Hysteresis phenomena in the interaction process of conical shock waves: experimental and numerical investigations

Abstract

The interaction of two conical shock waves, one converging and straight and the other diverging and curvilinear, in an axisymmetric flow was investigated both experimentally and numerically. A double-loop hysteresis was discovered in the course of the experimental investigation. The double-loop hysteresis consisted of a major one, associated with the interaction between the boundary layer and the wave configuration, and a minor one, associated with the dual-solution phenomenon, which is known to be non-viscous-dependent. The minor hysteresis loop was found to be an internal hysteresis loop of the major one. As expected the numerical Euler calculations failed to detect the viscous-dependent major hysteresis loop but did succeed in obtaining the non-viscous-dependent minor (internal) hysteresis loop. In addition, multiple hysteresis loops, associated with the interaction between the shock wave configuration and the edge of the curvilinear mobile cone were also observed. The non-viscous minor hysteresis loop involved different overall shock wave reflection configurations, and the other hysteresis loops involved the same shock wave reflection configuration but different flow patterns.

Hysteresis processes in the regular reflection↔Mach reflection transition in steady flows

“…As will be shown subsequently, the Euler solver, which was applied by Ben-Dor et al [38], failed, as expected, to reproduce the viscous dependent Type A wave configuration and the hysteresis loop that is associated with it. As a result only the non-viscousdependent internal hysteresis loop, i.e., the Type B-Type C hysteresis loop, was simulated.…”

“…Ben-Dor et al [38] also found that the just mentioned Type B-Type C transition at X E1:38 (between frames (h) and (i) in Fig. 16) was the origin of an additional internal hysteresis loop.…”

“…This in turn, led to the questions whether an actual RR wave configuration is indeed stable inside the dual-solution-domain, and whether the hysteresis process indeed exists in a purely two-dimensional flow. For this reason Chpoun et al [37] and Ben-Dor et al [38] designed an axisymmetric geometrical set-up, which was free of three-dimensional effect.…”

“…Ben-Dor et al [38] investigated this hysteresis process both experimentally and numerically. Their numerical investigation was limited by an inviscid flow model assumption.…”

“…The number of the humps is seen to increase as X is increased. There are three full humps for X ¼ 0:7 and 0.80 [frames (d) and Ben-Dor et al [38] found that the location of the curvilinear cone when a given hump detached from the rear edge of the curvilinear cone was different from the location of the curvilinear cone when the same hump was reattached. The attachment/detachment mechanism led to the identification of the above-mentioned additional minor hysteresis loops in which the wave configuration was always an oMR, but the flow patterns along the surface of the curvilinear cone were different.…”