Similarity analysis of compressor tip clearance flow structure

Abstract

A new approach is presented for analyzing compressor tip clearance flow. The basic idea is that the clearance velocity field can be (approximately) decomposed into independent through-flow and cross-flow, since chordwise pressure gradients are much smaller than normal pressure gradients in the clearance region. As in the slender body approximation in external aerodynamics, this description implies that the three-dimensional, steady, clearance flow can be viewed as a two-dimensional, unsteady flow. Using this approach, a similarity scaling for the cross-flow in the clearance region is developed and a generalized description of the clearance vortex is derived. Calculations based on the similarity scaling agree well with a wide range of experimental data in regard to flow features such as cross-flow velocity field, static pressure field, and tip clearance vortex trajectory. The scaling rules also provide a useful way of exploring the parametric dependence of the vortex trajectory and strength for a given blade row. The emphasis of the approach is on the vortical structure associated with the tip clearance because this appears to be a dominant feature of the endwall flow; it is also shown that this emphasis gives considerable physical insight into overall features seen in the data.