, and R365mfc as the working fluid and studied thermodynamic and economic properties of the organic Rankine cycle (ORC) system.The results showed that when the system reached the maximum output power, the corresponding heat exchanger energy consumption and economy were not the minimum.The type of organic working fluid also determined the maximum output power and economic performance of the system.Sebastian Eyerer 9 used R245fa and R1233ZD-E as the working fluid and analyzed the possibility of using R1233ZD-E to replace R245fa in the existing system.Usman et al. 10 compared the application potential of the new working fluid R1233ZD-E and R245fa and established a mathematical model to predict the performance of the ORC system at different temperatures.Molés et al. 11 experimentally evaluated the hcFo-1233ZD-E as a substitute of HFC-245fa in a fully monitored micro-scale ORC system.Pang et al. 12 performed experimental studies and compared the performance of two pure working fluids, that is, R123 and R245fa, and their mixtures in ORC systems.Heberle et al. 13 focused on exergy and environmental analysis of low global warming potential fluids such as isobutane or isobutane-propane R1233ZD or R1234yf instead of R134a and R245fa.Molés et al. 14 evaluated low GWP fluids R1234yf and R1234ZE, which were used as alternatives to R134a for cryogenic heat sources in the ORC system.
Fiaschi et al. 15 the basic ORC under different working fluids (including mixtures) and circulating conditions (including supercritical circulation) was analyzed and compared thermodynamically and economically.Zhao et al. 16 according to the mechanism and characteristics of the expansion device used in the ORC system, the structure and parameter selection of the device during the design process was proposed.Shen et al. 17 established an energy flow model for a typical ORC system.Kim et al. 18 established the feasibility of a low-grade thermal ORC, determined the optimal operating parameters relative to the heat source conditions, and modified the model according to the data.Yang et al. 19 introduced the construction and test of a 500 KW geothermal ORC system for geothermal resources of abandoned oil wells in the North China oilfield.Sun et al. 20 proposed a double-pressure ORC driven by a geothermal heat source.Li et al. 21presented the thermodynamic design of the ORC system under a given temperature and mass flow rate and evaluated its performance under several working conditions.Liu et al. 22 optimized and analyzed the simple superheat cycle and four working fluids recycling schemes.Li et al. 23,24 studied, designed, and tested a small R245fa ORC system test bench rated at 5 KW power output and the effects of pump speed and heat source parameters on the expander and the system performance were studied experimentally.Algieri et al. 25 investigated the energetic performances of small-scale ORCs to exploit low-temperature geothermal energy.A parametric analysis has been carried out, and the influence of the operating conditions and ORC configuration on system behavior have been estimated.Alshammari et al. 26 proposed a design method of the turbo expander for waste heat recovery ORC system.
In the direction of numerical simulation, Putra et al. 27 analyzed the secondary flows in the turbine guide vane passage through experiments and numerical simulation.Christoph et al. 28 used CFD software to analyze the change of secondary flow in the centripetal turbine runner with adjustable guide vane.Abidat et al. 29 studied the flow characteristics in the vortex chamber of a centrifugal turbo expander with RNG K-ε and SST model.Sauret et al. 30 selected R142a as the working fluid to perform thermodynamic calculations on the centripetal turbo expander, and used the CFX software to simulate the flow field inside the centripetal turbine, and analyzed the variable conditions.The results showed that the Mach number was an important factor that affects the turbine efficiency and the force of the moving blade, and the gas state equation selection NIST database defines the gas was more realistic than the P-R equation.Harinck et al. 31 designed a centriolar expander with a high expansion ratio, selected toluene as the working fluid and used CFD software to analyze the flow of the working fluid in the guide vane.Song et al. 32 established a one-dimensional analysis model for the intake turbine of the ORC system and studied the effect of workflow properties and ORC system working conditions on the performance of the expander.
Based on the above literature review, this paper first created three-dimensional models of the guide vane, moving vane, and the volute of the turbo expander.Then the CFX software was used to carry out the threedimensional numerical simulation and described the flow field characteristics induced by the turbo expander, the guide vane, and the moving vane, respectively.Moreover, according to the results obtained from the numerical simulation, the variable operating conditions of the turbo expander were analyzed, and the effect of different speeds, different inlet pressures, and different inlet temperatures on the efficiency and power of the expander were studied, respectively.

