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Hydrodynamic instabilities of a dual-mode air–SF6 interface induced by a cylindrically convergent shock

Published online by Cambridge University Press:  19 May 2023

Yu Liang Open the ORCID record for Yu Liang [Opens in a new window] ,
Lili Liu ,
Xisheng Luo Open the ORCID record for Xisheng Luo [Opens in a new window]  and
Chih-Yung Wen Open the ORCID record for Chih-Yung Wen [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 NYUAD Research Institute, New York University Abu Dhabi, Abu Dhabi 129188, UAE
Xisheng Luo*
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
Chih-Yung Wen*
Affiliation:
Department of Aeronautical and Aviation Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong
*
†Email addresses for correspondence: xluo@ustc.edu.cn, chihyung.wen@polyu.edu.hk
†Email addresses for correspondence: xluo@ustc.edu.cn, chihyung.wen@polyu.edu.hk
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Abstract

Shock-tube experiments are performed on the convergent Richtmyer–Meshkov (RM) instability of a multimode interface. The temporal growth of each Fourier mode perturbation is measured. The hydrodynamic instabilities, including the RM instability and the additional Rayleigh–Taylor (RT) effect, imposed by the convergent shock wave on the dual-mode interface, are investigated. The mode-coupling effect on the convergent RM instability coupled with the RT effect is quantified. It is evident that the amplitude growths of all first-order modes and second-order harmonics and their couplings depend on the variance of the interface radius, and are influenced by the mode-coupling from the very beginning. It is confirmed that the mode-coupling mechanism is closely related to the initial spectrum, including azimuthal wavenumbers, relative phases and initial amplitudes of the constituent modes. Different from the conclusion in previous studies on the convergent single-mode RM instability that the additional RT effect always suppresses the perturbation growth, the mode-coupling might result in the additional RT effect promoting the instability of the constituent Fourier mode. By considering the geometry convergence, the mode-coupling effect and other physical mechanisms, second-order nonlinear solutions are established to predict the RM instability and the additional RT effect in the cylindrical geometry, reasonably quantifying the amplitude growths of each mode, harmonic and coupling. The nonlinear solutions are further validated by simulations considering various initial spectra. Last, the temporal evolutions of the mixed mass and normalized mixed mass of a shocked multimode interface are calculated numerically to quantify the mixing of two fluids in the cylindrical geometry.

JFM classification

Compressible Flows: Shock waves
Type
JFM Papers
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Journal of Fluid Mechanics , Volume 963 , 25 May 2023 , A25
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© The Author(s), 2023. Published by Cambridge University Press

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