A Model for Accurate Prediction of Discharge Coefficients in Rotating Orifices with Different Wall Inclination Angles

Accurate prediction of discharge coefficients (Cd) in rotating orifices is essential for the design of aero-engine internal air systems, yet existing correlations usually treat axial and radial orifices separately and do not fully represent intermediate wall inclination angles. In this study, steady-state RANS simulations in a rotating reference frame, supported by validation against published data and by rotating orifice experiments, are used to investigate the combined effects of wall inclination angle α and length-to-diameter ratio L/d on Cd. The numerical results show that, under typical conditions (N = 3000 rpm, Π = 1.03, L/d = 1.5), Cd increases from 0.301 to 0.340 as α increases from π/2 to π, corresponding to a 12.96% increase. Under low rotational speeds and high pressure ratios, the Coriolis force reduces the relative tangential velocity and the incidence angle, thereby increasing Cd with α; however, at high rotational speeds and low pressure ratios, the centrifugal resistance to radial inflow becomes dominant, and at N = 7000 rpm, the Cd for the α = π orifice is 38.96% lower than that for the α = π/2 orifice. Increasing L/d promotes flow redevelopment and amplifies the Coriolis-force effect, leading to a larger Cd increase for orifices with larger α. Based on these mechanisms, a generalized incidence-angle formulation incorporating Coriolis and centrifugal effects is developed, and a Cd prediction model applicable to π/2 ≤ α ≤ π and different L/d values is proposed. Experimental validation shows that the maximum prediction error is reduced to 2.37%, demonstrating the accuracy of the proposed model for rotating inclined orifices.