| GEOTHERMAL ORC SYSTEM FLOW DESCRIPTION
The ORC system, which mainly consisted of an evaporator, a turbo expander, a condenser, and a working fluid pump, is shown in Figure 1.First, geothermal water entered the evaporator to exchange the heat with the organic working liquid at a low boiling point and heated the organic working liquid to steam.Second, the evaporated steam passed through the turbo expander to push the impeller to rotate and drive the generator, by which electricity was generated.Third, the steam was cooled to liquid with the condenser.After that, the pump was used to push the liquid back to the evaporator for another cycle.
The inlet liquid of the evaporator in the entire system is the geothermal water with a temperature of 90°C.The inlet and outlet temperatures of the cooling water are 25°C and 35°C, respectively.The evaporation temperature of the refrigerant is 80°C.The condensation temperature is 35°C, and the outlet temperature of the heat source is 71°C.Besides, the rated power is 200 kW, the organic working fluid is R245fa, the turbine efficiency is 0.8, the generator efficiency is 0.96, and the organic working pump efficiency is 0.85.The parameters of the system to be studied are shown in Table 1.
To simplify the calculation, several assumptions were made in this work: (1) the flow rate of the heat source water, the organic working fluid, and the cooling water kept constant under different working conditions; (2) the pressure loss through the whole process was ignorable; (3) efficiency of the expander and working fluid pump was fixed.
The thermodynamic design flow chart of the turbo expander is shown in Figure 3.According to the given design requirements and the parameters of the turbo expander obtained from the calculation of the ORC system, as shown in Table 2, the appropriate variable parameters were selected.Through REFPROP software, the enthalpy and entropy of the inlet and outlet of the turbo expander can be obtained, with the enthalpy drops of the turbo expander, the enthalpy drop distribution of the guide vane and the moving vane, and the aerodynamic parameters of the triangle of the inlet.The geometric dimensions and aerodynamic parameters of the turbo expander are shown in Table 3.
According to the parameters of the turbo expander listed in Table 3, the geometric shapes of guide vanes and The process diagram of the organic Rankine cycle.

F I G U R E 2 T-S diagram of the organic Rankine cycle (ORC).
T A B L E 1 System parameters of the geothermal organic Rankine cycle (ORC) power system.
Momentum equation: Energy equation:

| Turbulence equation
Menter 35 came up with the model SST (Shear stress transport).The model can simulate the separated flow with inverse pressure gradient in the turbulence model, so it is widely used in practical engineering.This paper mainly used SST turbulence model, which was apply the k-ɛ model to the mainstream area, the k-ω model in the near wall area, using a mixed function to combine the two models, thus synthesizing the advantages of the k-ɛ model and the k-ω model.
The k-ω model 36 has been revised by the eddy viscosity coefficient μ t and can be expressed as GUO ET AL.
| 3963 The transport equation of turbulent kinetic energy k and turbulent frequency ω is The value of these parameters in the model (γ,β,σ K ,σ ω ) can be expressed by the following formula: Among them, the mixing function F 1 is defined as ( ) .
The mixed function F 2 is defined as ( )

| Gas equation of state
The Peng-Robinson equation is an improvement of the Reddlich-Kwong equation.The accuracy of the Peng-Robinson equation in predicting vapor pressure and liquid density is much better than that of the Reddlich-Kwong equation.Moreover, the Peng-Robinson equation can be applied to polar materials and vapor-liquidvapor-liquid twophase systems.Therefore, for the numerical simulation of the turbo expander, the Peng-Robinson equation is more reasonable and more accurate than the Redlich-Kwong equation Two generalized parameters included in the Peng-Robinson equation are  ) m ω ω = 0.37464 + 1.54226 − 0.26992 .

| Meshing of volute and mesh independence verification
The mesh analysis function was used to assess the grid quality until the optimal grid was obtained.In this paper, unstructured grids were used, as shown in Figures 8  and 9, and the number of meshes was 3.23 × 10 6 .

