Prediction of mean flow and over-tip shock distribution in pressure-driven tip leakage flows

Abstract

The flow across the blade tip clearance in turbomachinery is simplified as pressure-driven tip leakage flow (TLF) by isolating it from the mainstream. Based on schlieren visualization and numerical simulations, several common features of TLF are achieved. Consequently, a diffusion model is proposed to evaluate the mean flow and shock motions within the clearance. It takes into consideration the effects of relative wall motion by superposing a fully developed Couette flow. In addition, the over-tip shock waves are treated as repeated sawtooth wave to model the propagation. This approach enables quick and accurate evaluations of the meanflow and shock motions under configurations of stationery and moving casing wall. Given the flow variables at boundaries of the shock region, the meanflow and the evolution of the over-tip shock waves can be achieved instantly with an error less than 2%. Another advantage of this model is it can be non-intrusive. Hence, the challenges, arising from spatial constraints in direct measuring of TLF within the clearance, are surmounted. This is beneficial for locating the tip flow loss and the shock-induced heat load. Two flow mechanisms are unveiled from the predictions: (1) The strongest shock–boundary interaction accompanied by strong momentum exchange occurs above the separation bubble. (2) The oscillation of over-tip shock waves is self-sustained by a feedback loop formed by the pressure-side vortex shedding, shock generation, and shock–boundary interactions.