Evolution and modeling of subgrid scales during rapid straining of turbulence

Shewen Liu, Joseph Katz and Charles Meneveau
Department of Mechanical Engineering
The Johns Hopkins University
Baltimore, Maryland 21218

ABSTRACT: The response, evolution, and modeling of subgrid-scale (SGS) stresses during rapid straining of turbulence is studied experimentally. Nearly isotropic turbulence with low mean velocity and Rl ~ 290 is generated in a water tank by means of spinning grids. Rapid straining (axisymmetric expansion) is achieved with two disks pushed towards each other. Time-resolved, two-dimensional velocity measurements are performed using cinematic PIV. The SGS stress is subdivided to a stress due to the mean distortion, cross term (the interaction between the mean and turbulence), and the turbulent SGS stress tij^T. Analysis of the time evolution of tij^T at various filter scales shows that all scales are more isotropic than the prediction of Rapid Distortion Theory, with increasing isotropy as scales decrease. A-priori tests show that rapid straining does not affect the high correlation exhibited by the similarity model, while the low correlation of the Smagorinsky model for isotropic turbulence shows some increase during rapid straining. Analysis of the evolution of total SGS energy dissipation reveals, surprisingly, that the Smagorinsky model with a constant coefficient under-predicts the dissipation during rapid straining. While the partial dissipationP_ij^T due only to the turbulent part of the stress is over-predicted by the Smagorinsky model, addition of the cross terms reverses the trend. The similarity model with a constant coefficient appropriate for isotropic turbulence, on the other hand, overpredicts SGS dissipation. These opposite trends suggest that the linear combination of both models (mixed model) may provide accurate prediction of SGS dissipation during rapid straining, as confirmed by the data. However, the mixed model with coefficients determined from dissipation balance underpredicts the SGS stress.

J. Fluid Mech 387, (1999), p. 281

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