The Compressible Shear Layer of a Mach Reflection

Abstract

A shear layer exists between two flows of different properties such as velocity or density. A finite thickness exists across a shear layer due to a velocity gradient forming on each side. The associated shear creates a region of mixing that increases in thickness from the point where the fluids first meet. Previous studies on shear layers [1, 2] revealed that the growth rate decreases as the shear velocity increases. Brown and Roshko [3] studied incompressible shear layers of different velocity and density ratios. Papamoschou [1] compared the visual growth rate of compressible shear layers to their incompressible values at the same velocity and density ratios. These values were plotted against M c , a parameter derived by Bogdanoff [4] in an attempt to investigate and correlate the effect of compressibility on the growth rate of the turbulent shear layer. Rikanati et al. [2] measured the spread angle of shear layers in a Mach reflection for a Mach number range of 1.55 to 2.78 and proposed a theoretical model similar to that found in Dimotakis [5]. The spread angle of the shear layer increased to a maximum of 8∘ before decreasing with the effect of compressibility. For Reynolds numbers (Re/mm) below 2 × 103 the theoretical model proposed by Rikanati failed to match the experimental spread angles. Previous work by Rubidge and Skews [6] revealed the Kelvin-Helmholtz Instability (KHI) occurring along the shear layer for Mach numbers of 1.34, 1.46 and 1.61. The spread angle of the shear layer was found to be approximately half of Rikanati’s measured angle, for the same Reynolds number.