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Appl. Sci. 2020, 10, 4168 13 of 26 Table 9. 3D CFD performance results. Variable Unit Value m ̇ kg/s W ̇ MW ηtt % ηts % ψ - φ - R - Πts - 372.5 108.5 69.87 63.05 1.34 0.511 0.355 5.51 Figure 5 shows relative Mach number (Mrel) distribution (absolute for stator) at three locations across the span. At the throat of the stator, the flow reaches its supersonic conditions with the onset of the trailing edge shock; high losses are associated with shockwaves which are mitigated by changing airfoil shape to lower Mach number values. Low Mach number values near the rotor pressure side (PS) leading edge is caused by incorrect incidence and the propagating suction side acceleration interacting with the presence of the rotor tip clearance; the area of incidence loss near the pressure side lessens from 10% to 90% span with the mean relative flow angle at rotor inlet β4 = 28.22◦ which is lower than the calculated flow angle from throughflow analysis (β4 = 45.50◦). The low Mrel values on the suction side indicate a region of flow separation that begins at SS leading edge and grows along the flow as end-span is approached (also reported in Dong et al.’s work [24]). Figure 5. Relative Mach number distribution at three spanwise turbine passage locations: (a) 10% span, (b) 50% span, (c) 90% span. (a) 10% span (b) 50% span Tip Hub Leading edge separation (c) 90% span Mrel [-] SS PSPDF Image | Radial Turbine Design for a Utility-Scale Supercritical CO2 Power
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