Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-25T11:16:17.207Z Has data issue: false hasContentIssue false
  • English
  • Français

Vortex-induced boundary-layer separation. Part 2. Unsteady interacting boundary-layer theory

Published online by Cambridge University Press:  26 April 2006

Vallorie J. Peridier ,
F. T. Smith  and
J. D. A. Walker
Vallorie J. Peridier
Affiliation:
Department of Mechanical Engineering, Temple University, Philadelphia, PA 19122, USA
F. T. Smith
Affiliation:
Department of Mathematics, University College London, Gower Street, 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 unsteady boundary layer induced by the motion of a rectilinear vortex above an infinite plane wall is calculated using interacting boundary-layer methods. The boundary-layer solution is computed in Lagrangian variables since it is possible to compute the flow evolution accurately in this formulation even when an eruption starts to evolve. Results are obtained over a range of Reynolds numbers, Re. For the limit problem Re → ∞ (studied in Part 1), a singularity develops in the non-interacting boundary-layer solution at finite time. The present results show that the interacting boundary-layer calculations also terminate in a singularity at a time which is earlier than in the limit problem and which decreases with decreasing Reynolds number. The computed results are compared with the length– and timescales predicted by recent asymptotic theories and are found to be in excellent agreement.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 232 , November 1991 , pp. 133 - 165
Copyright
© 1991 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

