Algebraic self-modeling solutions of two-dimensional transonic gas flow

Abstract

Approximate equations of the flow of gas in the transonic velocity range possess an important class of self-modeling solutions. Many of the transonic flow properties such as, for example, the character of flow at some distance from a body, the flow in Laval nozzles, etc., were analysed with such solutions as the main tool[1 to 3]. An analysis is made below of cases in which the self-modeling solutions are represented by algebraic functions. By resorting to parametric representation of the unknown magnitudes, it is possible to indicate in all cases a form of solution convenient for gas dynamical computations. Certain exact solutions of the Tricomi equation have been obtained in this manner, solutions which may be used in the analysis of new properties of transonic flows such as flow in a Laval nozzle with linked supersonic zones, flow in a nozzle with breaks in its wall, flow in the neighborhood of the intersection point of the sonic line with the sonic stream boundary, etc.