Unsteady flow of gas in laval nozzles with local supersonic zones: PMM vol. 39, n≗2, 1975, pp.271–279

Abstract

Exact particular solutions of nonlinear equations defining unsteady transonic flows of gas are derived. These solutions are used for analyzing unstable flows in Laval nozzles with local supersonic zones, Local supersonic zones in stationary flows were investigated with the use of the simplified equations for transonic flows of gas in [1] in plane nozzles and in [2] in nozzles of circular cross section. These solutions were then extended in [3] to three-dimensional flows in Laval nozzles. Since the investigation of variation of local supersonic zones with time is complicated by the nonlinearity of the equation for unstable transonic flows, hence even particular examples are of interest. A solution of this equation for an unsteady flow of the Taylor kind in a nozzle with two planes of symmetry was indicated in [3]. Similar solutions were later considered in [4] for unstable flows in plane nozzles. It was established that all of the above solutions can be extended. One of such generalized solutions of the transonic equation defining an unsteady flow of the Taylor kind in plane and axisymmetric Laval nozzles is presented in [5]. Here this solution is used for analyzing the variation of local supersonic zones with time (their onset, development, and joining at the nozzle axis, or the inverse process) for two classes of self-similar solutions.