Subgrid-scale effects in compressible variable-density decaying turbulence

Journal Article · Tue May 08 04:00:00 UTC 2018 · Journal of Fluid Mechanics

DOI: https://doi.org/10.1017/jfm.2018.281 · OSTI ID:1436961

GS, Sidharth  ^[1]; Candler, Graham V. ^[2]

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1. Univ. of Minnesota, Minneapolis, MN (United States). Aerospace Engineering and Mechanics; California Institute of Technology
2. Univ. of Minnesota, Minneapolis, MN (United States). Aerospace Engineering and Mechanics

We present that 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.

• Research Organization: California Inst. of Technology (CalTech), Pasadena, CA (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA), Office of Defense Programs (DP) (NA-10); US Air Force Office of Scientific Research (AFOSR)
• Grant/Contract Number: NA0002382
• OSTI ID: 1436961
• Journal Information: Journal of Fluid Mechanics, Journal Name: Journal of Fluid Mechanics Vol. 846; ISSN applab; ISSN 0022-1120
• Publisher: Cambridge University PressCopyright Statement
• Country of Publication: United States
• Language: English