Advertisement

A model for periodic structures in turbulent boundary layers

  • A. C. M. Beljaars
  • K. Krishna Prasad
Session I - Theory
Part of the Lecture Notes in Physics book series (LNP, volume 136)

Abstract

Many experimental studies emphasize the importance of periodic recognizable flow patterns for the transport process in turbulent flow. In this paper a model is formulated for the large scale part of the turbulent motion. The experimental observation that the structures in the outer region run in phase with the bursting cycle in the wall layer forms the basis of the model. The wall layer, where viscous stresses are important and the outer region where the inviscid approximation holds, are treated separately. The small scale part of the turbulent motion, which is assumed to be important in localized regions only (bursts regions), couples the wall region and the outer region.

The mean wall shear stress calculated with this model agrees reasonably well with the empirical formulae for the friction coefficient even for the more complex case of the transpired boundary layer. The main conclusion of the model calculations is that the transport of momentum can be very well explained in terms of turbulent structures. The model clearly illustrates how momentum is transported in three stages: (i) Thin elongated layers near the wall slow down as the result of viscous forces. (ii) The retarded fluid-is ejected in localized regions or bursts. (iii) The large scale motion in the outer region takes over the transport.

In this paper special attention will be given to the function of the longitudinal vortices in the wall layer. In turns out that they hardly influence the turbulent exchange, but that they are very important for the creation of locally unstable regions. It is believed that the strength of the longitudinal vortices is influenced by the large scale structures in the outer region. By this mechanism the large scales in the outer region can influence the burst frequency.

In a discussion some ideas are presented about what this can mean for special flow phenomena as: drag reduction by polymer solutions or along compliant walls and rapid shear stress change along curved walls.

