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.

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.

Table 4 shows the CFD numerical simulation results and errors. The errors

between the design and simulation values in the table are small and less than 3%, and the maximum error in the Mach number of the guide vane exit is 2.81% due to the supersonic flow of the guide vane gate exit. Overall, the simulation results agree well with the one-dimensional design values, and the design results basically meet the design requirements [5].

Figure 4 shows the change of pressure along the flow line, in which the change of pressure is small before the throat position of the guide impeller, and after the throat position, the change of pressure is large and drops to 0.58 MPa. The pressure in the impeller drops uniformly without any obvious jumps and fluctuations, which shows that the shape of the guide impeller and the impeller meets the design requirements.

According to Glassman’s empirical formula [11], the number of impeller blades can be calculated from Equation (1).

Z 1 = π 30 ( 110 − α ′ 1 ) tan α ′ 1 . (1)

K Z = Z N Z 1 . (2)

In the formula, α ′ 1 is the residual angle of impeller inlet airflow, Z_N is the number of blades of the guide impeller, and Z₁ is the ratio of the number of blades. The number of impeller blades is calculated as Z₁ = 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 show the effect of the ratio of the number of blades on the average speed and temperature at the outlet of the guide louvers, respectively. The average exit speed of the guide louvers shows an increasing trend with the change of the number of blades ratio, and the change amplitude decreases gradually, while the average temperature of the exit of the guide louvers is just the opposite with the change of the blade ratio. This is due to the increase in the number of blade ratio leads to an increase in the number of blades of the guide louvers, which increases the uniformity of airflow in the guide louvers

and reduces the generation of swirls; at the same time, the increase in the number of blades of the guide louvers increases the frictional losses in the guide louvers. As a result, the change in the average velocity at the outlet of the guide louvers slows down or even decreases as the number of blades increases.

The number of blade ratios and the number of impeller blades jointly affect the average exit velocity of the guide impeller, and Figure 5 is divided into five regions by the number of blade ratios. In regions I, II, III, IV and V, the blade ratios range from 1.19 - 1.32, 1.32 - 1.49, 1.49 - 1.56, 1.56 - 1.72 and 1.72 - 1.77, respectively. There is a difference in the priority of the numbers. The ranking in region I is: 19 > 21 > 17 > 13 > 15; region II is: 19 > 17 > 21 > 13 > 15, region III is: 19 > 17 > 13 > 21 > 15, region IV is: 17 > 19 > 13 > 21 > 15, region V is: 13 > 19 > 21 > 17 > 15 The pattern and order of the effect of the number of impeller and the number of blade ratios on the average exit temperature of the guide leaf grid in Figure 6 is exactly opposite to that in Figure 5, with the ranges of the blade ratios in regions I, II, III, IV and V being 1.19 - 1.29, 1.29 - 1.45, 1.45 - 1.55, 1.56 - 1.68 and 1.68 - 1.77, respectively.

Figure 7 shows the effect of the blade number ratio on the output power of the centripetal turbine. Due to the increase of the number of blades than the increase of the guide blade in the flow loss, resulting in the output power of the centripetal turbine are showing a downward trend, in order to the number of impeller blades 19 as an example, the blade ratio by 1.21 growth to 1.737 its output power by 31.2 kW reduced to 22.29 kW, indicating that the number of blades than to the turbine output power of the larger influence.

Figure 8 shows the effect of blade number ratio on the isentropic efficiency of

centripetal permeability. In the I region where the blade number ratio is 1.19 to 1.558, except the impeller blade number is 21, its isentropic efficiency is elevated with the change of blade ratio, when the impeller blade number is 21, its change trend is first elevated and then lowered and its peak is 89.1739%, the priority order of the impeller blade number in the I region is: 19 > 21 > 17 > 15 > 13; in the I region where the blade number is 1.588 to 1.558, its isentropic efficiency is elevated with the change of blade ratio. In the II region with the blade ratio of 1.72, when the blade ratio is 21, the isentropic efficiency shows a downward trend with the change of the blade ratio, and the rest shows an upward trend, and the priority ranking of the number of impeller blades in the II region is: 19 > 17 > 21 > 15 > 13; in the III region with the blade ratio of 1.72 to 1.77, the trend of the isentropic efficiency with the change of the blade ratio is consistent with the II region, and the priority ranking of the number of impeller blades in the II region is: 19 > 17 > 21 > 15 > 13. The priority order is 19 > 17 > 15 > 21 > 13.

In general, the blade number ratio in 1.19 - 1.588 region, the impeller blade number for 19 is the more ideal choice; And blade number ratio in 1.588 - 1.77 region, the impeller blade number for 17, 19 has better turbine performance. Consider the turbine performance and blade installation difficulty and other factors, this paper selects the impeller blade number is 17, blade number ratio is 1.5882 for the best blade number selection.

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.

Figure 9 shows the effect of the blade height of the guide cascade on the entropy efficiency and mass flow of the centripetal transparency. With the change of the blade height of the guide cascade, the mass flow rate shows a linear change trend, and the isentropic efficiency of the turbine shows an upward trend with the blade height, and its change range gradually decreases. According to the design working condition mass flow value of 1.1425 kg/s, the blade height of the guide vane is determined to be 2.7679 mm.

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

guide luffing; the isentropic efficiency of the centripetal turbine is increased by 3.84%, and the simulation results are more consistent with the design conditions.

Figure 10 shows the curve of the pressure versus flow line for the initial number of blades and the optimal number of blades. The trend of pressure in the guide impeller is approximately the same for both the initial and optimum number of blades. The differential pressure in the guiding impeller at optimum blade number increases, and the trend of pressure in the guiding impeller and the impeller is more uniform than before optimization.

Figure 11 and Figure 12 show the flow lines of the guide luff at the initially set number of blades and the optimum number of blades, respectively. Because of the high flow Mach number at the outlet of the guide luff, the excitation intensity

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.