Skip to main content
SpringerLink
Log in

Application of an Explicit Algebraic Reynolds Stress Model within a Hybrid LES–RANS Method

  • Published:
Flow, Turbulence and Combustion Aims and scope Submit manuscript

Abstract

Large-eddy simulations (LES) still suffer from extremely large resources required for the resolution of the near-wall region, especially for high-Re flows. That is the main motivation for setting up hybrid LES–RANS methods. Meanwhile a variety of different hybrid concepts were proposed mostly relying on linear eddy-viscosity models. In the present study a hybrid approach based on an explicit algebraic Reynolds stress model (EARSM) is suggested. The model is applied in the RANS mode with the aim of accounting for the Reynolds stress anisotropy emerging especially in the near-wall region. For the implementation into a CFD code this anisotropy-resolving closure can be formally expressed in terms of a non-linear eddy-viscosity model (NLEVM). Its extra computational effort is small, still requiring solely the solution of one additional transport equation for the turbulent kinetic energy. In addition to this EARSM approach, a linear eddy-viscosity model (LEVM) is used in order to verify and emphasize the advantages of the non-linear model. In the present formulation the predefinition of RANS and LES regions is avoided and a gradual transition between both methods is assured. A dynamic interface criterion is suggested which relies on the modeled turbulent kinetic energy and the wall distance and thus automatically accounts for the characteristic properties of the flow. Furthermore, an enhanced version guaranteeing a sharp interface is proposed. The interface behavior is thoroughly investigated and it is shown how the method reacts on dynamic variations of the flow field. Both model variants, i.e. LEVM and EARSM, have been tested on the basis of the standard plane channel flow and even more detailed on the flow over a periodic arrangement of hills using fine and coarse grids.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Abe, K., Jang, Y.-J., Leschziner, M.A.: An investigation of wall-anisotropy expressions and length-scale equations for non-linear eddy-viscosity models. Int. J. Heat Fluid Flow 24, 181–198 (2003)

    Article  Google Scholar 

  2. Abe, K.: A hybrid LES/RANS approach using an anisotropy-resolving algebraic turbulence model. Int. J. Heat Fluid Flow 26, 204–222 (2005)

    Article  Google Scholar 

  3. Batten, P., Goldberg, U., Chakravarthy, S.: LNS—An approach towards embedded LES. AIAA Paper 2002–0427 (2002)

  4. Batten, P., Goldberg, U., Chakravarthy, S.: Interfacing statistical turbulence closures with large-eddy simulation. AIAA J. 42(3), 485–492 (2004)

    Article  ADS  Google Scholar 

  5. Breuer, M., Rodi, W.: Large-eddy simulation of complex turbulent flows of practical interest. In: Hirschel, E.D. (ed.) Flow Simulation with High-Performance Computers II, Notes on Numerical Fluid Mechanics, vol. 52, pp. 258–274. Vieweg Verlag, Braunschweig (1996)

    Google Scholar 

  6. Breuer, M.: Large-eddy simulation of the sub-critical flow past a circular cylinder: numerical and modeling aspects. Int. J. Numer. Methods Fluids 28, 1281–1302 (1998)

    Article  MATH  ADS  Google Scholar 

  7. Breuer, M.: Direkte Numerische Simulation und Large-Eddy Simulation turbulenter Strömungen auf Hochleistungsrechnern, Habilitationsschrift. Univ. Erlangen–Nürnberg, Berichte aus der Strömungstechnik. ISBN: 3-8265-9958-6 (2002)

  8. Breuer, M.: New Reference Data for the Hill Flow Test Case. (2005) http://www.hy.bv.tum.de/DFG-CNRS/

  9. Breuer, M., Jaffrézic, B., Peller, N., Manhart, M., Fröhlich, J., Hinterberger, Ch., Rodi, W., Deng, G., Chikhaoui, O., S̆arić, S., Jakirlić, S.: A comparative study of the turbulent flow over a periodic arrangement of smoothly contoured hills. In: Lamballais, E., Friedrich, R., Geurts, B.J., Métais O. (eds.) Sixth Int. ERCOFTAC Workshop on DNS and LES: DLES-6, Poitiers, France, 12–14 Sept. 2005, ERCOFTAC Series, vol. 10, pp. 635–642. Direct and Large-Eddy Simulation VI, ISBN-10 1-4020-4909-9. Springer Science (2006)

