Design and Blade Number Ratio Analysis of Organic Rankine Cycle Radial-Inflow Turbine on Vehicle

The organic Rankine cycle is widely used in industrial waste heat, engine waste heat and other waste heat recovery applications, and as a key component of the system, it affects the efficiency and output power of the system. In this paper, a centripetal turbine is designed for the organic Rankine cycle, using vehicle exhaust gas as the heat source. Numerical simulations are performed to analyze the effect of the ratio of the number of guide vane blades to the number of impeller blades (vane number ratio) on the turbine performance and flow field. The results show that the effect of the number of impeller blades on the turbine entropy efficiency, the average exit velocity and the temperature of the guiding grate becomes less and less as the ratio of the number of blades increases. The optimum turbine performance is obtained when the number of impeller blades and the ratio of the number of blades are 17 and 1.5882, respectively, and the expansion performance of the guide impeller is improved and the isentropic efficiency of the turbine is improved by 3.84% compared with the preliminary number of blades.

energy [2], therefore, the engine of the exhaust waste heat utilization technology has a huge potential for energy saving and emission reduction, improve fuel utilization. The organic Rankine cycle is one of the most effective ways to recover the exhaust waste heat of the engine [3] [4]. As the core component of the organic Rankine cycle that affects the work done, the performance of the turbine expander directly affects the performance of the entire system. Therefore, it is important to design and optimize the turbine expander for the exhaust waste heat of the engine to improve the system performance.
Yue Song [5] designed a centripetal turbine for a medium-high temperature solar heat source and performed numerical simulations to verify the accuracy of the simulations by comparing the agreement between the simulated and designed values. Pei [6] designed a 3.3 kW radial turbine expander with 71% and 65% efficiency in simulations and experiments, respectively. Liu Pan [7] focused on the effect of lobe head clearance on centripetal turbulence. Numerical simulation and aerodynamic performance analysis of the turbine with different lobe top clearances were carried out by CFX, and the results showed that the lobe top clearance influenced the aerodynamic characteristics of the flow field. The results show that the lobe head clearance affects the aerodynamic characteristics of the flow field, and the temperature is the main cause of the deformation of the blades and disk during the turbine operation. Li Yan [8] optimized the structure of the centripetal turbine nozzle and impeller. The results showed that the overall performance was improved after optimization. It provides new ideas for the optimization method of centripetal turbine. Song Liming [9] proposed an automatic design parameterization method for the impeller based on the energy method, and carried out the aerodynamic optimization design for the small spreading chord ratio after loading impeller, and verified the correctness and practicality of the method.
The current research on centripetal turbines mainly focuses on the structure and variable operating performance of the guide impeller and the impeller, but there is a lack of research on the relationship between the number of impeller and impeller blades and their coupling. Therefore, in this paper, we design a centripetal turbine suitable for on-board organic Rankine cycle. The numerical simulation is used to analyze the effect of the number of blades on the performance of the turbine, and the performance and flow field are compared with that of a centripetal turbine with a preliminary number of blades.

Determination of System Working Principle and Turbine
Design Condition

Organic Rankine Cycle Systems
The system structure of organic Rankine cycle is shown in Figure 1, generally consisting of evaporator, condenser, pump and turbine expander four parts. Its workflow is: the engine high temperature exhausts in the evaporator and circulating workpiece heat exchange, so that the circulation of workpiece into high pressure and high temperature steam turbine expander work, heat energy into mechanical energy, low temperature and low pressure steam work into the condenser after cooling into the workpiece pump pressurization, into the next cycle.

Determination of the Centripetal Turbine Design Condition
The exhaust gas of a six-cylinder inline heavy-duty diesel engine is selected as the heat source, and the main technical parameters under the set conditions are: exhaust gas outlet temperature of 573 K, displacement of 13 L, maximum torque of 2500 N-m, exhaust gas mass flow rate of 0.75 kg·s −1 . The outlet temperature of the heat exchanger is set at 373 K, assuming that the system is running in a steady state, ignoring the pipeline pressure drop and heat loss [10]. The main components of the exhaust are shown in Table 1.
The thermophysical parameters of the exhaust gas are calculated using the thermophysical calculation software REFPROP according to the composition of the exhaust gas and the thermodynamic model of the organic Rankine cycle. The design parameters for the centripetal turbine are calculated as shown in Table 2.

