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Towards a new partially integrated transport model for coarse grid and unsteady turbulent flow simulations

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Abstract

A new two-equation model is proposed for large eddy simulations (LESs) using coarse grids. The modeled transport equations are obtained from a direct transposition of well-known statistical models by using multiscale spectrum splitting given by the filtering operation applied to the Navier–Stokes equations. The model formulation is compatible with the two extreme limits that are on one hand a direct numerical simulation and on the other hand a full statistical modeling. The characteristic length scale of subgrid turbulence is no longer given by the spatial discretization step size, but by the use of a dissipation equation. The proposed method is applied to a transposition of the well-known k-ε statistical model, but the same method can be developed for more advanced closures. This approach is intended to contribute to non-zonal hybrid models that bridge Reynolds-averaged Navier–Stokes (RANS) and LES, by using a continuous change rather than matching zones. The main novelty in the model is the derivation of a new ε equation for LES that is formally consistent with RANS when the filter width is very large. This approach is dedicated to applications to non-equilibrium turbulence and coarse grid simulations. An illustration is made of large eddy simulations of turbulence submitted to periodic forcing. The model is also an alternative approach to hybrid models.

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References

  1. Abe, K., Kondoh, T., Nagano, Y.: A new turbulence model for predicting fluid flow and heat transfer in separating and reattaching flows-I. Flow field calculations. Int. J. Heat Mass Transf. 37, 139–151 (1994)

    Google Scholar 

  2. Aupoix, B.: Application de modèles dans l’espace spectral à d’autres niveaux de fermeture en turbulence homogène. Dissertation, Université Lyon I (1987)

  3. Batten, P., Goldberg, U.C., Palaniswamy, S., Chakravarthy, S.R.: Hybrid RANS/LES: Spatial resolution and energy-transfer issues. In: Proc. Symp. on Turbulence and Shear Flow Phenomena, Second Int. Symp., KTH, Stockholm, vol. 2, pp. 159–164 (2001)

  4. Binder, G., Tardu, S., Vezin, P.: Cycle modulation of Reynolds stresses and length scales in pulsed channel flow. Proc. Roy. Soc. Lond. A 451, 121–139 (1995)

    Google Scholar 

  5. Binder, G., Kuény, J.L.: Measurements of the periodic oscillations near the wall in unsteady turbulent channel flow. In: Michel R., Cousteix J., Houdeville R. (eds.) Unsteady Turbulent Shear Flows. IUTAM Symp. Springer Berlin Heidelberg New York, pp. 100–109 (1981)

  6. Comte-Bellot, G., Corrsin, S.: The use of a contraction to improve the isotropy of grid generated turbulence. J. Fluid Mech. 25(4), 657–682 (1966)

    Google Scholar 

  7. Comte-Bellot, G., Corrsin, S.: Simple Eulerian time correlation of full and narrow-band velocity signals in grid-generated ‘isotropic’ turbulence. J. Fluid Mech. 48, 273–337 (1971)

    Google Scholar 

  8. Davidson, L., Peng, Shia-Hui: A hybrid LES-RANS model based on a one-equation SGS model and a two-equation k-ω model. Proc. Symp. on Turbulence and Shear Flow Phenomena, Second Int. Symp., KTH, Stockholm, vol. 2, pp. 175–180 (2001)

  9. Deardorff, J.W.: The use of subgrid transport equations in a three-dimensional model of atmospheric turbulence. J. Fluid Eng. ASME 95, 429–438 (1973)

    Google Scholar 

  10. Dejoan, A.: Simulation de grandes échelles turbulentes en écoulement de canal plan soumis à des perturbations instationnaires. Dissertation, Université d’Aix-Marseille II) (1998)

  11. Dejoan, A., Schiestel, R.: Simulation de grandes échelles en écoulement turbulent soumis à des perturbations instationnaires. Actes du 14ème Congrès Français de Mécanique, AUM, Toulouse. Communication réf. 453, 30 August–3 September (1999)

  12. Dejoan, A., Schiestel, R.: Large eddy simulations of non-equilibrium flows using transport equations subgrid scale model. Proc. Symp. on Turbulence and Shear Flow Phenomena, Second Int. Symp., KTH, Stockholm, vol. 2, pp. 341–346 (2001)

  13. Dejoan, A., Schiestel, R.: LES of unsteady turbulence via a one-equation subgrid scale transport model. Int. J. Heat Fluid Flow 23, 398–412 (2002)

    Google Scholar 

  14. Deschamps, V.: Simulation numérique de la turbulence dans un écoulement de canal plan. La Recherche Aérospatiale 3, 37–52 (1989)

    Google Scholar 

  15. Feng, M., Tardu, S., Binder, G.: Inner region of unsteady channel flow. In: So R.M.C., Speziale C.G., Launder B.E. (eds.) Near wall turbulent flows. Elsevier New York (1993)

