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Shear-improved Smagorinsky model for large-eddy simulation of wall-bounded turbulent flows

Published online by Cambridge University Press:  14 October 2021

E. Lévêque ,
F. Toschi ,
L. Shao  and
J.-P. Bertoglio
E. Lévêque
Affiliation:
Laboratoire de Physique, CNRS, Université de Lyon, École normale supérieure de Lyon, France
F. Toschi
Affiliation:
Istituto per le Applicazioni del Calcolo, CNR, Viale del Policlinico 137, I-00161, Roma, Italy INFN, Sezione di Ferrara, Via G. Saragat 1, I-44100 Ferrara, Italy
L. Shao
Affiliation:
Laboratoire de Mécanique des Fluides et d'Acoustique, CNRS, Université de Lyon, École centrale de Lyon, Université Lyon 1, INSA de Lyon, France
J.-P. Bertoglio
Affiliation:
Laboratoire de Mécanique des Fluides et d'Acoustique, CNRS, Université de Lyon, École centrale de Lyon, Université Lyon 1, INSA de Lyon, France
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Abstract

A shear-improved Smagorinsky model is introduced based on results concerning mean-shear effects in wall-bounded turbulence. The Smagorinsky eddy-viscosity is modified as vT =(Csδ)2(|S|—|〈S〉|): the magnitude of the mean shear |〈S〉|is subtracted from the magnitude of the instantaneous resolved rate-of-strain tensor |S|; CS is the standard Smagorinsky constant and Δ denotes the grid spacing. This subgrid-scale model is tested in large-eddy simulations of plane-channel flows at Reynolds numbers Reτ = 395 and Reτ = 590. First comparisons with the dynamic Smagorinsky model and direct numerical simulations for mean velocity, turbulent kinetic energy and Reynolds stress profiles, are shown to be extremely satisfactory. The proposed model, in addition to being physically sound and consistent with the scale-by-scale energy budget of locally homogeneous shear turbulence, has a low computational cost and possesses a high potential for generalization to complex non-homogeneous turbulent flows.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 570 , 10 January 2007 , pp. 491 - 502
Copyright
Copyright © Cambridge University Press 2007

