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Effect of chemical reaction on mixing transition and turbulent statistics of cylindrical Richtmyer–Meshkov instability

Published online by Cambridge University Press:  06 May 2022

Zheng Yan Open the ORCID record for Zheng Yan [Opens in a new window] ,
Yaowei Fu Open the ORCID record for Yaowei Fu [Opens in a new window] ,
Lifeng Wang ,
Changping Yu Open the ORCID record for Changping Yu [Opens in a new window]  and
Xinliang Li
Zheng Yan
Affiliation:
Institute of Applied Physics and Computational Mathematics, Beijing 100094, PR China
Yaowei Fu
Affiliation:
LHD, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, PR China
Lifeng Wang
Affiliation:
Institute of Applied Physics and Computational Mathematics, Beijing 100094, PR China Center for Applied Physics and Technology, HEDPS, Peking University, Beijing 100871, PR China
Changping Yu
Affiliation:
LHD, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China
Xinliang Li*
Affiliation:
LHD, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, PR China
*
†Email address for correspondence: lixl@imech.ac.cn
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Abstract

Direct numerical simulations of a three-dimensional cylindrical Richtmyer–Meshkov instability with and without chemical reactions are carried out to explore the chemical reaction effects on the statistical characteristics of transition and turbulent mixing. We adopt 9-species and 19-reaction models of non-premixed hydrogen and oxygen separated by a multimode perturbed cylindrical interface. A new definition of mixing width suitable for a chemical reaction is introduced, and we investigate the spatio-temporal evolution of typical flow parameters within the mixing regions. After reshock with a fuller mixing of fuels and oxygen, the chemical reaction becomes sufficiently apparent at affecting the evolution of the flow fields. Because of the generation of a combustion wave within the combustion regions and propagation, the growth of the mixing width with a chemical reaction is accelerated, especially around the outer radius with large temperature gradient profiles. However, the viscous dissipation rate in the early stage of the chemical reaction is greater because of heat release, which results in weakened turbulent mixing within the mixing regions. We confirm that small-scale structures begin to develop after reshock and then decay over time. During the developing process, helicity also begins to develop, in addition to kinetic energy, viscous dissipation rate, enstrophy, etc. In the present numerical simulations with cylindrical geometry, the fluctuating flow fields evolve from quasi-two-dimensional perturbations, and the generations of helicity can capture this transition process. The weakened fluctuations during shock compression can be explained as the inverse energy cascade, and the chemical reaction can promote this inverse energy cascade process.

JFM classification

Compressible Flows: Shock waves Mixing: Turbulent mixing Reacting Flows: Turbulent reacting flows

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JFM Papers
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Journal of Fluid Mechanics , Volume 941 , 25 June 2022 , A55
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© The Author(s), 2022. Published by Cambridge University Press

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