Hostname: page-component-8448b6f56d-sxzjt Total loading time: 0 Render date: 2024-04-24T22:04:20.762Z Has data issue: false hasContentIssue false
  • English
  • Français

The three-dimensional turbulent boundary layer near a plane of symmetry

Published online by Cambridge University Press:  26 April 2006

A. T. Degani ,
F. T. Smith  and
J. D. A. Walker
A. T. Degani
Affiliation:
Department of Mechanical Engineering and Mechanics, Lehigh University. Bethlehem, PA 18015, USA
F. T. Smith
Affiliation:
Department of Mathematics, University College, London WC1E 6BT, UK
J. D. A. Walker
Affiliation:
Department of Mechanical Engineering and Mechanics, Lehigh University. Bethlehem, PA 18015, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The asymptotic structure of the three-dimensional turbulent boundary layer near a plane of symmetry is considered in the limit of large Reynolds number. A selfconsistent two-layer structure is shown to exist wherein the streamwise velocity is brought to rest through an outer defect layer and an inner wall layer in a manner similar to that in two-dimensional boundary layers. The cross-stream velocity distribution is more complex and two terms in the asymptotic expansion are required to yield a complete profile which is shown to exhibit a logarithmic region. The flow in the inner wall layer is demonstrated to be collateral to leading order; pressure gradient effects are formally of higher order but can cause the velocity profile to skew substantially near the wall at the large but finite Reynolds numbers encountered in practice. The governing set of ordinary differential equations describing a self-similar flow is derived. The calculated numerical solutions of these equations are matched asymptotically to an inner wall-layer solution and the results show trends that are consistent with experimental observations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 234 , January 1992 , pp. 329 - 360
Copyright
© 1992 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

Anderson, S. D. & Eaton, J. K. 1987 An experimental investigation of pressure driven threedimensional turbulent boundary layers. Rep. MD-49. Stanford University.
Baldwin, B. S. & Lomax, H. 1978 Thin layer approximation and algebraic model for separated turbulent flows. AIAA 16th Aerosciences Meeting, Huntsville, Alabama, Jan. 16–18.
Barnwell, R. W. 1991 Nonadiabatic and three-dimensional effects in compressible turbulent boundary layers. 29th Aerospace Sciences Meeting, Reno, Nevada, AIAA-91-0528.
Bogucz, E. A. & Walker, J. D. A. 1988 The turbulent near wake at a sharp trailing edge. J. Fluid Mech. 196, 555–584.Google Scholar
Bradshaw, P. & Pontikos, N. S. 1985 Measurements in the turbulent boundary layer on an infinite swept wing. J. Fluid Mech. 159, 105–130.Google Scholar
Cantwell, B. J. 1981 Organized motion in turbulent flow. Ann. Rev. Fluid Mech. 13, 457–515.Google Scholar
Cebeci, T. 1975 Calculation of three-dimensional boundary layers II. Three-dimensional flow in Cartesian coordinates. AIAA J. 13, 1056–1064.Google Scholar
Cebeci, T. & Smith, A. M. O. 1974 Analysis of Turbulent Boundary Layers. Academic.
Chandrasekhar, N. & Swamy, N. V. C. 1976 Wall shear stress inference for three-dimensional turbulent boundary layer profiles. Trans. ASME E: J. Appl. Mech. 43, 20–27.Google Scholar
Clauser, F. H. 1954 Turbulent boundary layers in adverse pressure gradients. J. Aeronaut. Sci. 21, 91–108.Google Scholar
Clauser, F. H. 1956 The turbulent boundary layers. In Advances in Applied Mechanics, Vol. 4 (ed. Dryden, H. L. & von Kármán, T.), pp. 51–51. Academic.
Degani, A. T. 1991 The three-dimensional turbulent boundary layer — theory and application. Ph.D. thesis, Lehigh University.
Fendell, F. E. 1972 Singular perturbation and turbulent shear flow near walls. J. Astronaut. Sci. 20, 129–165.Google Scholar
Fernholz, H. H. & Vagt, J.-D. 1981 Turbulence measurements in an adverse-pressure-gradient three-dimensional turbulent boundary layer along a circular cylinder. J. Fluid Mech. 111, 233–269.Google Scholar
Francis, G. P. & Pierce, F. J. 1967 An experimental study of skewed turbulent boundary layers in low speed flows. Trans. ASME D: J. Basic Engng 89, 597–607.Google Scholar
Goldberg, U. & Reshotko, E. 1984 Scaling and modeling of three-dimensional pressure-driven turbulent boundary layers. AIAA J. 22, 914–920.Google Scholar
Hebbar, K. S. & Melnik, W. L. 1978 Wall region of a relaxing three-dimensional incompressible turbulent boundary layer. J. Fluid Mech. 85, 33–56.Google Scholar
Hinze, J. O. 1975 Turbulence. Mcgraw-Hill.
Hornung, H. G. & Joubert, P. N. 1963 The mean velocity profile in three-dimensional turbulent boundary layers. J. Fluid Mech. 15, 368–384.Google Scholar
Johnston, J. P. 1960 On three-dimensional turbulent boundary layers generated by secondary flow. Trans. ASME D: J. Basic Engng 82, 233–246.Google Scholar
Johnston, J. P. 1976 Experimental studies in three-dimensional turbulent boundary layers. Viscous Flow Symp., Lockheed-Georgia Co., June 22–23.
Klinksiek, W. F. & Pierce, F. J. 1970 Simultaneous lateral skewing in a three-dimensional turbulent boundary layer flow. Trans. ASME D: J. Basic Engng 92, 83–90.Google Scholar
Mellor, G. L. 1972 The large Reynolds number, asymptotic theory of turbulent boundary layers. Intl J. Engng Sci. 10, 851–873.Google Scholar
Mellor, G. L. & Gibson, D. M. 1966 Equilibrium turbulent boundary layers. J. Fluid Mech. 24, 225–253.Google Scholar
Melnik, R. E. 1981 Turbulent interactions on airfoils at transonic speeds — recent developments. In Computation of Viscous-Inviscid Interactions, AGARD-CP-291, Chap. 10.
Muller, U. R. 1982a Measurement of the Reynolds stresses and the mean-flow field in a three-dimensional pressure-driven boundary layer. J. Fluid Mech. 119, 121–153.Google Scholar
Muller, U. R. 1982b Comparison of three-dimensional turbulent boundary-layer calculations with experiment. IUTAM Symp. on Three-Dimensional Boundary Layers, Trondheim, Norway.
Nash, J. F. & Patel, V. C. 1972 Three-Dimensional Turbulent Boundary Layers. SBC Technical Book, Atlanta.
Neish, A. & Smith, F. T. 1988 The turbulent boundary layer and wake of an aligned flat plate. J. Engng Maths 22, 15–42.Google Scholar
Pierce, F. J., McAllister, J. E. & Tennant, M. H. 1983 A review of near-wall similarity models in three-dimensional turbulent boundary layers. Trans. ASME I: J. Fluids Engng 105, 251–262.Google Scholar
Pierce, F. J. & Zimmerman, B. B. 1973 Wall shear stress inference from two- and three-dimensional turbulent boundary layer velocity profiles. Trans. ASME I: J. Fluids Engng 95, 61–67.Google Scholar
Prahlad, T. S. 1973 Mean velocity profiles in three-dimensional incompressible turbulent boundary layers. AIAA J. 11, 359–365.Google Scholar
Smith, C. R., Walker, J. D. A., Haidari, A. H. & Sobrun, U. 1991 On the dynamics of near-wall turbulence. Phil. Trans. R. Soc. Lond. A 336, 131–175.Google Scholar
Smith, C. R., Walker, J. D. A., Haidari, A. H. & Taylor, B. K. 1990 Hairpin vortices in turbulent boundary layers: the implications for reducing drag. In Structure of Turbulence and Drag Reduction (ed. A. Gyr), pp. 58–58. Springer.
Van Den Berg, B. 1975 A three-dimensional law of the wall for turbulent shear flows. J. Fluid Mech. 70, 149–160.Google Scholar
Van Den Berg, B., Elsenaar, A., Lindhout, J. P. F. & Wesseling, P. 1975 Measurements in an incompressible three-dimensional turbulent boundary layer, under infinite swept-wing conditions, and comparison with theory. J. Fluid Mech. 70, 127–147.Google Scholar
Van Dyke, M. 1964 Perturbation Methods in Fluid Mechanics. Academic.
Walker, J. D. A. 1990a Wall layer eruptions in turbulent flows. In Structure of Turbulence and Drag Reduction (ed. A. Gyr). pp. 118–118. Springer.
Walker, J. D. A. 1990b Models based on dynamical features of the wall layer. Appl. Mech. Rev. 43, S232–S239.Google Scholar
Walker, J. D. A., Abbott, D. E., Scharnhorst, R. K. & Weigand, G. G. 1989 A wall-layer model for the velocity profile in turbulent flows. AIAA J. 27, 140–149.Google Scholar
Wie, Y.-S. & DeJarnette, F. R. 1988 Numerical investigation of three-dimensional flow separation using the boundary layer equations. AIAA Paper 88–0617.Google Scholar
Willmarth, W. W. 1975 Structure of turbulence in boundary layers. Adv. Appl. Mech. 1, 159–254.Google Scholar
Yajnik, K. S. 1970 Asymptotic theory of turbulent shear flows. J. Fluid Mech. 42, 411–427.Google Scholar
Yuhas, L. J. & Walker, J. D. A. 1982 An optimization technique for the development of two-dimensional steady turbulent boundary-layer models. Rep. FM-1, Dept. Mech. Engng and Mechs, Lehigh University; also AFOSR-TR-0417.