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Richtmyer–Meshkov instability of an unperturbed interface subjected to a diffracted convergent shock

Published online by Cambridge University Press:  27 September 2019

Liyong Zou ,
Mahamad Al-Marouf ,
Wan Cheng Open the ORCID record for Wan Cheng [Opens in a new window] ,
Ravi Samtaney ,
Juchun Ding Open the ORCID record for Juchun Ding [Opens in a new window]  and
Xisheng Luo Open the ORCID record for Xisheng Luo [Opens in a new window]
Liyong Zou
Affiliation:
Mechanical Engineering, Physical Science and Engineering Division, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia Laboratory for Shock Wave and Detonation Physics, Institute of Fluid Physics, China Academy of Engineering Physics, Mianyang 621900, China
Mahamad Al-Marouf
Affiliation:
Mechanical Engineering, Physical Science and Engineering Division, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia
Wan Cheng*
Affiliation:
Mechanical Engineering, Physical Science and Engineering Division, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia
Ravi Samtaney
Affiliation:
Mechanical Engineering, Physical Science and Engineering Division, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia
Juchun Ding
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, China
Xisheng Luo*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, China
*
†Email addresses for correspondence: wan.cheng@kaust.edu.sa, xluo@ustc.edu.cn
†Email addresses for correspondence: wan.cheng@kaust.edu.sa, xluo@ustc.edu.cn
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Abstract

The Richtmyer–Meshkov (RM) instability is numerically investigated on an unperturbed interface subjected to a diffracted convergent shock created by diffracting an initially cylindrical shock over a rigid cylinder. Four gas interfaces are considered with Atwood number ranging from $-0.18$ to 0.67. Results indicate that the diffracted convergent shock increases its strength gradually and reduces its amplitude quickly when it propagates towards the convergence centre. After the strike of the diffracted convergent shock, the initially unperturbed interface deforms with a bulge structure at the centre and two interface steps at both sides, which can be ascribed to the non-uniformity of the pressure distribution behind the diffracted convergent shock. With the decrease of Atwood number, the bulge structure becomes more pronounced. Quantitatively, the interface amplitude experiences a fast but short growing stage and then enters a linear stage. A good collapse of the dimensionless amplitude is found for all cases, which indicates a weak dependence of the growth rate on Atwood number in the deformed shock-induced RM instability. Then the impulsive theory is modified by eliminating the Atwood number and considering the geometry convergence, which well predicts the amplitude growth for the deformed shock-induced RM instability. Finally, the underlying mechanism is decoupled into three parts, and it is found that both the impulsive pressure perturbation and the geometry convergence promote the growth of interface perturbation while the continuous pressure perturbation inhibits the growth. As the Atwood number decreases, the impulsive perturbation plays an increasingly important role, which suggests that the impulsive perturbation dominates the deformed shock-induced RM instability at the linear stage.

JFM classification

Compressible Flows: Shock waves Instability: Nonlinear instability Mixing: Turbulent mixing

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 879 , 25 November 2019 , pp. 448 - 467
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© 2019 Cambridge University Press 

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