Numerical Simulations of Unsteady Shock Reflection Processes by a Ramp

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Numerical simulations of unsteady shock reflections by a ramp have been conducted. The two-dimensional Euler equations are solved numerically by a TVD scheme proposed by Harten with modified flux approach and resolution enhancement by artificial compression. The calculations have been carried out for regular reflections, single Mach reflections, complex Mach reflections and double Mach reflections under the conditions of shock Mach number from 1.34 to 3.10 and ramp angles from 35 to 48 degrees. The results show good agreements with experiments. In particular the slip layers and Mach stems in Mach reflections are captured with fine resolution. Also unsteady aerodynamic heating is simulated numerically by solving thin-layer approximated Navier-Stokes equations. The calculations have been carried out both for complex Mach reflection and for double Mach reflections under the conditions of shock Mach number of 2.35 and 2.75 respectively with ramp angle of 42.5 degrees. The unsteady aerodynamic heating induced by shock impingement is simulated numerically. The results show good agreements with experiments. In particular The second peak heating caused by the impingement of the slip layer generated from the triple point is fairly predicted. Also weak Mach reflection processes are simulated properly. Viscous effects to the shock reflection processes are proved to be significant for weak Mach reflection.
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