| Grid division of guide vane and moving vane and verification of grid independence
There is no correlation among the grids of vanes and moving vane, as shown in Table 4.The grid-independent verification of the turbo expander model used in the simulation is described in Table 4.The table shows that the difference between the working fluid flow rate and the expander efficiency corresponding to the three meshing results is not significant.Finally, the third meshing result was adopted.After meshing, the grid number of guide vanes and impeller blades is 541,000 and 945,000, respectively, as shown in Figures 10 and 11

| Analysis of flow field result of the turboexpander
Figure 12 shows the full-level distribution of the four aerodynamic parameters of the turbo expander.After absorbing heat in the evaporator, the low-temperature organic working fluid changed into saturated steam and flowed into the inlet of the volute.The steam was evenly distributed in the volute.It then entered the guide vane to expand and accelerate and then entered the moving blade to expand and push the impeller to rotate.From Figure 12A,B, it can be found that the distribution of pressure and temperature in the guide volute was relatively uniform, and there were no secondary vortices and reflux zones in the whole volute.But, there were high-pressure, hightemperature zones on the pressure surface of the guide vane, where there were flow inhomogeneity and air mixing phenomena.Meanwhile, the pressure and temperature in the moving vane decreased gradually, indicating that the working gas continued to expand in the moving vane .
Figure 12C showed the velocity streamline inside the turbo expander.The overall flow field of the organic working substance in the guide volute and the moving blade was pretty smooth.The streamline distribution in the guide volute was relatively regular and axisymmetric.No obvious secondary vortices or rotations of organic working substance occurred.The flow field in the guide vane exhibited nonuniformity, and there was gas mixing at 40% of the relative chord length on the pressure side of the guide vane.When the working fluid flow passed through 50% of the relative chord length of the guide vane, the flow field of the organic working fluid tended to be stable, and the streamline was smooth.
From the Mach number distribution in the turbo expander as of Figure 12D, it can be seen that the Mach number of organic working substance gas was basically unchanged, and its distribution was uniform.The change of Mach number mainly occurred at the outlet of the guide vane and the trailing edge of the impeller.There the organic working material expanded rapidly, completing the conversion from thermal and pressure energy to kinetic energy.There were peaks of Mach number at the outlet of guide vane.The Mach number of the organic working substance at the outlet of the guide vane was about 1, and the velocity of the working substance at the outlet of the moving vane exceeded sound speed.
From Figure 12, we can see that the organic working substance had completed the conversion from heat energy to work in the turbo expander.The high-temperature, highpressure organic working substance flowed into the guide volute.After the expansion acceleration was completed in the guide vane, the pressure and temperature of the organic working substance decreased continuously while the speed of the moving vane got higher, which pushed the rotating blade to rotate and output work.F I G U R E 13 Velocity vector of the volute.

| Flow field analysis of volute
Figure 13 shows the velocity vector of the volute, indicating that the velocity vector line was smooth and evenly distributed, and the velocity was basically symmetrical in the exit of volute, which ensured the uniformity of the guide vane inlet and the overall flow performance.Meanwhile, the flow of organic working substance gas in the guide volute was spiral, and there was no significant whirlpool structure or secondary flow.
From Figure 13B, it can be seen that there was no air mixing in the tail of the volute when the air entered from the volute entrance, and the flow field was stable.As shown in Figure 14, the pressure on the guide volute gradually decreased from the outer circular wall to the inner outlet section, and only the pressure at the volute was affected by the inlet mainstream, but the effect was minor.The pressure contour in the nozzle was vertical to the speed direction, and the pressure dropped uniformly.The pressure inside the volute decreased evenly from the outer wall to the inner wall, and the pressure distribution at the circumference near the outlet was basically the same, which helped the organic working gas enter the guide blade.As can be seen from the cross-sectional view of the volute from Figure 14B-D, there was no decrease at the cross-section of the takeover pipe.The pressure decreased from the outside to the inside.As a result, a high-pressure zone at the outlet of the outer wall and a low-pressure zone at the outlet of the inner wall was produced.
From Figure 15, we can see that the internal temperature field distribution and the pressure field were similar, and the temperature field contour was vertical to the velocity direction.From Figure 15C-F, the temperature in the external pipe decreased gradually due to heat dissipation.It can be seen from the cross-sectional view of the volute that the temperature contour in the volute coincided with the temperature contour in Figure 15A.The temperature F I G U R E 14 Pressure contour diagram of volute.As shown in (A), the pressure on the deflector housing gradually decreases from the outer circular wall to the inner outlet section.From the cross-sectional view of the volute in (B-F), it can be seen that the pressure drops from the outer to the inner side.
F I G U R E 15 Temperature contour diagram of volute.From (A), it can be seen that the temperature on the deflector housing gradually decreases from the outer circular wall to the inner outlet section.From (B-F), the temperature in the external pipe decreased gradually due to heat dissipation.
decreased from the high-temperature area on the outer wall to the low-temperature area on the inner wall.The temperature at the outlet reached the minimum, and there was no turbulence in the flow field.

