On mathematical modeling of a hypersonic flow past a thin wing with variable shape

Abstract

The present work is devoted to a further study of the spatial flowing of a thin wing of variable shape by a hypersonic flow of non-viscous gas. The head shock wave is considered to be attached to the leading edge of the wing. The use of the thin shock layer method for solving the system of gas dynamics equations makes it possible to build a mathematical model of the flow in question. It should also be noted that the analysis of boundary conditions makes it possible to determine the structure of the expansion of the quantities sought in a series and to construct approximate analytical solutions. In this case, in determining the first approximation corrections, two equations are integrated independently of the other equations. The application of the Euler—Ampere transform allows to construct a solution depending on two arbitrary functions and an unknown of the shock front. To determine these functions, previously it was obtained an integro-differential system of equations. This paper proposes one of the variants of the semi-inverse method for constructing the solution of this system, in which the form of one of arbitrary function is given. This approach allows you to additionally set the equation for the leading edge of the wing, and in the case when the head wave is attached along the entire leading edge and the inclination of the wing surface on it. The variant of the semi-inverse method presented in the work for the non-stationary spatial problem of the flow has made it possible to obtain a particular solution, which is a model for various flow regimes around the wing. Formulas are obtained to determine: the shape of the front of the shock wave, the shape of the surface of the streamlined body, the distance between the shock wave and the surface of the body, and the flow parameters on the wing surface.