  10. Breuer, M., Jaffrézic, B., Šarić, S., Jakirlić, S., Deng, G., Chikhaoui, O., Fröhlich, J., von Terzi, D., Manhart, M., Peller, N.: Issues in Hybrid LES–RANS and coarse grid LES of separated flows. EUROMECH Colloquium 469, Large-Eddy Simulation of Complex Flows. TU Dresden, Germany, 6–8 Oct. 2005

  11. Breuer, M., Jaffrézic, B., Arora, K.: Hybrid LES–RANS technique based on a one-equation near-wall model. J. Theor. Comput. Fluid Dyn. 22(3–4), 157–187 (2008)

    Google Scholar 

  12. Breuer, M., Peller, N., Rapp, Ch., Manhart, M.: Flow over periodic hills—numerical and experimental study in a wide range of Reynolds numbers. Int. J. Computers Fluids (2008, in press)

  13. Chen, H.C., Patel, V.C.: Near-wall turbulence models for complex flows including separation. AIAA J. 26(6), 641–648 (1988)

    Article  ADS  Google Scholar 

  14. Daly, B.J., Harlow, F.H.: Transport equations in turbulence. Phys. Fluids 13, 2634–2649 (1970)

    Article  ADS  Google Scholar 

  15. Davidson, L., Dahlström, S.: Hybrid LES–RANS: computation of the flow around a three-dimensional hill. In: Rodi, W., Mulas, M. (eds.) Engineering Turbulence Modeling and Experiments, vol. 6, pp. 319–328. Elsevier (2005)

  16. Davidson, L.: Hybrid LES–RANS: inlet boundary conditions. In: Skallerud, B., Andersson, H.I. (eds.) 3rd National Conf. on Computational Mechanics—MekIT’05, pp. 7–22. Trondheim, Norway, 11–12 May 2005

  17. Durbin, P.A.: Application of a near-wall turbulence model to boundary layers and heat transfer. Int. J. Heat Fluid Flow. 14, 316–323 (1993)

    Article  Google Scholar 

  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)

    Article  MATH  ADS  MathSciNet  Google Scholar 

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

    Article  MATH  ADS  MathSciNet  Google Scholar 

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

    Article  MATH  ADS  Google Scholar 

  21. Germano, M.: From RANS to DNS: towards a bridging model. In: Voke, P.R., Sandham, N.D., Kleiser, L. (eds.) Direct and Large-Eddy Simulation III, Proc. of the Isaac Newton Institute Symposium/ERCOFTAC Workshop on Direct and Large-Eddy Simulation, pp. 225–236. Cambridge, UK, 12–14 May 1999, ERCOFTAC Series, vol. 7. Kluwer Academic Publ., Dordrecht (1999)

  22. Grundestam, O., Wallin, S., Johansson, A.V.: Observations on the predictions of fully developed rotating pipe flow using differential and explicit algebraic Reynolds stress models. European J. Fluid Mech. B/Fluids 25, 95–112 (2006)

    Article  MATH  ADS  Google Scholar 

  23. Hanjalić, K., Hadžiabdić, M., Temmerman, L., Leschziner, M.A.: Merging LES and RANS strategies: zonal or seamless coupling?. In: Friedrich, et al. (eds.) Direct and Large-Eddy Simulation V, pp. 451–464. Kluwer Academic Publ., Netherlands (2004)

    Google Scholar 

  24. 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)

    Article  ADS  Google Scholar 

  25. Jaffrézic, B., Breuer, M., Chikhaoui, O., Deng, G., Visonneau, M.: Towards hybrid LES–RANS-coupling for complex flows with separation. In: Cancès, E., Gerbeau J.F. (eds.) ESAIM: Proceedings, CEMRACS 2005, Computational Aeroacoustics and CFD in Turbulent Flows, vol. 16, pp. 89–113. Marseille, France, July 18–Aug. 26, 2005 (2007)

  26. Jakirlić, S., Jester-Zürker, R., Tropea, C. (eds.): Report on 9th ERCOFTAC/IAHR/COST Workshop on Refined Flow Modeling. Darmstadt University of Technology. Germany, 4–5 Oct. 2001

  27. Kniesner, B., Jester-Zürker, R., Jakirlić, S., Hanjalić, K.: RANS–SMC and hybrid LES/RANS modelling of a backward-facing step flow subjected to increasingly enhanced wall heating. Fifth Int. Symp. on Turbulence and Shear Flow Phenomena. Garching, Germany, 27–29 August 2007