| Flow field analysis of guide vanes and impeller blades
Figure 16 shows the pressure distribution in the guide vane and the moving vane of the turbo expander.It can be seen that the pressure isoline on the guide vane was vertical to the direction of the flow channel.The pressure decreased along with the flow channel, and the working fluid expanded more uniformly.And there was a fluctuation of the pressure at the outlet of the suction surface, mainly due to the expansion of the organic working fluid in the chamfered part.In the flow direction of the moving blade, the flow of organic working fluid expanded in the channel, and the pressure continued to decrease.At the entrance of the moving blade, the static pressure contour was ideally distributed, which was basically vertical to the direction of the flow field, and there was no return flow and vortex.
From Figure 17, we can see that the flow line of the deflector was relatively smooth, without large vortices, and there was a relatively high-velocity zone near the suction surface at the outlet, which corresponded to the local lowpressure zone near the trailing edge of the suction surface mentioned above.The enlarged view of the trailing edge section showed that there were different flow directions at the trailing edge due to the influence of the trailing edge thickness on the working fluid flow, resulting in a local trailing flow loss.we can conclude that the guide vane had a certain thickness at the outlet, which affected the efficiency of the turbo expander.At the trailing edge of the moving blade, it can be seen that the arrow direction of the velocity vector had rotated.The eddy current generated at the trailing edge made the pressure field at the blade's trailing edge larger and decreased toward the surrounding areas.At the top of the moving blade, due to the existence of the rounded corner, there was a shock wave in the air flow, a pressure difference existed between the two sides at the front edge of   The effect of rotate speed on isentropic efficiency and expander power was shown in Figure 18.When the range of rotate speed varied from 6000 to 24,000 rad min −1 , the isentropic efficiency of the turbo expander first increased and then decreased, but the power of the expander increased continuously.It was easy to find that the rotate speed had a great impact on the performance of the turbo expander.When the rotated speed was 15,000 rad min −1 , the isentropic efficiency was the highest (about 85%), and the expander power was 245 KW, which was the best parameter.So, the optimal rotate speed was 15,000 rad min −1 .

| Effect of inlet pressure
Figure 19, with the increasing inlet pressure from 0.5 to 0.8 MPa, the turbo expander power linearly increased, but the isentropic efficiency of the turbo expander dropped sharply and then increased.When the inlet pressure rose to 0.7 MPa, the isotropic efficiency of the turbo expander decreased to 83.5%, which was the lowest point.With inlet pressure increasing from 0.5 to 0.8 MPa, the turbo expander power rose from 180.28 to 246.35 kW, which increased 36.6%.Combining Figure 18, when the inlet pressure was 0.59 MPa, the isentropic efficiency of the turbo expander was 85%, so we chose the inlet pressure of 0.59 MPa.

| Effect of inlet temperature
Figure 20 shows the influence of inlet temperature on the isentropic efficiency and turbo expander power, which indicates that the output power of the expander increased and the efficiency decreased with the rising inlet temperature.When the inlet temperature changed from 360 to 410 K, the output power of the expander increased from 251.45 to 275.48 KW, which increased 9.5%.On the contrary, the change of the isentropic efficiency was minor, which was less than 2.8%.It can conclude that the inlet temperature variation had little influence on the isentropic efficiency.So the influence of inlet temperature on the expander performance can be ignored.
The flow field analysis reveals 37,38 that vortices were generated at the trailing edge because the guide vane has a specific thickness at the exit.Shock waves appeared in the airflow at the top of the moving blades due to blade rounding.All these processes generated internal thermodynamic losses.Also, due to fluid friction, kinetic energy was converted into thermal energy, resulting in energy dissipation, and the energy dissipation caused by friction also causes internal flow losses.At lower rotational speeds, the losses due to fluid friction were smaller, and as the rotational speed increased, the flow shape was improved, and the increase in rotational speed has a positive effect on isentropic efficiency.While at higher rotational speeds, the energy loss increased with the increase in rotational speed, and the increase in speed can significantly damage the flow field, which is not conducive to the improvement of isentropic efficiency.The operation of a scroll expander in over-expansion mode is more detrimental to performance than operating under-expansion mode.So as the pressure increased, the isentropic efficiency of the turbo expander decreased.

