# Detailed Design and Aerodynamic Performance Analysis of a Radial-Inflow Turbine
## 5 Numerical Analysis
### CFD Results  
3D numerical simulations have been performed for design and off-design points. The mass flow rate map and the efficiency (total-to-total) map are illustrated in Figures 13 and 14. The maximum total-to-total efficiency is about 87.8% at a total-to-total velocity ratio of 0.73. The total-total efficiency at design point is about 1.3% less than the maximum efficiency. However, the total-to-total efficiency is more than 80% for a wide range of velocity ratio (\(0.5<v_{tt}<0.9\)) even at 80% of nominal speed. The corresponding points in Figures 13 and 14 show that the new design of the turbine will have a good aerodynamic performance at a low mass flow rate and off-design rotational speed. It shows that we could achieve a good design for a small radial-inflow turbine employed in an air cycle machine. In Figure 15, the total-to-total efficiency of the designed turbine was compared with that of current AUT turbine at the design speed. As illustrated in the figure, a 15% shift in efficiency is achieved at the design conditions. Figure 11: Grid independency for the rotor and nozzle blade rows. Figure 12: Comparison between experiments and CFD for the Ricardo RI turbine (2017). Figure 14: Mass flow rate map for the new design of RI turbine. Figure 13: Total-to-total efficiency map for the new design of RI turbine. Figure 15: Comparison between the efficiency of the designed turbine and the current version. Figures 16 and 17 present the evolution of total-to-static temperature ratio with pressure ratio and mass flow rate at various rotational speeds. The temperature ratio is important for the turbine in an air conditioning system due to the possibility of dehumidification and icing related to temperature drops. At the design point, the static temperature drops to about \(-25\)\({}^{\circ}\)C, while the static and total pressure is slightly more than 1 atm, making dehumidification possible. Since the low exit temperature for an RI turbine employed in air conditioning systems is unavoidable, the systems use an auxiliary passage to transfer hot air to the turbine exit. Although the possibility of the dehumidification is reduced by a reduction of mass flow rate and rotational speed, more studies and simulations with wet air are required. The meridional view of static pressure, static temperature and Mach number through stator and rotor flow passage have been presented in Figure 18. The exit station of stator has been slightly choked at design point with a maximum Mach number 1.05. The Mach and pressure contours presented in Figure 18 show that the flow expands gradually without any separation at hub. The static temperature at the exit station of the rotor change was from 273 K (0 \  
Figure 19 illustrates the streamline and Mach number contour at mid span (50% blade height) for design point conditions. According to the figure, a small local recirculation is noticeable along the first 10% of the suction surface of the rotor blade. The recirculation bubble size increases by reduction of rotational speed and mass flow rate (at off-design conditions). In Figure 20, the streamline and Mach contour at mid-span for the 65% of nominal rotational speed and PR\({}_{\text{fs}}\) = 2.0 is presented. Even at that off-design conditions, the local recirculation is only at first 20% of the suction surface. The effects of mass flow rate on the rotor leading edge recirculation are illustrated in Figure 21. As is shown in Figure 21, the recirculation is shifted from the suction surface to the pressure surface by a reduction of mass flow rate to 0.5 design value. The size of the recirculation is small enough (about 25% blade length) to have a noticeable negative effect on turbine efficiency. It shows that the new design of the RI turbine has an acceptable aerodynamic performance for a broad range of working conditions. Although circulation can be slightly improved by applying geometric modifications to the rotor blade leading edge (such as by using the elliptic leading edge), manufacturing costs will increase.