Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-19T13:43:36.025Z Has data issue: false hasContentIssue false
  • English
  • Français

Close interaction between a vortex filament and a rigid sphere

Published online by Cambridge University Press:  26 April 2006

Gianni Pedrizzetti
Gianni Pedrizzetti
Affiliation:
Dipartimento di Ingegneria Civile, Università di Firenze, via S. Marta 3. 50139 Firenze, Italy
Get access Rights & Permissions [Opens in a new window]

Abstract

The evolution of a linear vortex filament close to a rigid sphere is investigated at high Reynolds number. The limiting evolution in an ideal flow, is analysed using a cutoff method and the results are compared with those of a singular vortex approach able to account for a viscous effect on the vortex structure evolution. The computed results show the creation of a closed vortex structure in ideal flow and also, at low Reynolds number, an unrealistic reattachment of the vortex to the surface of the body. The nature of the boundary-layer development, when the no-slip condition is satisfied, is calculated near the symmetry plane. The solutions show the development of an unsteady, vortex-driven, separating boundary layer with the three-dimensional separations dependent on the initial distance of the filament from the wall. All the solutions ultimately show a rapid growth of the secondary vorticity field near the surface and suggest an ejection from the boundary layer, followed by a strong viscous-inviscid interaction.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 245 , December 1992 , pp. 701 - 722
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

Agishtein, M. E. & Migdal A. A. 1986 Computer simulation of three-dimensional vortex dynamics Mod. Phys. Lett. A 1, 221.Google Scholar
Aksman, M. J. & Novikov E. A. 1988 Reconnection of vortex filaments. Fluid Dyn. Res. 3, 239.Google Scholar
Aksman M. J., Novikov, E. A. & Orszag S. A. 1985 Vorton method in three-dimensional hydrodynamics. Phys. Rev. Lett. 54, 2410.Google Scholar
Batchelor G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Blondeaux, P. & De Bernardinis B. 1983 On the formation of vortex pairs near orifices. J. Fluid Mech. 135, 111.Google Scholar
Chorin A. J. 1982 The evolution of a turbulent vortex. Commun. Math. Phys. 83, 517.Google Scholar
Dhanak M. R. 1981 Interaction between a vortex filament and an approaching rigid sphere. J. Fluid Mech. 110, 129.Google Scholar
Dhanak, M. R. & De Bernardinis B. 1981 The evolution of an elliptic vortex ring. J. Fluid Mech. 109, 189.Google Scholar
Doligalski, T. L. & Walker J. D. A. 1984 The boundary layer due to a convected two-dimensional vortex. J. Fluid Mech. 139, 1.Google Scholar
Ersoy, S. & Walker J. D. A. 1987 The boundary layer due to a three-dimensional vortex loop. J. Fluid Mech. 185, 569.Google Scholar
Harvey, J. K. & Perry F. J. 1971 Flowfield produced by trailing vortices in the vicinity of the ground. AIAA J. 9, 1659.Google Scholar
Lighthill M. J. 1956 The image system of a vortex element in a rigid sphere. Proc. Camb. Phil. Soc. 52, 317.Google Scholar
Meiron D. I., Shelley M. J., Ashurst, W. T. & Orszag S. A. 1988 Numerical studies of vortex reconnection. Proc. SIAM Workshop on Vortex Dynamics, April 25–27. Leesburg, VA.
Moore D. W. 1972 Finite amplitude waves on aircraft trailing vortices. Aeronaut. Q. 23, 307.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.Google Scholar
Novikov E. A. 1983 Generalized dynamics of three-dimensional vortical singularities (vortons). Sov. Phys. JETP 57, 566.Google Scholar
Peace, A. J. & Riley N. 1983 A viscous vortex pair in ground effect. J. Fluid Mech. 129, 409.Google Scholar
Pedlosky J. 1979 Geophysical Fluid Dynamics. Springer.
Pedrizzetti G. 1991a Stretching of a vortex filament over an approaching sphere using the vortex singularities method. DIC I–3. Università di Firenze.Google Scholar
Pedrizzetti G. 1991b About modelling the close interaction between a vortex filament and a rigid sphere. Paper presented at EUROMECH 1st EFMC, September 16–20, Cambridge University.
Pedrizzetti G. 1992 Insight to singular vortex flows. Fluid Dyn. Res. (in the press).Google Scholar
Peridier V. J., Smith, F. T. & Walker J. D. A. 1991 Vortex-induced boundary layer separation. Part 1. The unsteady limit problem Re. J. Fluid Mech. 232, 99.Google Scholar
Perry, A. E. & Chong M. S. 1986 A series-expansion study of the Navier–Stokes equations with application to the three-dimensional separation pattern. J. Fluid Mech. 173, 207.Google Scholar
Perry, A. E. & Chong M. S. 1987 A description of eddying motion and flow pattern using critical-point concepts. Ann. Rev. Fluid Mech. 19, 125.Google Scholar
Perry, A. E. & Fairlie B. D. 1974 Critical points in flow patterns. Adv. Geophys. 18B, 299.Google Scholar
Pumir, A. & Siggia E. D. 1987 Vortex dynamics and the existence of solutions to the Navier–Stokes equations. Phys. Fluids 30, 1606.Google Scholar
Saffman P. G. 1980 Transition and Turbulence (ed. R. E. Meyer), p. 149. Academic.
Saffman P. G. 1989 A model of vortex reconnection. J. Fluid Mech. 112, 395.Google Scholar
Siggia E. D. 1985 Collapse and amplification of a vortex filament. Phys. Fluids 28, 794.Google Scholar
Smith C. R., Walker J. D. A., Haidair, A. H. & Sobrun U. 1991 On the dynamics of near-wall turbulence Phil. Trans. R. Soc. Lond. A 336, 131.Google Scholar
Van Dommelen L. L. 1990 On the Lagrangian description of unsteady boundary-layer separation. Part 2. The spinning sphere. J. Fluid Mech. 210, 627.Google Scholar
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.Google Scholar
Walker J. D. A. 1978 The boundary layer due to a rectilinear vortex Proc. R. Soc. Lond. A 359, 167.Google Scholar
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.Google Scholar
Winckelmans, G. & Leonard A. 1988 Improved vortex methods for three-dimensional flows. Proc. SIAM Workshop on Vortex Dynamics, April 25–27, Leesburg, VA.