Flow, Turbulence and Combustion

, Volume 60, Issue 1, pp 19–46 | Cite as

Computation of 3-D Turbulent Boundary Layers Using the V2F Model

  • S. Parneix
  • P.A. Durbin
  • M. Behnia


The V2F model makes use of the standard k–ε model, but extends it by incorporating near-wall turbulence anisotropy and non-local pressure-strain effects, while retaining a linear eddy viscosity assumption. It has the attraction of fewer equations and more numerical robustness than Reynolds stress models. The model is presented in a form that is completely independent of distance to the wall. This formalism is well suited to complex, 3-D, multi-zone configurations. It has been applied to the computation of two complex 3-D turbulent flows: the infinitely swept bump and the appendage-body junction; some preliminary results for the flow in a U-bend are also presented. Despite the use of a linear, eddy viscosity formula, the V2F model is shown to provide excellent predictions of mean flow quantities. The appendage-body test case involves very complex features, such as a 3-D separation and a horseshoe vortex. The V2F simulations have been shown to successfully reproduce these features, both qualitatively and quantitatively. The calculation of the complex flow structure inside and downstream of the U-bend also shows very promising results.

V2F turbulence modeling 3DTBL swept bump wing-body junction U-bend 


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  1. 1.
    Behnia, M., Parneix, S. and Durbin, P., Accurate predictions of jet impingement heat transfer. In: HTD-Vol. 343, National Heat Transfer Conference, Baltimore, Vol. 5 (1997) pp. 111–118.Google Scholar
  2. 2.
    Behnia, M., Parneix, S. and Durbin, P., Prediction of heat transfer in a jet impinging on a flat plate. International Journal of Heat and Mass Transfer 41 (1998) 1845–1855.CrossRefGoogle Scholar
  3. 3.
    Behnia, M., Parneix, S. and Durbin, P., Numerical simulation of jet impingement cooling of a heated pedestal. In: Proceedings of 10th International Symposium on Transport Phenomena. Kyoto (1997) Vol. 2, pp. 349–354.Google Scholar
  4. 4.
    Benek, J.A., Bunning, P.G. and Steger, P.G., Chimera: A grid-embedding technique. AIAA Paper No. 85-1523 (1985).Google Scholar
  5. 5.
    Benek, J.A., Donegan, T.L. and Suhs, J.L., Extended Chimera grid-embedding scheme with applications to viscous flows. AIAA Paper No. 87-1126 (1987).Google Scholar
  6. 6.
    Cheah, S.C., Iacovides, H., Jackson, D.C., Ji, H. and Launder, B. Measurements of an enclosed rotor-stator disc flow. In: Symposium on Laser Anemometry on Reciprocating, Reacting or Rotating Flow, University College of Swansea, 7-9 April (1992).Google Scholar
  7. 7.
    Cheah, S.C., Iacovides, H., Jackson, D.C., Ji, H. and Launder, B., LDA investigation of the flow development through rotating U-ducts. In: Proceedings International Gas-Turbine and Aero Congress, The Hague (1994) ASME paper 94-GT-55, pp. 590–596.Google Scholar
  8. 8.
    Chen, H.C., Assessment of a Reynolds stress closure model for appendage-hull junction flows. Journal of Fluid Engineering 117 (1995) 557–563.Google Scholar
  9. 9.
    Craft, T.J. and Launder, B.E., A Reynolds stress closure designed for complex geometries. International Journal of Heat and Fluid Flow 17 (1996) 245–254.CrossRefGoogle Scholar
  10. 10.
    Craft, T.J., Launder, B.E. and Suga, K., Prediction of turbulent transitional phenomena with a non-linear eddy-viscosity model. International Journal of Heat and Fluid Flow 18 (1997) 15–28.CrossRefGoogle Scholar
  11. 11.
    Deng, G., Rèsolution des èquations de Navier—Stokes tridimensionnelles. Application au calcul d'un raccord plaque plane-aile. Ph.D. Thesis, University of Nantes, France (1989).Google Scholar
  12. 12.
    Devenport, W. and Simpson, R., Time-dependent and time-averaged turbulence structure near the nose of a wing-body junction. Journal of Fluid Mechanics 210 (1990) 23–55.Google Scholar
  13. 13.
    Durbin, P., Near-wall turbulence closure without damping functions. Theoretical and Computational Fluid Dynamics 3(1) (1991) 1–13.Google Scholar
  14. 14.
    Durbin, P., A Reynolds-stress model for near-wall turbulence. Journal of Fluid Mechanics 249 (1993) 465–498.Google Scholar
  15. 15.
    Durbin, P., Application of a near-wall turbulence model to boundary layers and heat transfer. International Journal of Heat and Fluid Flow 14(4) (1993) 316–323.CrossRefGoogle Scholar
  16. 16.
    Durbin, P., On modeling three-dimensional turbulent wall layers. Physics of Fluids A 5 (1993) 1231–1238.CrossRefGoogle Scholar
  17. 17.
    Durbin, P., Separated flow computations with the k-ε-ν2— model. AIAA Journal 33(4) (1995) 659–664.Google Scholar
  18. 18.
    Bonnin, J.C., Buchel, T. and Rodi, W., Databases and testing of calculation methods for turbulent flows. Ercoftac Bulletin 28 (1996) 49–54.Google Scholar
  19. 19.
    Gibson, M.M. and Launder, B.E., Ground effects on pressure fluctuations in the atmospheric boundary layer. Journal of Fluid Mechanics 86 (1978) 491–511.Google Scholar
