Energy dissipation in LES: dependence on flow structure and effects of eigenvector alignments


Chad Higgins(1), C. Meneveau(2,3), Marc B. Parlange(1,3)

1 Department of Geography and Environmental Engineering 2 Department of Mechanical Engineering 3Center for Environmental and Applied Fluid Mechanics, The Johns Hopkins University, Baltimore MD 21218

ABSTRACT: Kinetic energy dissipation plays a vital role in large eddy simulations, and subgrid models must reproduce it accurately to prevent either overdamping of resolved scales, or underprediction which can lead to numerical instabilities. Equating mean subgrid-scale dissipation to molecular dissipation for the Smagorinsky model, Lilly (1967) derived a classic relationship between the eddy-viscosity parameter and the universal Kolmogorov constant, which is briefly reviewed. The SGS dissipation arises from correlations among the SGS stress tensor and the strain-rate tensor of the resolved motions, formally evaluated using a tensor contraction among these two tensors. Here, a geometric interpretation of this tensor contraction is derived with which the dependence of subgrid-scale (SGS) dissipation on alignment angles between the eigendirections of the SGS stress and the filtered strain rate tensors is explicitly known. Among others, it can be used to predict the recent field and laboratory observations that the SGS dissipation conditionally averaged on the so-called strain state parameter, , increases with increasin at indicating that high SGS dissipation is associated with axisymmetric extending motions.

In Festschrift “Turbulence and convection. Scientific inspirations by Douglas K. Lilly”, (2004, Cambridge University Press, 240p, E. Fedorovich, R. Rotunno, B. Stevens Eds.), 51-69.

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Charles Meneveau, Department of Mechanical Engineering, Johns Hopkins University, 3400 N. Charles Street, Baltimore MD 21218, USA, Phone: 1-410-516-7802, Fax: 1-(410) 516-7254, email: meneveau@jhu.edu

 
Last update: 03/17/2011