Abramowitz, M. & Stegun, I. A. 1964 Handbook of Mathematical Functions. US Government Printing Office, Washington, DC.
Acarlar, M. S. & Smith, C. R. 1987a A study of hairpin vortices in a laminar boundary layer. Part 1. Hairpin vortices generated by a hemisphere protuberance. J. Fluid Mech. 175, 1–41.Google Scholar
Acarlar, M. S. & Smith, C. R. 1987b A study of hairpin vortices in a laminar boundary layer. Part 2. Hairpin vortices generated by fluid injection. J. Fluid Mech. 175, 43–83.Google Scholar
Brotherton-Ratcliffe, R. V. & Smith, F. T. 1987 Complete breakdown of an unsteady interacting boundary layer (over a surface distortion or in a liquid layer). Mathematika 34, 86–100.Google Scholar
Brown, S. N., Cheng, H. K. & Smith, F. T. 1988 Nonlinear instability and break-up of separated flow. J. Fluid Mech. 193, 191–216.Google Scholar
Cebeci, T., Khattab, A. A. & schimke, S. M. 1988 Separation and reattachment near the leading edge of a thin oscillating airfoil. J. Fluid Mech. 188, 253–274.Google Scholar
Chu, C. C. & Falco, R. E. 1988 Vortex ring/viscous wall layer interaction model of the turbulence production process near walls. Exp. Fluids 6, 305.Google Scholar
Chuang, F. S. & Conlisk, A. T. 1989 Effect of interaction on the boundary layer induced by a convected rectilinear vortex. J. Fluid Mech. 200, 337–365.Google Scholar
Conlisk, A. T. 1989 The pressure field in intense vortex-boundary layer interaction. 27th Aerospace Sciences Meeting, Reno, NV, AIAA Paper 89–0293.
Cowley, S. J., Van Dommelen, L. L. & Lam, S. T. 1990 On the use of Lagrangian variables in the description of unsteady boundary-layer separation. Phil. Trans. R. Soc. Lond. A 333, 343–378.Google Scholar
Doligalski, T. L. & Walker, J. D. A. 1984 The boundary layer induced by a convected two-dimensional vortex. J. Fluid Mech. 139, 1–28.Google Scholar
Ece, M. C., Walkeb, J. D. A. & Doligalski, T. L. 1984 The boundary layer on an impulsively started rotating and translating cylinder. Phys. Fluids 23, 1077–1089.Google Scholar
Elliott, J. W., Cowley, S. J. & Smith, F. T. 1983 Breakdown of boundary layers: (i) on moving surfaces; (ii) in self-similar unsteady flow; (iii) in fully unsteady flow. Geophys. Astrophys. Fluid Dyn. 25, 77–138.Google Scholar
Ersoy, S. & Walker, J. D. A. 1985 Viscous flow induced by counterrotating vortices. Phys. Fluids 28, 2687–2698.Google Scholar
Ersoy, S. & Walker, J. D. A. 1986 Flow induced at a wall by a vortex pair. AIAA J. 24, 1597–1605.Google Scholar
Goldstein, S. 1948 On laminar boundary-layer flow near a point of separation. Q. J. Mech. Appl. Maths 1, 43–69.Google Scholar
Harvey, J. K. & Perry, F. J. 1971 Flowfield produced by trailing vortices in the vicinity of the ground. AIAA J. 9, 1659–1660.Google Scholar
Head, M. R. & Bandyopadhyay, P. 1981 New aspects of turbulent boundary layer structure. J. Fluid Mech. 107, 297–338.Google Scholar
Henkes, R. A. W. M. & Veldman, A. E. P. 1987 On the breakdown of the steady and unsteady interacting boundary-layer description. J. Fluid Mech. 179, 513–529.Google Scholar
Hoylb, J. M. 1991 Ph.D. thesis, University of London, in preparation.
Hoyle, J. M., Smith, F. T. & Walker, J. D. A. 1991 On sublayer eruption and vortex formation. Comput. Phys. Commun. 65, 151–157.Google Scholar
Lou, T.-W. 1990 Interactive boundary-layer solutions for vortex-induced separation. M.Sc. thesis, Lehigh University.
Napolitano, M., Werle, M. J. & Davis, R. T. 1978 Numerical solution of the triple-deck equations for supersonic and subsonic flow past a hump. David Taylor Naval Shipyard Research and Development Center Rep. AFL78–6–42.
Peridier, V., Smith, F. T. & Walker, J. D. A. 1991 Vortex-induced boundary-layer separation. Part 1. The limit problem Re. J. Fluid Mech. 232, 99–131.Google Scholar
Peridier, V. J. & Walker, J. D. A. 1988 An algorithm for unsteady flows with strong convection. NASA Tech. Mem. 100828; ICOMP-88–5. NASA Lewis Research Center.
Peridier, V. J. & Walker, J. D. A. 1989 Vortex induced boundary layer separation. AFOSR Rep. FM-13. Department of Mechanical Engineering and Mechanics, Lehigh University; AFOSR-TR-90–0458 (also available AD-221564).
Perry, A. E. & Chong, M. S. 1982 On the mechanisms of wall turbulence. J. Fluid Mech. 119, 173–217.Google Scholar
Riley, N. & Vasantha, R. 1989 Unsteady high Reynolds number flows. J. Fluid Mech. 205, 243–262.Google Scholar
Sears, W. R. & Telionis, D. P. 1971 Unsteady boundary-layer separation. In Recent Research on Unsteady Boundary Layers, pp. 404–447. Laval University Press, Quebec.
Sears, W. R. & Telionis, D. P. 1975 Boundary-layer separation in unsteady flow. SIAM J. Appl. Maths 28, 215–235.Google Scholar
Smith, F. T. 1982 On the high Reynolds number theory of laminar flows. IMA J. Appl. Maths 28, 207–281.Google Scholar
Smith, F. T. 1988a Finite-time breakup can occur in any unsteady interacting boundary layer. Mathematica 35, 256–273.Google Scholar
Smith, F. T. 1988B A reversed-flow singularity in interacting boundary layers. Proc. R. Soc. Lond. A 420, 21–52.Google Scholar
Smith, F. T. & Khorrami, A. F. 1991 The interactive breakdown in supersonic ramp flow. J. Fluid Mech. 224, 197–215.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 (in press).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 surface drag. In Structure of Turbulence and Drag Reduction (ed. A. Gyr), pp. 51–58. Springer.
Stewartson, K. 1974 Multistructured boundary layers on flat plates and related bodies. Adv. Appl. Mech. 14, 145–239.Google Scholar
Van Dommelen, L. L. 1981 Unsteady boundary-layer separation. Ph.D. dissertation, Cornell University.
Van Dommelen, L. L. & Shen, S. F. 1980 The spontaneous generation of the singularity in a separating boundary layer. J. Comput. Phys. 38, 125–140.Google Scholar
Van Dommelen, L. L. & Shen, S. F. 1982 The genesis of separation. In Proc. Symp. on Numerical and Physical Aspects of Aerodynamic Flow, Long Beach, California (ed. T. Cebeci), pp. 283–311. Springer.
Walker, J. D. A. 1978 The boundary layer due to a rectilinear vortex. Proc. R. Soc. Lond. A 359, 167–188.Google Scholar
Walker, J. D. A. 1990a Wall-layer eruptions in turbulent flows. In Structure of Turbulence and Drag Reduction (ed. A. Gyr), pp. 109–110. Springer.
Walker, J. D. A. 1990b Models based on dynamical features of the wall layer. Appl. Mech. Rev. 43, S232–S232.Google Scholar
Walker, J. D. A., Abbott, D. E., Scharnhorst, R. K. & Weigand, G. G. 1989 Wall-layer model for velocity profile in turbulent flows. AIAA J. 27, 140–149.Google Scholar
Walker, J. D. A., Smith, C. R., Doligalski, T. L. & Cerra, A. W. 1987 Impact of a vortex ring of a wall. J. Fluid Mech. 181, 99–140.Google Scholar