Divergent Richtmyer–Meshkov instability on a heavy gas layer

Abstract

Experiments on divergent Richtmyer–Meshkov (RM) instability at a heavy gas layer are performed in a specially designed shock tube. A novel soap-film technique is extended to generate gas layers with controllable thicknesses and shapes. An unperturbed gas layer is first examined and its two interfaces are found to move uniformly at the early stage and be decelerated later. A general one-dimensional theory applicable to an arbitrary-thickness layer is established, which gives a good prediction of the layer motion in divergent geometry. Then, six kinds of perturbed SF $_6$ layers with various thicknesses and shapes surrounded by air are examined. At the early stage, the amplitude growths of the inner interface for various-thickness layers collapse quite well and also can be predicted by the Bell model for cylindrical RM instability at a single interface, which indicates a negligible interface coupling effect. Later, a rarefaction wave accelerates the inner interface, causing a dramatic rise in the growth rate. It is found that a thicker gas layer will result in a larger extent that the rarefaction wave can promote the instability growth. A modified Bell model accounting for both Rayleigh–Taylor (RT) instability and interface stretching caused by a rarefaction wave is established, which well reproduces the quick instability growth. At late stages, reverberating waves inside the layer are negligibly weak such that the inner interface growth is dominated by RM instability and RT stability. The major factors driving the outer interface development are a compression wave and interface coupling. A new interface coupling phenomenon existing uniquely in divergent geometry caused by the gradual thinning of the gas layer is observed and also modelled.

Effects of reverberating waves and interface coupling on a divergent Richtmyer–Meshkov instability

“…Thus quasi-one-dimensional (quasi-1-D) experiments corresponding to an unperturbed SF 6 layer surrounded by air impacted by a divergent shock are required to examine the background flow. Fortunately, these quasi-1-D experiments have been reported recently by Zhang et al (2023). A sequence of schlieren images (upper) and schematic diagrams (lower) illustrating the evolution of the SF 6 layer driven by a cylindrical divergent shock are given in figure 2.…”

“…Rich experimental data for various types of gas layers obtained in this work provide the first opportunity to fully examine the validity of the linear theory of Mikaelian (2005). The present work together with that of Zhang et al (2023) will constitute a systematic study of divergent RM instability at a perturbed heavy gas layer.…”

“…Specifically, a divergent shock becomes weaker and weaker with time, thus a non-uniform, unsteady pressure field is established behind it, which leads to interface deceleration (i.e. RT stability/instability) (Li et al 2020b;Zhang et al 2023). Also, for a gas layer moving in a divergent geometry, the layer becomes progressively thinner with time due to geometric divergence and thus exhibits an increasingly strong interface coupling effect (Zhang et al 2023).…”

“…RT stability/instability) (Li et al 2020b;Zhang et al 2023). Also, for a gas layer moving in a divergent geometry, the layer becomes progressively thinner with time due to geometric divergence and thus exhibits an increasingly strong interface coupling effect (Zhang et al 2023). Moreover, for divergent RM instability, nonlinearity and compressibility are much weaker than those of convergent RM instability (Li et al 2020b).…”

“…A gas layer could present four configurations in terms of shape: sinusoidal inner interface and unperturbed outer interface (configuration I); unperturbed inner interface and sinusoidal outer interface (configuration II); sinusoidal inner and outer interfaces that present the same phase (configuration III); sinusoidal inner and outer interfaces that present opposite phases (configuration IV). Divergent RM instability at a gas layer of configuration I has been examined by Zhang et al (2023) in a specially designed divergent shock tube. It was found that reverberating waves inside the layer produce influences on the instability growth that are more pronounced than those of planar and convergent RM instabilities.…”