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

    Google Scholar 

  17. Hamba, F.: An attempt to combine large eddy simulation with the k-epsilon model in a channel flow calculation. Theor. Comput. Fluid Dyn. 14(5), 323–336 (2001)

    Google Scholar 

  18. Hamba, F.: A hybrid RANS/LES simulation of turbulent channel flow. Theor. and Comput. Fluid Dyn. 16(5), 387–403 (2003)

  19. Hanjalic, K., Hadziabdic, M., Temmerman, L., Leschziner, M.: Merging LES and RANS strategies: zonal or seamless coupling? In: Direct and Large-Eddy Simulation n°V (Proceedings of the Fifth International ERCOFTAC Workshop on Direct and Large-Eddy Simulation. Held at the Munich University of Technology, Germany, August 27–29, Friedrich, R., Geurts, B., Métais, O. (eds.), Ercoftac series vol. 9, Kluwer, Dordrecht, pp. 451–464 (2004)

  20. Hinze, J.O.: Turbulence, 2nd edn. McGraw-Hill, New York (1975)

  21. Horiuti, K., Yoshizawa, A.: Large-eddy simulation of turbulent channel flow by 1-equation model. In: Schumann, U., Friedrich R. (eds.) Notes on Numerical Fluid Mechanics vol. 15. Direct and Large-eddy Simulation of Turbulence. Proc. EUROMECH Coll. No 199, Munich, 1985. Vieweg-Verlag Wiesbaden, pp. 119–134 (1986)

  22. Hughes, T.J.R., Oberai, A.A., Mazzei, L.: Large eddy simulation of turbulent channel flow by the variational multiscale method. Phys. Fluids 13(6), 1784–1799 (2001)

    Google Scholar 

  23. Hussain, A.K.M.F., Reynolds, W.C.: Measurements in fully developed turbulent channel flow. J. Fluids Eng. Trans. ASME I 97, 568–578 (1975)

    Google Scholar 

  24. Jones, W.P., Launder, B.E.: The prediction of laminarization with a two-equation model of turbulence. Int. J. Heat Mass Transf. 15, 301–313 (1972)

    Google Scholar 

  25. Krajnovic, S., Davidson, L.: A mixed one-equation subgrid scale model for large eddy simulation. Int. J. Heat Fluid Flow 23, 413–425 (2002)

    Google Scholar 

  26. Kwak, D., Reynolds, W.C., Ferziger, J.H.: Three-dimensional time-dependent computation of turbulent flows. Dept. of Mech. Eng., Stanford Univ., Calif., Report TF-5 (1975)

  27. Laufer, J.: Investigation of turbulent flow in a two-dimensional channel. NACA Report 1053 (1951)

  28. Launder, B.E., Sharma, B.I.: Application of the energy-dissipation model of turbulence to the calculation of flow near a spinning disc. Lett Heat Mass Transf. 1, 131–138 (1974)

    Google Scholar 

  29. Lesieur, M.: Turbulence in fluids, 2nd edn. . Kluwer Dordrecht (1990)

  30. Métais, O., Lesieur, M.: Spectral large-eddy simulation of isotropic and stably stratified turbulence. J. Fluid Mech. 125, 475–503 (1992)

    Google Scholar 

  31. Moin, P., Kim, J.: Numerical investigation of turbulent channel flow. J. Fluid Mech. 118, 341–377 (1982)

    Google Scholar 

  32. Moser, R.D., Kim, J., Mansour, N.N.: Direct numerical simulation of turbulent channel flow up to Reτ=590, Phys. Fluids 11(4), 943–945 (1999)

    Google Scholar 

  33. Nikitin, N.V., Nicoud, F., Wasistho, B., Squires, K.D., Spalart, P.R.: An approach to wall modeling in large-eddy simulations. Phys. Fluids Letters 12(7), 1629–1632 (2000)

    Google Scholar 

  34. Patel, V.C., Rodi, W., Scheuerer, G.: Turbulence models for near wall and low Reynolds number flows: a review. AIAA J 23(9), 1308–1319 (1985)

    Google Scholar 

  35. Piomelli, U., Balaras, E., Pasinato, H., Squires, K.D., Spalart, Ph.R.: The inner-outer interface in large eddy simulations with wall-layer models. Int. J. Heat Fluid Flow 24, 538–550 (2003)

    Google Scholar 

  36. Piomelli, U., Moin, P., Ferziger, J.H.: Model consistency in large eddy simulation of turbulent channel flow. Phys. Fluids 31(7), 1884–1891 (1988)

    Google Scholar 

  37. Rubinstein, R., Zhou, Ye: Analytical theory of the destruction terms in dissipation rate transport equations. Phys. Fluids 8(11), 3172–3178 (1996)

