An analytical study into steady-state and unsteady-state flows involving the use of Prandtl–Meyer and Riemann invariants

The results of studies into steady-state, plane, supersonic isentropic flows are given in [1, 2]. It is demonstrated that an analytical study results in a qualitatively correct description of the main singularities of flow, and the numerical and experimental results support the results of analytical solution. In particular, it is found that the distribution of the gasdynamic parameters on the boundaries, characteristic curves, and contour of a Laval nozzle is nonmonotonic. The results of [1, 2] are generalized to the case of one-dimensional steady-state flows, as well as plain jet flows into a low-pressure space. Steady-state and unsteady-state flows are investigated using Prandtl–Meyer and Riemann invariants. An analysis is performed of such flows with a certain set of initial and boundary conditions. For a plane steady-state case, flows are treated in channels of different shapes, including flows in a channel with straight walls and in an adjacent Laval nozzle, as well as in a jet flowing into a low-pressure space. For an unsteady-state one-dimensional case, flows are treated in a channel with straight walls with closed ends and with open ends, as well as with an extended piston.