Irregular reflection of weak acoustic shock pulses on rigid boundaries : Schlieren experiments and direct numerical simulation based on a Navier-Stokes solver

Abstract

The local interactions occurring between incident and reflected shock waves in the vicinity of rigid surfaces are investigated. Both regular and irregular — also called von Neumann — regimes of reflection are studied, via experimental and numerical simulations. Shock waves are produced experimentally with a 20 kV electrical spark source which allows the generation of spherically diverging acoustic shocks. The behaviour of the resulting weak acoustic shocks near rigid boundaries is visualized with a Schlieren optical technique which allows the spatial structure of the shocks to be studied. In particular, the evolution of the Mach stem forming above a flat surface is examined, and its height is observed to be directly linked to the angle of incidence and the pressure amplitude of the incident shock. The propagation of an acoustic shock between two parallel rigid boundaries is also studied. It is shown that the strong interactions between the Mach stems emerging from the two boundaries can lead to a drastic modification of the morphology of the acoustic field in the waveguide. Experimental results are compared to numerical results obtained from high-order finite-difference based simulations of the 2D Navier-Stokes equations. The good agreement between the experimental distribution of the acoustic field and numerical results suggests that numerical simulations are promising as a predictive tool to study nonlinear acoustic propagation of acoustic waves in complex geometrical configurations with rigid boundaries.