Numerical Study of Triple-Shock-Wave Structure in Steady Irregular ...
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Numerical Study of Triple-Shock-Wave Structure in Steady Irregular ...
Abstract. The viscosity effects on strong and weak shock wave reflection are investigated with the Navier-Stokes and. DSMC flow solvers. It is shown that the ...
Numerical Study of Triple-Shock-Wave Structure in Steady Irregular Reflection G.V. Shoev, D.V. Khotyanovsky, Ye.A. Bondar, A.N. Kudryavtsev and M.S. Ivanov Khristianovich Institute of Theoretical and Applied Mechanics, Institutskaya 4/1, Novosibirsk, Russia, 630090 Abstract. The viscosity effects on strong and weak shock wave reflection are investigated with the Navier-Stokes and DSMC flow solvers. It is shown that the viscosity plays a crucial role in the vicinity of three-shock intersection. Instead of a singular triple point, in viscous flow there is a smooth three shock transition zone, where one-dimensional shock jump relations cannot be applied. At the flow parameters corresponding to the von Neumann reflection, when no inviscid three-shock solution exists, the computations predict an irregular shock-wave configuration similar to that observed previously in experiments. The existence of a viscous zone in the region of shock-wave interaction allows a continuous transition from the parameters behind the Mach stem to the parameters behind the reflected shock, which is impossible in the inviscid three-shock theory. Keywords: von Neumann paradox, irregular shock wave reflection. PACS: 47.40.Ki, 47.35.Lf.
INTRODUCTION Many interesting phenomena that occur in oblique shock wave reflection have been discovered in the past. The main feature herein is the existence of two possible configurations of shocks, regular and irregular. Irregular reflection, which is shown in the figure 1, is shock wave pattern that combines the incident (IS) and reflected (RS) shock waves and the Mach stem (MS). Classical theoretical methods such as the shock polar analysis and the three-shock theory based on Rankine– Hugoniot jump conditions across oblique shocks were developed by J. von Neumann to describe shock wave configurations. These theoretical methods predict well most of the features of shock wave interaction. However, in reflection of weak shock waves (M∞
