Analytical Study on Post-Shock Expansion in Transonic Flow

A simple analytical method for the interaction between weak normal shock waves and turbulent boundary layers on flat surfaces is presented. The flow is assumed to be adiabatic, two-dimensional and to follow the power-law form. An empirical relation for a normal shock wave in transonic flow is taken into account, and momentum and energy integral equations for the turbulent boundary layer are applied. This study is aimed to analyze the post-shock expansion caused by the shock/boundary layer interaction. The results show that the post-shock expasion is iargely positioned outside the edge of boundary layer and the extent of it scales with the flow Mach number, and also show the qualitative agreement with experimental results. 1. Introdution In transonic flows such as those in aerofoils, turbine blades, compressors, diffusers and nozzles, neary-normal shock waves occur and interact with the boundary layer developing along the wall surface. When the free • stream Mach number just upstream of the shock wave excceeds about 1.1 and 1.33`L', respectively, in the cases laminar and turbulent bound-ary layers, it has been well known that the flow separation occur, i.e. shock-induced separation. There are still many discussions even up to now on whether the shock wave