Pneumatic Design of the Centripetal Turbine
The thermal and pneumatic design of the centripetal turbine is carried out by  Table 3.
According to the calculated dimensional parameters of the centripetal turbine impeller and the guide impeller, the selected coordinates of the TC series pneumatic impeller of MPEI were imported into UG software to generate the pattern World Journal of Engineering and Technology  curves and model the guide impeller. ANSYS-BladeGen software was used to enter the dimensional parameters of the impeller in the thickness/angle mode, and the impeller was modeled by radial spatial stacking of different leaf height cross-sections. The completed three-dimensional models of the guide vane and impeller are shown in Figure 2 and Figure 3. Import the coordinates of the guiding impeller runner and impeller model into TurboGrid and divide the structured mesh. The inlet boundary conditions are total pressure and total temperature inlet, the outlet boundary conditions are static pressure, the heat transfer model is Total Energy model, and the turbulence model is k ε − model.

Effect of Blade Number Ratio on Centripetal Turbulence Performance
According to Glassman's empirical formula [11], the number of impeller blades can be calculated from Equation (1).
In the formula, 1 α ′ is the residual angle of impeller inlet airflow, Z N is the number of blades of the guide impeller, and Z 1 is the ratio of the number of blades. The number of impeller blades is calculated as Z 1 = 14.2803. When the conditions allow, it should be ensured that there is no convention between ZZ and ZZ, and it is better to use prime numbers, followed by odd numbers [10].
Therefore, the effect of the number of blades ratio on the turbulence performance is investigated when the number of impeller blades is 13, 15, 17, 19 and 21, respectively.
The main function of the guide louvers is to convert the energy of the materials into kinetic energy with high efficiency, and the lower the outlet temperature and higher the speed of the guide louvers, the better the performance of the guide louvers. Figure 5 and Figure 6 Figure 6 is exactly opposite to that in Figure

Influence of the Height of the Guide Vanes on the Mass Flow Rate
The blade height and blade exit angle of the guide cascade have a significant effect on the flow rate of the centripetal turbine [12]. In order to reduce errors and make the mass flow more consistent with the design conditions, the influence of the blade height of the guide cascade on the mass flow and isentropic efficiency of the centripetal turbine is analyzed, and the blade height of the guide cascade is determined.  Table 5 shows the numerical simulation results for the initial number of blades versus the optimal number of blades. Compared with the initial number of blades, the exit temperature of the guide luffing is reduced by 4.012 K and the exit velocity is increased by 14.352 m/s, which improves the performance of the       is higher, which deflects the flow at the outlet of the guide luff. The deflection of the flow at the outlet of the guide luff is improved at the optimal number of blades, which is due to the increase in the number of blades of the guide luff, which improves the uniformity of the airflow in the guide luff. Figure 13 and Figure 14 show the clouds and flow lines of the Mach number distribution at 50% of the leaf height for the initial number of blades and the optimal number of moving leaves. Due to the existence of negative impulse angle at the moving leaf inlet, there is a low Mach region at the pressure surface of the moving leaf inlet for both the initial number of leaves and the optimum number of leaves, which causes airflow separation, which is improved at the optimum number of leaves due to the increase of the number of moving leaves. From the figure, it can be seen that at the optimum number of leaves, due to the back pressure gradient, there is a vortex at the suction surface of the moving leaf, which increases the turbulent flow loss and requires further optimization analysis of the moving leaf shape and the meridional flow path.

Conclusions
In this paper, the design and numerical simulation of the centripetal turbine were carried out with R123 as the working mass for the engine exhaust heat source. The results show that the relative errors between the simulation results  2) By comparing the initial number of blades with the optimal number of blades, the performance of the guide louvers was improved at the optimal number of blades, and the isentropic efficiency of the turbine was improved by 3.84%. The pressure change along the flow line was more uniform at the optimum number of blades, and the deflection of the flow line at the outlet of the guide impeller was also improved. The airflow separation at the pressure surface at the impeller inlet was reduced, but the swirl generated at the suction surface increased the flow loss in the impeller, requiring further analysis and research.