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

Published online by Cambridge University Press:  03 September 2020

Rui Sun ,
Juchun Ding Open the ORCID record for Juchun Ding [Opens in a new window] ,
Zhigang Zhai Open the ORCID record for Zhigang Zhai [Opens in a new window] ,
Ting Si Open the ORCID record for Ting Si [Opens in a new window]  and
Xisheng Luo Open the ORCID record for Xisheng Luo [Opens in a new window]
Rui Sun
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei230026, PR China
Juchun Ding*
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei230026, PR China
Zhigang Zhai
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei230026, PR China
Ting Si
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei230026, PR China
Xisheng Luo
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei230026, PR China
*
†Email address for correspondence: [email protected]
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Abstract

The convergent Richtmyer–Meshkov instability (RMI) of an $\textrm {SF}_6$ layer with a uniform outer surface and a sinusoidal inner surface surrounded by air (generated by a novel soap film technique) is studied in a semiannular convergent shock tube using high-speed schlieren photography. The outer interface initially suffers only a slight deformation over a long period of time, but distorts quickly at late stages when the inner interface is close to it and produces strong coupling effects. The development of the inner interface can be divided into three stages. At stage I, the interface amplitude first drops suddenly to a lower value due to shock compression, then decreases gradually to zero (phase reversal) and later increases sustainedly in the negative direction. After the reshock (stage II), the perturbation amplitude exhibits long-term quasi-linear growth with time. The quasi-linear growth rate depends weakly on the pre-reshock amplitude and wavelength, but strongly on the pre-reshock growth rate. An empirical model for the growth of convergent RMI under reshock is proposed, which reasonably predicts the present results and those in the literature. At stage III, the perturbation growth is promoted by the Rayleigh–Taylor instability caused by a rarefaction wave reflected from the outer interface. It is found that both the Rayleigh–Taylor effect and the interface coupling depend heavily on the layer thickness. Therefore, controlling the layer thickness is an effective way to modulate the late-stage instability growth, which may be useful for the target design.

JFM classification

Compressible Flows: Shock waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 902 , 10 November 2020 , A3
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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