The Mott-Smith solution to the regular shock reflection problem

Abstract

The classical Mott-Smith solution for one-dimensional normal shock wave structure is extended to the two-dimensional regular shock reflection problem. The solution for the non-equilibrium molecular velocity distribution function along the symmetry-plane streamline is obtained as a weighted sum of four Maxwellians. An analysis of applicability of the solution has been performed using the results of direct simulation Monte Carlo calculations for a range of incident shock wave intensities. Accuracy of the solution improves with increasing $Ma_n$ , the Mach number normal to the shock front, so that the solution becomes rather accurate for strong shocks with $Ma_n>8$ .

Regular reflection of shock waves in steady flows: viscous and non-equilibrium effects

“…2019; Timokhin et al. 2022). The NSF equations less accurate in this regard predict quantitatively different results than the more accurate R13 equations and the benchmark Boltzmann equation (or DSMC method).…”

“…Its important to note that the analysed effects are essentially non-equilibrium which is related to strong non-Maxwellian shape of the molecular velocity distribution (see Bondar et al 2019;Timokhin et al 2022). The NSF equations less accurate in this regard predict quantitatively different results than the more accurate R13 equations and the benchmark Boltzmann equation (or DSMC method).…”

“…2019; Timokhin et al. 2022), interesting features determined by the effects of viscosity, heat conduction and thermal non-equilibrium were observed for the RR problem. The main goal of the present work is a detailed investigation of these effects in the RR flow of a dilute monatomic gas (argon) for the case of a strong IS and its qualitative comparison with the case of the planar shock wave.…”

“…Then it changes direction again to the direction of the incoming flow in the reflected shocks (RS). Note that the inviscid solution of this problem consists of four zones of a uniform supersonic flow (1), ( 2), ( 3) and (4) (zone (3) is symmetrical to zone (2)) divided by four straight-line discontinuities (compare with two uniform flow zones divided by one discontinuity in the 1-D shock case) (Timokhin, Kudryavtsev & Bondar 2022). As in the 1-D case, the solution can be determined analytically if one knows the incoming flow Mach number and the IS angle (in the 1-D case, it is sufficient to know only the Mach number).…”