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Richtmyer–Meshkov instability on two-dimensional multi-mode interfaces

Published online by Cambridge University Press:  15 October 2021

Yu Liang Open the ORCID record for Yu Liang [Opens in a new window] ,
Lili Liu ,
Zhigang Zhai Open the ORCID record for Zhigang Zhai [Opens in a new window] ,
Juchun Ding Open the ORCID record for Juchun Ding [Opens in a new window] ,
Ting Si Open the ORCID record for Ting Si [Opens in a new window]  and
Xisheng Luo Open the ORCID record for Xisheng Luo [Opens in a new window]
Yu Liang
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China NYUAD Research Institute, New York University Abu Dhabi, Abu Dhabi 129188, UAE
Lili Liu
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
Zhigang Zhai*
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
Juchun Ding
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
Ting Si
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
Xisheng Luo*
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
*
†Email addresses for correspondence: sanjing@ustc.edu.cn, xluo@ustc.edu.cn
†Email addresses for correspondence: sanjing@ustc.edu.cn, xluo@ustc.edu.cn
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Abstract

Shock-tube experiments on eight kinds of two-dimensional multi-mode air–SF$_6$ interface with controllable initial conditions are performed to examine the dependence of perturbation growth on initial spectra. We deduce and demonstrate experimentally that the amplitude development of each mode is influenced by the mode-competition effect from quasi-linear stages. It is confirmed that the mode-competition effect is closely related to initial spectra, including the wavenumber, the phase and the initial amplitude of constituent modes. By considering both the mode-competition effect and the high-order harmonics effect, a nonlinear model is established based on initial spectra to predict the amplitude growth of each individual mode. The nonlinear model is validated by the present experiments and data in the literature by considering diverse initial spectra, shock intensities and density ratios. Moreover, the nonlinear model is successfully extended based on the superposition principle to predict the growths of the total perturbation width and the bubble/spike width from quasi-linear to nonlinear stages.

JFM classification

Compressible Flows: Shock waves Mixing: Turbulent mixing
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 928 , 10 December 2021 , A37
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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