Flow, Turbulence and Combustion

, Volume 68, Issue 2, pp 167–192 | Cite as

Reynolds Stress Budgets in Couette and Boundary Layer Flows

  • Jukka Komminaho
  • Martin Skote
Article

Abstract

Reynolds stress budgets for both Couette and boundary layer flows are evaluated and presented. Data are taken from direct numerical simulations of rotating and non-rotating plane turbulent Couette flow and turbulent boundary layer with and without adverse pressure gradient. Comparison of the total shear stress for the two types of flows suggests that the Couette case may be regarded as the high Reynolds number limit for the boundary layer flow close to the wall. The limit values of turbulence statistics close to the wall for the boundary layer for increasing Reynolds number approach the corresponding Couette flow values. The direction of rotation is chosen so that it has a stabilizing effect, whereas the adverse pressure gradient is destabilizing. The pressure-strain rate tensor in the Couette flow case is presented for a split into slow, rapid and Stokes terms. Most of the influence from rotation is located to the region close to the wall, and both the slow and rapid parts are affected. The anisotropy for the boundary layer decreases for higher Reynolds number, reflecting the larger separation of scales, and becomes close to that for Couette flow. The adverse pressure gradient has a strong weakening effect on the anisotropy. All of the data presented here are available on the web [36].

boundary layer flow Couette flow DNS RST budget 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Abe, H., Kawamura, H. and Matsuo, Y., Direct numerical simulation of a fully developed turbulent channel flow with respect to the Reynolds number dependence. J. Fluids Engrg. 123 (2001) 382-393.CrossRefGoogle Scholar
  2. 2.
    Antonia, R.A., Djenidi, L. and Spalart, P.R., Anisotropy of the dissipation tensor in a turbulent boundary layer. Phys. Fluids 6(7) (1994) 2475-2479.MATHADSCrossRefGoogle Scholar
  3. 3.
    Aronson, D., Johansson, A.V. and Löfdahl, L., Shear-free turbulence near a wall. J. Fluid Mech. 338 (1997) 363-385.MathSciNetADSCrossRefGoogle Scholar
  4. 4.
    Basdevant, C., Technical improvement for direct numerical simulation of homogeneous threedimensional turbulence. J. Comput. Phys. 50(2) (1983) 209-214.MATHMathSciNetADSCrossRefGoogle Scholar
  5. 5.
    Bech, K. and Andersson, H.I., Secondary flow in weakly rotating turbulent plane Couette flow. J. Fluid Mech. 317 (1996) 195-214.MATHADSCrossRefGoogle Scholar
  6. 6.
    Bech, K.H., Simulation of rotating and non-rotating turbulent plane Couette flow. Ph.D. Thesis, Department of Applied Mechanics, Thermodynamics and Fluid dynamics, Norwegian Institute of Technology, Trondheim (1995).Google Scholar
  7. 7.
    Bech, K.H. and Andersson, H.I., Very-large-scale structures in DNS. In: Voke, P.R., Kleiser, L. and Chollet, J.-P. (eds.), Direct and Large-Eddy Simulations I. Kluwer Academic Publishers, Dordrecht (1994) pp. 13-24.Google Scholar
  8. 8.
    Bech, K.H., Tillmark, N., Alfredsson, P.H. and Andersson, H.I., An investigation of turbulent Couette flow at low Reynolds numbers. J. Fluid Mech. 286 (1995) 291-325.ADSCrossRefGoogle Scholar
  9. 9.
    Ching, C.Y., Djenidi, L. and Antonia, R.A., Low-Reynolds-number effects in a turbulent boundary layer. Exp. Fluids 19 (1995) 61-68.CrossRefGoogle Scholar
  10. 10.
    Fernholz, H.H. and Finley, P.J.,: 1996, The incompressible zero-pressure-gradient turbulent boundary layer: An assessment of the data. Progr. Aerospace Sci. 32 (1996) 245-311.ADSCrossRefGoogle Scholar
  11. 11.
    Gibson, M.M. and Launder, B.E., Ground effects on pressure fluctuations in the atmospheric boundary layer. J. Fluid Mech. 86 (1978) 491-511.MATHADSCrossRefGoogle Scholar
  12. 12.
    Greenspan, H.P., The Theory of Rotating Fluids. Cambridge University Press, Cambridge (1968).MATHGoogle Scholar
  13. 13.
    Groth, J., Description of the pressure effects in the Reynolds stress transport eqautions. Phys. Fluids A 3(9) (1991) 2276-2277.ADSCrossRefGoogle Scholar
  14. 14.
    Hallbäck, M., Groth, J. and Johansson, A.V., An algebraic model for nonisotropic turbulent dissipation rate term in Reynolds stress closures. Phys. Fluids A 2(10) (1990) 1859-1866.MATHADSCrossRefGoogle Scholar
  15. 15.
    Hunt, J.C.R. and Graham, J.M.R., Free-stream turbulence near plane boundaries. J. FluidMech. 84 (1978) 209-235.MATHMathSciNetADSGoogle Scholar
  16. 16.
    Kim, J., Moin, P. and Moser, R., Turbulence statistics in fully developed channel flow. J. Fluid Mech. 177 (1987) 133-166.MATHADSCrossRefGoogle Scholar
  17. 17.
