Irregular self-similar configurations of shock-wave impingement on shear layers

Abstract

An oblique shock impinging on a shear layer that separates two uniform supersonic streams, of Mach numbers $M_{1}$ and $M_{2}$, at an incident angle $\unicode[STIX]{x1D70E}_{i}$ can produce regular and irregular interactions with the interface. The region of existence of regular shock refractions with stable flow structures is delineated in the parametric space $(M_{1},M_{2},\unicode[STIX]{x1D70E}_{i})$ considering oblique-shock impingement on a supersonic vortex sheet of infinitesimal thickness. It is found that under supercritical conditions, the oblique shock fails to deflect both streams consistently and to provide balanced flow properties downstream. In this circumstance, the flow renders irregular configurations which, in the absence of characteristic length scales, exhibit self-similar pseudosteady behaviours. These cases involve shocks moving upstream at constant speed and increasing their intensity to comply with equilibrium requirements. Differences in the variation of propagation speed among the flows yield pseudosteady configurations that grow linearly with time. Supercritical conditions are described theoretically and reproduced numerically using highly resolved inviscid simulation.

Specific heat effects in two-dimensional shock refractions

“…Specifically, the maximum pressure and deflection provided by the incident and transmitted shocks may not be sufficiently close to be matched between them through a third reflected wave. In that case, the flow evolves instead into a self-similar irregular structure that grows with time [27]. Another possibility arises when considering a subsonic flow in the lower gaseous stream, which makes the analytical treatment even more complicated.…”

“…Although the non-linear system described above must be solved numerically, due to the trigonometric and implicit relationships involved, a qualitative description of the variable specific heat ratio can be withdrawn with use made of the well-known polar Henderson-Neumann diagrams [25,27]. First, each curve shown in Fig.…”

“…Inside these combustion devices, an intricate interplay between shocks and streams of reactants yields a stable power output. A great number of scientific studies has been performed to clarify many relevant details of this kind of compressible problems, including shock interactions with canonical turbulence [4][5][6][7][8], planar interactions with gaseous interfaces [9][10][11], shock-shock interactions [12,13], shock reflections on solid walls [14][15][16][17] and boundary-layer effects [18][19][20][21][22] that may include separation processes [23,24], or transmission of flow discontinuities across tangential layers [25][26][27], to name a few.…”

Refraction of Oblique Shock Wave on a Tangential Discontinuity

“…The 2D steady potential flow equation is employed to describe the motion of the fluid. Supercritical conditions are described theoretically and reproduced numerically using highly resolved inviscid simulation in [34].…”

Interaction between Shock Waves Travelling in the Same Direction

“…These include the emergence of local supersonic regions with λ-shaped shock waves on the upper surface of the wing profile during a wave crisis, as well as the formation of overtaking shocks on a needle extended into a supersonic flow in front of the body in order to reduce resistance, or when supplying energy to a supersonic flow with the formation of plasma [19]. Irregular refractions of a shock wave on a mixing layer are considered in [20]. Supersonic flows are complex numerical simulation problems.…”