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On the properties of similarity subgrid-scale models as deduced from measurements in a turbulent jet

Published online by Cambridge University Press:  26 April 2006

Shewen Liu ,
Charles Meneveau  and
Joseph Katz
Shewen Liu
Affiliation:
Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA
Charles Meneveau
Affiliation:
Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA
Joseph Katz
Affiliation:
Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA
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Abstract

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The properties of turbulence subgrid-scale stresses are studied using experimental data in the far field of a round jet, at a Reynolds number of Rλ ≈ 310. Measurements are performed using two-dimensional particle displacement velocimetry. Three elements of the subgrid-scale stress tensor are calculated using planar filtering of the data. Using a priori testing, eddy-viscosity closures are shown to display very little correlation with the real stresses, in accord with earlier findings based on direct numerical simulations at lower Reynolds numbers. Detailed analysis of subgrid energy fluxes and of the velocity field decomposed into logarithmic bands leads to a new similarity subgrid-scale model. It is based on the ‘resolved stress’ tensor Lij, which is obtained by filtering products of resolved velocities at a scale equal to twice the grid scale. The correlation coefficient of this model with the real stress is shown to be substantially higher than that of the eddy-viscosity closures. It is shown that mixed models display similar levels of correlation. During the a priori test, care is taken to only employ resolved data in a fashion that is consistent with the information that would be available during large-eddy simulation. The influence of the filter shape on the correlation is documented in detail, and the model is compared to the original similarity model of Bardina et al. (1980). A relationship between Lij and a nonlinear subgrid-scale model is established. In order to control the amount of kinetic energy backscatter, which could potentially lead to numerical instability, an ad hoc weighting function that depends on the alignment between Lij and the strain-rate tensor, is introduced. A ‘dynamic’ version of the model is shown, based on the data, to allow a self-consistent determination of the coefficient. In addition, all tensor elements of the model are shown to display the correct scaling with normal distance near a solid boundary.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 275 , 25 September 1994 , pp. 83 - 119
Copyright
© 1994 Cambridge University Press

