Application of the principle of minimum entropy production to shock wave reflections. I. Steady flows

Abstract

The properties of curved oblique shocks associated with the reflection of weak shock waves AIP Conf.Based on new experimental results of Chpoun, Passerel, Li, and Ben-Dor ͓J. Fluid Mech. 301, 19 ͑1995͔͒ and numerical results of Vuillon, Zeitoun, and Ben-Dor ͓J. Fluid Mech. 301, 37 ͑1995͔͒ regarding the shock wave reflection transitions from regular to Mach reflection and from Mach to regular reflection in steady flows of perfect gases which contradicted the present understanding regarding these processes ͓Hornung and Robinson, J. Fluid Mech. 123, 155 ͑1982͔͒, we present a new approach for better understanding the supersonic flow deflection over straight wedges and the transition of steady shock wave reflections over straight wedges. The new approach is based on the principle of minimum entropy production which enables one to choose the physical ͑stable͒ solutions out of a variety of possible mathematical ones. To the best of our knowledge the new transition criteria which are proposed in this study agree with all the available experimental results.

Time history of regular to Mach reflection transition in steady supersonic flow

“…This plane is divided by two curves (the von Neumann criterion θ = θ N (M 0 ) and the detachment criterion θ = θ D (M 0 )) into three branches: lower branch for only RR, upper branch for only MR and middle branch where both RR and MR are possible depending on the history that the actual steady flow is built (see Ben-Dor 2007 and references therein). Although both RR and MR are stable with small disturbances in the dual solution domain (Teshukov 1989;Li & Ben-Dor 1996), RR may transit to MR if the amplitude of the disturbance exceeds a certain level (Ivanov et al 1997(Ivanov et al , 1998(Ivanov et al , 2000Kudryavtsev et al 2002). The earlier investigations (e.g.…”

Theoretical study on regular reflection of shock wave–boundary layer interactions

“…Some researchers attempt to explain the shock interaction principles from the view of entropy. Li & Ben-Dor (1996 a , b ) firstly employ the minimum entropy production principle (MEP) to propose new criteria for the RR–MR transition, which have been proved by experiments (see Chpoun et al 1995). Accordingly, in the work conducted by Wang et al (2018), MEP is employed to analyse the configurations as well as RR to MR transition of separation shock–separation shock interactions, as shown in figure 4, which agree well with experimental results.…”

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

“…Li and Ben-Dor [11] analytically proved, by applying the principle of minimum entropy production, that the RR wave configuration is stable in most of the dual-solutiondomain.…”