The laminar boundary layer in compressible flow

Abstract

The paper is concerned with the integration of the laminar boundary-layer equations for a compressible fluid and is in three parts. In Part I the boundary-layer equations for a compressible fluid are derived, reduced to nondimensional form, and their relation to the corresponding equations for an incompressible fluid discussed. Methods of integrating them are considered, and it is shown that, provided there is no pressure gradient in the main stream, the methods employed for incompressible flow are of practical value. If there is a pressure gradient, then the complications introduced by compressibility are such that general algebra must cease and numerical integration take its place at an early stage. This means that approximate methods (such as Pohlhausen’s) of calculating separation lose their simplicity, and there are indications that their accuracy will also suffer; so it is natural to consider the practicability of direct integration of the equations, probably by series expansions. In Part II, suitable expansions in one independent variable with coefficients which are functions of the other are obtained. It is found that the independent variables can be so chosen that the differential equations for the coefficients in the expansions have the same general structure as for an incompressible fluid. The boundary conditions and the limiting forms of the equations for zero Mach number are investigated. The application of iterative methods to the equations is discussed. In Part III the ENIAC is briefly described, and the methods of applying it to obtain solutions of the equations derived in Part II are described in some detail. It is shown that, by proper choice of independent variable, the results for zero pressure gradient can be put into a form in which they vary only slowly with Linear interpolation in between the tabulated values will thus provide reliable first estimates of these quantities, and the accuracy can be improved, if required, by an iterative process. Tables of results are given.