Concerning the effect of compressibility on lam inar boundary layers and their separation

Abstract

The theory of compressible flow in a laminar boundary layer has been developed for the case when the viscosity is assumed to be proportional to the absolute temperature and the Prandtl number is unity. (These assumptions may be compared with the empirical relations u∝ oc T® and σ = 0*715 suggested by Cope.) It is shown that a transformation of the ordinate normal to the layer can lead to a simplified form of equation of motion very similar to the ordinary incompressible equation but modified by a multiplicative factor G in the pressure term. This factor is greater than unity at the boundary and tends to one at the outside of the layer. Several particular solutions are considered including accelerated flow with a linearly increasing velocity and retarded flow along a flat plate with a linearly decreasing velocity. The general implications of the theory are discussed and qualitative conclusions are drawn when the mainstream velocity starts from a stagnation point, rises to a maximum and subsequently falls. It is concluded that for such a velocity distribution increasing compressibility will reduce the skin friction, increase the boundary layer thickness and cause earlier separation as compared with the incompressible flow with the same mainstream velocity distribution and the kinematic viscosity corresponding to conditions at the stagnation point.