Hostname: page-component-745bb68f8f-s22k5 Total loading time: 0 Render date: 2025-01-10T06:13:30.438Z Has data issue: false hasContentIssue false
  • English
  • Français

On the magnitude of the subgrid-scale eddy coefficient in large-eddy simulations of turbulent channel flow

Published online by Cambridge University Press:  21 April 2006

P. J. Mason  and
N. S. Callen
P. J. Mason
Affiliation:
Meteorological Office, London Road, Bracknell, Berkshire RG12 2SZ
N. S. Callen
Affiliation:
Meteorological Office, London Road, Bracknell, Berkshire RG12 2SZ
Get access Rights & Permissions [Opens in a new window]

Abstract

A series of large-eddy simulations of plane Poiseuille flow are discussed. The subgrid-scale motions are represented by an eddy viscosity related to the flow deformation — the ‘Smagorinsky’ model. The resolution of the computational mesh is varied independently of the value of the coefficient Cs which determines the magnitude of this subgrid eddy viscosity. To ensure that results are from a statistically steady state unrealistic initial conditions are used and sufficient time is allowed for the flow to become independent of the initial conditions. In keeping with previous work it is found that for large Cs the resolved-scale motions are damped out; however, this critical value of Cs is found to depend on the mesh resolution. Only with a fine mesh does the value of Cs previously found to be appropriate for homogeneous turbulence (≈ 0.2) give simulations with sustained resolved-scale motions. The ratio l0/δ of the channel width 2δ to the scale of the ‘Smagorinsky’ mixing length, l0 = CsΔ where Δ is a typical mesh spacing), is found to be the key parameter determining the ‘turbulent’ eddy-viscosity ‘Reynolds number’ of the resolved-scale motions. A fixed value of 10 is regarded as determining the separation of scales into resolved and subgrid. The value of l0 is regarded as a measure of numerical resolution and values of Cs less than about 0.2 correspond to inadequate resolution.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 162 , January 1986 , pp. 439 - 462
Copyright
© 1986 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Antonopoulos-Domis, M. 1981 Large-eddy simulation of a passive scalar in isotropic turbulence. J. Fluid Mech. 104, 55–79.Google Scholar
Bardina, J., Ferziger, J. H. & Reynolds, W. C. 1983 Improved turbulence models based on large eddy simulation of homogeneous, incompressible, turbulent flows. Stanford University Rep. TF-19.Google Scholar
Cambon, C., Jeandel, D. & Mathieu, J. 1981 Spectral modelling of homogeneous non-isotropic turbulence. J. Fluid Mech. 104, 247–62.Google Scholar
Comte-Bellot, G. 1963 Contribution a I'étude de la turbulence de conduite. Doctoral thesis, University of Grenoble.
Deardorff, J. W. 1970a On the magnitude of the subgrid-scale eddy coefficient. J. Comp. Phys. 7, 120–133.Google Scholar
Deardorff, J. W. 1970a A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers. J. Fluid Mech. 41, 453–480.Google Scholar
Deardorff, J. W. 1974 Three-dimensional numerical study of the height and mean structure of a heated planetary boundary layer. Boundary-Layer Met. 7, 81–106.Google Scholar
Hussain, A. K. M. F. & Reynolds, W. C. 1975 Measurements in fully developed turbulent channel flows. Trans. ASME I: J. Fluids Engng 97, 568–578Google Scholar
Kalnay de Rivas, E. 1972 On the use of non-uniform grids in finite-difference equations. J. Comp. Phys. 10, 202.Google Scholar
Kraichnan, R. H. 1976 Eddy viscosity in two and three-dimensions. J. Atmos. Sci. 33, 1521–1536.Google Scholar
Kwak, D., Reynolds, W. C. & Ferziger, J. H. 1975 Three-dimensional time-dependent computation of turbulent flow. Stanford University Rep. TF-5.Google Scholar
Laufer, J. 1951 Investigation of turbulent flow in a two-dimensional channel. NACA rep. 1053.
Launder, B. E. & Spalding, D. B. 1972 Mathematical Models of Turbulence. Academic.
Leonard, A. 1974 Energy cascade in large-eddy simulations of turbulent fluid flows. Adv. Geophys. 18 A, 237–248.Google Scholar
Leslie, D. C. & Quarini, G. L. 1979 The application of turbulence theory to the formulation of subgrid modelling procedures. J. Fluid Mech. 91, 65–91.Google Scholar
Lilly, D. K. 1967 The representation of small-scale turbulence in numerical simulation experiments. In Proc. IBM Scientific Computing Symposium on Environmental Sciences, IBM Form No. 320–1951, pp. 195–210.
Mason, P. J. & Sykes, R. I. 1978 A simple Cartesian model of boundary layer flow over topography. J. Comp. Phys. 28, 198–210.Google Scholar
Mcmillan, O. J. & Ferziger, J. H. 1979 Direct testing of subgrid-scale models. A1AA J. 17, 1340–1346.Google Scholar
Moin, P. & Kim, J. (M & K) 1982 Numerical investigation of turbulent channel flow. J. Fluid Mech. 118, 341–377.Google Scholar
Moin, P., Reynolds, W. C. & Ferziger, J. H. 1978 Large-eddy simulation of incompressible turbulent channel flow. Rep. No. TF-12 Dept. of Mech. Engng, Stanford University.
Orszag, S. A. & Kells, L. C. 1980 Transition to turbulence in plane Poiseuille and plane Couette flow. J. Fluid Mech. 96, 159–205.Google Scholar
Piacsek, S. A. & Williams, G. P. 1970 Conservation properties of convection difference schemes. J. Comp. Phys. 6, 392–405.Google Scholar
Roache, P. J. 1972 Computational Fluid Dynamics. Albuquerque: Hermosa.
Runstodler, P. W., Kline, S. J. & Reynolds, W. C. 1963 An investigation of the flow structure of the turbulent boundary layer. Dept Mech. Eng. Stanford University Rep. MD-8.Google Scholar
Sabot, J. & Comte-Bellot, G. 1976 Intermittency of coherent structures on the core region of fully developed turbulent pipe flow. J. Fluid Mech. 74, 767.Google Scholar
Schumann, U. 1975 Subgrid-scale model for finite difference simulations of turbulent flows in plane channels and annuli. J. Comp. Phys. 18, 376–404.Google Scholar
Smagorinsky, J. 1963 General circulation experiments with the primitive equations: 1. The basic experiment. Mom. Wea. Rev. 91, 99–164.Google Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow. Cambridge University Press.
Van Driest, E. R. 1956 On turbulent flow near a wall. J. Aero. Sci. 23, 1007–1011.Google Scholar
Williams, G. P. 1969 Numerical integration of the three-dimensional Navier-Stokes equations for incompressible flow. J. Fluid Mech. 37, 727–750.Google Scholar