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Analysis of the equilibrium wall model for high-speed turbulent flows

Prahladh S. Iyer*

Mujeeb R. Malik†

  • National Institute of Aerospace, Hampton, Virginia 23666, USA

  • NASA Langley Research Center, Hampton, Virginia 23681, USA

  • *prahladh.iyer@nianet.org
  • †mujeeb.r.malik@nasa.gov
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Phys. Rev. Fluids 4, 074604 – Published 25 July, 2019

DOI: https://doi.org/10.1103/PhysRevFluids.4.074604

Abstract

We perform a priori and a posteriori analyses of the equilibrium wall model for high-speed wall-bounded turbulent flows. The time-averaged flow from various direct numerical simulation (DNS) databases is used as input to the wall model and the accuracy of the predictions in terms of wall shear stress and wall temperature (or heat flux for isothermal wall boundary conditions) are assessed. Two different mixing-length-based eddy-viscosity models and various damping functions are tested in this study. Both mixing-length models involve two adjustable parameters: (i) the von Kármán constant κ, which varies in the literature from 0.37 to 0.44, and (ii) a viscous damping constant A+ (for the van Driest damping function). Also, for compressible flows, multiple scalings can be used for the viscous wall-normal spacing in the damping function. The sensitivity of the results to these model parameters is reported and it is found that the predictions of skin friction and wall temperature (or heat flux) are sensitive to the constants used, damping function scaling, and the wall-model exchange location. Wall-modeled large-eddy simulation (WMLES) is performed for (i) supersonic channel flow with a cold wall and (ii) an axisymmetric supersonic boundary layer for the adiabatic wall condition, to verify the a priori trends observed with respect to the damping functions. A posteriori WMLES results are consistent with the trends observed in the a priori analysis of DNS data, thus indicating the usefulness of the a priori analysis. We introduce a damping function scaling, which works well over a range of Mach numbers and thermal wall conditions.

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Outline

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Phys. Rev. Fluids 4, 074604– Published 25 July, 2019
  • Received 26 March 2019
Article part of CHORUS
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