Definition of the Existence Region of the Solution of the Problem of an Arbitrary Gas-dynamic Discontinuity Breakdown at Interaction of Flat Supersonic Jets with Formation of Two Outgoing Compression Shocks

П В Булат ,Mikhail Pavlovich Bulat

doi:10.19026/rjaset.9.1378

П В Булат , Mikhail Pavlovich Bulat

Open Access

https://doi.org/10.19026/rjaset.9.1378

Copy DOI

Abstract

We have considered the modern theory of breakdown of an arbitrary gas-dynamic discontinuity for the space-time dimension equal to two. The regions of solutions existence for a one-dimensional non-stationary case and a two-dimensional stationary case have been compared. The Riemann problem of breakdown of an arbitrary discontinuity of parameters of two flat flows angle collision is considered. The problem is solved in accurate setting. The problem parameter areas where outgoing waves appear as two jumps are specified. Two depression waves solution are not covered. The special Mach numbers of interacting flows dividing the parameter plane into areas with different outgoing discontinuities are given.

Highlights

We consider the problem of breakdown of an arbitrary gas-dynamic discontinuity in space-time with dimensionality equal to two
In a number of technical applications, the problem of breakdown of discontinuities needs to be solved in accurate setting, with no simplification
Possible types of solution: As you know, simplectic geometry specifies the reflection of the gas-dynamic variables space, as well as the specifics of transformation of shock-waves and wave fronts in the even-dimensional space

Summary

INTRODUCTION

We consider the problem of breakdown of an arbitrary gas-dynamic discontinuity in space-time with dimensionality equal to two. In a number of technical applications (flow around the airfoil sharp edge, shock-wave reflection from an obstacle, shockwave processes in jet streams, detonation burning), the problem of breakdown of discontinuities needs to be solved in accurate setting, with no simplification. This is especially for study such fine gas-dynamic phenomena as the Neumann paradox (Neuman, 1963). For definiteness P1≥P2, that an outgoing discontinuity R1 depending on relation of values P1v1, P2v2 may be both a depression wave and a compression shock. The following are qualitative pictures for the region of existence of the solution with two outgoing jumps

MATERIALS AND METHODS

RESULTS AND DISCUSSION

CONCLUSION