Effects of a sharp pressure rise on a compressible laminar boundary layer, when the Prandtl number is σ = 0.72

Abstract

SynopsisFollowing an earlier paper (Curle 1978) we consider a compressible laminar boundary layer with uniform pressure when the distance x along the wall satisfies x < x0 and a prescribed large adverse pressure gradient when x > x0. The viscosity and absolute temperature are again taken to be proportional, but the Prandtl number is no longer assumed to be unity. After applying the Illingworth-Stewartson transformation, the transformed external velocity u1(x) is chosen so thatis large and constant, where Ts is the stagnation temperature, Tw is the (constant) Wall temperature and u0 is the upstream value of u1(x).The flow reacts to this sharp pressure rise mainly in a thin inner sublayer, so inner and outer asymptotic expansions are derived and matched for functions F and S which determine the stream function and the temperature.The skin friction, heat transfer, displacement thickness and momentum thickness are determined as functions of , andinvolve two parameters B1, B2, which depend upon the Mach number and the walltemperature. Detailed numerical calculations are presented here for σ = 0.72. In particular, it is seen that the heat transfer rate varies roughly like σ⅓ except near to separation, where it varies like σ¼.