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Dynamic one-equation-based subgrid model for large-eddy simulation of stratified turbulent flows

R. Ranjan1,*, M. K. Venkataswamy2,†, and S. Menon2,‡

  • 1Department of Mechanical Engineering, University of Tennessee at Chattanooga 615 McCallie Avenue, Chattanooga, Tennessee 37403, USA
  • 2School of Aerospace Engineering, Georgia Institute of Technology 270 Ferst Drive, Atlanta, Georgia 30332, USA

  • *reetesh-ranjan@utc.edu
  • †mvenkataswamy3@gatech.edu
  • ‡suresh.menon@ae.gatech.edu
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Phys. Rev. Fluids 5, 064601 – Published 3 June, 2020

DOI: https://doi.org/10.1103/PhysRevFluids.5.064601

Abstract

In this study, the dynamic one-equation-based subgrid model for large-eddy simulation (LES) of turbulent flows is extended to account for the effects of density stratification under the Boussinesq approximation. The model utilizes an eddy viscosity closure by solving a modeled transport equation for the subgrid-scale (SGS) turbulent kinetic energy (ksgs) to obtain the characteristic velocity scale. The closure of the SGS density flux is attained through an algebraic eddy diffusivity-based approach using the eddy viscosity and the turbulent Prandtl number. The transport equation for ksgs gets modified due to density stratification, which leads to a coupling of the SGS stress and the SGS density flux. All the model coefficients are determined locally in a dynamic manner. The dynamic model is evaluated by simulating a fully developed turbulent flow in a periodic channel under neutral and stratified conditions at frictional Reynolds number (Reτ) of 180, 550, and 950 and frictional Richardson number (Riτ) of 0, 60, 120, and 240. The LES predictions are compared with direct numerical simulation results. A comprehensive assessment is performed by examining the behavior of the model coefficients, comparison of static and dynamic approaches for the model coefficients, along with comparison with other well-established algebraic closures for the SGS stress and the SGS density flux at Reτ=550. The results show that the proposed model appropriately responds to the changes in the behavior of the flow due to stratification, at both the resolved and the SGS levels, particularly in the regions away from the wall where internal waves tend to coexist with the shear-generated turbulence. An explicit coupling of the SGS buoyancy flux with the SGS kinetic energy in the dynamic model, which is absent in the other algebraic models, allows improved accuracy in capturing the instantaneous and the statistical features of both the resolved and the SGS quantities.

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Phys. Rev. Fluids 5, 064601– Published 3 June, 2020
  • Received 19 June 2019
  • Accepted 6 May 2020
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