Advertisement

Theoretical and Computational Fluid Dynamics

, Volume 28, Issue 1, pp 1–21 | Cite as

Wall modeling for implicit large-eddy simulation and immersed-interface methods

  • Zhen Li Chen
  • Stefan HickelEmail author
  • Antoine Devesa
  • Julien Berland
  • Nikolaus A. Adams
Original Article

Abstract

We propose and analyze a wall model based on the turbulent boundary layer equations (TBLE) for implicit large-eddy simulation (LES) of high Reynolds number wall-bounded flows in conjunction with a conservative immersed-interface method for mapping complex boundaries onto Cartesian meshes. Both implicit subgrid-scale model and immersed-interface treatment of boundaries offer high computational efficiency for complex flow configurations. The wall model operates directly on the Cartesian computational mesh without the need for a dual boundary-conforming mesh. The combination of wall model and implicit LES is investigated in detail for turbulent channel flow at friction Reynolds numbers from Re τ  = 395 up to Re τ =100,000 on very coarse meshes. The TBLE wall model with implicit LES gives results of better quality than current explicit LES based on eddy viscosity subgrid-scale models with similar wall models. A straightforward formulation of the wall model performs well at moderately large Reynolds numbers. A logarithmic-layer mismatch, observed only at very large Reynolds numbers, is removed by introducing a new structure-based damping function. The performance of the overall approach is assessed for two generic configurations with flow separation: the backward-facing step at Re h = 5,000 and the periodic hill at Re H = 10,595 and Re H = 37,000 on very coarse meshes. The results confirm the observations made for the channel flow with respect to the good prediction quality and indicate that the combination of implicit LES, immersed-interface method, and TBLE-based wall modeling is a viable approach for simulating complex aerodynamic flows at high Reynolds numbers. They also reflect the limitations of TBLE-based wall models.