| CONCLUSIONS
According to the characteristics of low-temperature geothermal energy in this study, an expander based on ORC power generation was designed.CFX was used to simulate the flow field of the turbo expander in the geothermal energy ORC system.Through the flow field analysis of the turbo expander, volute, guide vane, and the rotor blade and the variable working condition analysis of the turbo expander can be obtained as follows: efficiency, and an increase in inlet pressure was also detrimental to the isentropic efficiency.The optimum rotational speed of the turbo expander was 15,000 rad min −1 and the optimum inlet pressure was 0.59 MPa.
In this study, an expander based on ORC power generation was designed based on the characteristics of low-temperature geothermal energy, and this device can be used to productively utilize waste heat and reduce thermal pollution.

F I G U R E 4
Three-dimensional diagram of guide vane.F I G U R E 5 Three-dimensional diagram of impeller blade.F I G U R E 6 Three-dimensional diagram of volute.F I G U R E 7 Schematic diagram of whole turbo expander.

α
in Equation (5) is a function of specific temperature Tr and eccentricity factor ω

F I G U R E 8
The meshing diagram of volute inlet.

F I G U R E 9 9 F
The mesh created for the whole volute.T A B L E 4 Grid independent verification of vane and moving vane blade for turboexpander.I G U R E 10 The meshing diagram of guide vane.

F
I G U R E 11 The meshing diagram of impeller blade.T A B L E 5 Boundary and initial conditions of nozzle and impeller blade for the 200 kW turboexpander

F I G U R E 12
Distribution of thermal parameters of the turbo expander.

F
I G U R E 16 Pressure contour of guide vane and impeller blade.
the impeller.So the working fluid on the suction surface side expands, the speed increases, and the pressure decreases.The working fluid on the pressure side was compressed by the impact, the speed decreased, and the pressure increased.

4. 4 |
Analysis of the turbo expander under different working conditions 4.4.1 | Effects of rotate speed

F
I G U R E 17 Velocity vector diagram of different blade positions.F I G U R E 18 Isentropic efficiency and expander power as a function of rotate speed.
(a) From the flow field analysis of the expander, the pressure and temperature distribution in the volute were relatively uniform, and there were uneven flow and air mixing in some regions of the guide vane, and the working fluid gas continually expanded in the moving vane.The flow field of the organic working fluid in the guide volute and the moving blade was relatively smooth.And the velocity streamlines distribution in the guide volute was relatively neat and had axial symmetry.(b) Analysis of the volute flow field showed that the velocity vector line was smooth and evenly distributed.The flow of the organic working fluid gas in the guide volute was spiral, with no significant vortex structure or secondary flow.The pressure on the guide volute gradually decreased from the outer circular wall to the inner outlet section, and only at the volute tongue was the pressure affected by the inlet mainstream.(c) Flow field from the guide vane and moving vane, the pressure decreased along the flow channel, and the expansion of the working fluid was relatively uniform.In the moving blade along the flow direction, the organic working fluid flow expanded in the channel, and the pressure was continuously reduced.(d) Analysis of the variable operating conditions of the expander showed that either too high or too low a rotational speed was detrimental to the isentropic F I G U R E 19 Isentropic efficiency and power changes as a function of inlet pressure.F I G U R E 20 Isentropic efficiency and turbo expander power as a function of inlet temperature. 34 34e initial parameters of the turbo expander.34 Design flow diagram of the turbo expander.T A B L E 2

Table 5 shows
the values of parameters in preprocessing.