Similarity Analysis of Compressor Tip Clearance Flow Structure

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 throughflow and crossflow, 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 crossflow 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 crossflow 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.