Filtering, averaging, and scale dependency in homogeneous variable density turbulence

Journal Article · Wed Feb 24 00:00:00 EST 2021 · Physics of Fluids

DOI:https://doi.org/10.1063/5.0040337· OSTI ID:1835782

Saenz, Juan Antonio  ^[1]; Aslangil, Denis  ^[1]; Livescu, Daniel  ^[1]

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1. Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

We investigate relationships between statistics obtained from filtering and from ensemble or Reynolds-averaging turbulence flow fields as a function of length scale. Generalized central moments in the filtering approach are expressed as inner products of generalized fluctuating quantities, $q\text{'}(\xi ,x)=q\left(\xi \right)-\overline{q}\left(x\right)$, representing fluctuations of a field $q\left(\xi \right)$, at any point ξ, with respect to its filtered value at x. For positive-definite filter kernels, these expressions provide a scale-resolving framework, with statistics and realizability conditions at any length scale. In the small-scale limit, scale-resolving statistics become zero. In the large-scale limit, scale-resolving statistics and realizability conditions are the same as in the Reynolds-averaged description. Using direct numerical simulations (DNS) of homogeneous variable density turbulence, we diagnose Reynolds stresses, ${\mathcal{T}}_{ij}$, resolved kinetic energy, kr, turbulent mass-flux velocity, a_i, and density-specific volume covariance, b, defined in the scale-resolving framework. These variables, and terms in their governing equations, vary smoothly between zero and their Reynolds-averaged definitions at the small and large scale limits, respectively. At intermediate scales, the governing equations exhibit interactions between terms that are not active in the Reynolds-averaged limit. For example, in the Reynolds-averaged limit, b follows a decaying process driven by a destruction term; at intermediate length scales, it is a balance between production, redistribution, destruction, and transport, where b grows as the density spectrum develops and then decays when mixing becomes strong enough. This work supports the notion of a generalized, length-scale adaptive model that converges to DNS at high resolutions and to Reynolds-averaged statistics at coarse resolutions.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA)
• Grant/Contract Number: 89233218CNA000001
• OSTI ID: 1835782
• Alternate ID(s): OSTI ID: 1767319
• Report Number(s): LA-UR-20-29879; TRN: US2300250
• Journal Information: Physics of Fluids, Vol. 33, Issue 2; ISSN 1070-6631
• Publisher: American Institute of Physics (AIP)
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS