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Refined modelling of the single-mode cylindrical Richtmyer–Meshkov instability

Published online by Cambridge University Press:  03 December 2020

Jinxin Wu Open the ORCID record for Jinxin Wu [Opens in a new window] ,
Han Liu  and
Zuoli Xiao Open the ORCID record for Zuoli Xiao [Opens in a new window]
Jinxin Wu
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing100871, PR China
Han Liu
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing100871, PR China
Zuoli Xiao*
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing100871, PR China HEDPS and Center for Applied Physics and Technology, College of Engineering, Peking University, Beijing100871, PR China Beijing Innovation Center for Engineering Science and Advanced Technology, Peking University, Beijing100871, PR China
*
†Email address for correspondence: [email protected]
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Abstract

Evolution of the two-dimensional single-mode Richtmyer–Meshkov (RM) instability in a cylindrical geometry is numerically investigated through direct numerical simulation. A proper decomposition of the measured initial perturbation amplitude is found to be crucial for a comparative study between the numerical simulation and benchmark experiment. A refined compressible model is proposed based on the Bell equation by taking the premixed width of the initial interface into consideration. The modified model can accurately reproduce the development history of a single-mode perturbed gaseous interface between the first shock-interface interaction and reshock based on the evolution data of the unperturbed interface under the same premixing condition. The detailed effects of the RM instability, Rayleigh–Taylor stabilization and compressibility coupled with the Bell–Plesset effect are also specified with the aid of this model. It turns out that the refined Bell model can be further applied to the post-reshock stage of the RM instability before the appearance of strong nonlinearity.

JFM classification

Compressible Flows: Shock waves Mixing: Turbulent mixing
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 908 , 10 February 2021 , A9
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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