Expansion Procedures and Similarity Laws for Transonic Flow Part I. Slender Bodies at Zero Incidence

Abstract

The purpose of this report is to provide a detailed and comprehensive account of a transonic approximation as applied to flows past wings and bodies. It is mainly concerned with the derivation of approximate equations, boundary conditions, etc., rather than with the more difficult problem of the solution of transonic flow problems. Thus the report contains for the most part a re-examination of the basic ideas, as presented for example, in Ref. 1. The essential new point of view introduced here is to regard the approximate transonic equations as part of a systematic expansion procedure. Thus, it becomes possible, in principle, to compute the higher terms of this approximation or at least to estimate errors. In the next section the form of the expansion and the reasons for it are explained. In the succeeding sections the equations of motion, shock relations, and boundary conditions for the flow problem are presented and then the expansion procedure is applied systematically. The resulting system of equations for the first, second, and higher approximations i s presented in Section 5. The main results of interest for practical applications concern similarity laws and the pressure coefficient on the surface of slender bodies and these appear in Section 6. The remaining section treats bodies of non-circular cross-section.