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Evaluating the stretching/compression effect of Richtmyer–Meshkov instability in convergent geometries

Published online by Cambridge University Press:  03 August 2022

Jin Ge Open the ORCID record for Jin Ge [Opens in a new window] ,
Haifeng Li Open the ORCID record for Haifeng Li [Opens in a new window] ,
Xinting Zhang  and
Baolin Tian
Jin Ge
Affiliation:
Sino-French Engineer School, Beihang University, Beijing 100191, PR China
Haifeng Li*
Affiliation:
Institute of Applied Physics and Computational Mathematics, Beijing 100094, PR China
Xinting Zhang
Affiliation:
Sino-French Engineer School, Beihang University, Beijing 100191, PR China
Baolin Tian*
Affiliation:
Institute of Applied Physics and Computational Mathematics, Beijing 100094, PR China HEDPS, Center for Applied Physics and Technology, and College of Engineering, Peking University, Beijing 100871, PR China
*
†Email addresses for correspondence: tylihaifeng@163.com, tian_baolin@iapcm.ac.cn
†Email addresses for correspondence: tylihaifeng@163.com, tian_baolin@iapcm.ac.cn
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Abstract

Richtmyer–Meshkov (RM) instability in convergent geometries (such as cylinders and spheres) plays a fundamental role in natural phenomena and engineering applications, e.g. supernova explosion and inertial confinement fusion. Convergent geometry refers to a system in which the interface converges and the fluids are compressed correspondingly. By applying a decomposition formula, the stretching or compression (S(C)) effect is separated from the perturbation growth as one of the main contributions, which is defined as the averaged velocity difference between two ends of the mixing zone. Starting from linear theories, the S(C) effect in planar, cylindrical and spherical geometries is derived as a function of geometrical convergence ratio, compression ratio and mixing width. Specifically, geometrical convergence stretches the mixing zone, while fluid compression compresses the mixing zone. Moreover, the contribution of geometrical convergence in the spherical geometry is more important than that in the cylindrical geometry. A series of cylindrical cases with high convergence ratio is simulated, and the growth of perturbations is compared with that of the corresponding planar cases. As a result, the theoretical results of the S(C) effect agree well with the numerical results. Furthermore, results show that the S(C) effect is a significant feature in convergent geometries. Therefore, the S(C) effect is an important part of the Bell–Plesset effect. The present work on the S(C) effect is important for further modelling of the mixing width of convergent RM instabilities.

JFM classification

Instability: Nonlinear instability Convection: Buoyancy-driven instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 946 , 10 September 2022 , A18
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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