Some exact solutions of the problem of super- and hypersonic gas flow about a yawed wing with fence

Abstract

Individual examples are known of bodies of three-dimensional form for which it is possible to construct the solution of the flow problem, for example, bodies of star-shaped (polygonal) cross section [1, 2], or bodies of revolution (cone, ellipsoid) at an angle of attack, and so on. The role of such individual solutions is important in clarifying the characteristic features of the three-dimensional flow about bodies. The application of the hypersonic method of small perturbations [3], which reduces the problem of three-dimensional flow to the problem of the unsteady motion of a gas in two dimensions, and also the use of one of the known families of exact solutions of the two-dimensional problem on unsteady motion [4] make it possible to study the flow about a yawed wing with a tip plate in a hypersonic flow in certain particular cases. In the present paper, we construct a more general class of threedimensional bodies of thi s type (combinations of a yawed or triangular wing with tip plate directed parallel to the free stream) for which it is possible to construct simple exact solutions of the supersonic and hypersonic flow problem without use of the method of small perturbations. In a particular case, these solutions describe the flow about two mutually intersecting yawed wings. The example of flow about these bodies reveals an interesting phenomenon of strong interference at high velocities, when, as a result of the interference, local pressures are developed which far exceed the pressures on the isolated wing. w 1. Let us consider a supersonic gas flow about a portion of a triangular (or sweptback) wing similar to that shown in Fig. 1, with thefreestream directed opposite to the x coordinate axis.