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Research Papers

# LES of Wall-Bounded Flows Using a New Subgrid Scale Model Based on Energy Spectrum Dissipation

[+] Author and Article Information
I. Veloudis, Z. Yang, J. J. McGuirk

Department of Aeronautical and Automotive Engineering, Loughborough University, Loughborough, LE11 3TU Leicestershire, UK

J. Appl. Mech 75(2), 021005 (Feb 20, 2008) (11 pages) doi:10.1115/1.2775499 History: Received October 01, 2006; Revised July 09, 2007; Published February 20, 2008

## Abstract

A new one-equation subgrid scale (SGS) model that makes use of the transport equation for the SGS kinetic energy $(kSGS)$ to calculate a representative velocity scale for the SGS fluid motion is proposed. In the $kSGS$ transport equation used, a novel approach is developed for the calculation of the rate of dissipation of the SGS kinetic energy $(ε)$. This new approach leads to an analytical computation of $ε$ via the assumption of a form for the energy spectrum. This introduces a more accurate representation of the dissipation term, which is then also used for the calculation of a representative length scale for the SGS based on their energy content. Therefore, the SG length scale is not associated simply with the grid resolution or the largest of the SGS but with a length scale representative of the overall SGS energy content. The formulation of the model is presented in detail, and the new approach is tested on a series of channel flow test cases with Reynolds number based on friction velocity varying from 180 to 1800. The model is compared with the Smagorinsky model (1963, “General Circulation Experiments With the Primitive Equations: 1. The Basic Experiment  ,” Mon. Weather Rev., 91, pp. 90–164) and the one-equation model of Yoshizawa and Horiuti (1985, “A Statistically-Derived Subgrid Scale Kinetic Energy Model for the Large Eddy Simulation of Turbulent Flows  ,” J. Phys. Soc. Jpn., 54(8), pp. 2834–2839). The results indicate that the proposed model can provide, on a given mesh, a more accurate representation of the SG scale effects.

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## Figures

Figure 1

Schematic of energy distribution among wave numbers

Figure 2

Variation of f(ε) with ε for κcmax

Figure 3

Variation of f(ε) with ε for κcmin

Figure 4

U+ versus y+ for (a) Reτ=180 and (b) Reτ=395

Figure 5

U+ versus y+ for (a) Reτ=640 and (b) Reτ=1800

Figure 6

U+ versus y+ for Reτ=180 using the ESD model and Inagi (28) function with CT=5.0 and 10.0

Figure 7

Nondimensional rms values of u′¯+, v′¯+, and w′¯+ versus y+ for Reτ=180

Figure 8

Nondimensional rms values of u′¯+, v′¯+, and w′¯+ versus y+ for Reτ=395

Figure 9

Nondimensional rms values of u′¯+, v′¯+, and w′¯+ versus y+ for Reτ=640

Figure 10

Nondimensional rms values of u′¯+, v′¯+, and u′v′¯+ versus y+ for Reτ=1800

Figure 11

Discriminant isocontour for the Smagorinsky model (case 2)

Figure 12

Discriminant isocontour for the kSGS-equation model (case 2)

Figure 13

Discriminant isocontour for the ESD model (case 2)

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