  38. Rubinstein, R., Zhou, Ye: Schiestel’s Derivation of the epsilon equation and two equations modeling of rotating turbulence. NASA/CR-2001-211060, ICASE Report No 2001–24, pp. 1–6 (2001)

  39. Sarkar, A., So, R.M.C.: A critical evaluation of near-wall two-equation models against direct numerical simulation data. Int. J. Heat Fluid Flow 18(2), 197–208 (1997)

    Google Scholar 

  40. Schiestel, R.: Sur la modélisation des écoulements turbulents en non-équilibre spectral. C.R. Acad. Sci., Paris, 302, series II, (11), pp. 727–730 (1986)

  41. Schiestel, R.: Multiple time scale modeling of turbulent flows in one point closures. Phys. Fluids 30(3), 722–731 (1987)

    Google Scholar 

  42. Schiestel, R.: Les écoulements turbulents, modélisation et simulation, 2nd edn. Hermès Paris (1998)

  43. Schiestel, R., Viazzo, S.: A Hermitian-Fourier numerical method for solving the incompressible Navier–Stokes equations. Comput Fluids 24(6), 739–752 (1995)

    Google Scholar 

  44. Schumann, U.: Subgrid scale model for finite difference simulations of turbulent flows in plane channels and annuli. J. Comp. Phys. 18, 367–404 (1975)

    Google Scholar 

  45. Scotti, A., Meneveau, C., Lilly, D.K.: Generalized Smagorinsky model for anisotropic grids. Phys. Fluids A 5(9), 2306–2308 (1975)

    Google Scholar 

  46. Scotti, A., Piomelli, U.: Numerical simulation of pulsating turbulent channel flow. Phys. Fluids 13(5), 1367–1384 (2001)

    Google Scholar 

  47. Scotti, A., Piomelli, U.: Turbulence models in pulsating flows. AIAA J 40(3), 537–544 (2002)

    Google Scholar 

  48. Spalart, P.R., Jou, W.H., Strelets, M., Allmaras, S.R.: Comments of the feasibility of LES for wings, and of a hybrid RANS/LES approach. First AFOSR Int. Conf. On DNS/LES, Ruston, LA, 4–8, August 1997. In: Liu, C., Liu Z. (eds.) Advances in DNS/LES. Greyden Columbus, OH (1997)

  49. Tardu, S.: Control of drag reduction by time-space periodical suctionand blowing. Proc. 11th Symp. on Turbulent Shear Flows, Grenoble, September 1997, pp. 9.1–9.6 (1997)

  50. Tardu, S., Binder, G.: Wall shear stress modulation in an unsteady turbulent channel flow with height imposed frequencies. Phys. Fluids A 5(8), 2028–2037 (1993)

    Google Scholar 

  51. Tardu, S., Binder, G., Blackwelder, R.: Turbulent channel flow with large amplitude velocity oscillations. J. Fluid Mech. 267, 109–151 (1994)

    Google Scholar 

  52. Travin, A., Shur, M., Strelets, M., Spalart, P.R.: Physical and numerical upgrades in the detached eddy simulations of complex turbulent flows. In: Friedrich, R., Rodi W. (eds.) Advances in LES of Complex Flows. Kluwer Dordrecht, pp. 239–254 (2002)

  53. Vasilyev, O.V., Lund, T.S., Moin, P.: A General class of commutative filters for LES in Complex Geometries. J. Comput. Phys. 146, 82–104 (1998)

    Google Scholar 

  54. Viazzo, S., Schiestel, R.: Simulations des grandes échelles turbulentes en canal à l’aide d’un schéma hermitien. Comptes Rendus de l’Académie des Sciences, 321, series IIb, pp. 225–232 (1995)

  55. Wei, T., Willmarth, W.: Examination of V-Velocity Fluctuations in a Turbulent Channel Flow in the Context of Sediment Transport. J. Fluid Mech. 223, 241–252 (1991)

    Google Scholar 

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Author notes

  1. Anne Dejoan

    Present address: Aeronautics Department, Imperial College, London, Prince Consort, South Kensington, London, SW7 2AZ, UK

Authors and Affiliations

  1. Institut de Recherche sur les Phénomènes Hors Equilibre, I.R.P.H.E., U.M.R. 6594 CNRS/Universités d’Aix-Marseille I & II, 49 rue Frédéric Joliot Curie, B.P. 146, Technopôle de Château-Gombert, 13384, Marseille Cedex 13, France

    Roland Schiestel & Anne Dejoan

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  1. Roland Schiestel
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Correspondence to Roland Schiestel.

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T.B. Gatski

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47.27.Eq

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Schiestel, R., Dejoan, A. Towards a new partially integrated transport model for coarse grid and unsteady turbulent flow simulations. Theoret. Comput. Fluid Dynamics 18, 443–468 (2005). https://doi.org/10.1007/s00162-004-0155-z

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