  20. 20.
    Goldberg, U. and Reshotko, E., Scaling and modeling of three-dimensional, pressure-driven turbulent boundary layers. AIAA Journal 22 (1984) 914–920.Google Scholar
  21. 21.
    Hanjalic, K., Advanced turbulence closure models: A view of current status and future prospects. International Journal of Heat and Fluid Flow 15 (1994) 178–203.CrossRefGoogle Scholar
  22. 22.
    Iacovides, H. and Launder, B.E., Computational fluid dynamics applied to internal gas-turbine blade cooling: A review. International Journal of Heat and Fluid Flow 16 (1995) 454–470.CrossRefGoogle Scholar
  23. 23.
    Iacovides, H., Launder, B.E. and Li, H.Y., The computation of flow development through stationary and rotating U-ducts of strong curvature. International Journal of Heat and Fluid Flow 17 (1996) 22–33.CrossRefGoogle Scholar
  24. 24.
    Ji, H., An experimental investigation of two rotating turbulent shear flows with gas turbine applications. Ph.D. Thesis, Department of Mechanical Engineering, UMIST (1994).Google Scholar
  25. 25.
    Johnston, J.P. and Flack, K.A., Review — Advances in three-dimensional turbulent boundary layers with emphasis on the wall-layer regions. Journal of Fluid Engineering 118 (1996) 219–232.Google Scholar
  26. 26.
    Launder, B.E., Turbulence modelling for flows in arbitrarily complex domains. In: Eccomas. John Wiley & Sons, New York (1996).Google Scholar
  27. 27.
    Martinuzzi, R. and Tropea, C., The flow around surface-mounted, prismatic obstacles placed in a fully developed channel flow. Journal of Fluid Engineering 115 (1993) 85–92.Google Scholar
  28. 28.
    Moin, P., Shih, T.H., Driver, D.M and Mansour, N.M., Direct numerical simulation of a three dimensional turbulent boundary layer. Physics of Fluids A 2 (1990) 601–639.Google Scholar
  29. 29.
    Simoneau, R.J. and Simon, F.F., Progress towards understanding and predicting heat transfer in the turbine gas path. International Journal of Heat and Fluid Flow 14 (1993) 106–127.CrossRefGoogle Scholar
  30. 30.
    Ölçmen, S. and Simpson, R., An experimental study of a three-dimensional pressure-driven turbulent boundary layer. Journal of Fluid Mechanics 290 (1995) 225–262.Google Scholar
  31. 31.
    Ölçmen, S. and Simpson, R., Some features of a turbulent wing-body junction vortical flow. In: 35th Aerospace Sciences Meeting and Exhibit. (1997) AIAA Paper No. 97-0651.Google Scholar
  32. 32.
    Praisner, T.J., Seal, C.V., Takmaz, L. and Smith, C.R., Spatial-temporal turbulent flow-field and heat transfer behavior in end-wall junctions. International Journal of Heat and Fluid Flow 18 (1997) 142–151.CrossRefGoogle Scholar
  33. 33.
    Rodi W., Bonnin, J.C., Buchal, T. and Laurence, D., Testing of Calculation Methods for Turbulent Flows: Workshop Results for 5 Test-Cases. EDF Report. EFD (1998) 98NB00004, ISSN 1161-0611.Google Scholar
  34. 34.
    Rodi, W. and Mansour, N.N., Low Reynolds number k-ε modeling with the aid of direct simulation data. Journal of Fluid Mechanics 250 (1993) 509–529.Google Scholar
  35. 35.
    Rogers, S.E. and Kwak, D., Upwind differencing scheme for the time-accurate incompressible Navier—Stokes equations. AIAA Journal 28 (1990) 253–262.Google Scholar
  36. 36.
    Schwarz, W. and Bradshaw, P., Turbulence structural changes for a three-dimensional turbulent boundary layer in a 30° bend. Journal of Fluid Mechanics 272 (1994) 183–209.Google Scholar
  37. 37.
    Spencer, M.C., Jones, T.V. and Lock, G.D., Endwall heat transfer measurements in an annular cascade of nozzle guide vanes at engine representative Reynolds and Mach numbers. International Journal of Heat and Fluid Flow 17 (1996) 139–147.CrossRefGoogle Scholar
  38. 38.
    Sung, C.H. and Yang, C.I., Validation of turbulent horseshoe vortex flows. In: 17th Symposium on Naval Hydrodynamics, The Hague (1988).Google Scholar
  39. 39.
    Xie, Q. and Wroblewski, D., Effect of periodic unsteadiness on heat transfer in a turbulent boundary layer downstream of a cylinder-wall junction. International Journal of Heat and Fluid Flow 17 (1996) 107–115.Google Scholar
  40. 40.
    Webster, D.R., DeGraaff, D.B. and Eaton, J.K., Turbulence characteristics of a boundary layer over a two-dimensional bump. Journal of Fluid Mechanics 320 (1996) 53–69.Google Scholar
  41. 41.
    Webster, D.R., DeGraaff, D.B. and Eaton, J.K., Turbulence characteristics of a boundary layer over a swept bump. Journal of Fluid Mechanics 323 (1996) 1–22.Google Scholar
  42. 42.
    Wu, X. and Squires, K.D., Nonequilibrium turbulent flow over a bump: A comparison of LES and RANS with experiments. AIAA Journal 38 (1998) 799–808.Google Scholar
  43. 43.
    Wu, X. and Squires, K.D., Prediction of the three-dimensional turbulent boundary layer over a swept bump. AIAA Journal 36(4) (1998) 505–514. Google Scholar

Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • S. Parneix
  • P.A. Durbin
  • M. Behnia

There are no affiliations available

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