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A Non-Linear SGS Model Based On The Spatial Velocity Increment

Application to LES of fully developed pipe flow and round turbulent jet

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Abstract

A new subgrid scale (SGS) modelling concept for large-eddy simulation (LES) of incompressible flow is proposed based on the three-dimensional spatial velocity increment δ u i . The new model is inspired by the structure function formulation developed by Métais and Lesieur [39] and applied in the context of the scale similarity type formulation. First, the similarity between the SGS stress tensor τ ij and the velocity increment tensor Q ij = δ u i δ u j is analyzed analytically and numerically using a priori tests of fully developed pipe flow at Re τ = 180. Both forward and backward energy transfers between resolved and unresolved scales of the flow are well predicted with a SGS model based on Q ij . Secondly, a posteriori tests are performed for two families of turbulent shear flows. LES of fully developed pipe flow up to Re τ = 520 and LES of round turbulent jet at Re D = 25000 carried out with a dynamic version of the model provide promising results that confirm the power of this approach for wall-bounded and free shear flows.

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References

  1. Antonia, R.A., Kim, J., Browne, L.W.B.: Some characteristics of small-scale turbulence in a turbulent duct flow. J. Fluid Mech. 233, 369–388 (1991)

    Article  ADS  Google Scholar 

  2. Bardina, J., Ferziger, J.H., Reynolds, W.C.: Improved subgrid-scale models for large-eddy simulations. AIAA Paper 80, 1357 (1980)

    Google Scholar 

  3. Batchelor, G.K.: The Theory of Homogeneous Turbulence. Cambridge University Press (1953)

  4. Benzi, R., Amati, G., Casciola, C.M., Toschi, F., Piva, R.: Intermittency and scaling laws for wall bounded turbulence. Phys. Fluids 11(6), 1284–1286 (1999)

    Article  ADS  Google Scholar 

  5. Borue, V., Orszag, S.A.: Local energy flux and subgrid-scale statistics in three-dimensional turbulence. J. Fluid Mech. 366, 1–31 (1998)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  6. Brun, C., Friedrich, R.: The spatial velocity increment as a tool for SGS modeling. In: Geurts B.J. (ed.) Modern Simulation Strategies for Turbulent Flow. R.T. Edwards Publishing House, pp. 57–84 (2001a)

  7. Brun, C., Friedrich, R.: Modelling the SGS tensor T ij. An issue in the dynamic approach. Phys. Fluids 13(8), 2373–2385 (2001b)

    Article  ADS  Google Scholar 

  8. Crow, S.C., Champagne, F.H.: Orderly structures in jet turbulence. J. Fluid Mech. 48, 547–591 (1971)

    Article  ADS  Google Scholar 

  9. Cerutti, S., Meneveau, C.: Intermittency and relative scaling of subgrid-scale energy dissipation in isotropic turbulence. Phys. Fluids 10(4), 928–937 (1998)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  10. Domaradzki, J.A., Loh, K.C.: The subgrid-scale estimation model in the physical space. Phys. Fluids 11, 2330 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  11. Ducros, F., Comte, P., Lesieur, M.: Large-Eddy Simulation of transition to turbulence in a boundary layer developing spatially over a flat plate. J. Fluid Mech. 326, 1–36 (1996)

    Article  MATH  ADS  Google Scholar 

  12. Eggels, J.G.M., Unger, F., Weiss, F., Westerweel, J., Adrian, R.J., Friedrich, R., Nieuwstadt, F.T.M.: Fully developed turbulent pipe flow: A comparison between direct numerical simulation and experiment. J. Fluid Mech. 268, 175–209 (1994)

    Article  ADS  Google Scholar 

  13. Frisch, U.: Turbulence. The legacy of A.N. Kolmogorov. Cambridge University Press (1995)

  14. Germano, M., Piomelli, U., Moin, P., Cabot, W.H.: A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A 3(7), 1760–1765 (1991)

    Article  MATH  ADS  Google Scholar 

  15. Germano, M.: Private communication (2000)

  16. Geurts, B.J., Fröhlich, J.: Numerical effects contaminating LES; a mixed story. In: Geurts, B.J. (ed.) Modern Simulation Strategies for Turbulent Flow. R.T. Edwards Publishing House, pp. 309–322 (2001a)

  17. Geurts, B.J., Fröhlich, J.: A framework for predicting accuracy limitations in large-eddy simulation. Phys. Fluids 14(6), 41–44 (2001b)

