Experiments On The Richtmyer-Meshkov Instability With An Imposed, Random Initial Perturbation

Abstract

The Richtmyer-Meshkov instability is studied in vertical shock tube experiment. The instability is initiated by the passage of an incident shock wave over an interface between two dissimilar gases. The interface is formed by opposed gas flows in which air and SF₆ enter the shock tube from the top and from the bottom of the shock tube driven section. The gases exit the test section through a series of small holes in the test section side walls, leaving behind a flat, diffuse membrane-free interface at that location. Random three-dimensional perturbations are imposed on the interface by oscillating the column of gases in the vertical direction, using two loud speakers mounted in the shock tube wall. The development of the turbulent mixing is observed as a result of the shock-interface interaction. The flow is visualized using planar Mie scattering in which the light from a laser sheet is scattered by smoke particles seeded in one of the experimental gases and image sequences are captured using high-speed CMOS cameras. The primary interest of the study is the determination of the growth rate of the turbulent mixing layer that develops after an impulsive acceleration of the perturbed interface between the two gases (air/SF₆) by a weak M=1.2 incident shock wave. Measurements of the mixing layer width following the initial shock interaction show a power law growth h ~ tᶿ similar to those observed in previous experiments and simulations with θ ~ 0.40. The experiments reveal that the growth rate of the mixing width significantly varies from one experiment to another. This is attributed to the influence of initial perturbations imposed on the interface. However, better consistency for the mixing layer growth rate is obtained from the mixing generated by the reflected shock wave. A novel approach that is based on mass and linear momentum conservation laws in the moving reference frame leads to a new definition of the spike and bubble mixing layer widths, which does not depend on the initial conditions.