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TECHNICAL PAPERS

Index of Resolution Quality for Large Eddy Simulations

[+] Author and Article Information
I. B. Celik

Mechanical and Aerospace Engineering, West Virginia University, P.O. Box 6106, Morgantown, WV, 25506-6106ismail.celik@mail.wvu.edu

Z. N. Cehreli, I. Yavuz

Mechanical and Aerospace Engineering, West Virginia University, P.O. Box 6106, Morgantown, WV, 25506-6106

J. Fluids Eng 127(5), 949-958 (Sep 01, 2005) (10 pages) doi:10.1115/1.1990201 History:

In the light of rapidly increasing applications of large-eddy simulations (LES), it is deemed necessary to impose some quality assessment measures for such studies. The verification of LES calculations is difficult because of the fact that both the subgrid scale (SGS) model contribution and numerical discretization errors are functions of the grid resolution. In this study, various indexes of quality measures, hereafter referred to as LES̱IQ, are proposed. The recommended LES̱IQ is based on the Richardson extrapolation concept. This method has been applied to various cases and the calculated LES̱IQ results are compared with the relative total experimental and direct numerical simulation (DNS) error, defined as IQ̱EX and IQ̱DNS, respectively. It is postulated that in practical applications of LES, numerical dissipation will always be a significant part of the overall dissipation, and it must be accounted for in any assessment of the quality of LES. It is further suggested that LES̱IQ of 75% to 85% can be considered adequate for most engineering applications that typically occur at high Reynolds numbers; the proposed index is an indicator of good resolution (i.e., verification), but not necessarily a good or accurate model (i.e., validation).

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Copyright © 2005 by American Society of Mechanical Engineers
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Figures

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Figure 1

The variation of subgrid activity parameter along the streamwise direction for LES of the wake of a turning ship (Cehreli, 2004 (31)).

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Figure 2

Index of quality versus h∕ηk or ⟨vt,eff⟩∕v

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Figure 3

(a) The resolved kinetic energy. (b) Large-eddy simulation index of quality (LES̱IQ) [Eqs. 15,16] for flow around a square cylinder (Sohankar , 1999 (26)). (The numbers in parentheses in the legend indicate grid nodes in the x-,y-,z directions, respectively).

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Figure 4

(a) The resolved turbulence kinetic energy. (b) LES̱IQ [Eq. 18] and IQ̱EX [Eq. 17] for the mixing layer simulation (Badeau, 2003 (27)). (The numbers in parentheses in the legend indicate grid nodes in the x-,y-,z directions, respectively).

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Figure 5

(a) The resolved turbulence kinetic energy. (b) LES̱IQ [Eq. 18] and IQ̱EX [Eq. 17] for the channel flow simulation (Shi, 2001 (28)): Curve fit to experiments was done by the present authors. (The numbers in parentheses in the legend indicate grid nodes in the x-,y-,z directions, respectively).

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Figure 6

(a) The resolved turbulence kinetic energy. (b) LES̱IQ [Eqs. 15,16] for surface piercing flat-plate boundary layer simulation (Sreedhar and Stern, 1998 (22)) for the uniform grid and 3% stretching in the transverse direction (The numbers in parentheses in the legend indicate grid nodes in the x-,y-,z directions, respectively).

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Figure 7

(a) Resolved turbulence kinetic energy normalized with respect to its inlet value, kinlet=3.3E−0.3 (ship cruising on a straight track). (b) LES̱IQ [Eqs. 15,16] along centerline of the wake. (The numbers in parentheses in the legend indicate grid nodes in the x-,y-,z directions, respectively).

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Figure 8

Vertical buoyant jet. (a) Comparison of resolved TKE from DREAM® simulations (300×238×238; 150×107×107; and 75×56×56) to experiments (Anwar, 1969 (40)) at x∕Din=20 (normalized with respect to the square of the inlet velocity), (b). Corresponding LES̱IQ and IQEX of the above data  * (wrms for the experimental data was estimated by the authors as wrms≅vrms).

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Figure 9

(a) Resolved turbulence kinetic energy decay versus time for Δ∕h=2; (b) Calculated LES̱IQ [Eq. 20] and IQ̱DNS [Eq. 17]. A curve fit to the turbulent kinetic energy data from Geurts and Froehlich (2001) (18) was used in our analysis.

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