Skip to main content

The Scale-Adaptive Simulation Method for Unsteady Turbulent Flow Predictions. Part 1: Theory and Model Description

Flow, Turbulence and Combustion volume 85, pages 113–138 (2010)Cite this article

Abstract

The article gives an overview of the Scale-Adaptive Simulation (SAS) method developed by the authors during the last years. The motivation for the formulation of the SAS method is given and a detailed explanation of the underlying ideas is presented. The derivation of the high-Reynolds number form of the equations as well as the calibration of the constants is provided. The concept of SAS is explained using several generic examples and test cases. In a companion article, the model is applied to more complex industrial-type applications.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

References

  1. Baldwin, B.S., Barth, T.J.: A one-equation turbulence transport model for aerodynamic flows. AIAA Paper 92-0439 (1992)

  2. Coles, D., Wadcock, A.J.: Flying hot-wire study of flow past an NACA 4412 airfoil at maximum lift. AIAA J. 17(4), 312–329 (1979)

    Article  ADS  Google Scholar 

  3. 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(Part 2), 273–337 (1971)

    Article  ADS  Google Scholar 

  4. Craft, T.J., Launder, B.E., Suga, K.: Development and application of a cubic eddy-viscosity model of turbulence. Int. J. Heat Fluid Flow 17(2), 108–115 (1996)

    Article  Google Scholar 

  5. Davidson, L.: Evaluation of the SST–SAS model: channel flow, asymmetric diffuser and axi-symmetric hill. In: Proceedings European Conference on Comp. Fluid Dyn. ECCOMAS CFD (2006)

  6. Egorov, Y., Menter, F.R.: Development and application of SST–SAS model in the DESIDER project. In: Advances in Hybrid RANS–LES Modelling. Notes on Num. Fluid Mech. Multidiscip. Des., vol. 97, Springer (2008)

  7. Egorov, Y., Menter, F.R., Cokljat, D.: The scale-adaptive simulation method for unsteady turbulent flow predictions. Part 2: application to complex flows. Flow Turbul. Combust. (2010). doi:10.1007/s10494-010-9265-4

    MATH  Google Scholar 

  8. Fröhlich, J., Mellen, C.P., Rodi, W., Temmerman, L., Leschziner, M.: Highly resolved large-eddy simulation of separated flow in a channel with streamwise periodic constrictions. J. Fluid Mech. 526, 19–66 (2005)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  9. Fröhlich, J., von Terzi, D.: Hybrid LES/RANS methods for simulation of turbulent flows. Prog. Aerosp. Sci. 44(5), 349–377 (2008)

    Article  Google Scholar 

  10. Gatski, T.B., Speziale, C.G.: On explicit algebraic stress models for complex turbulent flows. J. Fluid Mech. 254, 59–78 (1993)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  11. Kim, S.E.: Large Eddy simulation using unstructured meshes and dynamic subgrid-scale turbulence models. AIAA Paper no. 2004-2548 (2004)

  12. Launder, B.E., Spalding, D.B.: The numerical computation of turbulent flows. Comput. Methods. Appl. Mech. Eng. 3, 269–289 (1974)

    Article  MATH  Google Scholar 

  13. Launder, B.E., Reece, G.J., Rodi, W.: Progress in the development of a Reynolds-stress turbulence closure. J. Fluid Mech. 68, 537 (1975)

    Article  MATH  ADS  Google Scholar 

  14. Menter, F.R.: Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J. 32(8), 1598–1605 (1994)

    Article  ADS  Google Scholar 

  15. Menter, F.R.: Eddy viscosity transport equations and their relation to the k–ε model. NASA-TM-108854 (1994)

  16. Menter, F.R.: Eddy viscosity transport equations and their relation to the k–ε model. J. Fluids Eng. 119, 876–884 (1997)

    Article  Google Scholar 

  17. Menter, F.R, Kuntz, M., Bender R.: A scale-adaptive simulation model for turbulent flow predictions. AIAA Paper 2003-0767 (2003)

  18. Menter, F.R., Egorov, Y.: Re-visiting the turbulent scale equation. In: Proc. IUTAM Symp. One Hundred Years of Boundary Layer Research. Springer, Göttingen (2004)

    Google Scholar 

  19. Menter, F.R., Egorov, Y.: A scale-adaptive simulation model using two-equation models. AIAA Paper 2005-1095, Reno/NV (2005)

  20. Menter, F.R., Egorov, Y.: Turbulence models based on the length-scale equation. In: Fourth International Symposium on Turbulent Shear Flow Phenomena, Williamsburg, 2005—Paper TSFP4-268 (2005)

  21. Menter, F.R., Egorov, Y.: SAS turbulence modelling of technical flows. In: DLES 6—6th ERCOFTAC Workshop on Direct and Large Eddy Simulation September, Poitiers (2005)

  22. Menter, F.R., Egorov, Y., Rusch D.: Steady and unsteady flow modelling using the \(k-\sqrt k L\) model. In: Hanjalic, K., Nagano, Y., Jakirlic, S. (eds.) Proc. Turbulence, Heat and Mass Transfer, vol. 5 (2006)

