A Method for the Calculation of the Wall Layers Inside the Passage of a Compressor Cascade With and Without Tip Clearance

Abstract

A method is presented for calculating the wall shear layers of a compressor cascade. The integrated across the blade spacing Navier-Stokes equations are used. Closure is obtained using an integral equation of the boundary layer type and the secondary vorticity generation equation. The calculation is performed inside the passage and a dialogue is established between the longitudinal velocity profile, associated with the primary vorticity (generated and diffused) and the transverse profile, associated with the secondary vorticity, which is generated by the primary one. A unique feature of the method is that it takes into account the velocities induced by the secondary vorticity in the “free stream” flow (the problem is elliptic in the transverse direction). The influence of the tip clearance vortex is included in the method and comparisons with experimental results for two heavily loaded cascades with and without tip clearance show good agreement.