Experimental study of wall conductivity influence on shock wave reflection

Abstract

In the conventional von Neumann theoretical treatment of two-dimensional shock wave reflection off a surface, it is assumed that the flow is inviscid and that the reflecting surface is perfectly smooth, rigid, non-porous, and adiabatic. These theoretical predictions have been found to be good predictions of reflection over a significant range where regular reflection exists and for a limited range around Mach 2 for strong shocks in the case of Mach reflection. However, experiments on regular reflection have shown that this pattern persists to a small extent beyond what the theory predicts. This effect has been ascribed to the development of a viscous boundary layer behind the point of reflection, and some studies have been done on the effect of surface roughness on reflection topology. The possibility of thermal effects and heat transfer from the shock-heated gas to the wall and on the boundary layer has, on the other hand, been almost totally neglected. To study this, two surfaces of different conductivities have been placed at the same angle, symmetrically in a shock tube, and impacted by a single plane shock wave and the reflection patterns examined. Tests were conducted over a range of Mach numbers between 1.28 and 1.4, and incident shock wave angles between $36^\circ$ and $70^\circ$ covering both regular and Mach reflection. Both quantitative and qualitative tests show that there is a difference in the angles between the reflected waves and the reflecting surfaces based on the material thermal conductivity. In the quantitative tests the value of this angle was larger for materials with a lower thermal conductivity, and vice versa. A material, such as aluminium, with mid-range thermal conductivity had angles that lay within the limits of the two extreme values for glass and copper. The qualitative images supported these findings, showing asymmetry in reflection topography, with the intersection of the two reflected shock waves lying closer to the material with a higher thermal conductivity.