    Article  Google Scholar 

  18. Ghosal, S., Lund, T.S., Moin, P., Akselvoll, K.: A dynamic localisation model for large-eddy simulation of turbulent flows. J. Fluid Mech. 286, 229–255 (1995)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  19. Goutorbe, T., Laurence, D., Maupu, V.: A-priori test of a subgrid scale stress tensor model including anisotropy and backscatter effects. In: Voke, P.R. et al. (eds.) Direct and Large-Eddy Simulation I. Kluwer Academic Publishers, pp. 121–131 (1994)

  20. Härtel, K., Kleiser, L., Unger, F., Friedrich, R.: Subgrid-scale energy transfer in the near-wall region of turbulent flows. Phys. Fluids 6(9), 3131–3143 (1994)

    Article  Google Scholar 

  21. Howard, R.: Private communication (2004)

  22. Hunt, J.C.R., Wray, A.A., Moin, P.: Eddies, stream and convergence zones in turbulent flows., Report CTR-S88, Center for Turbulence Research, NASA Ames\Stanford Univ (1988)

  23. Hussein, H.J., Capp, S.P., George, W.K.: Velocity measurements in a high-Reynolds-number, momentum conserving, axisymmetric, turbulent jet. J. Fluid Mech. 258, 31–75 (1994)

    Article  ADS  Google Scholar 

  24. Hüttl, T.J., Friedrich, R.: Direct numerical simulation of turbulent flows in curved and helically coiled pipes. Comput. & Fluids 30(5), 591–605 (2001)

    Article  MATH  Google Scholar 

  25. Kolmogoroff, A.N.: The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. C.R. Acad. Sci. U.R.S.S. 30, 301 (1941)

    MathSciNet  Google Scholar 

  26. Kravchenko, A.G., Moin, P.: On the effect of numerical errors in large eddy simulations of turbulent flows. J. Comp. Phys. 286, 229–255 (1997)

    Google Scholar 

  27. Krogstad, P.A., Torbergsen, L.E.: Invariant analysis of turbulent pipe flow. Flow Turb. Combust. 64(3), 161–181 (2000)

    Article  MATH  Google Scholar 

  28. Lamballais, E., Métais, O., Lesieur, M.: Spectral-dynamic model for large-eddy simulations of turbulent rotating channel flow. Theor. Comp. Fluid Dyn. 12, 149–177 (1998)

    Article  MATH  Google Scholar 

  29. Leonard, A.: On the energy cascade in large-eddy simulations of turbulent flows. Adv. Geophys. A18, 237 (1974)

    ADS  Google Scholar 

  30. Lesieur, M., Métais, O.: New trends in large-eddy simulations of turbulence. Annu. Rev. Fluid. Mech. 28, 45–82 (1996)

    Article  ADS  Google Scholar 

  31. Lesieur, M.: Turbulence in Fluids, 3rd edn, revised and enlarged. Kluwer Academic Publishers (1997)

  32. Lele, S.K.: Compact finite difference schemes with spectral-like resolution. J. Comp. Phys. 103, 16–42 (1992)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  33. Lilly, D.K.: A proposed modification of the Germano subgrid-scale closure method. Phys. Fluids A 4, 633–635 (1992)

    Article  ADS  Google Scholar 

  34. Liu, S., Meneveau, C., Katz, J.: On the properties of similarity subgrid-scale models as deduced from measurements in a turbulent jet. J. Fluid Mech. 275, 83–119 (1994)

    Article  ADS  Google Scholar 

  35. Lund, T.S., Kaltenbach, H.-J.: Experiments with explicit filtering for LES using a finite-difference method., Annual Research Briefs 1995, Center for Turbulence Research, NASA Ames\Stanford Univ., pp. 91–105 (1996)

  36. Mathew, J., Lechner, R., Foysi, H., Sesterhenn, J., Friedrich, R.: An explicit filtering method for large eddy simulation of compressible flows. Phys. Fluids 15(8), 2279–2289 (2003)

    Article  ADS  Google Scholar 

  37. Meneveau, C., Lund, T., Cabot, W.: A Lagrangian dynamic subgrid-scale model of turbulence. J. Fluid Mech. 319, 353–386 (1996)

    Article  MATH  ADS  Google Scholar 

  38. Meneveau, C., Katz, J.: Scale-invariance and turbulence models for large-eddy simulation. Ann. Rev. Fluid. Mech. 28, 45–82 (2001)

    Google Scholar 

  39. Métais, O., Lesieur, M.: Spectral large-eddy simulation of isotropic and stably stratified turbulence. J. Fluid Mech. 239, 157–194 (1992)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  40. Monin, A.S., Yaglom, A.M.: Statistical Fluid Mechanics. MIT Press (1975)

  41. Oberlack, M.: Symmetries of the Navier–Stokes equations and their implications for subgrid-models in large-eddy simulation of turbulence. In: Fundamental Problematic Issues in Turbulence, (eds. A. Gyr, W. Kinzelbach, A. Tsinober, Trends in Mathematics), Birkhäuser Verlag (1999)

