The influence of the downstream pressure on the shock wave reflection phenomenon in steady flows

Abstract

The effect of the downstream pressure (defined here as the wake pressure behind the tail of the reflecting wedge) on shock wave reflection in steady flows is investigated both numerically and analytically. The dependence of the shock wave configurations on the downstream pressure is studied. In addition to the incident-shock-waveangle-induced hysteresis, which was discovered a few years ago, a new downstreampressure-induced hysteresis has been found to exist. The numerical study reveals that when the downstream pressure is sufficiently high, an inverse-Mach reflection wave configuration, which has so far been observed only in unsteady flows, can be also established in steady flows. Very good agreement between the analytical predictions and the numerical results is found.

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

“…Thus Ben-Dor et al's [22] study confirmed the hypothesis of Henderson and Lozzi [9] and showed both numerically and analytically how the RR and the MR wave configurations depend on the downstream pressure.…”

“…Following their numerical study, which was published in an English journal, many investigators using a variety of numerical codes numerically simulated the hysteresis process. Additional direct simulation Monte Carlo (DSMC) calculations were published by Ivanov et al [17], Ben-Dor et al [18] and Ivanov et al [19]; Ivanov et al [17] also presented high resolution FCT scheme calculations; calculations based on total variation diminishing (TVD) scheme were presented by Shirozu and Nishida [20]; calculations based on Godunov and van Leer scheme were conducted by Chpoun and Ben-Dor [21], calculations based on HLLE MUSCL TVD scheme were conducted by Ivanov et al [19]; and calculations based on Steger and Warming flux splitting scheme were presented by Ben-Dor et al [22]. It should be noted here that unlike the experiments the abovementioned numerical simulations were purely twodimensional.…”

“…Ben-Dor et al [22] investigated, both numerically and analytically, the effect of the downstream pressure 2 on the shock wave reflection. They discovered, in the course of their investigation, a downstream-pressure-variationinduced hysteresis.…”

Effects of Laser Energy Deposition on the Transition Characteristics of Shock Reflection in the Dual Solution Domain

“…Many studies on Mach reflections and regular reflections in supersonic flows have been conducted for this purpose, which can be useful for improving the performance of a supersonic intake. However, few studies have made realistic models or structures to control or generate favorable operating conditions in the supersonic region, although the transition between regular reflection and Mach reflections has been confirmed by many experiments and numerical simulations [4,[13][14][15][16][17][18][19].…”

Geometric criterion for RR↔MR transition in hypersonic double-wedge flows

“…The hysteresis phenomenon has been proved by experiments when quiet supersonic test facilities became available [6][7][8][9][10][11] and by computations when high-performance computers were available. [12][13][14][15][16][17][18] The research on shock wave interactions is still active in recent times. 1,[19][20][21][22][23][24] The shock wave interactions have significant impacts on the performance and reliability of a high-speed aircraft.…”