  28. Lumley, J.L., Newman, G.: The return to isotropy of homogeneous turbulence. J. Fluid Mech. 82, 161–178 (1977)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  29. Manceau, R., Bonnet, J.-P., Leschziner, M.A., Menter, F. (eds.): 10th Joint ERCOFTAC SIG-15/IAHR/QNET-CFD Workshop on Refined Flow Modeling. Université de Poitiers, France, 10–11 Oct. 2002

    Google Scholar 

  30. Mellen, C.P., Fröhlich, J., Rodi, W.: Large-eddy simulation of the flow over periodic hills. In: Deville, M., Owens, R. (eds.) Proceedings of 16th IMACS World Congress. Lausanne, Switzerland, (2000)

    Google Scholar 

  31. Menter, F.R., Kuntz, M.: Adaptation of eddy-viscosity turbulence models to unsteady separated flow behind vehicles. In: McCallen, R., Browand, F., Ross, J. (eds.) Symp. on “The aerodynamics of heavy vehicles: trucks, buses and trains”, Monterey, USA, 2–6 Dec. 2002. Springer, Berlin Heidelberg New York (2004)

  32. Moser, R.D., Kim, J., Mansour N.N.: DNS of turbulent channel flow up to Re τ  = 590. Phys. Fluids 11, 943–945 (1999)

    Article  ADS  MATH  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. 12(7), 1629–1632 (2000)

    Article  ADS  Google Scholar 

  34. Piomelli, U., Chasnov, J.R.: Large-eddy simulations: theory and applications. In: Hallbäck, M., Henningson, D.S., Johansson, A.V., Alfredson, P.H. (eds.) Turbulence and Transition Modeling, pp. 269–331. Kluwer (1996)

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

    Article  MATH  ADS  Google Scholar 

  36. Pope, S.B.: Turbulent Flows. Cambridge University Press (2000)

    MATH  Google Scholar 

  37. Rhie, C.M., Chow, W.L.: Numerical study of the turbulent flow past an airfoil with trailing-edge separation. AIAA J. 21, 1525–1532 (1983)

    Article  MATH  ADS  Google Scholar 

  38. Rodi, W., Mansour, N.N., Michelassi, V.: One-equation near-wall turbulence modeling with the aid of direct simulation data. J. Fluids Eng. 115, 196–205 (1993)

    Article  Google Scholar 

  39. Sagaut, P.: Large-Eddy Simulation for Incompressible Flows—An Introduction. Springer (2001)

  40. Šarić, S., Jakirlić, S., Breuer, M., Jaffrézic, B., Deng, G., Chikhaoui, O., Fröhlich, J., von Terzi, D., Manhart, M., Peller, N.: Evaluation of detached-eddy simulations for predicting the flow over periodic hills. In: Cancès, E., and Gerbeau, J.F. (eds.) ESAIM: Proceedings, CEMRACS 2005, Computational Aeroacoustics and CFD in Turbulent Flows, vol. 16 pp. 133–145, 18 July–26 Aug. 2005. Marseille, France (2007)

  41. Schlüter J.U., Pitsch, H., Moin, P.: Large-eddy simulation inflow conditions for coupling with reynolds-averaged flow solvers. AIAA J. 42(3), 478–484 (2004)

    Article  ADS  Google Scholar 

  42. Schumann, U.: Subgrid-scale model for finite-difference simulations of turbulent flows in plane channels and annuli. J. Comput. Phys. 18, 376–404 (1975)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  43. Shur, M., Spalart, P.R., Strelets, M., Travin, A.: Detached-eddy simulation of an airfoil at high angle of attack. In: Rodi, W., Laurence, D. (eds.) Fourth Int. Symp. on Engineering Turbulence Modeling and Measurements, Corsica, France, 24–26 May 1999. Engineering Turbulence Modeling and Experiments, vol. 4, pp. 669–678. Elsevier, Amsterdam (1999)

    Google Scholar 

  44. Smagorinsky, J.: General circulation experiments with the primitive equations, I, the basic experiment. Month. Weather Rev. 91, 99–165 (1963)

    Article  ADS  Google Scholar 

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

    Google Scholar 

  46. Spalart, P.R., Jou, W.-H., Strelets, M., Allmaras, S.R.: Comments on the feasibility of LES for wings, and on a hybrid RANS/LES approach. In: Liu, C., Liu, Z. (eds.) Advances in DNS/LES, 1st AFOSR Int. Conf. on DNS/LES. Greyden Press, Columbus, OH, 4–8 Aug. 1997

    Google Scholar 

  47. Spalart, P.R.: Trends in turbulence treatments. AIAA Paper 2000-2306, FLUIDS 2000, Computational Fluid Dynamics Symp. Denver, Colorado, USA, 19–22 June 2000

