Application of the TURBIT-3 Subgrid Scale Model to Scales between Large Eddy and Direct Simulations

  • Günther Grötzbach
Chapter
Part of the Notes on Numerical Fluid Mechanics book series (NONUFM)

Summary

A method is presented to calculate the coefficients of subgrid scale models. The theory accounts for all details of the finite difference scheme as it is actually used in a simulation code. The dominating model coefficients are found to depend on local flow parameters. This method as it is implemented in the TURBIT-3-code makes the subgrid scale model selfadaptive to all scales from direct to large eddy simulations. This feature is verified by simulations for turbulent liquid metal flows in annuli. According to the domination of large scales due to the large conductivity of the fluid the theory automatically switches the subgrid scale heat flux model gradually or totally off. It is necessary for successful verification of the results to really use the predicted radially space-dependent coefficients at all intermediate scales between large eddy and direct simulations. For an internally heated horizontal convection layer the predicted model coefficients are compared to direct simulations on grids with different resolution. The agreement of the maximum grid widths allowable for a direct simulation found on both ways shows that the theory to calculate the model coefficients can also be used to check the spatial resolution capabilities of grids in advance to direct numerical simulations.

Keywords

Rayleigh Number Large Eddy Simulation Direct Numerical Simulation Peclet Number Finite Difference Scheme 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References

  1. /1/.
    P.R. Voke, M.W. Collins: Large eddy simulation: Retrospect and prospect Physico Chemical Hydrodynamics 4, 1983, p. 119 – 161.Google Scholar
  2. /2/.
    R.S. Rogallo, P. Moin: Numerical simulation of turbulent flows Ann. Rev. Fluid Mech. 16, 1984, p. 99 – 137.CrossRefGoogle Scholar
  3. /3/.
    P. Moin, J. Kim: Numerical investigation of turbulent channel flow J. Fluid Mech. 118, 1982, p. 341 – 377.MATHGoogle Scholar
  4. /4/.
    U. Schumann, G. Grötzbach, L. Kleiser: Direct numerical simulation of turbulence In: Prediction Methods for Turbulent Flows, Ed.: W. Kollmann, Hemisphere Publ. Corp. 1980, p. 123 – 258.Google Scholar
  5. /5/.
    G. Grötzbach: Direct numerical and large eddy simulation of turbulent channel flows in: Encyclopedia of Fluid Mechanics, Ed.N.P. Cheremisinoff, Gulf Publishing, Vol. 6 (in press), preprint as KfK report 01.02.06.P49A, 1984.Google Scholar
  6. /6/.
    U. Schumann: Subgrid scale model for finite difference simulations of turbulent flows in plane channels and annuli J. Comp. Physics 18, 1975, p. 376 – 404.MathSciNetMATHCrossRefGoogle Scholar
  7. /7/.
    G. Grötzbach, U. Schumann: Direct numerical simulation of turbulent velocity-, pressure-, and temperature-fields in channel flows Turbulent Shear Flows I, Ed.F. Durst et al., Springer 1979, p. 370–385.Google Scholar
  8. /8/.
    D.K. Lilly: The representation of small-scale turbulence in numerical simulation experiments Proc. IBM Scientific Comp. Symp. on Environmental Sciences, IBM Form No. 320–1951, 1967, p. 195–210.Google Scholar
  9. /9/.
    U. Schumann: Ein Verfahren zur direkten numerischen Simulation turbulenter Strömungen in Platten- und Ringspaltkanälen und über seine Anwendung zur Untersuchung von Turbulenzmo Enllen Dissertation, Universität Karlsruhe, 1973, KfK 1854, English translation in NASA-TT-F-15391.Google Scholar
  10. /10/.
    G. Grötzbach: Direkte numerische Simulation turbulenter Geschwindigkeits-, Druck- und Temperaturfelenr bei Kanalströmungen Dissertation, Universität Karlsruhe, 1977, KfK 2426, English translation in DOE-tr-61.Google Scholar
  11. /11/.
    M.S. Uberoi, L.S.G. Kovasznay: On mapping and measurement of random fields Quart.Appl.Math. 10, 1952, p. 375–393.MathSciNetGoogle Scholar
  12. /12/.
    G. Grötzbach: Spatial resolution requirements for direct numerical simulation of the Rayleigh-Bénard convection J. Comp. Physics 49, 1983, p. 241–264.MATHCrossRefGoogle Scholar
  13. /13/.
    G. Grötzbach: Numerical simulation of turbulent temperature fluctuations in liquid metals Int.J. Heat Mass Transfer 24, 1981, p. 475–490.CrossRefGoogle Scholar
  14. /14/.
    C.J. Lawn: Turbulent temperature fluctuations in liquid metals Int.J. Heat Mass Transfer 20, 1977, p. 1035–1044.CrossRefGoogle Scholar
  15. /15/.
    M. Jahn: Holographische Untersuchung Enr freien Konvektion in einer Kernschmelze Dissertation, Techn. Universität Hannover, F.R.G., 1975.Google Scholar
  16. /16/.
    G. Grötzbach: Direct numerical simulation of the turbulent momentum and heat transfer in an internally heated fluid layer Heat Transfer 1982, Ed. U. Grigull, E. Hahne, K. Stephan, J. Straub, Hemisphere 1982, Vol. 2, p. 141–146.Google Scholar

Copyright information

© Springer Fachmedien Wiesbaden 1986

Authors and Affiliations

  • Günther Grötzbach
    • 1
  1. 1.Kernforschungszentrum Karlsruhe GmbHInstitut für ReaktorentwicklungKarlsruheFederal Republic of Germany

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