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Research Papers: Fundamental Issues and Canonical Flows

Evaluation of Turbulence Models Using Direct Numerical and Large-Eddy Simulation Data

[+] Author and Article Information
Hassan Raiesi1

Department of Mechanical and Material Engineering, Queen’s University, Kingston, ON, K7L 3N6, Canadaraiesi@me.queensu.ca

Ugo Piomelli, Andrew Pollard

Department of Mechanical and Material Engineering, Queen’s University, Kingston, ON, K7L 3N6, Canada

1

Corresponding author.

J. Fluids Eng 133(2), 021203 (Mar 02, 2011) (10 pages) doi:10.1115/1.4003425 History: Received September 13, 2010; Published March 02, 2011; Online March 02, 2011; Revised November 29, 2011

The performance of some commonly used eddy-viscosity turbulence models has been evaluated using direct numerical simulation (DNS) and large-eddy simulation (LES) data. Two configurations have been tested, a two-dimensional boundary layer undergoing pressure-driven separation, and a square duct. The DNS and LES were used to assess the kε, ζf, kω, and Spalart–Allmaras models. For the two-dimensional separated boundary layer, anisotropic effects are not significant and the eddy-viscosity assumption works well. However, the near-wall treatment used in kε models was found to have a critical effect on the predictive accuracy of the model (and, in particular, of separation and reattachment points). None of the wall treatments tested resulted in accurate prediction of the flow field. Better results were obtained with models that do not require special treatment in the inner layer (ζf, kω, and Spalart–Allmaras models). For the square duct calculation, only a nonlinear constitutive relation was found to be able to capture the secondary flow, giving results in agreement with the data. Linear models had significant error.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Boundary layer, Reδin∗=550. (a) Vertical velocity profile along the top boundary. (b) Distribution of friction coefficient. (c) Profiles of the streamwise velocity component; ◼, ●, △ DNS (10); — present DNS; −⋅⋅− LES.

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Figure 2

Mean streamlines, Reδin∗=2200.

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Figure 3

Prediction of friction coefficient and streamwise velocity profiles obtained using the exact eddy-viscosity 18; — LES; −⋅⋅− RANS

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Figure 4

Distribution of friction coefficient. (a) k−ε model; — LES; −⋅−νT from Eq. 19; --- two-layer wall treatment; −⋅⋅− low-Re model. (b) k−ω model; — LES; --- νT from Eq. 15; −⋅⋅−νT from Eq. 19. (c) ζ−f model; — LES; --- model prediction; −⋅⋅− model prediction with exact k and ε.

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Figure 6

(a) Profiles of the friction coefficient and (b) streamwise velocity component. — LES; −⋅⋅− Spalart–Allmaras model; --- k−ω model

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Figure 7

(a) Profiles of the friction coefficient and (b) streamwise velocity component. — LES; −⋅⋅− low-Re model; --- RNG k−ε model with two-layer wall treatment.

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Figure 8

Distribution of friction coefficient (a) and streamwise velocity profiles (b): ζ−f model; — LES; --- model prediction

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Figure 9

Geometry of the square duct

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Figure 10

Flow statistics along the lines y/h=0.3 and y/h=0.7; — fine grid simulation; --- coarse-grid simulation; ◼ Ref. 17. (a) Mean streamwise velocity; (b) mean spanwise velocity; ((c) and (d)) root-mean-square of streamwise velocity fluctuations; ((e) and (f)) root-mean-square of spanwise velocity fluctuations.

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Figure 11

Isocontours of the cross-stream Reynolds stresses (contour increments of [max(τij)−min(τij)]/12). The dashed lines correspond to negative values. (a) τyz from DNS results; (b) τyz obtained from eddy-viscosity model; (c) τyy from DNS results; (d) τyy obtained from eddy-viscosity model.

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Figure 12

Distribution of wall shear stress. — DNS; −⋅− linear model; --- nonlinear model.

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Figure 13

Flow statistics along the line y/h=0.3. (a) Mean streamwise velocity; (b) mean spanwise velocity; (c) root-mean-square spanwise velocity fluctuations; (d) turbulent kinetic energy; — DNS; −⋅− linear model; --- nonlinear model.

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Figure 5

Distribution of u′v′¯. (a) LES; (b) k−ω; (c) k−ε; (d) profiles of u′v′¯ along a streamline (—) as marked in (a)–(c); --- LES;— k−ω; −⋅−k−ε

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