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Effects of non-periodic portions of interface on Richtmyer–Meshkov instability

Published online by Cambridge University Press:  20 December 2018

Xisheng Luo Open the ORCID record for Xisheng Luo [Opens in a new window] ,
Yu Liang ,
Ting Si Open the ORCID record for Ting Si [Opens in a new window]  and
Zhigang Zhai Open the ORCID record for Zhigang Zhai [Opens in a new window]
Xisheng Luo
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, China State Key Laboratory of Fire Science, University of Science and Technology of China, Hefei 230026, China
Yu Liang
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, China
Ting Si
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, China
Zhigang Zhai*
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, China
*
†Email address for correspondence: [email protected]
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Abstract

The development of a non-periodic $\text{air}\text{/}\text{SF}_{6}$ gaseous interface subjected to a planar shock wave is investigated experimentally and theoretically to evaluate the effects of the non-periodic portions of the interface on the Richtmyer–Meshkov instability. Experimentally, five kinds of discontinuous chevron-shaped interfaces with or without non-periodic portions are created by the extended soap film technique. The post-shock flows and the interface morphologies are captured by schlieren photography combined with a high-speed video camera. A periodic chevron-shaped interface, which is multi-modal (81 % fundamental mode and 19 % high-order modes), is first considered to evaluate the impulsive linear model and several typical nonlinear models. Then, the non-periodic chevron-shaped interfaces are investigated and the results show that the existence of non-periodic portions significantly changes the balanced position of the initial interface, and subsequently disables the nonlinear model which is applicable to the periodic chevron-shaped interface. A modified nonlinear model is proposed to consider the effects of the non-periodic portions. It turns out that the new model can predict the growth of the shocked non-periodic interface well. Finally, a method is established using spectrum analysis on the initial shape of the interface to separate its bubble structure and spike structure such that the new model can apply to any random perturbed interface. These findings can facilitate the understanding of the evolution of non-periodic interfaces which are more common in reality.

JFM classification

Compressible Flows: Compressible Flows Compressible Flows: Shock waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 861 , 25 February 2019 , pp. 309 - 327
Copyright
© 2018 Cambridge University Press 

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