Convergent Richtmyer–Meshkov instability of a heavy gas layer with perturbed outer interface

Abstract

The evolution of an $\text{SF}_{6}$ layer surrounded by air is experimentally studied in a semi-annular convergent shock tube by high-speed schlieren photography. The gas layer with a sinusoidal outer interface and a circular inner interface is realized by the soap-film technique such that the initial condition is well controlled. Results show that the thicker the gas layer, the weaker the interface–coupling effect and the slower the evolution of the outer interface. Induced by the distorted transmitted shock and the interface coupling, the inner interface exhibits a slow perturbation growth which can be largely suppressed by reducing the layer thickness. After the reshock, the inner perturbation increases linearly at a growth rate independent of the initial layer thickness as well as of the outer perturbation amplitude and wavelength, and the growth rate can be well predicted by the model of Mikaelian (Physica D, vol. 36, 1989, pp. 343–357) with an empirical coefficient of 0.31. After the linear stage, the growth rate decreases continuously, and finally the perturbation freezes at a constant amplitude caused by the successive stagnation of spikes and bubbles. The convergent geometry constraint as well as the very weak compressibility at late stages are responsible for this instability freeze-out.

Convergent Richtmyer–Meshkov instability of heavy gas layer with perturbed inner surface

“…Specifically, the thicker the gas layer, the slower the development of the outer interface, and the quicker the development of the inner interface. The present results are different from those in the outer perturbation case (Ding et al 2019), where the layer thickness affects the instability growth from a very early time. This work is an important step towards a complete understanding of hydrodynamic instabilities at a perturbed layer, and the findings may be useful for the target design.…”

“…In Cases 1 and 2, this seeded perturbation suffers very slow growth for a long time (), which indicates a negligible coupling effect between the inner and outer interfaces. We note that this behaviour is completely different from that of the outer perturbation case, where the initially-undisturbed inner interface deforms quickly from a very early time (Ding et al 2019). In Case 3, where the inner and outer interfaces are much closer together, the outer interface presents rapid instability growth at .…”

“…At late stages, both spikes and bubbles saturate gradually and finally stop growing. This type of instability freeze-out has also been observed in the outer perturbation case (Ding et al 2019), and the physical mechanisms are given below. As the circumferentially distributed spikes (carrying heavy ) move to the geometric centre at a high speed (), air in the vicinity of the geometric centre is continuously compressed and produces a drag force (i.e.…”

“…It is also observed that the small perturbation on the outer interface seeded by the distorted shock TS 3 experiences very slow growth for a long time. This is different from the outer perturbation case (Ding et al 2019), where the seeded perturbation on the initially uniform interface grows considerably from a very early time. Such slow instability growth may be ascribed to the following factors.…”

“…It should be stressed that the inner perturbation case is more critical for ICF, because the inner interface of such a layer may exhibit rapid instability growth, which would directly entrain the inside fuel to the outside and hence impede the ignition. We show in the present work that the evolution of an inner perturbation layer is distinctly different from the outer perturbation case (Ding et al 2019), and we discuss the reasons for such a difference. The growth behaviours of perturbations on both the outer and inner interfaces of the inner perturbation layer are carefully analysed and the underlying flow regimes are discussed.…”