Keywords

Large-eddy simulation Wall model Turbulent boundary layer equations Immersed-boundary method 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Adams E.W., Johnstont J.P.: Flow structure in the near-wall zone of a turbulent separated flow. AIAA J. 26(8), 932–939 (1988)CrossRefGoogle Scholar
  2. 2.
    del Alamo J.C., Jiménez J., Zandonade P., Moser R.D.: Scaling of the energy spectra of turbulent channels. J. Fluid Mech. 500, 135–144 (2004)CrossRefzbMATHGoogle Scholar
  3. 3.
    Baggett, J.S.: Some modeling requirements for wall models in large eddy simulation. CTR Annu. Res. Briefs 123–134 (1997)Google Scholar
  4. 4.
    Baggett, J.S., Jiménez, J., Kravchenko, A.: Resolution requirements in large-eddy simulation of shear flows. CTR Annu. Res. Briefs 51–66 (1997)Google Scholar
  5. 5.
    Balaras, E., Benocci, C.: Subgrid-scale models in finite-difference simulations of complex wall bounded flows AGARD 2.1–2.5 (1994)Google Scholar
  6. 6.
    Balaras E., Benocci C., Piomelli U.: Two-layer approximate boundary conditions for large-eddy simulations. AIAA J. 34, 1111–1119 (1996)CrossRefzbMATHGoogle Scholar
  7. 7.
    Baldwin, B.S., Lomax, H.: Thin Layer Approximation and Algebraic Model for Separated Turbulent Flows. AIAA paper (78-257) (1978)Google Scholar
  8. 8.
    Bhattacharya, A., Das, A., Moser, R.D.: A filtered-wall formulation for large-eddy simulation of wall-bounded turbulence. Phys. Fluids 20, 115104-1–115104-16 (2008)Google Scholar
  9. 9.
    Brasseur, J., Wei, T.: Designing large-eddy simulation of the turbulent boundary layer to capture law-of-the-wall scaling. Phys. Fluids 22, 021303-1–021303-21 (2010)Google Scholar
  10. 10.
    Breuer M., Jaffrézic B., Arora K.: Hybrid LES-RANS technique based on a one-equation near-wall model. J. Theor. Comput. Fluid Dyn. 22, 157–187 (2008)CrossRefzbMATHGoogle Scholar
  11. 11.
    Breuer M., Kniazev B., Abel M.: Development of wall models for LES of separated flows using statistical evaluations. Comput. Fluids 36, 817–837 (2007)CrossRefzbMATHGoogle Scholar
  12. 12.
    Cabot, W.H.: Wall models in large eddy simulation of separated flow. CTR Annu. Res. Briefs 97–106 (1997)Google Scholar
  13. 13.
    Cabot W.H., Moin P.: Approximate wall boundary conditions in the large-eddy simulation of high Reynolds number flows. Flow Turbul. Combust. 63, 269–291 (1999)CrossRefGoogle Scholar
  14. 14.
    Choi J.I., Oberoi R.C., Edwards J.R., Rosati J.A.: An immersed boundary method for complex incompressible flows. J. Comput. Phys. 224, 757–784 (2007)CrossRefzbMATHMathSciNetGoogle Scholar
  15. 15.
    Cristallo A., Verzicco R.: Combined immersed boundary/large-eddy-simulations of incompressible three dimensional complex flows. Flow Turbul. Combust. 77, 3–26 (2006)CrossRefzbMATHGoogle Scholar
  16. 16.
    Deardorff J.W.: A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers. J. Fluid Mech. 41, 453–465 (1970)CrossRefzbMATHGoogle Scholar
  17. 17.
    Fadlun E.A., Verzicco R., Orlandi P., Mohd-Yusof J.: Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations. J. Comput. Phys. 161, 35–60 (2000)CrossRefzbMATHMathSciNetGoogle Scholar
  18. 18.
    Fröhlich J., Mellen C.P., Rodi W., Temmerman L., Leschziner M.A.: Highly resolved large-eddy simulation of separated flow in a channel with streamwise periodic constrictions. J. Fluid Mech. 526, 19–66 (2005)CrossRefzbMATHMathSciNetGoogle Scholar
  19. 19.
    Fröhlich J., von Terzi D.: Hybrid LES/RANS methods for the simulation of turbulent flows. Prog. Aerosp. Sci. 44, 349–377 (2008)CrossRefGoogle Scholar
  20. 20.
    Fureby C., Grinstein F.F.: Large eddy simulation of high-Reynolds number free and wall-bounded flows. J. Comput. Phys. 181, 68–97 (2002)CrossRefzbMATHMathSciNetGoogle Scholar
  21. 21.
    Garnier E., Mossi M., Sagaut P., Deville M.: On the use of shock-capturing schemes for large-eddy simulation. J. Comput. Phys. 153, 273–311 (1999)CrossRefzbMATHGoogle Scholar
  22. 22.
    Grinstein F.F., Fureby C.: From canonical to complex flows: Recent progress on monotonically integrated LES. Comp. Sci. Eng. 6, 36–49 (2004)CrossRefGoogle Scholar
  23. 23.
    Grinstein F.F., Margolin L.G., Rider W.J.: Implicit Large Eddy Simulation. Cambridge University Press, Cambridge (2007)CrossRefzbMATHGoogle Scholar
  24. 24.
    Hickel, S., Adams, N.A.: On implicit subgrid-scale modeling in wall-bounded flows. Phys. Fluids 19, 105106-1–105106-13 (2007). doi: 10.1063/1.2773765 Google Scholar
  25. 25.
    Hickel S., Adams N.A.: A proposed simplification of the adaptive local deconvolution method. Eur. Ser. Appl. Ind. Math. 16, 66–76 (2007). doi: 10.1051/proc:2007008 zbMATHMathSciNetGoogle Scholar
  26. 26.
    Hickel S., Adams N.A.: Implicit LES applied to zero-pressure-gradient and adverse-pressure-gradient boundary-layer turbulence. Int. J. Heat Fluid Flow 29(3), 626–639 (2008). doi: 10.1016/j.ijheatfluidflow.2008.03.008 CrossRefGoogle Scholar
  27. 27.
