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Appl. Sci. 2018, 8, 2038 5 of 16 edge loss, rotor backface windage loss, and rotor exit energy loss. All of these loss models are well established by some scholars and widely used in numerous open literature reports. The loss happened in the nozzle is evaluated by the model presented by Rodger [7], as Equation (3): C42 0.05 3tanα4 scosα4 ∆hn=2Re0.2 s/c + b . (3) The incidence loss that happened in rotor inlet is caused by the difference between flow direction and rotor blade direction, and it is the energy used to turn the flow to the correct direction. The model presented by NASA [6] is adopted, as Equation (4): ∆hi = 12W42 sin2β4 − β4,opt. (4) The rotor passage loss is a summation of different loss items that happened in the rotor passage. It mainly concerns the cross flow and the secondary flow. The CETI (Concepts NREC LLC, White River Junction, VT, USA) passage loss model presented by Whitfield [8] is selected here, as Equation (5): L H r2cosβ 1 5 b5 W42+W52 +0.68 1− πb4 b5 ∆hp=Kp 1 4πrb 2πr2−r2 DH= 44 + 5s 5h . (5) (6) (7) in which, r4 (b5/c) 2 LH=4 Zr−2 + r4−r5h−2 , DH 2 2πr4 + Zrb4 π(r5s − r5h) + Zrb5 The rotor tip clearance loss is evaluated by the model presented by Dambach [29], which considers the interaction of axial clearance flow and radial clearance flow, as Equation (8), ∆h=U43ZrKεC+KεC+K εεCC, (8) c 8π aaa rrr a,r arar where, in most cases, Ka = 0.4, Kr = 0.75, Ka,r = −0.3, results in good agreement with experimental data: Ca = 1−(r6s/r4), (9) Cm4 b4 r6s Zr − b4 Cr= r C rb. (10) 4 m666 The trailing edge loss refers to the loss due to the sudden expansion when fluid passes the trailing edge. The model presented by Glassman [30] is adopted as Equation (11): ρ6W62,rms Nrt6,rms 2 ∆P0,te= 2 π(r +r )cosβ . (11) 6h 6s 6,rms The windage loss happens between rotor backface and casing, and the model presented by Daily et al. [31] is used to evaluate this loss, as Equation (12): ρ U 43 r 42 ∆hw = k f 2mW62 , (12) 3.7(εb/r4)0.1 5 kf = Re1/2 forRe<1×10, (13)PDF Image | Design and Optimization Approach for Radial Inflow Turbines
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