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Instability evolution on a shock-accelerated cylindrical fluid layer with arbitrary Atwood numbers

Published online by Cambridge University Press:  25 November 2024

Ming Yuan Open the ORCID record for Ming Yuan [Opens in a new window] ,
Zhiye Zhao Open the ORCID record for Zhiye Zhao [Opens in a new window] ,
Luoqin Liu Open the ORCID record for Luoqin Liu [Opens in a new window] ,
Pei Wang ,
Nan-Sheng Liu Open the ORCID record for Nan-Sheng Liu [Opens in a new window]  and
Xi-Yun Lu Open the ORCID record for Xi-Yun Lu [Opens in a new window]
Ming Yuan
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, PR China
Zhiye Zhao*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, PR China Department of Mechanical and Aerospace Engineering, The Hong Kong University of Science and Technology, Hong Kong, PR China
Luoqin Liu*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, PR China
Pei Wang
Affiliation:
Institute of Applied Physics and Computational Mathematics, Beijing 100094, PR China
Nan-Sheng Liu
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, PR China
Xi-Yun Lu
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, PR China
*
†Email addresses for correspondence: [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected]
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Abstract

Developing a model to describe the shock-accelerated cylindrical fluid layer with arbitrary Atwood numbers is essential for uncovering the effect of Atwood numbers on the perturbation growth. The recent model (J. Fluid Mech., vol. 969, 2023, p. A6) reveals several contributions to the instability evolution of a shock-accelerated cylindrical fluid layer but its applicability is limited to cases with an absolute value of Atwood numbers close to $1$, due to the employment of the thin-shell correction and interface coupling effect of the fluid layer in vacuum. By employing the linear stability analysis on a cylindrical fluid layer in which two interfaces separate three arbitrary-density fluids, the present work generalizes the thin-shell correction and interface coupling effect, and thus, extends the recent model to cases with arbitrary Atwood numbers. The accuracy of this extended model in describing the instability evolution of the shock-accelerated fluid layer before reshock is confirmed via direct numerical simulations. In the verification simulations, three fluid-layer configurations are considered, where the outer and intermediate fluids remain fixed and the density of the inner fluid is reduced. Moreover, the mechanisms underlying the effect of the Atwood number at the inner interface on the perturbation growth are mainly elucidated by employing the model to analyse each contribution. As the Atwood number decreases, the dominant contribution of the Richtmyer–Meshkov instability is enhanced due to the stronger waves reverberated inside the layer, leading to weakened perturbation growth at initial in-phase interfaces and enhanced perturbation growth at initial anti-phase interfaces.

JFM classification

Compressible Flows: Shock waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1000 , 10 December 2024 , A9
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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