Keywords

Wall Shear Stress Large Eddy Simulation Turbulent Boundary Layer Outer Region Wall Region 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Acton, E., (1976). The modelling of large eddies in a two-dimensional shear layer, J. Fluid Mech., 76, 561.MATHCrossRefADSGoogle Scholar
  2. Bark, F.H., (1975). On the wave structure of the wall region of a turbulent boundary layer, J. Fluid Mech., 70, 229.CrossRefADSGoogle Scholar
  3. Beljaars, A.C.M., (1979). A model for turbulent exchange in boundary layers, Ph.D. thesis, Eindhoven University of Technology, Eindhoven, Netherlands.Google Scholar
  4. Beljaars, A.C.M., Krishna Prasad, K. and Vries, D.A. de, (1980). A structural model for turbulent exchange in boundary layers, submitted to J. Fluid Mech.Google Scholar
  5. Blackwelder, R.F. and Eckelmann, H., (1979). Streamwise vortices associated with the bursting phenomenon, J. Fluid Mech., 24, 577.CrossRefADSGoogle Scholar
  6. Blackwelder, R.F., and Kaplan, R.E., (1972). The intermittent structure of the wall region of a turbulent boundary layer, Univ. S. Calif. Rep. USCAE, 1-22.Google Scholar
  7. Blackwelder, R.F., and Kaplan, R.E., (1976). On the wall structure of turbulent boundary layers, J. Fluid Mech., 76, 89.CrossRefADSGoogle Scholar
  8. Blackwelder, R.F., and Kovasznay, L.S.G., (1972). Time scales and correlation in a turbulent boundary layer, Phys. Fluids, 15, 1545.CrossRefADSGoogle Scholar
  9. Bradshaw, P., (1973). Effects of streamline curvature on turbulent flow. AGARDograph No. 169.Google Scholar
  10. Bradshaw, P., (1973). The strategy of calculation methods for complex turbulent flows, Imperial College Aero report 73-05.Google Scholar
  11. Brodkey, R.S., Wallace, J.M., and Eckelmann, H., (1974). Some Properties of Truncated Turbulence Signals in Bounded Shear Flows. J. Fluid Mech., 63, 209.CrossRefADSGoogle Scholar
  12. Brown, G.L., and Roshko, A., (1974). On density effects in turbulent mixing layers, J. Fluid Mech., 64, 775.CrossRefADSGoogle Scholar
  13. Brown, G.L., and Thomas, A.S.W., (1977). Large structures in a turbulent boundary layer, Phys. Fluids, 20, S243.CrossRefADSGoogle Scholar
  14. Bushnell, O.M., J.N. Hefner and R.L. Ash, (1977). Compliant wall drag reduction for turbulent boundary layers. Phys. Fluids, 20, S31.CrossRefADSGoogle Scholar
  15. Cebeci, T., and Smith, A.M.O., (1974). Analysis of turbulent boundary layers, Academic Press, New York.MATHGoogle Scholar
  16. Corino, E.R., and Brodkey, R.S., (1969). A visual investigation in the wall region of turbulent flow, J. Fluid, Mech., 37, 1.CrossRefADSGoogle Scholar
  17. Deardorff, J.W., (1970). A numerical study of three-dimensional turbulent channel flow at large Reynolds number, J. Fluid Mech., 41, 453.MATHCrossRefADSGoogle Scholar
  18. Eckelmann, H., (1974). The structure of the viscous sublayer and the adjacent wall region in a turbulent channel flow, J. Fluid Mech., 65, 439CrossRefADSGoogle Scholar
  19. Einstein, H.A., and Li, H., (1956). The viscous sublayer along a smooth boundary, J. Engng. Mech. Div. Am. Soc. Civ. Engrs., 82 (EM2), 945.Google Scholar
  20. Falco, R.E., (1977). Coherent motion in the outer region of turbulent boundary layers, Phys. Fluids, 20, S124.CrossRefADSGoogle Scholar
  21. Fendell, F.E., (1972). Singular perturbation and turbulent shear flow near walls, J. Astronautical Sc., 20, 129.ADSGoogle Scholar
  22. Fortuna, G. and Hanratty, T.J., (1972). The influence of drag-reducing polymers on turbulence in the viscous sublayer, J. Fluid Mech., 53, 575.CrossRefADSGoogle Scholar
  23. Hanratty, T.J., (1956). Turbulent exchange of mass and momentum with a boundary, A.I.Ch.E.Je, 2, 359.Google Scholar
  24. Hinze, J.O., (1975). Turbulence, McGrawhill, New York, 2nd ed.Google Scholar
  25. Johnston, J.P., (1972). The Suppression of shear-layer turbulence in rotating systems. ARARD Conf. Proc. 93.Google Scholar
  26. Kim, H.T., Kline, S.J., and Reynolds, W.C., (1971). The production of turbulence near a smooth wall in a turbulent boundary layer, J. Fluid Mech., 50, 133.CrossRefADSGoogle Scholar
  27. Kim, J. & Moin, P., (1979). Large eddy simulation of turbulent channel flow — Illiac IV Calculation, AGARD Symposium on Turbulent Boundary Layer-Experiment, Theory, and Modelling.Google Scholar
  28. Kline, S.J., (1968). Discussion, Proc. of AFOSR-IFP-Stanford Conf. on computation of Turbulent Boundary Layers. Ed: S.J. Kline et al., Vol. 1 p. 527.Google Scholar
  29. Kline, S.J., Reynolds, W.C., Schraub, F.A. and Rundstadler, P.W., (1967). The structure of turbulent boundary layers. J. Fluid Mech., 30, 741.CrossRefADSGoogle Scholar
