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

Published online by Cambridge University Press:  06 September 2019

Juchun Ding Open the ORCID record for Juchun Ding [Opens in a new window] ,
Jianming Li ,
Rui Sun ,
Zhigang Zhai Open the ORCID record for Zhigang Zhai [Opens in a new window]  and
Xisheng Luo Open the ORCID record for Xisheng Luo [Opens in a new window]
Juchun Ding
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, China
Jianming Li
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, China
Rui Sun
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, China
Zhigang Zhai
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, China
Xisheng Luo*
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, China
*
†Email address for correspondence: [email protected]
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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.

JFM classification

Compressible Flows: Shock waves Mixing: Turbulent mixing Instability: Nonlinear instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 878 , 10 November 2019 , pp. 277 - 291
Copyright
© 2019 Cambridge University Press 

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