Transition to Mach reflexion of shock waves in steady and pseudosteady flow with and without relaxation

Abstract

Experiments were conducted in the free-piston shock tube and shock tunnel with dissociating nitrogen and carbon dioxide, ionizing argon and frozen argon to measure the transition condition in pseudosteady and steady flow. The transition condition in the steady flow, in which the wall was eliminated by symmetry, agrees with the calculated von Neumann condition. I n the real gases this calculation assumed thermodynamic equilibrium after the reflected shock. I n the pseudosteady flow of reflexion from a wedge the measured transition angle lies on the Mach-reflexion side of the calculated detachment condition by an amount which may be explained in terms of the displacement effect of the boundary layer on the wedge surface. A single criterion based on the availability of a length scale a t the reflexion point explains the difference between the pseudosteady and steady flow transition condition and predicts a hysteresis effect in the transition angle when the shock angle is varied during steady flow. No significant effects on the transition condition due to finite relaxation length could be detected. However, new experiments in which interesting relaxation effects should be evident are suggested.

Non-uniqueness of solutions in asymptotically self-similar shock reflections

“…For parameters M i = 6.6 and γ = 1.2, the determined transition between regular and Mach reflection of 44.5 • ± 0.5 • over the wedge with a sharp corner is in good agreement with the sonic criterion [6], modelled by two-shock theory. This criterion predicts a transition at θ w = 44.47 • ± 0.01 • .…”

“…While viscous effects and the presence of relaxation reduce the transition wedge angle [6], these length scales vanish asymptotically as the reflection grows. Their effects only dominate the solution at early times, while the later time solution may still be influenced by the start-up conditions, as illustrated in the present study.…”

“…It has also been shown that the transition angle decreases with radius of curvature [18], tending towards the transition angle of a reflection off a straight wedge. The transition angle for a reflection over a concave circle has been analytically predicted using the sonic criterion [6] by BenDor and Takayama [10] but the proposed models are independent of the radius of curvature. Their model "A" predicts a transition at θ w ≈ 63 • for M = 6.6 and γ = 1.2 on the concave circle.…”

“…This overlap has been observed in both steady and pseudosteady flows. Much attention has been devoted to the many types of reflection configurations, the conditions under which they occur, and which factors favour the appearance of one type over another, especially under conditions where both regular and Mach reflections are possible solutions [3][4][5][6].…”

Numerical investigation on three-dimensional shock wave reflection over two perpendicularly intersecting wedges

“…the hysteresis phenomena in steady shock wave reflections [7][8][9][10], and the application of new experimental facilities [11]. However, the previous results are mainly on two-dimensional (2D) cases, and 3D shock wave reflection has not yet been investigated widely.…”