Subgrid Scale Modeling of Turbulence for the Dynamic Procedure Using Finite Difference Method and Its Assessment on the Thermally Stratified Turbulent Channel Flow

[+] Author and Article Information
Makoto Tsubokura

Department of Mechanical Engineering and Intelligent Systems,  The University of Electro-Communications, Chofugaoka 1-5-1, Chofu-shi, Tokyo 182-8585, Japantsubo@mce.uec.ac.jp

J. Appl. Mech 73(3), 382-390 (Oct 14, 2005) (9 pages) doi:10.1115/1.2150236 History: Received December 16, 2003; Revised October 14, 2005

Previously proposed methods for subgrid-scale (SGS) stress modeling were re-investigated and extended to SGS heat-flux modeling, and various anisotropic and isotropic eddy viscosity/diffusivity models were obtained. On the assumption that they are used in a finite-difference (FD) simulation, the models were constructed in such a way that they are insensitive to numerical parameters on which calculated flows are strongly dependent in the conventional Smagorinsky model. The models obtained, as well as those previously proposed, were evaluated a priori in a stably stratified open channel flow, which is considered to be a challenging application of large eddy simulation and suitable for testing both SGS stress and heat-flux models. The most important feature of the models proposed is that they are insensitive to the discretized test filtering parameter required in the dynamic procedure of Germano (1991, Phys. Fluids, 3, pp. 1760–1765) in FD simulation. We also found in SGS heat-flux modeling that the effect of the grid (resolved)-scale (GS) velocity gradient plays an important role in the estimation of the streamwise heat flux, and an isotropic eddy diffusivity model with the effect of the GS velocity is proposed.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 3

One-dimensional power spectra of streamwise velocity at y+∼16 for longitudinal (top) and transverse (bottom) directions

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Figure 4

Exact SGS stress and heat flux obtained from the DNS data

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Figure 5

Plane-averaged correlation coefficient between the exact and modeled rate of SGS turbulence production

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Figure 6

SGS energy production by SGS models using the dynamic procedure; Δ¯∕h=4∕3 and Δ̃∕h=4

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Figure 7

SGS eddy viscosity coefficient by (a) the proposed isotropic model and (b) the Smagorinsky models for various filter parameters Δ¯∕h and Δ̃∕h; α=(Δ̃∕Δ¯)2. (엯, exact values obtained from the DNS data.)

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Figure 8

Plane-averaged correlation coefficient between the exact and modeled (a) SGS temperature gradient (comparison between the isotropic and the anisotropic representations), (b) SGS temperature gradient (effect of velocity gradient term), and (c) rate of SGS temperature variance

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Figure 9

SGS turbulent Prandtl number predicted by the proposed isotropic and the Smagorinsky models for various filter parameters Δ¯∕h and Δ̃∕h; α=(Δ̃∕Δ¯)2. (엯, exact values obtained from the DNS data.)

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Figure 10

(a) Mean velocity, (b) rms velocity, and (c) GS streamwise and normal-wall temperature gradient: lines, DNS (GS); open symbols, LES of Eqs. 11,13(iso+v.g.); closed symbols, LES of Eqs. 11,12 (iso). Filter parameters: Δ¯∕h=2 and Δ̃∕h=4.

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Figure 1

Stably stratified, open channel flow

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Figure 2

(a) Mean velocity and temperature and (b) rms velocity fluctuations. (DNS: neutral case by Moser (see Ref. 16) at Reτ=590, stable case by Iida (see Ref. 17) at Reτ=150, Riδ=0.04,0.09)




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