The Turbulent Boundary Layer in Compressible Flow

Abstract

The flow of a compressible gas past a fiat plate is investigated for a turbulent boundary layer. The local and mean skin-friction coefficients are calculated for both power and log laws of velocity distribution. The calculations show a considerable reduction of both coefficients with increasing M. In the course of the analysis assumptions have been made whose accuracy is not proven, though they are consistent with those made in incompressible gas dynamics. The results are applied to calculate the contribution to fR of skin friction for a typical projectile of various calibres. The calculation shows that it should be possible by a properly selected series of wind-tunnel and full-scale experiments to ascertain if the large reduction in skin friction occurs, but that it is unlikely that it will be possible to discriminate between the two hypotheses about velocity distribution. Historical Note.--The introduction proper gives the reasons which lead to the writing of this paper and for a long time security considerations prevented its publication. Recently, however, work on similar lines both at the Royal Aircraft Establishment and in America (e.g., van Driest or Wilson in J.Ae.Sc.) have both confirmed the general accuracy of the picture presented and to a considerable extent superseded it as a technical contribution. Nevertheless it seems still to have some value technically and to be of great interest historically as a very early contribution to the literature of the subject. The preparation of a paper of this kind for publication raises questions of rewriting so as to bring it up to date which are very difficult to decide. In the present case it has been decided to leave it untouched except to change the details of the references if the subject matter has since been published. The main reasons for this decision are that adequate modern treatments (such as those cited above) now exist, and that therefore to rewrite it would merely add one more to them and to no useful purpose, while at the same time it would diminish almost to vanishing point the historical value of the paper. The work was carried out as part of the National Physical Laboratory programme of work for the fighting services.