  48. Spalart, P.R.: Strategies for turbulence modeling and simulations. Int. J. Heat Fluid Flow 21, 252–263 (2000)

    Article  Google Scholar 

  49. Spalart, P.R., Deck, S., Shur, M.L., Squires, K.D., Strelets, M., Travin, A.: A new version of detached-eddy simulation resistant to ambiguous grid densities. J. Theor. Comput. Fluid Dyn. 20, 181–195 (2006)

    Article  MATH  ADS  Google Scholar 

  50. Speziale, C.G.: Turbulence modeling for time-dependent RANS and VLES: a review. AIAA J. 36(2), 173–184 (1996)

    Article  ADS  Google Scholar 

  51. Speziale, C.G.: A combined large-eddy simulation and time-dependent RANS capability for high-speed compressible flows. J. Sci. Comput. 13, 253–274 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  52. Strelets, M.: Detached-eddy simulation of massively separated flows. AIAA Paper 2001-0879 (2000)

  53. Squires, K.D., Forsythe, J.R., Spalart, P.R.: Detached-eddy simulation of the separated flow around a forebody cross-section. In: Geurts, B.J., Friedrich, R., Métais, O. (eds.) Fourth Workshop on Direct and Large-Eddy Simulation, pp. 484–500. Enschede, The Netherlands, 18–20 July 2001. ERCOFTAC Series, Direct and Large-Eddy Simulation IV. Kluwer Academic Publ., Dordrecht (2001)

  54. 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 streamwise periodic constrictions. Int. J. Heat Fluid Flow 24, 157–180 (2003)

    Article  Google Scholar 

  55. Temmerman, L., Hadžiabdić, M., Leschziner, M.A., Hanjalić, K.: A hybrid two-layer URANS–LES approach for large-eddy simulation at high reynolds numbers. Int. J. Heat Fluid Flow 26, 173–190 (2005)

    Article  Google Scholar 

  56. Travin, A., Shur, M., Strelets, M., Spalart, P.R.: Detached-eddy simulations past a circular cylinder. J. Flow, Turbulence Combustion 63 (1/4), 293–313. Kluwer Academic Publ., Dordrecht (2000)

  57. Travin, A., Shur, M., Strelets, M., Spalart, P.R.: Physical and numerical upgrades in the detached-eddy simulation of complex turbulence flows. In: Fluid Mechanics and Its Application: Advances in LES of Complex Flows (2002)

  58. Travin, A.K., Shur, M.L., Spalart, P.R., Strelets, M.K.: Improvement of delayed detached-eddy simulation for LES with wall modelling. In: Wesseling, P., Onate, E., Periaux, J. (eds.) European Conf. of Comput. Fluid Dynamics, ECCOMAS CFD TU Delft. The Netherlands (2006)

  59. von Terzi, D., Hinterberger, C., García-Villalba, M., Fröhlich, J., Rodi, W., Mary, I.: LES with downstream RANS for flow over periodic hills and a model combustor flow. EUROMECH Colloquium 469, Large-Eddy Simulation of Complex Flows. TU Dresden, Germany, 6–8 Oct. 2005

  60. Wagner, C., Hüttl, T., Sagaut, P. (eds.): Large-Eddy Simulation for Acoustics. ISBN-13: 978052-187-1440, ISBN-10: 052-187-1441. Cambridge University Press (2007)

  61. 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  ADS  MathSciNet  Google Scholar 

  62. Wolfshtein, M.: The velocity and temperature distribution in one-dimensional flow with turbulence augmentation and pressure gradient. Int. J. Heat Mass Trans. 12, 301–318 (1969)

    Article  Google Scholar 

  63. Yoshizawa, A., Horiuti, K.: A statistically-derived subgrid-scale kinetic energy model for the large-eddy simulation of turbulent flows. J. Phys. Soc. Japan 54(8), 2834–2839 (1985)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Fluid Mechanics, University of Erlangen–Nürnberg, Cauerstr. 4, 91058, Erlangen, Germany

    B. Jaffrézic & M. Breuer

Authors
  1. B. Jaffrézic
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Breuer
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Breuer.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jaffrézic, B., Breuer, M. Application of an Explicit Algebraic Reynolds Stress Model within a Hybrid LES–RANS Method. Flow Turbulence Combust 81, 415–448 (2008). https://doi.org/10.1007/s10494-008-9146-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10494-008-9146-2

Keywords

Search

Navigation