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The boundary layer due to a three-dimensional vortex loop

Published online by Cambridge University Press:  21 April 2006

S. Ersoy  and
J. D. A. Walker
S. Ersoy
Affiliation:
Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA 18015, USA Present address: 9 Eylül University, Izmir, Turkey.
J. D. A. Walker
Affiliation:
Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA 18015, USA
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Abstract

The nature of the boundary layer induced by the motion of a three-dimensional vortex loop towards a plane wall is considered. Initially the vortex is taken to be a ring approaching a plane wall at an angle of attack in an otherwise stagnant fluid; the ring rapidly distorts into a loop shape due to the influence of the wall and the trajectory is computed from a numerical solution of the Biot-Savart integral. As the vortex loop moves, an unsteady boundary-layer flow develops on the wall. A method is described which allows the computation of the flow velocities on and near the symmetry plane of the vortex loop within the boundary layer. The computed results show the development of a variety of complex three-dimensional separation phenomena. Some of the solutions ultimately show strong localized boundary-layer growth and are suggestive that a boundary-layer eruption and a strong viscous-inviscid interaction will be induced by the moving vortex.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 185 , December 1987 , pp. 569 - 598
Copyright
© 1987 Cambridge University Press

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References

Acarlar, M. S. & Smith, C. R. 1984 An experimental study of hairpin vortices as a potential flow structure of turbulent boundary layers. Rep. FM-5. Department of Mechanical Engineering and Mechanics, Lehigh University.
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 protruberance. 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
Batchelor, G. K. 1970 An Introduction to Fluid Dynamics. Cambridge University Press.
Bippes, H. 1972 Sitzungber. Heidel. Akad. Wiss. Math. Naturwiss. K1, 103.
Callegari, A. J. & Ting, L. 1978 Motion of a curved vortex filament with decaying vortical core and axial velocity. SIAM J. Appl. Maths 35, 148–174.Google Scholar
Cerra, A. W. & Smith, C. R. 1983 Experimental observation of vortex ring interaction with fluid adjacent to a surface. Rep. FM-4. Department of Mechanical Engineering and Mechanics, Lehigh University.
Dhanak, M. R. 1981 Interaction between a vortex filament and an approaching rigid sphere. J. Fluid Mech. 109, 129–147.Google Scholar
Dhanak, M. R. & De Bernardinis, B. 1981 The evolution of an elliptic vortex ring. J. Fluid Mech. 109, 189–216.Google Scholar
Didden, N. & Ho, C.-M. 1985 Unsteady separation in a boundary layer produced by an impinging jet. J. Fluid Mech. 160, 235–256.Google Scholar
Doligalski, T. L. & Walker, J. D. A. 1978 Shear layer breakdown due to vortex motion. In Proc. Workshop on Coherent Structure of Turbulent Boundary Layers (ed. C. R. Smith & D. E. Abbott), pp. 288–339. Lehigh University.
Doligalski, T. L. & Walker, J. D. A. 1984 The boundary layer due to a convected two-dimensional vortex. J. Fluid Mech. 139, 1–28.Google Scholar
Elliot, J. W., Smith, F. T. & Cowley, S. J. 1983 Breakdown of boundary layers: (i) on moving surfaces; (ii) in semi-similar unsteady flow; (iii) in fully unsteady flow. Geophys. Astrophys. Fluid Dyn. 25, 77–138.Google Scholar
Ersoy, S. & Walker, J. D. A. 1985a Viscous flow induced by counter-rotating vortices. Phys. Fluids 28, 2687–2698.Google Scholar
Ersoy, S. & Walker, J. D. A. 1985b The viscous flow induced near a wall by counter-rotating vortex pairs and vortex loops. Rep. FM-8. Department of Mechanical Engineering and Mechanics, Lehigh University.
Ersoy, S. & Walker, J. D. A. 1986 The flow induced at a wall by a vortex pair. AIAA J. 24, 1597–1605.Google Scholar
Falco, R. E. 1977 Coherent motions in the outer region of a turbulent boundary layer. Phys. Fluids 20, S124–S132.Google Scholar
Falco, R. E. 1982 A synthesis and model of turbulence structure in the wall region. In Structure of Turbulence in Heat and Mass Transfer (ed. Z. P. Zaric), Hemisphere.
Falco, R. E. 1983 New results, a review and synthesis of the mechanism of turbulence production in boundary layers and its modification. AIAA Paper 83–0377.
Falco, R. E. & Wiggert, D. C. 1980 The effects of dilute polymer additives on vortex ring/wall interactions – a mechanism for drag reduction. In Viscous Flow Drag Reduction (ed. G. Hough), Prog. Astronaut. Aeronaut. 72, 275–289.
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. & Bandyophadyay, P. 1981 New aspects of turbulent boundary-layer structure. J. Fluid Mech. 107, 297–337.Google Scholar
Hon, L.-T. & Walker, J. D. A. 1987 An analysis of motion and effects of hairpin vortices. Rep. FM-11. Department of Mechanical Engineering and Mechanics, Lehigh University.
Lamb, H. 1932 Hydrodynamics. Cambridge University Press.
Leonard, A. 1980 Vortex methods for flow simulation. J. Comp. Phys. 37, 289–335.Google Scholar
Leonard, A. 1985 Computing three-dimensional incompressible flows with vortex filaments. Ann. Rev. Fluid Mech. 17, 523–559.Google Scholar
Lighthill, M. J. 1963 Boundary layer theory. In Laminar Boundary Layers (ed. L. Rosenhead), pp. 46–109. Oxford University Press.
Mehta, R. D. & Lim, T. T. 1984 Flow visualization study of a vortex/wing interaction. NASA Tech. Memo. 86656.
Moore, D. W. 1972 Finite amplitude waves on aircraft trailing vortices. Aero. Q. 23, 307–314.Google Scholar
Moore, D. W. & Saffman, P. G. 1972 The motion of a vortex with axial flow. Phil. Trans. R. Soc. Lond. A 272, 403–429.Google Scholar
Smith, C. R. 1984 A synthesized model of the near-wall behavior in turbulent boundary layers. In Proc. Eighth Bienniel Symp. on Turbulence (ed. G. K. Patterson & J. L. Zakin), pp. 299–325. University of Missouri-Rolla, Missouri.
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 a singularity in a separating laminar boundary layer. J. Comp. Phys. 38, 125–140.Google Scholar
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., Scharnhorst, R. K. & Weigand, G. G. 1986 Wall layer models for the calculation of velocity and heat transfer in turbulent boundary layers. AIAA Paper 86–0213, Reno, Nevada; to appear in AIAA J.
Walker, J. D. A., Smith, C. R., Cerra, T. & Doligalski, T. L. 1987 The impact of a vortex ring on a wall. J. Fluid Mech. 181, 99–140.Google Scholar