Prediction of Ingress Through Turbine Rim Seals—Part II: Combined Ingress

In Part I of this two-part paper, the orifice equations were solved for the case of externally induced (EI) ingress, where the effects of rotational speed are negligible. In Part II, the equations are solved, analytically and numerically, for combined ingress (CI), where the effects of both rotational speed and external flow are significant. For the CI case, the orifice model requires the calculation of three empirical constants, including $Cd,e,RI$ and $Cd,e,EI$⁠, the discharge coefficients for rotationally induced (RI) and EI ingress. For the analytical solutions, the external distribution of pressure is approximated by a linear saw-tooth model; for the numerical solutions, a fit to the measured pressures is used. It is shown that although the values of the empirical constants depend on the shape of the pressure distribution used in the model, the theoretical variation of $Cw,min$ (the minimum nondimensional sealing flow rate needed to prevent ingress) depends principally on the magnitude of the peak-to-trough pressure difference in the external annulus. The solutions of the orifice model for $Cw,min$ are compared with published measurements, which were made over a wide range of rotational speeds and external flow rates. As predicted by the model, the experimental values of $Cw,min$ could be collapsed onto a single curve, which connects the asymptotes for RI and EI ingress at the respective smaller and larger external flow rates. At the smaller flow rates, the experimental data exhibit a minimum value of $Cw,min$⁠, which undershoots the RI asymptote. Using an empirical correlation for $Cd,e$⁠, the model is able to predict this undershoot, albeit smaller in magnitude than the one exhibited by the experimental data. The limit of the EI asymptote is quantified, and it is suggested how the orifice model could be used to extrapolate the effectiveness data obtained from an experimental rig to engine-operating conditions.