Steady Shock Refraction in Hypersonic Ramp Flow

Abstract

This paper discusses features of a supersonic flow with a transversal Mach number stratification when encountering a ramp. A flow of this nature can occur for a variety of reasons around a hypersonic vehicle. Formation of a heated wall boundary layer, external fuel injection on the compression ramp, energy deposition, and film or transpiration cooling are just some of the processes that will establish a flow where a wall near layer features a distinct difference in Mach number compared to the outer flow. This paper will introduce a flow topology framework that will help to understand phenomena associated with this stratification. Shock refraction is identified as the main mechanism which causes a redirection of the flow additional to the ramp deflection. It will be shown how, depending on the Mach number ratios between the layers, shocks or expansion fans will be created that will interact with the surface. This can be the cause for undesired or unexpected temperature and pressure distributions along the wall when shock refraction is not taken into account. As a possible application, it will be shown how shock refraction can act as a virtual external compression ramp. CFD computations are performed using the DLR TAU code, a finite volume, second order accuracy, compressible flow solver. Nomenclature M Mach number γ Ratio of specific heats u Flow speed c Speed of sound β Shock angle ϑ Deflection angle M Molecular weight R Universal gas constant p Pressure T Temperature n Refractive index ξ, ζ, η Fitting parameters s Compression stage

Refraction of Oblique Shock Wave on a Tangential Discontinuity

“…A numerical study of the Richtmyer-Meshkov instability in the interaction of a strong shock wave with a discontinuity in the density of a rectilinear and sinusoidal shape is carried out in [19]. The refraction of a shock wave upon its interaction with a near-wall layer of a heated gas is investigated in [20]. A wide range of issues related to the interaction of shock waves with contact discontinuities and the formation of the Richtmyer-Meshkov instability are discussed in [21].…”