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Analysis of second moments and their budgets for Richtmyer-Meshkov instability and variable-density turbulence induced by reshock

Man Long Wong*

Jon R. Baltzer

Daniel Livescu

Sanjiva K. Lele

  • Department of Aeronautics and Astronautics, & Center for Turbulence Research, Stanford University, Stanford, California 94305, USA

  • XTD-IDA, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

  • CCS-2, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

  • Department of Aeronautics and Astronautics, Department of Mechanical Engineering, & Center for Turbulence Research, Stanford University, Stanford, California 94305, USA

  • *mlwong@alumni.stanford.edu
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Phys. Rev. Fluids 7, 044602 – Published 11 April, 2022

DOI: https://doi.org/10.1103/PhysRevFluids.7.044602

Abstract

Nonlinear Richtmyer-Meshkov instability and the mixing transition induced by a Mach 1.45 shock and subsequent reshock at an interface between two ideal gases (sulfur hexafluoride and air) with high Atwood number are studied with second-moment analysis using data from high-resolution compressible Navier-Stokes simulations. The analysis first addresses the importance of two second-order moments: turbulent mass flux and density-specific-volume covariance, together with their transport equations. These quantities play an essential role in the development of Favre-averaged Reynolds stress and turbulent kinetic energy in this variable-density flow. Then, grid sensitivities and the time evolution of the turbulent quantities, which include the second moments, are investigated, followed by a detailed study of the transport equations for the second moments, including the Reynolds stress and the turbulent kinetic energy with well-resolved data before reshock. After reshock, budgets of the same but large-scale turbulent quantities are studied with the effects of the subfilter-scale stress taken into account. The budgets of these large-scale quantities are shown to have an insignificant influence from the numerical regularization. Finally, the effects of the subfilter-scale stress on the budgets of the large-scale turbulent quantities with different degrees of filtering are also examined.

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Phys. Rev. Fluids 7, 044602– Published 11 April, 2022
  • Received 19 November 2021
  • Accepted 18 March 2022
Article part of CHORUS
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