  42. Piomelli, U., Moin, P., Ferziger, J.H.: Model consistency in LES of turbulent channel flows. Phys. Fluids 31, 1884–1884 (1988)

    Article  ADS  Google Scholar 

  43. Piomelli, U., Yunfang, Y., Adrian, J.A.: Subgrid-scale energy transfer and near-wall turbulence structure. Phys. Fluids 8(1), 215–224 (1996)

    Article  MATH  ADS  Google Scholar 

  44. Pope, S.B.: Turbulent flows. Cambridge University Press (2000)

  45. Rogallo, R.S., Moin, P.: Numerical simulation of turbulent flows. Ann. Rev. Fluid. Mech. 16, 99–137 (1984)

    Article  ADS  Google Scholar 

  46. Salvetti, M.V., Beux, F.: The effect of the numerical scheme on the subgrid-scale term in large-eddy simulation. Phys. Fluids 10, 3020 (1998)

    Article  ADS  Google Scholar 

  47. da Silva, C.B., Métais, O.: Vortex control of bifurcating jets: a numerical study. Phys. Fluids 14(11), 3798–3819 (2002a)

    Article  ADS  Google Scholar 

  48. da Silva, C.B., Métais, O.: On the influence of coherent structures upon interscale interactions in turbulent plane jets. J. Fluid Mech. 473, 103–145 (2002b)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  49. den Toonder, J.M.J., Nieuwstadt, F.T.M.: Reynolds number effects in a turbulent pipe flow for low to moderate Re. Phys. Fluids 9, 3398–3409 (1997)

    Article  ADS  Google Scholar 

  50. Urbin, G., Métais, O.: Large-eddy simulations of the three-dimensional spatially developing round jet. In: Chollet, J.P. et al. (eds.) Direct and Large-Eddy Simulation II. Kluwer Academic Publishers (1997)

  51. Van Driest, E.R.: J. Aerospace Sci. 23, 1007 (1956)

    Google Scholar 

  52. Vreman, B., Geurts, B.J., Kuerten, H.: Realizability conditions for the turbulent stress tensor in large-eddy simulation. J. Fluid Mech. 278, 351–362 (1994)

    Article  MATH  ADS  Google Scholar 

  53. Vreman, B., Geurts, B.J., Kuerten, H.: Large-eddy simulation of the turbulent mixing layer. J. Fluid Mech. 339, 357–390 (1997)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  54. Vreman, A.W.: An eddy-viscosity subgrid-scale model for turbulent shear flow : algebraic theory and applications. Phys. Fluids 16(10), 3670–3681 (2004)

    Article  ADS  Google Scholar 

  55. Van de Water, W., Herweijer, J.A.: High-order structure functions of turbulence. J. Fluid Mech. 387, 3–37 (1999)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  56. Winckelmans, G.S., Wray, A.A., Vasilyev, O.V., Jeanmart, H.: Explicit-filtering large-eddy simulation using the tensor-diffusivity model supplemented by a dynamic Smagorinsky term. Phys. Fluids 13(5), 1385–1403 (2001)

    Article  ADS  Google Scholar 

  57. Zaman, K.B.M.Q., Hussain, A.K.M.F.: Vortex pairing in a circular jet under controlled excitation. part 1. General jet response. J. Fluid Mech. 101, 449–491 (1980)

    Article  ADS  Google Scholar 

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Author notes

  1. Christophe Brun

    Present address: Polytech'Orléans/LME, 8, rue Léonard de Vinci, 45072, Orleans CEDEX 2, France

  2. Carlos B. da Silva

    Present address: Instituto Soperior Técnico, Pau Mecânica I, 1o Andar, Av. Rovisco Pais, 1049-001, Lisboa, Portugal

Authors and Affiliations

  1. Fachgebiet Strömungsmechanik, Technische Universität München, Boltzmannstr, 15, 85748, Garching, Germany

    Christophe Brun & Rainer Friedrich

  2. LEGI/MoST, Institut de Mécanique de Grenoble, BP 53, 38041, Grenoble Cedex 09, France

    Carlos B. da Silva

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  1. Christophe Brun
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Correspondence to Christophe Brun.

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Communicated by R. D. Moser

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Brun, C., Friedrich, R. & da Silva, C.B. A Non-Linear SGS Model Based On The Spatial Velocity Increment. Theor. Comput. Fluid Dyn. 20, 1–21 (2006). https://doi.org/10.1007/s00162-005-0006-6

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  • DOI: https://doi.org/10.1007/s00162-005-0006-6

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