Equation of nonsteady transonic flows of an ideal gas

Abstract

At the present time, there are several different equations for describing a transonic, nonsteady, irrotational flow of an ideal perfect gas ([1], Table 1), depending on the ratios between the small characteristic parameters of the flow. In order to extend the range of application of these equations, a composite equation is formed from them (for example, the equations for small and large Strouhal numbers in the theory of oscillation of a wing are combined). In this paper, a more general equation is obtained for the plane flow of this class by means of natural orthogonal coordinates ψΨ (family of equipotential lines and streamlines) without the use of ɛ estimates, for which the equation by comparison with the composite equation contains a new nonlinear term. Accurate solutions of the equation are found, describing nonsteady transonic flows in plane nozzles; one of them describes the process of the establishment of a design cycle in Laval nozzles with immovable walls.