  23. Menter, F.R., Egorov, Y.: Formulation of the Scale-Adaptive Simulation (SAS) model during the DESIDER Project. In: Haase, W., Braza, M., Revell, A. (eds.) Notes on Num. Fluid Mech. and Multidisc. Design, vol. 103, Springer (2009)

  24. Menter, F.R., Garbaruk A., Smirnov P.: Scale adaptive simulation with artificial forcing. In: Proc. 3rd Symposium on Hybrid RANS–LES Methods (2009)

  25. Moffatt, H.K.: Turbulence and stochastic processes: Kolmogorov’s ideas 50 years on. In: Hunt, J.C.R., Phillips, O.M., Williams, D. (eds.) Proceedings of the Royal Society, London, A, vol. 434, 1991, pp. 1–240 (1991)

  26. Nicoud, F., Ducros, F.: Subgrid-scale stress modelling based on the square of the velocity gradient tensor. Flow Turbul. Combust. 62, 183–200 (1999)

    Article  MATH  Google Scholar 

  27. Pope, S.B.: A more general effective-viscosity hypothesis. J. Fluid Mech. 72, 331–340 (1975)

    Article  MATH  ADS  Google Scholar 

  28. Rodi, W.: A new algebraic relation for calculating the Reynolds stresses. Z. Angew. Math. Mech. 56, 219–221 (1976)

    Article  MathSciNet  Google Scholar 

  29. Rodi, W.: Turbulence modelling for boundary layer calculations. In: Proc. IUTAM Symp. One Hundred Years of Boundary Layer Research, Göttingen, Springer (2004)

  30. Rodi, W., Mansour, N.N.: Low Reynolds number modelling with the aid of direct numerical simulation data. J. Fluid Mech. 250, 509–529 (1993)

    Article  MATH  ADS  Google Scholar 

  31. Rotta, J.C.: Statistische theorie nicht-homogener turbulenz I und II. Z. Phys. 129, 547–572; 131, 51–77 (1951)

    Google Scholar 

  32. Rotta, J.C.: Über eine methode zur Berechnung turbulenter Scherströmungen, aerodynamische Versuchsanstalt Göttingen. Rep. 69 A14 (1968)

  33. Rotta, J.C.: Turbulente Strömumgen. BG Teubner Stuttgart (1972)

  34. Sagaut, P., Deck, S., Terracol, M.: Multiscale and Multiresolution Approaches in Turbulence. Imperial College Press, London (2006)

    Book  Google Scholar 

  35. Spalart, P.R., Allmaras, S.R.: A one-equation turbulence model for aerodynamic flows. La Recherche Aerospatiale n 1, 5–21 (1994)

    Google Scholar 

  36. Spalart, P.R.: Strategies for turbulence modelling and simulations. Int. J. Heat Fluid Flow. 21, 2 (2000)

    Article  Google Scholar 

  37. Spalart, P.R., Jou, W., Strelets, M., Allmaras, S.: Comments on the feasibility of LES for wings, and on a hybrid RANS/LES approach. In: Advances in DNS/LES, 1st AFOSR Int. Conf. on DNS/LES (1997)

  38. Sjunnesson, A., Henriksson, R., Lofstrom C.: CARS measurements and visualization of reacting flows in bluff body stabilized flame. AIAA Paper. 92-3650 (1992)

  39. Strelets, M.: Detached Eddy simulation of massively separated flows. AIAA Paper 2001-879 (2001)

  40. Temmerman, L., Leschziner, M.A.: Large eddy simulation of separated flow in a streamwise periodic channel constriction. In: Proceedings, 2nd Symp. on Turbulence and Shear-Flow Phenomena, Stockholm (2001)

  41. Tennekes, H., Lumley, J.L.: A First Course in Turbulence. MIT Press, London (1992)

    Google Scholar 

  42. Travin, A., Shur, M., Spalart, P.R., Strelets, M.: On URANS solutions with LES-like behaviour. In: Proc. ECCOMAS 2004, Jyväskylä (2004)

  43. Wallin, S., Johansson, A.V.: An explicit algebraic Reynolds stress model for incompressible and compressible turbulent flows. J. Fluid Mech. 403, 89–132 (2000)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  44. Wilcox, D.C.: Turbulence Modeling for CFD. DCW Industries Inc., 2. Edition (1998)

Download references

Author information

Authors and Affiliations

  1. ANSYS Germany GmbH, Staudenfeldweg 12, 83624, Otterfing, Germany

    F. R. Menter & Y. Egorov

Authors
  1. F. R. Menter
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Y. Egorov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to F. R. Menter.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Menter, F.R., Egorov, Y. The Scale-Adaptive Simulation Method for Unsteady Turbulent Flow Predictions. Part 1: Theory and Model Description. Flow Turbulence Combust 85, 113–138 (2010). https://doi.org/10.1007/s10494-010-9264-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10494-010-9264-5

Keywords

  • Turbulence model
  • Scale-adaptive simulation
  • SAS
  • Hybrid RANS–LES