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References

REFERENCES

Benzi, R., Amati, G., Casciola, C., Toschi, F. & Piva, R. 1999 Intermittency and scaling laws for wall bounded turbulence. Phys. Fluids 11 (6), 1284–1286.CrossRefGoogle Scholar
Berselli, L. C., Iliescu, T. & Layton, W. J. 2005 Mathematics of Large Eddy Simulation of Turbulent Flows. Springer.Google Scholar
Casciola, C. M., Gualtieri, P., Benzi, R. & Piva, R. 2003 Scale-by-scale budget and similarity laws for shear turbulence. J. Fluid Mech. 176, 105–114.CrossRefGoogle Scholar
Craya, A. 1958 Contribution à l'analyse de la turbulence associée à des vitesses moyennes. P. S. T. Ministère de l'Air 345.Google Scholar
Danaila, L., Antonia, R. & Burattini, P. 2004 Progress in studying small-scale turbulence using exact two-point equations. New J. Phys. 6, 128.CrossRefGoogle Scholar
Deardorff, J. W. 1970 A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers. J. Fluid Mech. 41, 453.CrossRefGoogle Scholar
van Driest, E. R. 1956 On turbulent flow near a wall. J. Aero. Sci. 23, 1007–1011.CrossRefGoogle Scholar
Dubois, T., Jauberteau, F. & Temam, R. 1999 Dynamic Multilevel Methods and the Numerical Simulation of Turbulence. Cambridge University Press.Google Scholar
Frisch, U. 1995 Turbulence: The Legacy of A. N. Kolmogorov. Cambridge University Press.CrossRefGoogle Scholar
Germano, M. 1992 Turbulence: the filtering approach. J. Fluid Mech. 238, 325–336.CrossRefGoogle Scholar
Germano, M., Piomelli, U., Moin, P. & Cabot, W. H. 1991 A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A 3, 1760.CrossRefGoogle Scholar
Ghosal, S. & Moin, P. 1995 The basic equations for the large eddy simulation of turbulent flows in complex geometry. J. Comput. Phys. 118, 24–37.CrossRefGoogle Scholar
Hinze, J. O. 1976 Turbulence. McGraw–Hill.Google Scholar
Hoyas, S. & Jimenez, J. 2006 Scaling of velocity fluctuations in turbulent channels up to Reτ = 2000. Phys. Fluids 18, 011702, http://torroja.dmt.upm.es/ftp/channels/data/.CrossRefGoogle Scholar
Hughes, T. J. R., Mazzei, L. & Jansen, K. E. 2000 Large eddy simulation and the variational multiscale method. Compu. Visualiz. Sci. 3, 47.CrossRefGoogle Scholar
Hughes, T. J. R., Oberai, A. & Mazzei, L. 2001 Large eddy simulation of turbulent channel flows by the variational multiscale method. Phys. Fluids 13 (6), 1784–1799.CrossRefGoogle Scholar
Kim, J., Moin, P. & Moser, R. D. 1987 Turbulent statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133.CrossRefGoogle Scholar
Kraichnan, R. H. 1976 Eddy-viscosity in two and three dimensions. J. Atmos. Sci. 33, 1521–1536.2.0.CO;2>CrossRefGoogle Scholar
Leonard, A. 1974 Energy cascade in large-eddy simulations of turbulent fluid flows. Adv. Geophys. A 18, 237–248.CrossRefGoogle Scholar
Lesieur, M. 1997 Turbulence in Fluids, 3rd edn. Kluwer.CrossRefGoogle Scholar
Lesieur, M. & Metais, O. 1996 New trends in large-eddy simulations of turbulence. Annu. Rev. Fluid. Mech. 28, 45–82.CrossRefGoogle Scholar
Lilly, D. K. 1967 The representation of small-scale turbulence in numerical simulation experiments. In Proc. IBM Sci. Comput. Symp. Environ. Sci, p. 195.Google Scholar
Liu, S., Katz, J. & Meneveau, C. 1999 Evolution and modelling of subgrid scales during rapid straining of turbulence. J. Fluid Mech. 387, 281–320.CrossRefGoogle Scholar
Meneveau, C. & Katz, J. 2000 Scale-invariance and turbulence models for large-eddy simulation. Annu. Rev. Fluid Mech. 32, 1–32.CrossRefGoogle Scholar
Moin, P. & Kim, J. 1982 Numerical investigation of turbulent channel flow. J. Fluid Mech. 118, 341–377.CrossRefGoogle Scholar
Monin, A. S. & Yaglom, A. M. 1975 Statistical Fluid Mechanics. MIT Press, Cambridge MA.Google Scholar
Moser, R. D., Kim, J. & Mansour, N. N. 1999 Direct numerical simulation of turbulent channel flow up to Reτ = 590. Phys. Fluids 11 (4), 943–945, http://www.tam.uiuc.edu/Faculty/Moser.CrossRefGoogle Scholar
Perot, B. & Moin, P. 1995 Shear-free turbulent boundary layers. Part 1. Physical insights into near wall turbulence. J. Fluid Mech. 295, 199–227.CrossRefGoogle Scholar
Piomelli, U. 1993 High Reynolds number calculations using the dynamic subgrid-scale stress model. Phys. Fluids A 5 (6), 1484.CrossRefGoogle Scholar
Piomelli, U. 1999 Large-eddy simulation: achievements and challenges. Prog. Aerosp. Sci. 35, 335–362.CrossRefGoogle Scholar
Piomelli, U. & Balaras, E. 2002 Wall-layer models for large-eddy simulations. Annu. Rev. Fluid Mech. 34, 349–374.CrossRefGoogle Scholar
Piomelli, U. & Zang, T. A. 1991 Large-eddy simulation of transitional channel flow. Comput. Phys. Commun. 65, 224–230.CrossRefGoogle Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Rogallo, R. S. & Moin, P. 1984 Numerical simulation of turbulent flows. Annu. Rev. Fluid Mech. 16, 99–137.CrossRefGoogle Scholar
Ruiz-Chavarria, G., Ciliberto, S., Baudet, C. & Lévéque, E. 2000 Scaling properties of the streamwise component of velocity in a turbulent boundary layer. Physica D 141, 183–198.CrossRefGoogle Scholar
Sagaut, P. 2001 Large Eddy Simulation for Incompressible Flows. Springer.CrossRefGoogle Scholar
Sagaut, P., Deck, S. & Terracol, M. 2006 Multiscale and Multiresolution Approaches in Turbulence. Imperial College Press.CrossRefGoogle Scholar
Schumann, U. 1975 Subgrid scale model for finite difference simulations of turbulent flows in plane channels and annulli. J. Comput. Phys. 18, 376–404.CrossRefGoogle Scholar
Shao, L., Sarkar, S. & Pantano, C. 1999 On the relationship between the mean flow and subgrid stresses in large eddy simulation of turbulent shear flows. Phys. Fluids 11 (5), 1229–1248.CrossRefGoogle Scholar
Smagorinsky, J. 1963 General circulation experiments with the primitive equations. 1. The basic experiment. Mon. Weather Rev. 91, 99.2.3.CO;2>CrossRefGoogle Scholar
Sullivan, P., McWilliams, J. C. & Moeng, C.-H. 1994 A subgrid-scale model for large-eddy simulation of planetary boundary-layer flows. Boundary-Layer Met. 71, 247–276.CrossRefGoogle Scholar
Toschi, F., Amati, G., Succi, S., Benzi, R. & Piva, R. 1999 Intermittency and structure functions in channel flow turbulence. Phys. Rev. Lett. 82, 5044–5047.CrossRefGoogle Scholar
Toschi, F., Lévéque, E. & Ruiz-Chavarria, G. 2000 Shear effects in nonhomogeneous turbulence. Phys. Rev. Lett. 85, 1436.CrossRefGoogle ScholarPubMed
Xu, C. X., Zhang, Z. & Nieuwstatd, F. M. 1996 Origin of high kurtosis in viscous sublayer. Phys. Fluids 85, 1938.CrossRefGoogle Scholar