References

Akhavan, R., Ansari, A. & Mangiavacci, N. 1993 Subgrid-scale modeling of energy transfer in turbulent shear flows. Bull. Am. Phys. Soc. 38, 2231.Google Scholar
Akselvoll, K. & Moin, P. 1993 Application of the dynamic localization model to large-eddy simulation of turbulent flow over a backward facing step. In Engineering Applications of Large Eddy Simulations (ed. U. Piomelli & S. Ragab) ASME-FED, vol. 162, p. 1.
Bardina, J., Ferziger, J. H. & Reynolds, W. C. 1980 Improved subgrid scale models for large eddy simulation. AIAA Paper 80-1357.
Chasnov, J. R. 1991 Simulation of the Kolmogorov inertial subrange using an improved subgrid model. Phys. Fluids A 3, 188.Google Scholar
Chollet, J. & Lesieur, M. 1981 The parameterization of small scales of three-dimensional isotropic turbulence utilizing spectral closures. J. Atmos. Sci. 38, 2747.Google Scholar
Clark, R. A., Ferziger, J. H. & Reynolds, W. C. 1979 Evaluation of subgrid models using an accurately simulated turbulent flow. J. Fluid Mech. 91, 1.Google Scholar
Deardorff, J. W. 1970 A numerical study of three-dimensional turbulent channel flow at large reynolds numbers. J. Fluid Mech. 41, 453.Google Scholar
Dong, R., Chu, S. & Katz, J. 1992 Quantitative visualization of the flow structure within the volute of a centrifugal pump, part a: Technique. Trans. ASME I: J. Fluids Engng 114, 390.Google Scholar
Ferziger, J. H. 1977 Large eddy numerical simulations of turbulent flows. AIAA J. 15, 1261.Google Scholar
Ganapathy, S. & Katz, J. 1993 Lift and drag forces on bubbles entrained by a vortex ring within non-uniform unsteady flows. In ‘Cavitation and Multiphase Flow Forum’, Washington DC, June, 1993, p. 165. ASME.
Germano, M. 1986 A proposal for a redefinition of the turbulent stresses in the filtered Navier–Stokes equations. Phys. Fluids 29, 2323.Google Scholar
Germano, M. 1992 Turbulence: the filtering approach. J. Fluid Mech. 238, 325.Google Scholar
Germano, M., Piomelli, U., Moin, P. & Cabot, W. H. 1991 A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A 3, 1760.Google Scholar
Ghosal, S., Lund, T. S. & Moin, P. 1992 A local dynamic model for large eddy simulation. In Center for Turbulence Research, Annual Research Briefs, Stanford University, vol. 3.
Horiuti, K. 1989 The role of the Bardina model in large eddy simulation of turbulent channel flow. Phys. Fluids A 1, 426.Google Scholar
Horiuti, K. 1993 A proper velocity scale for modeling subgrid-scale eddy viscosities in large eddy simulation. Phys. Fluids A 5, 146.Google Scholar
Kraichnan, R. H. 1976 Eddy viscosity in two and three dimensions. J. Atmos. Sci. 33, 1521.Google Scholar
Leonard, A. 1974 Energy cascade in large-eddy simulations of turbulent fluid flows. Adv. Geophys. 18, 237.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.Google Scholar
Lilly, D. K. 1967 The representation of small-scale turbulence in numerical simulation experiments. In Proc. IBM Scientific Computing Symp. on Environmental Sciences, p. 195.
Lilly, D. K. 1992 A proposed modification of the germano subgrid scale closure method. Phys. Fluids A 4, 633.Google Scholar
Liu, S., Meneveau, C. & Katz, J. 1994a Experimental study of similarity subgrid-scale models of turbulence in the far field of a jet. In Direct and Large Eddy Simulation I (ed. P. R. Voke, L. Kleiser and J. P. Chollet), pp. 37–48. Kluwer.
Liu, S., Meneveau, C. & Katz, J. 1994b Experimental studies of similarity subgrid-scale models of turbulence using conditional averaging. ASME-FED (to appear).
Lumley, J. L. 1970 Towards a turbulent constitutive relation. J. Fluid Mech. 41, 413.Google Scholar
Lund, T. 1993 Numerical experiments with highly-variable eddy viscosity models. In Engineering Applications of Large Eddy Simulations (ed. U. Piomelli & S. Ragab). ASME-FED, vol. 162, p. 7.
Lund, T. & Novikov, E. A. 1992 Parametrization of subgrid-scale stress by the velocity gradient tensor. In Center for Turbulence Research, Annual Research Briefs, Stanford University, vol. 27.
McMillan, O. J. & Ferziger, J. H. 1979 Direct testing of subgrid-scale models. AIAA J. 17, 1340.Google Scholar
Meneveau, C. 1994 Statistics of turbulence subgrid-scale stresses: Necessary conditions and experimental tests. Phys. Fluids 6, 815.Google Scholar
Meneveau, C., Lund, T. & Moin, P. 1992 Search for subgrid scale parametrization by projection pursuit regression. In Proc. Summer Program 1992 Stanford University, vol. IV, p. 61.
Métais, O. & Lesieur, M. 1992 Spectral large-eddy simulation of isotropic and stably stratified turbulence. J. Fluid Mech. 239, 157.Google Scholar
Piomelli, U. 1993 High Reynolds number calculations using the dynamic subgrid-scale stress model. Phys. Fluids A 5, 1484.Google Scholar
Piomelli, U., Moin, P. & Ferziger, J. H. 1988 Model consistency in large eddy simulation of turbulent channel flows. Phys. Fluids 31, 1884.Google Scholar
Reynolds, W. C. 1990 The potential and limitations of direct and large eddy simulations. In Whither Turbulence? or Turbulence at Crossroads (ed. J. L. Lumley), p. 313. Springer.
Rogallo, R. & Moin, P. 1984 Numerical simulation of turbulent flows. Ann. Rev. Fluid. Mech. 16, 99.Google Scholar
Schmidt, H. & Schumann, U. 1989 Coherent structure of the convective boundary layer derived from large-eddy simulations. J. Fluid Mech. 200, 511.Google Scholar
Schumann, U. 1975 Subgrid scale model for finite difference simulations of turbulent flows in plane channels and annuli. J. Comput. Phys. 18, 376.Google Scholar
Smagorinsky, J. 1963 General circulation experiments with the primitive equations, i. the basic experiment. Mon. Weath. Rev. 91, 99.Google Scholar
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. MIT Press.
Yoshizawa, A. 1989 Subgrid-scale modeling with a variable length scale. Phys. Fluids A 1, 1293.Google Scholar
Zang, Y., Street, R. L. & Koseff, J. 1993 A dynamic mixed subgrid-scale model and its application to turbulent recirculating flows. Phys. Fluids A 5, 3186.Google Scholar