An experimental investigation of Richtmyer-Meshkov instability

Abstract

In this study, the interaction of a shock wave with an interface between two gases is studied experimentally. The basic mechanism for the initial growth of perturbations on the interface is the baroclinic generation of vorticity which results from the misalignment of the pressure gradient in the shock and the density gradient at the interface. The growth of perturbations soon enters into a nonlinear regime with the appearance of bubbles of light fluid rising into heavy fluid and spikes of heavy fluid falling into light fluid. In the nonlinear regime, interaction between various scales and the appearance of other instabilities, such as Kelvin-Helmholtz instability, along the boundaries of the spikes occur, which results in the breakup of the interface. These processes lead to a turbulent mixing zone (TMZ) which grows with time. The main focus of this study is to understand the growth of TMZ with time in a cylindrical geometry with square cross section and for the the first time study the effect of area convergence in a conical geometry on its growth rate. The present set of experiments is done in the GALCIT 17 in. shock tube with air and sulfur hexafluoride as light and heavy gases. The growth of the TMZ is studied in a straight test section for single-mode initial perturbation consisting of two different wavelength and amplitude combinations at incident shock Mach number of 1.55. The multimode initial perturbation growth at late times is studied in a conical geometry to study the effect of area convergence at incident Mach numbers of 1.55 and 1.39. The results are compared with the experiments of Vetter which were done in the same shock tube with a straight test section with no area convergence and at the same Mach number. In the study of the Richtmyer-Meshkov (RM) instability of single-scale perturbations on air/sulfur-hexafluoride interface in a straight test section, the initially sinusoidal interface is formed by a polymeric membrane of thickness 1.5 micron and the flow visualization is done using schlieren imaging technique. The interface thickness is measured visually from the photographs. It is found that the growth rate decreases rapidly with time with a small dependence on the initial wavelength persisting until late times. In the case of the RM instability, growth of multimode initial perturbations in a conical geometry, it is found from the schlieren flow visualization images that the interface thickness grows about 40-50 % more rapidly than in Vetter's experiments. Experimental results for laser-induced scattering at late times are presented for air/He gas combinations at the interface. In situations when the rear of the interface is not clearly demarcated, the thickness is determined by an image processing technique. This technique is also used to determine the possible dominant eddy/blob size in the TMZ from the schlieren images. Some inviscid computational studies, with a planar or spherical shock interacting with a planar or spherical initial interface in light-heavy (air/sulfur-hexafluoride) and heavy-light (air/He) configurations, are also presented. In the conical geometry there is a reflected shock originating from the triple point. This reflection is a consequence of the transition from the cylindrical shock tube to the converging cone. Due to the vorticity created by the interaction of reflected shock from the cone wall with the interface in initial stage, it is found that the interface curves toward or away from the apex of the cone, depending on the sign of density gradient. This curving of the interface could have a role to play in the diffuse rear boundary of the interface in schlieren flow visualization images but the laser-induced scattering image shows that the mixing zone indeed does not have a well-defined rear boundary. Rather, small blobs of fluids on the right are scattered in the mixing zone. An inviscid computational study is also done on cylindrical and conical test section geometries to study the effect of transverse reflected waves on the growth of small sinusoidal initial perturbations. It is found by comparison with cylindrical geometry (where reflected waves do not exist) that the transverse reflected waves do not affect the growth of perturbations on the interface.