    Komminaho, J., Lundbladh, A. and Johansson, A.V., Very large structures in plane turbulent Couette flow. J. Fluid Mech. 320 (1996) 259-285.MATHADSCrossRefGoogle Scholar
  18. 18.
    Komminaho, J., Lundbladh, A. and Johansson, A.V., Determination of the transition Reynolds number in plane Couette flow through study of relaminarization. In: Liu, C. and Liu, Z. (eds.), First AFOSR International Conference on DNS/LES, Ruston, LA. Greyden Press, Columbus (1997) pp. 233-240.Google Scholar
  19. 19.
    Kreiss, H.-O. and Oliger, J., Comparison of accurate methods for the integration of hyperbolic equations. Tellus 24 (1972) 199-215.MathSciNetADSCrossRefGoogle Scholar
  20. 20.
    Le, H. and Moin, P., Direct numerical simulation of turbulent flow over a back-ward facing step. In: Annual Research Briefs. Stanford University Center for Turbulence Research (1992) pp. 161-173.Google Scholar
  21. 21.
    Lumley, J.L. and Newman, G.R., The return to isotropy of homogenous turbulence. J. Fluid Mech. 82 (1977) 161-178.MATHMathSciNetADSCrossRefGoogle Scholar
  22. 22.
    Lundbladh, A. and Johansson, A.V., Direct simulation of turbulent spots in plane Couette flow. J. Fluid Mech. 229 (1991) 499-516.MATHADSCrossRefGoogle Scholar
  23. 23.
    Mansour, N.N., Kim, J. and Moin, P., Reynolds-stress and dissipation-rate budgets in a turbulent channel flow. J. Fluid Mech. 194 (1988) 15-44.ADSCrossRefGoogle Scholar
  24. 24.
    Moin, P. and Kim, J., Numerical investigation of turbulent channel flow. J. Fluid Mech. 118 (1982) 341-377.MATHADSCrossRefGoogle Scholar
  25. 25.
    Moser, R.D., Kim, J. and Mansour, N.N., Direct numerical simulation of turbulent channel flow up to ReT = 590. Phys. Fluids 11(4) (1999) 943-945.ADSCrossRefMATHGoogle Scholar
  26. 26.
    Na, Y. and Moin, P., Direct numerical simulation of studies of turbulent boundary layers with adverse pressure gradient and separation. Technical Report TF-68, Thermosciences Division, Department of Mechanical Engineering, Stanford University (1996).Google Scholar
  27. 27.
    Nagano, Y., Tagawa, M. and Tsuji, T., Effects of adverse pressure Gradients on mean flows and turbulence statistics in a boundary layer. In: Durst, F., Friedrich, R., Launder, B.E., Schmitd, F.W., Schumann, U. and Whitelaw, J.H. (eds.), Turbulent Shear Flows 8. Springer-Verlag, Berlin (1992) pp. 7-21.Google Scholar
  28. 28.
    Orszag, S.A., Numerical methods for the simulation of turbulence. Phys. Fluids Suppl. II 12 (1969) 250-257.MATHCrossRefADSGoogle Scholar
  29. 29.
    Orszag, S.A., Transform method for the calulation of Vector-coupled sums: Application to the spectral form of the vorticity equation. J. Atmos. Sci. 27 (1970) 890-895.ADSCrossRefGoogle Scholar
  30. 30.
    Perot, J.B. and Moin, P., Shear-free turbulent boundary layers. Part 1. Physical insights into near-wall turbulence. J. Fluid Mech. 295 (1995) 199-227.MATHMathSciNetADSCrossRefGoogle Scholar
  31. 31.
    Sahay, A. and Sreenivasan, K., The wall-normal position in pipe and channel flow at which viscous and turbulent shear stresses are equal. Phys. Fluids 11(10) (1999) 3186-3188.ADSCrossRefMATHGoogle Scholar
  32. 32.
    Sjögren, T. and Johansson, A.V., Development and calibration of algebraic nonlinear models for terms in the Reynolds stress transport equations. Phys. Fluids 12(6) (2000) 1554-1572.ADSCrossRefMATHGoogle Scholar
  33. 33.
    Skote, M., Henkes, R.A.W.M. and Henningson, D.S., Direct numerical simulation of selfsimilar turbulent boundary layers in adverse pressure gradients. Flow, Turbulence and Combustion 60 (1998) 47-85.MATHCrossRefGoogle Scholar
  34. 34.
    Skote, M. and Henningson, D., Analysis of the data base from a DNS of a separating turbulent boundary layer. In: Annual Research Briefs. Center for Turbulence Research (1999) pp. 225-237.Google Scholar
  35. 35.
    Skote, M. and Henningson, D.S., DNS of a separated turbulent boundary layer. J. Fluid Mech. (2002) accepted.Google Scholar
  36. 36.
    Skote, M. and Komminaho, J., http://nallo.mech.kth.se/~mskote/html_lib/data.html (2001).Google Scholar
  37. 37.
    Spalart, P.R., Direct simulation of a turbulent boundary layer up to Reθ = 1410. J. Fluid Mech. 187 (1988) 61-98.MATHADSCrossRefGoogle Scholar
  38. 38.
    Spalart, P.R. and Watmuff, J.H., Experimental and numerical study of a turbulent boundary layer with pressure gradients. J. Fluid Mech. 249 (1993) 337-371.ADSCrossRefGoogle Scholar
  39. 39.
    Tillmark, N. and Alfredsson, P.H., Experiments on transition in plane Couette flow. J. Fluid Mech. 235 (1992) 89-102.ADSCrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Jukka Komminaho
    • 1
  • Martin Skote
    • 1
  1. 1.Department of MechanicsKTHStockholmSweden

Personalised recommendations