Skip to main content
Log in

Anisotropy Invariant Reynolds Stress Model of Turbulence (AIRSM) and its Application to Attached and Separated Wall-Bounded Flows

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

Abstract

Numerical predictions with a differential Reynolds stress closure, which in its original formulation explicitly takes into account possible states of turbulence on the anisotropy-invariant map, are presented. Thus the influence of anisotropy of turbulence on the modeled terms in the governing equations for the Reynolds stresses is accounted for directly. The anisotropy invariant Reynolds stress model (AIRSM) is implemented and validated in different finite-volume codes. The standard wall-function approach is employed as initial step in order to predict simple and complex wall-bounded flows undergoing large separation. Despite the use of simple wall functions, the model performed satisfactory in predicting these flows. The predictions of the AIRSM were also compared with existing Reynolds stress models and it was found that the present model results in improved convergence compared with other models. Numerical issues involved in the implementation and application of the model are also addressed.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

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

    Article  MATH  ADS  MathSciNet  Google Scholar 

  2. Lumley, J.L.: Computational modeling of turbulent flows. Adv. Appl. Mech. 18, 123–176 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  3. Jovičić, N., Breuer, M., Jovanović, J.: Anisotropy–invariant mapping of turbulence in a flow past an unswept airfoil at high angle of attack. J. Fluids Eng. 128(3), 559–567 (2006)

    Article  Google Scholar 

  4. Jovanović, J.: The Statistical Dynamics of Turbulence. Springer, New York (2004)

    MATH  Google Scholar 

  5. Shir, C.C.: A preliminary study of atmospheric turbulent flow in the idealized planetary boundary layer. J. Atmos. Sci. 30, 1327–1339 (1973)

    Article  ADS  Google Scholar 

  6. Hällback, M., Groth, J., Johansson, A.V.: An algebraic model for non-isotropic turbulent dissipation rate in Reynolds stress closure. Phys. Fluids A 2, 1859–1866 (1990)

    Article  ADS  Google Scholar 

  7. Kolmogorov, A.N.: Local structure of turbulence in an incompressible fluid at very high Reynolds numbers. Dokl. Akad. Nauk SSSR 30, 299–303 (1941)

    ADS  Google Scholar 

  8. Speziale, C.G., Sarkar, S., Gatski, T.B.: Modeling of pressure-strain correlation of turbulence: an invariant dynamical system approach. J. Fluid Mech. 227, 245–272 (1991)

    Article  MATH  ADS  Google Scholar 

  9. Launder, B.E., Reece, G.J., Rodi, W.: Progress in the development of a Reynolds-stress turbulence closure. J. Fluid Mech. 68, 537–566 (1975)

    Article  MATH  ADS  Google Scholar 

  10. Durst, F., Schäfer, M., Wechsler, K.: Efficient simulation of incompressible viscous flows on parallel computers. Notes Numer. Fluid Mech. 52, 87–101 (1996)

    Google Scholar 

  11. Grotjans, H.: Turbulenzmodelle höherer Ordnung für komplexe Anwendungen. PhD thesis, TU München (1999)

  12. Jakirlic, S. Hanjalić, K.: A new approach to modelling near-wall turbulence energy and stress dissipation. J. Fluid Mech. 459, 139–166 (2002)

    Article  MATH  ADS  Google Scholar 

  13. Manceau, R., Hanjalić, K.: Elliptic blending model: a new near-wall Reynolds-stress turbulence closure. Phys. Fluids 14(2), 744–754 (2002)

    Article  ADS  Google Scholar 

  14. Launder, B.E., Li, S.-P.: On the elimination of wall-topography parameters from second-moment closure. Phys. Fluids 6(2), 999–1006 (1994)

    Article  MATH  ADS  Google Scholar 

  15. Dianat, M., Fairweather, M., Jones, W.P.: Reynolds stress closure applied to axisymmetric, impinging turbulent jets. Theoret. Comput. Fluid Dyn. 8, 435–447 (1996)

    MATH  ADS  Google Scholar 

  16. Craft, T.J., Launder, B.E.: A Reynolds stress closure designed for complex geometries. Int. J. Heat Fluid Flow 17(3), 245–254 (1996)

    Article  Google Scholar 

  17. Moser, R.D., Kim, J., Mansour, N.N.: Direct numerical simulation of turbulent channel flow up to Re τ  = 590. Phys. Fluids 11, 943–946 (1999)

    Article  MATH  ADS  Google Scholar 

  18. Obi, S., Aoki, K., Masuda, S.: Experimental and computational study of turbulent separated flow in an asymmetric diffuser. In: Proc. 9th Symp. on Turbulent Shear Flows, Kyoto (1993)

  19. Buice, C.U., Eaton, J.K.: Experimental investigation of flow through an asymmetric plane diffuser. Technical report, Center of Turbulence Research, Stanford University, CTR Annual Research Briefs (1996)

  20. Durbin, P.A.: On the k-ϵ stagnation point anomaly. Int. J. Heat Fluid Flow 17, 89–91 (1996)

    Article  Google Scholar 

  21. Iaccarino, G.: Predictions of a turbulent separated flow using commercial CFD codes. ASME J. Fluids Eng. 123, 819–828 (2001)

    Article  Google Scholar 

  22. Apsley, D.D., Leschziner, M.A.: Advanced turbulence modelling of separated flow in a diffuser. J. Flow Turbul. Combust. 63, 81–112 (1999)

    Article  Google Scholar 

  23. Kaltenbach, H.J., Fatica, M., Mittal, R., Lund, T.S., Moin, P.: Study of flow in a planar asymmetric diffuser using large-Eddy simulation. J. Fluid Mech. 390, 151–185 (1999)

    Article  MATH  ADS  Google Scholar 

  24. Schlüter, J.U., Wu, X., Pitsch, H.: Large-Eddy Simulation of a Separated Plane Diffuser. AIAA Paper (2005)

  25. Driver, D.M., Seegmiller, H.L.: Feature of a reattachment turbulent shear layer in a divergent channel flow. AIAA J. 23, 163–171 (1985)

    Article  ADS  Google Scholar 

  26. Lasher W.C., Taulbee, D.B.: On the computation of turbulent backstep flow. Int. J. Heat Fluid Flow 13(1), 30–40 (1992)

    Article  ADS  Google Scholar 

  27. Hanjalić, K., Jakirlić, S.: Contribution towards the second-moment closure modelling of separating turbulent flows. Comput. Fluids 27(2), 137–156 (1998)

    Article  MATH  Google Scholar 

  28. Guilmineau, E., Piquet, J., Queutey, P.: Two-dimensional turbulent viscous flow simulation past airfoils at fixed incidence. Comput. Fluids, 26, 135–162 (1997)

    Article  MATH  Google Scholar 

  29. Coles, D., Wadcock, A.J.: Flying hot-wire study of flow past a NACA 4412 airfoil at maximum lift. AIAA J. 17, 321–329 (1979)

    Article  ADS  Google Scholar 

  30. Wadcock, A.J.: Two-dimensional stalled airfoil. In: Proceedings of the 1980-81 AFOSR-HTTM-Stanford Conference on Complex Turbulent Flows, pp. 234–252. Thermosciences Divison, Mechanical Engineering Department, Stanford University, Stanford, California (1981)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to M. Breuer.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kumar, V., Frohnapfel, B., Jovanović, J. et al. Anisotropy Invariant Reynolds Stress Model of Turbulence (AIRSM) and its Application to Attached and Separated Wall-Bounded Flows. Flow Turbulence Combust 83, 81–103 (2009). https://doi.org/10.1007/s10494-008-9190-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10494-008-9190-y

Keywords

Navigation