Boundary-layer tables for similar compressible flow

Abstract

T HE similar solutions of the compressible, laminar boundary-layer equations depend on a pressure gradient parameter |8 and on the wall-to-inviscid stagnation temperature ratio gw. However, derived quantities, such as various thicknesses, also depend on a speed parameter 5. A comprehensive table of results is therefore three-dimensional and, in fact, does not exist. One of the more extensive tabulations is due to Back. His three-dimensional table, however, is scanty, lacking results for negative /3 and for gw > 1 . Furthermore, the spacing on gw and S is nonuniform and inadequate for interpolation or extrapolation. These remarks are not criticisms, since a comprehensive three-dimensional table is a prohibitive undertaking and, even it is existed, would be difficult and awkard to use. We provide a new formulation that enables all quantities of interest to be determined by a set of two-dimensional tables in which j8 and gw are the only entree parameters. With such a set, accurate values can be found for the skin-friction coefficient, Stanton number, and the five most common viscous and thermal boundary-layer thicknesses for arbitrary values of S. We use the compressible similarity equations under the traditional assumptions of steady flow of a perfect gas with unity values for the Prandtl number and Chapman-Rubesin parameter. The bounding wall is assumed impermeable, and the flow is two-dimensional or axisymmetric. Our nomenclature is usually that of Ref. 1 or may be found in the full paper. For the subsequent derivation, we need the following collection of integrals, all of which are exact: