Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-19T04:00:32.724Z Has data issue: false hasContentIssue false
  • English
  • Français

A structural model for turbulent exchange in boundary layers

Published online by Cambridge University Press:  20 April 2006

A. C. M. Beljaars ,
K. Krishna Prasad  and
D. A. De Vries
A. C. M. Beljaars
Affiliation:
Laboratory for Fluid Dynamics and Heat Transfer, University of Technology, Eindhoven, Netherlands Present Address: Royal Netherlands Meteorological Institute, De Bilt, Netherlands.
K. Krishna Prasad
Affiliation:
Laboratory for Fluid Dynamics and Heat Transfer, University of Technology, Eindhoven, Netherlands
D. A. De Vries
Affiliation:
Laboratory for Fluid Dynamics and Heat Transfer, University of Technology, Eindhoven, Netherlands
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper a model is presented that incorporates characteristic features of the turbulent structures as revealed by recent experimental observations. The principal characteristic features are the occurrence of periodicity and intermittency, not only at the edge of the boundary layer, but also close to the wall.

By an averaging procedure, equations are derived for the large-scale part of the turbulent motion. The unknown terms, representing the small-scale turbulent stress, are assumed to be zero except in the so-called burst regions which occupy only a small fraction of the total flow field and arise from local instability of the large-scale flow field. In the model distinction is made between a thin layer near the wall where viscous forces play an important role and the remaining part of the boundary layer where inviscid equations are valid. The momentum transport takes place in three different stages with different mechanisms. First of all the fluid in the wall region is retarded by viscous forces and collected in long narrow regions (streaks). After this a rapid exchange takes place in the burst regions where the low-momentum fluid is ejected into the outer region. Finally the large-scale structures in the outer region take over the transport.

It turns out that the transport properties of a turbulent boundary layer can be calculated reasonably well with this deterministic model. It can be concluded that the coherent part of the turbulent motion is very important in the transport process.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 112 , November 1981 , pp. 33 - 70
Copyright
© 1981 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Acton, E. 1976 The modelling of large eddies in a two-dimensional shear layer. J. Fluid Mech. 76, 561.Google Scholar
Beljaars, A. C. M. 1978 A quantitative model for momentum exchange by coherent motions in a turbulent wall boundary layer. Lett. Heat & Mass Transfer 5, 231.Google Scholar
Beljaars, A. C. M. 1979 A model for turbulent exchange in boundary layers. Ph.D. thesis, Eindhoven University of Technology, Netherlands.
Bakewell, H. P. & Lumley, J. L. 1967 Viscous sublayer and adjacent wall region in turbulent pipe flow. Phys. Fluids 10, 1880.Google Scholar
Bark, F. H. 1975 On the wave structure of the wall region of a turbulent boundary layer. J. Fluid Mech. 70, 229.Google Scholar
Black, T. J. 1968 An analytical study of the measured wall pressure field under supersonic turbulent boundary layers. N.A.S.A. CR-888.
Blackwelder, R. F. & Eckelmann, H. 1979 Streamwise vortices associated with the bursting phenomenon. J. Fluid Mech. 94, 577.Google Scholar
Blackwelder, R. F. & 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
Blackwelder, R. F. & Kovasznay, L. S. G. 1972 Time scales and correlation in a turbulent boundary layer. Phys. Fluids 15, 1545.Google Scholar
Brown, G. L. & Roshko, A. 1974 On density effects in turbulent mixing layers. J. Fluid Mech. 64, 775.Google Scholar
Brown, G. L. & Thomas, A. S. W. 1977 Large structure in a turbulent boundary layer. Phys. Fluids Suppl. 20, 243.
Cebeci, T. & Smith, A. M. O. 1974 Analysis of Turbulent Boundary Layers. Academic.
Chorin, A. J. & Bernard, P. S. 1972 Discretization of a vortex sheet, with an example of roll-up. Univ. Calif. Rep. FM-72–5.Google Scholar
Clements, R. R. 1977 Flow representation, including separated regions, using discrete vortices. VKI Lecture Series, Computational fluid mechanics, Rhode-Saint-Genèse, Belgium.
Corino, E. R. & Brodkey, R. S. 1969 A visual investigation in the wall region of turbulent flow. J. Fluid Mech. 37, 1.Google Scholar
Dinckelakker, A., Hessel, M., Meier, G. E. A. & Schewe, G. 1977 Investigation of pressure fluctuations beneath a turbulent boundary layer by means of an optical method. Phys. Fluids 20, S216.Google Scholar
Eckelmann, H. 1974 The structure of the viscous sublayer and the adjacent wall region in a turbulent channel flow. J. Fluid Mech. 65, 439.Google Scholar
Einstein, H. A. & Li, H. 1956 The viscous sublayer along a smooth boundary. Proc. A.S.C.E. J. Engng Mech. Div. 82 (EM2), 945.Google Scholar
Falco, R. E. 1977 Coherent motion in the outer region of turbulent boundary layers. Phys. Fluids Suppl. 20, 124.Google Scholar
Favre, A., Gaviglio, J. & Dumas, R. 1967 Structure of velocity space—time correlations in a boundary layer. Phys. Fluids Suppl. 10, 138.Google Scholar
Fendell, F. E. 1972 Singular perturbation and turbulent shear flow near walls. J. Astronautical Soc. 20, 129.Google Scholar
Gupta, A. K., Laufer, J. & Kaplan, R. E. 1971 Spatial structure in the viscous sublayer. J. Fluid Mech. 50, 493.Google Scholar
Hanratty, T. J. 1956 Turbulent exchange of mass and momentum with a boundary. A.I.Ch.E. J. 2, 359.Google Scholar
Head, M. R. & Bandyopadhyay, P. 1979 Flow visualization of turbulent boundary layer structure. AGARD Symp. on Turb., The Hague.
Hinze, J. O. 1975 Turbulence, 2nd edn. McGraw-Hill.
Kim, H. T., Kline, S. J. & Reynolds, W. C. 1971 The production of turbulence near a smooth wall in a turbulent boundary layer. J. Fluid Mech. 50, 133.Google Scholar
Kline, S. J., Reynolds, W. C., Schraub, F. A. & Rundstadler, P. W. 1967 The structure of turbulent boundary layers. J. Fluid Mech. 30, 741.Google Scholar
Kovasznay, L. S. G., Kibens, V. & Blackwelder, R. F. 1970 Large-scale motion in the intermittent region of a turbulent boundary layer. J. Fluid Mech. 41, 283.Google Scholar
Lamb, H. 1932 Hydrodynamics, 6th edn. Cambridge University Press.
Landahl, M. T. 1965 A wave-guide model for turbulent shear flow. N.A.S.A. CR-317.
Landahl, M. T. 1967 A wave-guide model for turbulent shear flow. J. Fluid Mech. 29, 441.Google Scholar
Landahl, M. T. 1975 Wave breakdown and turbulence. SIAM J. Appl. Mech. 28, 735.Google Scholar
Laufer, J. 1972 Recent developments in turbulent boundary layer research. Inst. Naz. Alta. Mat., Symp. Math. 9, 299.Google Scholar
Laufer, J. & Badri Narayanan, M. A. 1971 The mean period of the production mechanism in a boundary layer. Phys. Fluids 14, 182.Google Scholar
Mager, A. 1964 Three-dimensional laminar boundary layers. In Theory of Laminar Flows (ed. F. K. Moore). Princeton University Press.
Mellor, G. L. 1972 The large Reynolds number asymptotic theory of turbulent boundary layers. Int. J. Engng Sci. 10, 851.Google Scholar
Nychas, S. G., Hershey, H. C. & Brodkey, R. S. 1973 A visual study of turbulent shear flow. J. Fluid Mech. 61, 513.Google Scholar
Offen, G. R. & Kline, S. J. 1974 Combined dye-streak and hydrogen bubble visual observations of a turbulent boundary layers. J. Fluid Mech. 62, 223.Google Scholar
Offen, G. R. & Kline, S. J. 1975 A proposed model of the bursting process in turbulent boundary layers. J. Fluid Mech. 70, 209.Google Scholar
Ooms, G., Groen, G., de Graag, D. P. & Ballintijn, J. F. 1978 On turbulent pipe flow with heat transfer and chemical reaction. 6th Int. Heat Transfer Conf., Toronto, paper FC(b)-35.
Praturi, A. K. & Brodkey, R. S. 1978 A stereoscopic visual study of coherent structures in turbulent shear flow. J. Fluid Mech. 89, 251.Google Scholar
Rao, K. N., Narasimha, R. & Badri Narayanan, M. A. 1971 The bursting phenomenon in a turbulent boundary layer. J. Fluid Mech. 48, 339.Google Scholar
Schubert, G. & Corcos, G. M. 1967 The dynamics of turbulence near a wall according to a linear model. J. Fluid Mech. 29, 113.Google Scholar
Shen, S. F. 1964 Stability of laminar flows. In Theory of Laminar Flows (ed. F. K. Moore). Princeton University Press.
Sternberg, J. 1962 A theory for the viscous sublayer of a turbulent flow. J. Fluid Mech. 13, 241.Google Scholar
Stuart, J. T. 1965 The production of intense shear layers by vortex stretching and convection. AGARD Rep. 514.Google Scholar
Tennekes, H. 1968 Outline of a second-order theory for turbulent pipe flow. A.I.A.A. J. 6, 1735.Google Scholar
Thomas, L. C., Chung, B. T. F. & Mahaldar, S. K. 1971 Temperature profiles for turbulent flow of high Prandtl number fluids. Int. J. Heat Mass Transfer 14, 1465.Google Scholar
Townsend, A. A. 1961 Equilibrium layers and wall turbulence. J. Fluid Mech. 11, 97.Google Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow, 2nd edn. Cambridge University Press.
Ueda, H. & Hinze, J. O. 1975 Fine structure turbulence in the wall region of a turbulent boundary layer. J. Fluid Mech. 67, 125.Google Scholar
Van Dongen, F. G., Beljaars, A. C. M. & De Vries, D. A. 1978 A periodic and intermittent model for the wall region of a turbulent boundary layer. Int. J. Heat Mass Transfer 21, 1099.Google Scholar
Van Dyke, M. 1975 Perturbation Methods in Fluid Mechanics. Stanford, California: Parabolic.
Willmarth, W. W. 1975a Structure of turbulence in boundary layers. Adv. Appl. Mech. 15, 159.Google Scholar
Willmarth, W. W. 1975b Pressure fluctuations beneath turbulent boundary layers. Ann. Rev. Fluid Mech. 7, 13.Google Scholar
Willmarth, W. W. & Wooldridge, C. E. 1962 Measurements of the fluctuating pressure at the wall beneath a thick turbulent boundary layer. J. Fluid Mech. 14, 187.Google Scholar
Wills, J. A. B. 1971 Measurements of the wave-number/phase velocity spectrum of wall pressure beneath a turbulent boundary layer. J. Fluid Mech. 45, 65.Google Scholar
Witting, H. 1958 Über den Einfluss der Strömlinienkrümmung auf die Stabilität laminarer Strömungen. Arch. Rat. Mech. Anal. 2, 243.Google Scholar