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Appl. Sci. 2020, 10, 4168 16 of 26 An additional plane at rotor exit with contours of total pressure in the rotating frame of reference is plotted in Figure 9. The warm-coloured patches (regions tending to red) are areas with the highest total pressure, whilst cooler-coloured tones (tending to blue) are zones where total pressure is lost. The large tip clearance leakage area, visible at the rotor exit stream-section, adds to the amount of entropy/loss generation which leads to low efficiency values. Figure 9. Relative total pressure contours at rotor exit stream section. 3.3.3. Off-Design Turbine Analysis The turbine performance maps are generated using 2D CFD simulations rather than the full 3D ones, on account of the computational resources available as well as the long time required for the 3D simulations. The conditions extend over the range of total-to-static pressure ratio between 2 and 7 at three rotational speeds of 19,268 rpm, 21,409 rpm and 23,550 rpm. The variation of mass flow rate and stator outlet Mach number with the off-design conditions is shown in Figure 10. In general, the mass flow is expected to increase with higher pressure ratios but have lower values at higher rotational speeds, until choking occurs whereby the mass flow rate reaches its maximum asymptote. The radial turbine becomes choked at around Πts = 3, thus for the operating range of the design, the turbine will almost always experience supersonic flows. Minimum pressure loss region SS PS Tip Tip clearance leakage Rotor wake Hub P0,rel [bar] 375 370 365 360 355 350 345 340 335 330 Operating range 19268 rpm 21409 rpm 23550 rpm 1.5 1.4 1.3 1.2 1.1 1 0.9 0.8 0.7 DP ṁ [kg/s] (a) M4 [-] 19268 rpm 21409 rpm 23550 rpm DP 0.6 234567234567 Πts [-] (b) Πts [-] Non-choked region Figure 10. Variation of parameters with total-to-static pressure ratio at three rotational speeds: (a) Mass flow, (b) Stator outlet Mach number. Both total-to-total and total-to-static efficiency maps are plotted in Figure 11. The difference between the efficiency values is solely attributed to the loss in the available kinetic energy at rotor outlet, i.e., related to the exit swirl (α5), because the axial velocity is not a function of rotational speed (but is related to pressure ratio). The trend for both efficiencies are broadly similar except for the value difference due to the mentioned loss. The highest efficiency value occurs with a pressure ratio of aboutPDF Image | Radial Turbine Design for a Utility-Scale Supercritical CO2 Power
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