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Vortex-induced boundary-layer separation. Part 1. The unsteady limit problem Re → ∞

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
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Abstract

The unsteady boundary-layer flow produced by a two-dimensional vortex in motion above an infinite plane wall in an otherwise stagnant fluid is considered in the limit of infinite Reynolds number. This study is part of a continuing investigation into the nature of the physical processes that occur near the surface in transitional and fully turbulent boundary layers. The adverse pressure gradient due to the vortex leads to the development of a zone of recirculation in the viscous flow near the surface, and the boundary-layer flow then focuses rapidly toward an eruption along a band which is very narrow in the stream wise direction. The evolution of the unsteady boundary layer is posed in Lagrangian coordinates and computed using an efficient, factored ADI numerical method. The boundary-layer solution is found to develop a separation singularity and to evolve toward a terminal stage which is generic in two-dimensional unsteady flows. The computed results are compared with the results of asymptotic theory of two-dimensional boundary-layer separation and the agreement is found to be excellent.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 232 , November 1991 , pp. 99 - 131
Copyright
© 1991 Cambridge University Press

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References

Acarlar, M. S. & Smith, C. R. 1987a A study of hairpin vortices in a laminar boundary layer. Part 1. Hairpin vortices generated by hemisphere protuberances. 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
Beam, R. M. & Warming, R. F. 1978 An implicit factored scheme for the compressible Navier-Stokes equations. AlAA J. 16, 393–402.Google Scholar
Cebeci, T. 1986 Unsteady boundary layers with an intelligent numerical scheme. J. Fluid Mech. 163, 129–140.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
Collins, W. M. & Dennis, S. C. R. 1973 Flow past an impulsively started circular cylinder. J. Fluid Mech. 60, 105–127.Google Scholar
Conlisk, A. T. 1989 The pressure field in intense vortex-boundary layer interaction. 27th Aerospace Sciences Meeting, Reno, NV, AlAA Paper. 89–0293.
Cousteix, J. 1986 Three-dimensional and unsteady boundary-layer computations, Ann. Rev. Fluid Mech. 18, 173–196.Google Scholar
Cowley, S. J. 1983 Computer extension and analytic continuation of Blasius' expansion for impulsive flow past a circular cylinder. J. Fluid Mech. 135, 389–405.Google Scholar
Cowley, S. J., Van Dommelen, L. L. & Lam, S. T. 1990 On the use of Lagrangian variables in descriptions of unsteady boundary-layer separation. Phil. Trans. R. Soc. Lond. A 333, 343–378.Google Scholar
Doligalski, T. L. & Walker, J. D. A. 1978 Shear layer breakdown due to vortex motion. In Coherent Structure of Turbulent Boundary Layers (ed. C. R. Smith & D. E. Abbott), pp. 288–332. AFOSR/Lehigh University Workshop.
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., Walker, 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. Geophy. Astrophys. Fluid Dyn. 25, 77–138.Google Scholar
Elliott, J. W. & Smith, F. T. 1987 Dynamic stall due to unsteady marginal separation. J. Fluid Mech. 179, 489–512.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. App. 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
Hoyle, J. M., SmithF. T. & Walker, J. D. A. 1991 On sublayer eruption and vortex formation. Comput. Phys. Commun. 65, 151–157.Google Scholar
Lam, S. T. 1988 On high-Reynolds-number-laminar flows through a curved pipe, and past a rotating cylinder. Ph.D. thesis, University of London.
McCroskey, W. J. 1982 Unsteady Airfoils. Ann. Rev. Fluid Mech. 14, 285–311.Google Scholar
Moore, F. K. 1958 On the separation of the unsteady boundary layer. In Boundary Layer Research (ed. H. G. Görtler), pp. 296–311. Springer.
Peridier, V. J., Smith, F. T. & Walker, J. D. A. 1988 Methods for the calculation of unsteady separation. AIAA Paper 88–0604.
Peridier, V. J., Smith, F. T. & Walker, J. D. A. 1991 Vortex-induced boundary-layer separation. Part 2. Unsteady interacting boundary-layer theory. J. Fluid Mech. 232, 133–165.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, Rep. FM-13. Dept. of Mechanical Engineering and Mechanics, Lehigh University; AFOSR-TR-90–0458 (available as ADA-221564).
Proudman, I. & Johnson, K. 1962 Boundary-layer growth near a rear stagnation point. J. Fluid Mech. 12, 161–168.Google Scholar
Riley, N. 1975 Unsteady laminar boundary layers. SIAM Rev. 17, 274–297.Google Scholar
Riley, N. & Vasantha, R. 1989 Unsteady high Reynolds number flows. J. Fluid Mech. 205, 243–262.Google Scholar
Rott, N. 1956 Unsteady viscous flow in the vicinity of a stagnation point. Q. Appl. Maths. 13, 444–451.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 Concerning dynamic stall, Aeron. Q. Nov./Dec.Google Scholar
Smith, F. T. 1988 Finite-time breakup can occur in unsteady interacting boundary layer. Mathematika 35, 256–273.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 2nd IUTAM Symp. on Structure of Turbulence and Drag Reductions, (ed. A. Gyr). Springer.
Van Dommelen, L. L. 1981 Unsteady boundary-layer separation, Ph.D dissertation, Cornell University.
Van Dommelen, L. L. & Cowley, S. J. 1990 On the Lagrangian description of unsteady boundary-layer separation. Part 1. General theory. J. Fluid Mech. 210, 593–626.Google Scholar
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 2nd IUTAM Sym. On Structure of Turbulence and Drag Reduction (ed. A. Gyr). Springer; also NASA Tech. Mem. 102362, ICOMP-89–26.
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., Sharnhorst, 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 The impact of a vortex ring on a wall. J. Fluid Mech. 181, 99–140.Google Scholar
Williams, J. C. 1977 Incompressible boundary-layer separation. Ann. Rev. Fluid Mech. 9 113–144.Google Scholar