    Hickel S., Adams N.A., Domaradzki J.A.: An adaptive local deconvolution method for implicit LES. J. Comput. Phys. 213, 413–436 (2006). doi: 10.1016/j.jcp.2005.08.017 CrossRefzbMATHMathSciNetGoogle Scholar
  28. 28.
    Hoyas, S., Jiménez, J.: Scaling of the velocity fluctuations in turbulent channels up to Re τ = 2003. Phys. Fluids 18, 011702-1–011702-4 (2006)Google Scholar
  29. 29.
    Hutchins, N., Marusic, I. (2007) Large-scale influences in near-wall turbulence. Philos. Trans. R. Soc. A 365, 647–664Google Scholar
  30. 30.
    Jovic, S.: An Experimental Study of a Separated/Reattached Flow Behind a Backward-Facing Step. Re h = 37,000. NASA TM 110384 (1996)Google Scholar
  31. 31.
    Jovic, S., Driver, D.M.: Backward-Facing Step Measurements at Low Reynolds Number, Re h = 5000. NASA TM 108807 (1994)Google Scholar
  32. 32.
    Kang S., Iaccarino G., Ham F., Moin P.: Prediction of wall-pressure fluctuation in turbulent flows with an immersed boundary method. J. Comput. Phys. 228, 6753–6772 (2009)CrossRefzbMATHGoogle Scholar
  33. 33.
    Kobayashi H., Ham F., Wu X.: Application of a local SGS model based on coherent structures to complex geometries. Int. J. Heat Fluid Flow 29(3), 640–653 (2008)CrossRefGoogle Scholar
  34. 34.
    Le H., Moin P., Kim J.: Direct numerical simulation of turbulent flow over a backward-facing step. J. Fluid Mech. 330, 349–74 (1997)Google Scholar
  35. 35.
    Meyer M., Devesa A., Hickel S., Hu X.Y., Adams N.A.: A conservative immersed interface method for large-eddy simulation of incompressible flows. J. Comput. Phys. 18, 6300–6317 (2010). doi: 10.1016/j.jcp.2010.04.040 CrossRefMathSciNetGoogle Scholar
  36. 36.
    Meyer M., Hickel S., Adams N.A.: Assessment of implicit large-eddy simulation with a conservative immersed-interface method for turbulent cylinder flow. Int. J. Heat Fluid Flow. 31, 368–377 (2010). doi: 10.1007/978-3-642-13872-0_12 CrossRefGoogle Scholar
  37. 37.
    Mittal R., Iaccarino G.: Immersed boundary methods. Annu. Rev. Fluid Mech. 37, 239–261 (2005)CrossRefMathSciNetGoogle Scholar
  38. 38.
    Moser R.D., Kim J., Mansour N.N.: Direct numerical simulation of turbulent channel flow up to Re τ = 590. Phys. Fluids 11(4), 943–945 (1999)CrossRefzbMATHGoogle Scholar
  39. 39.
    Nicoud F., Baggett J.S., Moin P., Cabot W.: Large eddy simulation wall-modeling based on suboptimal control theory and linear stochastic estimation. Phys. Fluids 13(10), 2968–2984 (2001)CrossRefGoogle Scholar
  40. 40.
    Piomelli U.: Wall-layer models for large eddy simulations. Prog. Aerosp. Sci. 44, 437–446 (2008)CrossRefGoogle Scholar
  41. 41.
    Piomelli U., Balaras E.: Wall-layer models for large-eddy simulation. Annu. Rev. Fluid Mech. 34, 349–374 (2002)CrossRefMathSciNetGoogle Scholar
  42. 42.
    Piomelli U., Moin P., Ferziger J.H., Kim J.: New approximate boundary conditions for large-eddy simulations of wall-bounded flows. Phys. Fluids A 1, 1061–1068 (1989)CrossRefGoogle Scholar
  43. 43.
    Rapp, C., Breuer, M., Manhart, M., Peller, N.: 2D Periodic Hill Flow. http://qnet.cfms.org.uk (2010)
  44. 44.
    Roman, F., Armenio, V., Fröhlich, J.: A simple wall-layer model for large eddy simulation with immersed boundary method. Phys. Fluids 12, 101701-1–101701-4 (2009)Google Scholar
  45. 45.
    Schumann U.: Subgrid scale model for finite difference simulations of turbulent flows in plane channels and annuli. J. Comput. Phys. 18, 376–404 (1975)CrossRefzbMATHMathSciNetGoogle Scholar
  46. 46.
    Stolz S., Adams N.A.: An approximate deconvolution procedure for large-eddy simulation. Phys. Fluids 11(4), 1699–1701 (1999)CrossRefzbMATHGoogle Scholar
  47. 47.
    Temmerman L., Leschziner M.A., Mellen C.P., Fröhlich J.: Investigation of wall-function approximations and subgrid-scale models in large-eddy simulation of separated flow in a channel with periodic constrictions. Int. J. Heat Fluid Flow 24, 157–180 (2003)CrossRefGoogle Scholar
  48. 48.
    Tessicini, F., Iaccarino, G., Wang, M., Verzicco, R.: Wall modeling for large-eddy simulation using an immersed-boundary method. CTR Annu. Res. Briefs 181–187 (2002)Google Scholar
  49. 49.
    ̆Sarić, S., Jakirlić, S., Breuer, M., Jaffrézic, B., Deng, G., Chikhaoni, O.: Evaluation of detached-eddy simulations for predicting the flow over periodic hills. In: Cancès, E., Gerbeau, J.F. (eds.) ESAIM Proceedings CEMRACS 2005: Computational aeroacoustics and computational fluid dynamics in turbulent flows. Marseille, France (July 18–August 26, 2005)Google Scholar
  50. 50.
    Wang M., Moin P.: Dynamic wall modeling for large-eddy simulation of complex turbulent flows. Phys. Fluids 14(7), 2044–2051 (2002)MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Zhen Li Chen
    • 1
    • 2
  • Stefan Hickel
    • 1
    Email author
  • Antoine Devesa
    • 1
  • Julien Berland
    • 1
  • Nikolaus A. Adams
    • 1
  1. 1.Institute of Aerodynamics and Fluid MechanicsTechnische Universität MünchenGarchingGermany
  2. 2.Institute of Fluid DynamicsNorthwestern Polytechnical UniversityXi’anPeople’s Republic of China

Personalised recommendations