Development of perturbations of a shock-accelerated interface between two gases

Abstract

It is known [1] that the interface between two media of unequal densities is unstable if a constant acceleration is directed from the light medium toward the heavier one. In that case small initial perturbations grow exponentially. Conversely, if the acceleration is directed from the heavy liquid toward the light one, the interface remains stable.Richtmyer [2] analyzed the case where the acceleration is of pulse-like nature and, in particular, when the interface is accelerated by a stationary shock wave passing out of the light medium into the heavier one. In that case, for small initial sinusoidal perturbation, its amplitude grows linearly with time da dt ao n u R, a(0) = a0, where n = 2~'/)~; )~ is the perturbation wavelength; u is the contact interface velocity; R = (p2-pl)/(p~+pl) is the Atwood number; pl and p2 are the densities of the gases at the interface, compressed by the shock wave.The experimental results [3] confirmed the conclusions [2] in a qualitative sense. In addition, the interface was found to be unstable in the case where the shock wave passes out of the heavy gas into the light one. The interface perturbation amplitude grows linearly with time in both cases, except the initial stage.At present, there are many papers on the development of interface sinusoidal perturbations after passage of a shock wave (see, for instance, [4-9]); numerical solutions are given to two problems in [8, 10], where the development of finite "step-like" perturbations is investigated.This paper reports the results of experimental and numerical investigations on the development of finite perturbations of various shapes. The initial perturbation amplitudes under consideration A0 (being measured from an upper to a lower point of the perturbation) fall in the range 0.2~ ~ z~0 <~ 0.8)~. In the case of a perturbation y = a0 cos nx, Ao = 2a0 (here A0 is the "step" height).Experimental Investigation. 1. The experiments were carried out in a shock tube using the technique described in [3].The measuring section of the shock tube consisted of butt-joined units. A thin organic film of mass-length ratio (3-4) 9 10 -5 g/cm was placed at joints between the units. The units were filled with gases of various densities. The joints (and thus the interfaces between the gases) were specially shaped to obtain a certain shape of the initial interface perturbation.The interface under study is accelerated by a plane shock wave, initiated in the channel of the shock tube. The channel of the measuring section of the shock tube has transparent walls, thus permitting observation of the flow process. The process was recorded by means of the shadow-image equipment IAB-451 combined with the optical superfast photocamera SFR-2M in the frame-by-frame mode.2. The development of the initial perturbations of the interface between gases of various density has been studied in the experiments: air (p0 = 1.205 g/liter, "), = 1,405) and Freon-12 (p0 = 5,13 g/liter, = 1,138).Institute of Experimental Physics, Arzamas-16 607200.

Hydrodynamic instability in strong media

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Review of experimental Richtmyer–Meshkov instability in shock tube: From simple to complex

“…In the experimental study on shock-interface interaction, spherical or cylindrical gaseous bubbles, and single-mode interface are the most common interface types while other interface types are rarely under consideration. Bakhrakh et al 86 considered the case of a 2D disturbance with a complex shape ('saw' and 'step', as sketched in Figure 12(a) and (b)). In their experiments, the measuring section of the shock tube consisted of butt-joined units.…”

“…[98][99][100] However, the investigation on the evolution of an inclined interface impacted by a shock wave is insufficient. In experiments, an inclined interface was created by organic films 86 or a nitrocellulose membrane with a support. 101 Unfortunately, the pieces of the membrane and the support could have adverse effects on the flow evolution.…”

“…Bakhrakh et al. 86 considered the case of a 2D disturbance with a complex shape (‘saw’ and ‘step’, as sketched in Figure 12(a) and (b)). In their experiments, the measuring section of the shock tube consisted of butt-joined units.…”