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A new subgrid eddy-viscosity model for large-eddy simulation of anisotropic turbulence

Published online by Cambridge University Press:  14 June 2007

G. X. CUI*
Affiliation:
Department of Engineering Mechanics, Tsinghua University, Beijing, China
C. X. XU
Affiliation:
Department of Engineering Mechanics, Tsinghua University, Beijing, China
L. FANG
Affiliation:
Department of Engineering Mechanics, Tsinghua University, Beijing, China Laboratory of Fluid Mechanics and Acoustics, Ecole Centrale de Lyon, France
L. SHAO
Affiliation:
Laboratory of Fluid Mechanics and Acoustics, Ecole Centrale de Lyon, France
Z. S. ZHANG
Affiliation:
Department of Engineering Mechanics, Tsinghua University, Beijing, China
*
Author to whom correspondence should be addressed: demzzs@mail.tsinghua.edu.cn; cgx@mail.tsinghua.edu.cn.

Abstract

A new subgrid eddy-viscosity model is proposed in this paper. Full details of the derivation of the model are given with the assumption of homogeneous turbulence. The formulation of the model is based on the dynamic equation of the structure function of resolved scale turbulence. By means of the local volume average, the effect of the anisotropy is taken into account in the generalized Kolmogorov equation, which represents the equilibrium energy transfer in the inertial subrange. Since the proposed model is formulated directly from the filtered Navier–Stokes equation, the resulting subgrid eddy viscosity has the feature that it can be adopted in various turbulent flows without any adjustments of model coefficient. The proposed model predicts the major statistical properties of rotating turbulence perfectly at fairly low-turbulence Rossby numbers whereas subgrid models, which do not consider anisotropic effects in turbulence energy transfer, cannot predict this typical anisotropic turbulence correctly. The model is also tested in plane wall turbulence, i.e. plane Couette flow and channel flow, and the major statistical properties are in better agreement with those predicted by DNS results than the predictions by the Smagorinsky, the dynamic Smagorinsky and the recent Cui–Zhou–Zhang–Shao models.

Type
Papers
Copyright
Copyright © Cambridge University Press 2007

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References

REFERENCES

Bardina, J., Ferziger, J. & Reynolds, W. C. 1987 Improved subgrid model for large-eddy simulation. AIAA Paper 801357.Google Scholar
Cambon, C., Mansour, N. N. & Godeferd, F. S. 1997 Energy transfer in rotating turbulence. J. Fluid Mech. 337, 303.CrossRefGoogle Scholar
Cambon, C., Rubinstein, R. & Godeferd, F. S. 2004 Advances in wave turbulence: rapidly rotating flows. New J. Phys. 6, 73.CrossRefGoogle Scholar
Casciola, C. M., Gualtieri, P., Benzi, R. & Piva, R. 2004 Scale by scale budget and similarity law for shear turbulence. J. Fluid Mech. 476, 105.CrossRefGoogle Scholar
Chollet, J. P. & Lesieur, M. 1981 Parameterisation for small scales of three dimensional isotropic turbulence using spectral closure. J. Atmos. Sci. 38, 27472757.Google Scholar
Cui, G. X., Zhou, H. B., Zhang, Z. S. & Shao, L. 2004 A new dynamic subgrid eddy viscosity model with application to turbulent channel flow. Phys. Fluids 16 (8), 2835.CrossRefGoogle Scholar
Gemano, M., Piomelli, U., Moin, P. & Cabot, W. H. 1991 A dynamic subgrid-scale eddy viscosity model. Phys. Fluids, A3, 1760.CrossRefGoogle Scholar
Geurts, B. J. 2004 Elements of Direct and Large-Eddy Simulation. Edwards.Google Scholar
Hill, R. J. 2002 Exact second-order structure function relationship. J. Fluid Mech. 468, 317.Google Scholar
Horiuti, K. 2006 Transformation properties of dynamic subgrid-scale models in a frame of reference undergoing rotation. J. Turbulence 7, 1.CrossRefGoogle Scholar
Jacquin, L., Leuchter, O., Cambon, C. & Mathieu, J. 1990 Homogeneous turbulence in the presence of rotation. J. Fluid Mech. 220, 1.CrossRefGoogle Scholar
Jimenez, J. & Moser, R. D. 2000 Large-eddy simulation: where are we and what can we expect? AIAA J. 38, 605.CrossRefGoogle Scholar
Kawamura, H., Abe, H. & Matsuo, Y. 1999 DNS of turbulent heat transfer in channel flow with respect to Reynolds and Prandtl number effects. Intl J. Heat Fluid Flow 20, 196207.CrossRefGoogle Scholar
Kraichnan, R. 1976 Eddy viscosity in two and three dimensions. J. Atmos. Sci. 15211536.Google Scholar
Meneveau, C. 1994 Statistics of turbulence subgrid-scale stress: necessary conditions and experimental tests. Phys. Fluids A 6, 815833.Google Scholar
Métais, O. & Lesieur, M. 1992 Spectral large-eddy simulation of isotropic and stably stratified turbulence. J. Fluid Mech. 256, 157194.CrossRefGoogle Scholar
Monin, A. S. & Yaglom, A. M. 1975 Statistical Fluid Mechanics. Mechanics of Turbulence, Vol. 2. MIT Press.Google Scholar
Moser, R. D., Kim, J. & Moin, P. 1999 Direct numerical simulation of turbulent channel flow up to Re τ = 590. Phys Fluids 8, 1076.Google Scholar
Nicoud, F. & Ducros, F. 1999 Subgrid-scale stress modeling based on the square of the velocity gradient tensor. Flow, Turbulence Combust 63, 183200.CrossRefGoogle Scholar
Pope, S. 2004 Ten questions concerning the large eddy simulation of turbulent flows. New J. Phys. 6, 124.Google Scholar
Pope, S. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Rogallo, R. S. 1981 Numerical experiments in homogeneous turbulence. NASA Rep. 81315.Google Scholar
Sagaut, P. 2002 Large Eddy Simulation for Incompressible Flows. Springer.CrossRefGoogle Scholar
Skrbek, L. & Stalp, S. R. 2000 On the decay of homogeneous turbulence. Phys. Fluids 12 (8), 1997.CrossRefGoogle Scholar
Smagorinsky, J. 1963. General circulation experiments with primitive equation. Mon. Weather Rev. 91, 99.Google Scholar
Vreman, A. W. 2004 An eddy-viscosity subgrid-scale mode for turbulent shear flow: algebraic theory and applications. Phys. Fluids 16, 36703681.Google Scholar
Xu, C., Zhang, Z. & Nieuwstadt, F. T. M. 1996. Origin of high kurtosis in viscous sublayer. Phys. Fluids 8, 19381942.Google Scholar
Yang, X. & Domaraski, J. A. 2004 Large eddy simulation of decaying turbulence. Phys. Fluids 16 (11), 4088.CrossRefGoogle Scholar