  30. Kovasznay, L.S.G., Kibens, V., and Blackwelder, R.F., (1970). Large scale motion in the intermittent region of a turbulent boundary layer, J. Fluid Mech., 41, 283.CrossRefADSGoogle Scholar
  31. Landahl, M.T., (1965). A wave-guide model for turbulent shear flow, NASA, CR-317.Google Scholar
  32. Landahl, M.T., (1967). A wave-guide model for turbulent shear flow, J. Fluid Mech., 29, 441.MATHCrossRefADSGoogle Scholar
  33. Landahl, M.T., (1975). Wave breakdown and turbulence, SIAM, J. Appl. Mech., 28, 735.CrossRefMATHGoogle Scholar
  34. Laufer, J., and Badri Narayanan, M.A., (1971). The mean period of the production mechanism in a boundary layer, Phys. Fluids, 14, 182.CrossRefADSGoogle Scholar
  35. Mager, A., (1964). Three-dimensional laminar boundary layers in “Theory of Laminar flows”, Ed. F.K. Moore, Princeton University Press.Google Scholar
  36. Mellor, G.L., (1972). The large Reynolds number asymptotic theory of turbulent boundary layers. Int. J. Engng. Sci., 10, 851.CrossRefMathSciNetGoogle Scholar
  37. Mizushina, T., and Usui, H., (1977). Reduction of eddy diffusion for momentum and heat in viscoleastic fluid flow in a circular tube. Phys. Fluids, 20, S100.CrossRefADSGoogle Scholar
  38. Nychas, S.G., Hershey, H.C., and Brodkey, R.S., (1973). A visual study of turbulent flow, J. Fluid Mech., 61, 513.CrossRefADSGoogle Scholar
  39. Offen, G.R., and Kline, S.J., (1974). Combined dye-streak and hydrogen bubble visual observations of a turbulent boundary layer, J. Fluid Mech., 62, 223.CrossRefADSGoogle Scholar
  40. Offen, G.R., and Kline, S.J., (1975). A proposed model of the bursting process in turbulent boundary layers, J. Fluid Mech., 70, 209.CrossRefADSGoogle Scholar
  41. Orszag, S.A., (1978). Prediction of compliant wall drag reduction-Part II, Cambridge Hydrodynamics Report 11.Google Scholar
  42. Praturi, A.K., and Brodkey, R.S., (1978). A stereoscopic visual study of coherent structures in turbulent shear flow, J. Fluid Mech., 89, 251.CrossRefADSGoogle Scholar
  43. Rajagopalan, S., and Antonia, R.A., (1979). Some properties of the large structures in a fully developed turbulent duct flow, Phys. Fluids, 22, 614.CrossRefADSGoogle Scholar
  44. Ramapriyan, B.R. and B.G. Shivaprasad, (1977). Mean flow measurements in turbulent boundary layers along mildly curved surfaces. AIAA Journal, 15, 189.ADSCrossRefGoogle Scholar
  45. Ramapriyan, B.R., and B.G. Shivaprasad, (1978). The structure of turbulent boundary layers along mildly curved surfaces, J. Fluid Mech., 76, 561.Google Scholar
  46. Schumann, U. (1975). Subgrid scale model for finite difference simulations of turbulent flows in plane channels and annuli, J. Comp. Phys., 18, 376.MATHCrossRefADSMathSciNetGoogle Scholar
  47. Senda, M., Susuki, K. and Sats, T., (1979). Turbulence structure related to the heat transfer in a turbulent boundary layer with injection, 2nd symposium on Turbulent Shear Flows, London, 1979.Google Scholar
  48. Shen, S.F., (1964). Stability of laminar flows, in: Theory of laminar flows, edited by F.K. Moore, Princeton Univ. Press, New Jersey.Google Scholar
  49. Shubert, G., and Corcos, G.M., (1967). The dynamics of turbulence near a wall according to a linear model, J. Fluid Mech., 29, 113.CrossRefADSGoogle Scholar
  50. Sternberg, J., (1962). A theory for the viscous sublayer of a turbulent flow, J. Fluid Mech., 13, 241.MATHCrossRefADSGoogle Scholar
  51. Sternberg, J., (1968). Discussion, Proc. of AFOSR-IFP-Stanford Conf. on computations of turbulent boundary layers. Ed: S.J. Kline et al., Vol. 1, p. 411.Google Scholar
  52. Stuart, J.T., (1965). The production of intense shear layers by vortex stretching and convection, AGARD Rep. 514.Google Scholar
  53. Tennekes, H., and Lumley, J.L., (1974). A first course in turbulence, MIT Press, Cambridge.Google Scholar
  54. Virk, P.S., (1975). Drag reduction fundamentals, AICHE J., 21, 625.CrossRefGoogle Scholar
  55. Willmarth, W.W., (1975). Structure of turbulence in boundary layers, Adv. App. Mech., vol. 15, p. 159., Academic Press.CrossRefGoogle Scholar
  56. Willmarth, W.W., and Woodridge, G.E., (1962). Measurements of the fluctuating pressure at the wall beneath a thick turbulent boundary layer, J. Fluid Mech., 14, 187.MATHCrossRefADSGoogle Scholar
  57. Witting, H., (1958). Ober den Einfluss der Strömlinien-Krümmung auf die stabilität Laminarer Strömingen, Arch. Rat. Mech. Anal., 2, No. 3, 243.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • A. C. M. Beljaars
    • 1
  • K. Krishna Prasad
    • 2
  1. 1.Royal Netherlands Meteorological InstituteDe BiltThe Netherlands
  2. 2.Eindhoven University of TechnologyEindhovenThe Netherlands

Personalised recommendations