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Subgrid-scale effects in compressible variable-density decaying turbulence

Published online by Cambridge University Press:  08 May 2018

Sidharth GS Open the ORCID record for Sidharth GS [Opens in a new window]  and
Graham V. Candler
Sidharth GS*
Affiliation:
Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN 55455, USA
Graham V. Candler
Affiliation:
Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN 55455, USA
*
†Email address for correspondence: [email protected]
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Abstract

Many turbulent flows are characterized by complex scale interactions and vorticity generation caused by compressibility and variable-density effects. In the large-eddy simulation of variable-density flows, these processes manifest themselves as subgrid-scale (SGS) terms that interact with the resolved-scale flow. This paper studies the effect of the variable-density SGS terms and quantifies their relative importance. We consider the SGS terms appearing in the density-weighted Favre-filtered equations and in the unweighted Reynolds-filtered equations. The conventional form of the Reynolds-filtered momentum equation is complicated by a temporal SGS term; therefore, we derive a new form of the Reynolds-filtered governing equations that does not contain this term and has only double-correlation SGS terms. The new form of the filtered equations has terms that represent the SGS mass flux, pressure-gradient acceleration and velocity-dilatation correlation. To evaluate the dynamical significance of the variable-density SGS effects, we carry out direct numerical simulations of compressible decaying turbulence at a turbulent Mach number of 0.3. Two different initial thermodynamic conditions are investigated: homentropic and a thermally inhomogeneous gas with regions of differing densities. The simulated flow fields are explicitly filtered to evaluate the SGS terms. The importance of the variable-density SGS terms is quantified relative to the SGS specific stress, which is the only SGS term active in incompressible constant-density turbulence. It is found that while the variable-density SGS terms in the homentropic case are negligible, they are dynamically significant in the thermally inhomogeneous flows. Investigation of the variable-density SGS terms is therefore important, not only to develop variable-density closures but also to improve the understanding of scale interactions in variable-density flows.

JFM classification

Turbulent Flows: Compressible turbulence Turbulent Flows: Isotropic turbulence Mixing: Turbulent mixing
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 846 , 10 July 2018 , pp. 428 - 459
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Copyright
© 2018 Cambridge University Press 

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