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A compressible Reynolds-averaged mixing model considering turbulent composition and heat fluxes

Published online by Cambridge University Press:  23 September 2025

Hansong Xie ,
Tengfei Luo Open the ORCID record for Tengfei Luo [Opens in a new window] ,
Yaomin Zhao Open the ORCID record for Yaomin Zhao [Opens in a new window] ,
Yousheng Zhang Open the ORCID record for Yousheng Zhang [Opens in a new window]  and
Jianchun Wang Open the ORCID record for Jianchun Wang [Opens in a new window]
Hansong Xie
Affiliation:
HEDPS, Center for Applied Physics and Technology and School of Mechanics and Engineering Science, Peking University, Beijing 100871, PR China
Tengfei Luo
Affiliation:
Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, PR China Center for Ocean Research in Hong Kong and Macau and Division of Environment and Sustainability, Hong Kong University of Science and Technology, Hong Kong, PR China
Yaomin Zhao*
Affiliation:
HEDPS, Center for Applied Physics and Technology and School of Mechanics and Engineering Science, Peking University, Beijing 100871, PR China
Yousheng Zhang*
Affiliation:
HEDPS, Center for Applied Physics and Technology and School of Mechanics and Engineering Science, Peking University, Beijing 100871, PR China Institute of Applied Physics and Computational Mathematics, Beijing 100094, PR China National Key Laboratory of Computational Physics, Beijing 100088, PR China
Jianchun Wang
Affiliation:
Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, PR China
*
Corresponding authors: Yaomin Zhao, yaomin.zhao@pku.edu.cn; Yousheng Zhang, zhang_yousheng@iapcm.ac.cn
Corresponding authors: Yaomin Zhao, yaomin.zhao@pku.edu.cn; Yousheng Zhang, zhang_yousheng@iapcm.ac.cn
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Abstract

In typical nature and engineering scenarios, such as supernova explosion and inertial confinement fusion, mixing flows induced by hydrodynamic interfacial instabilities are essentially compressible. Despite their significance, accurate predictive tools for these compressible flows remain scarce. For engineering applications, the Reynolds-averaged Navier–Stokes (RANS) simulation stands out as the most practical approach due to its outstanding computational efficiency. However, existing RANS studies focus primarily on cases where the compressible effect plays an insignificant role in mixing development, with quite limited attention given to scenarios with significant compressibility influence. Moreover, most of the existing RANS mixing models demonstrate significantly inaccurate predictions for the latter. This study develops a novel compressible RANS mixing model by incorporating physical compressibility corrections into the $K$–$L$–$\gamma$ mixing transition model recently proposed by Xie et al. (J. Fluid Mech. 1002, 2025, A31). Specifically, taking the density-stratified Rayleigh–Taylor mixing flows as representative compressible cases, we first analyse the limitations of the existing model for compressible flows, based on high-fidelity data and local instability criteria. Subsequently, the equation of state for a perfect gas is employed to derive comprehensive compressibility corrections. The crucial turbulent composition and heat fluxes are integrated into the closure of the key turbulent mass flux term of the turbulent kinetic energy equation. These corrections enable the model to accurately depict compressible mixing flows. Systematic validations confirm the efficacy of the proposed modelling scheme. This study offers a promising strategy for modelling compressible mixing flows, paving the way for more accurate predictions in complex scenarios.

JFM classification

Mixing: Turbulent mixing Turbulent Flows: Turbulence modelling Turbulent Flows: Compressible turbulence

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1019 , 25 September 2025 , A56
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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