Implication of Mismatch Between Stress and Strain-Rate in Turbulence Subjected to Rapid Straining and Destraining on Dynamic LES Models

Abstract

Planar straining and destraining of turbulence is an idealized form of turbulence-meanflow interaction that is representative of many complex engineering applications. This paper studies experimentally the response of turbulence subjected to a process involving planar straining, a brief relaxation and destraining. Subsequent analysis quantifies the impact of the applied distortions on model coefficients of various eddy viscosity subgrid-scale models. The data are obtained using planar particle image velocimetry (PIV) in a water tank, in which high Reynolds number turbulence with very low mean velocity is generated by an array of spinning grids. Planar straining and destraining mean flows are produced by pushing and pulling a rectangular piston towards and away from the bottom wall of the tank. The velocity distributions are processed to yield the time evolution of mean subgrid dissipation rate, the Smagorinsky and dynamic model coefficients, as well as the mean subgrid-scale momentum flux during the entire process. It is found that the Smagorinsky coefficient is strongly scale dependent during periods of straining and destraining. The standard dynamic approach overpredicts the dissipation based Smagorinsky coefficient, with the model coefficient at scale Δ in the standard dynamic Smagorinsky model being close to the dissipation based Smagorinsky coefficient at scale 2Δ. The scale-dependent Smagorinsky model, which is designed to compensate for such discrepancies, yields unsatisfactory results due to subtle phase lags between the responses of the subgrid-scale stress and strain-rate tensors to the applied strains. Time lags are also observed for the SGS momentum flux at the larger filter scales considered. The dynamic and scale-dependent dynamic nonlinear mixed models do not show a significant improvement. These potential problems of SGS models suggest that more research is needed to further improve and validate SGS models in highly unsteady flows.