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SPECIAL SECTION ON RANS/LES/DES/DNS: THE FUTURE PROSPECTS OF TURBULENCE MODELING

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

[+] Author and Article Information
Jun Chen

Department of Mechanical Engineering,  Johns Hopkins University, 223 Latrobe Hall, 3400 North Charles Street, Baltimore, MD 21218junchen@jhu.edu

Joseph Katz

Department of Mechanical Engineering,  Johns Hopkins University, 118 Latrobe Hall, 3400 North Charles Street, Baltimore, MD 21218katz@jhu.edu

Charles Meneveau

Department of Mechanical Engineering,  Johns Hopkins University, 127 Latrobe Hall, 3400 North Charles Street, Baltimore, MD 21218meneveau@jhu.edu

J. Fluids Eng 127(5), 840-850 (Jun 01, 2005) (11 pages) doi:10.1115/1.1989360 History: Received August 05, 2004; Revised June 01, 2005

## 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.

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## Figures

Figure 1

Schematic description of (a) the experimental facility and (b) the activity grid

Figure 2

Schematics of the instrumentation and control system

Figure 3

Piston motion trajectory

Figure 4

Mean flow streamline patterns at (a) t=1.160s and (b) t=2.160s

Figure 5

Evolution of mean strain, spatially averaged rate S11 (squares) and −S22 (triangles). The error bars represent the standard deviation of spatial distribution of S(t).

Figure 6

Spatial distribution of rms velocity fluctuations of the initial turbulence (t=0.210s) (a) u1 and (b) u2

Figure 7

Kinetic energy spectra of the initial equilibrium turbulence (t=0.210s)

Figure 8

Evolution of mean SGS dissipation

Figure 9

Evolution of the term TΔ=2Δ2⟨∣S̃∣S̃ijS̃ij⟩ at different scales

Figure 10

Evolution of the dissipation based Smagorinsky model coefficients (CSΔ)2 at three different filter scales. Squares+dash line: Δ=25η0, triangles+dashdot line: Δ=50η0, diamonds+dashdotdot line: Δ=100η0, and solid line: CSΔ=0.16.

Figure 11

Evolution of standard dynamic model coefficients (squares and dash lines) and comparison with the dissipation based Smagorinsky model coefficients (triangles and dashdot lines, given in Fig. 1). (a) Δ=25η0 and (b) Δ=50η0.

Figure 12

Evolution of standard dynamic model coefficient at scale Δ (squares and dash lines) compared to the evolution of the dissipation-based Smagorinsky model coefficient at scale 2Δ (triangles and dashdot lines). (a) Δ=25η0 and (b) Δ=50η0.

Figure 13

Evolution of scale-dependent dynamic model coefficient CSΔ,SDDM (squares+dash line) in comparison to the dissipation-based Smagorinsky model coefficient CSΔ (dotted line), and the standard dynamic model coefficient CSΔ,DM (triangles+dashdot line). Δ=25η0 for all three curves.

Figure 14

Evolution of the coefficient CSΔ,DM (squares+dash line) and CS2Δ,DM (triangles+dashdot line) for Δ=25η0, which are used in the scale-dependent dynamic approach, Eq. 13

Figure 15

Evolution of standard dynamic coefficient (CS,NLΔ,DM)2 of Eq. 15 (triangles and dashdot lines) in the mixed model in comparison with the dissipation-based model coefficient obtained by balancing SGS dissipation (squares and dash lines). (a) Δ=25η0 and (b) Δ=50η0.

Figure 16

Evolution of scale-dependent dynamic nonlinear model coefficient (CS,NLΔ,SDDM)2 of Eq. 16 (triangles and dashdot lines) in comparison with the dissipation-based nonlinear model coefficients (squares and dash lines).

Figure 17

Evolution of the modeled and dissipation-based mean SGS stress anisotropy tensor terms (b11 and b22). (a) Δ=25η0 and (b) Δ=100η0. Open squares+dash lines: b11, solid squares+dotted lines: b11mod, open triangles+dash lines: b22, and solid triangles+dotted lines: b22mod.

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