Hostname: page-component-cb9f654ff-mwwwr Total loading time: 0 Render date: 2025-09-03T01:15:36.295Z Has data issue: false hasContentIssue false
  • English
  • Français

Vortex motion in doubly connected domains

Published online by Cambridge University Press:  10 October 2008

L. ZANNETTI ,
F. GALLIZIO  and
G. M. OTTINO
L. ZANNETTI
Affiliation:
DIASP, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
F. GALLIZIO
Affiliation:
DIASP, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
G. M. OTTINO
Affiliation:
DIASP, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
Get access Rights & Permissions [Opens in a new window]

Abstract

The unsteady two-dimensional rotational flow past doubly connected domains is analytically addressed. By concentrating the vorticity in point vortices, the flow is modelled as a potential flow with point singularities. The dependence of the complex potential on time is defined according to the Kelvin theorem. The general case of non-null circulations around the solid bodies is discussed. Vortex shedding and time evolution of the circulation past a two-element airfoil and past a two-bladed Darrieus turbine are presented as physically coherent examples.

Information

Type
Papers
Information
Journal of Fluid Mechanics , Volume 612 , 10 October 2008 , pp. 143 - 152
Copyright
Copyright © Cambridge University Press 2008

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.)

Article purchase

Temporarily unavailable

References

REFERENCES

Clements, R. R. 1973 An inviscid model of two-dimensional vortex shedding. J. Fluid Mech. 57, 321–336.CrossRefGoogle Scholar
Crowdy, D. G. & Marshall, J. S. 2005 The motion of a point vortex around multiple circular islands. Phys. Fluids 17, 56602–13.CrossRefGoogle Scholar
Ferrari, C. 1930 Sulla trasformazione conforme di due cerchi in due profili alari. Mem. R. Acc. Sci. Torino 68, 1–15.Google Scholar
Ives, D. C. 1976 A modern look at conformal mapping, including multiply connected regions. AIAA J. 14, 1006–1011.CrossRefGoogle Scholar
Johnson, E. R. & McDonald, N. R. 2004 The motion of a vortex near two circular cylinders. Proc. R. Soc. Lond. A 460, 939–954.CrossRefGoogle Scholar
Johnson, E. R. & McDonald, N. R. 2005 Vortices near barriers with multiple gaps. J. Fluid Mech. 531, 335–358.CrossRefGoogle Scholar
Kiya, M. & Arie, M. 1977 A contribution to an inviscid vortex-shedding model for an inclined flat plate in uniform flow. J. Fluid Mech. 82, 223–243.CrossRefGoogle Scholar
Lagally, M. 1929 Die reibungslose stromung im aussengbiet zweier kreise. Z. Angew. Math. Mech. 9, 299–305.CrossRefGoogle Scholar
Lin, C. C. 1941 On the motion of vortices in two dimensions. Proc. Nat. Acad. Sci. USA 27, 570–577.CrossRefGoogle ScholarPubMed
Milne-Thomson, L. M. 1968 Theoretical Hydrodynamics. Dover.CrossRefGoogle Scholar
Pullin, D. I. 1978 The large-scale structure of unsteady self-similar rolled-up vortex-sheets. J. Fluid Mech. 88, 401–430.CrossRefGoogle Scholar
Routh, E. J. 1881 Some application of conjugate functions. Proc. Lond. Math. Soc. 12, 73–89.Google Scholar
Saffman, P. G. 1992 Vortex Dynamics. Cambridge University Press.Google Scholar
Sarpkaya, T. 1975 An inviscid model of two-dimensional vortex shedding for transient and asymptotically steady separated flow over an inclined flat plate. J. Fluid Mech. 68, 109–129.CrossRefGoogle Scholar
Tricomi, F. 1951 Funzioni ellittiche. Zanichelli, Bologna.Google Scholar
Zannetti, L. & Franzese, P. 1994 The non-integrability of the restricted problem of two vortices in closed domains. Physica D 76, 99–109.Google Scholar
Zannetti, L. & Iollo, A. 2003 Passive control of the vortex wake past a flat plate at incidence. Theor. Comput. Fluid Dyn. 16, 211–230.CrossRefGoogle Scholar
Zannetti, L., Gallizio, F. & Ottino, G. 2007 Vortex capturing vertical axis wind turbine. J. Phys. Conf. Series doi:10.1088/1742-6596/75/1/012029 75, 1–10.CrossRefGoogle Scholar