Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-19T06:37:12.907Z Has data issue: false hasContentIssue false
  • English
  • Français

Hollow wakes past arbitrarily shaped obstacles

Published online by Cambridge University Press:  01 February 2011

H. TELIB  and
L. ZANNETTI
H. TELIB
Affiliation:
DIASP, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Turin, Italy
L. ZANNETTI*
Affiliation:
DIASP, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Turin, Italy
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

An analytical solution is presented for steady inviscid separated flows modelled by hollow vortices, that is, by closed vortex sheets bounding a region with fluid at rest. Steady flows past arbitrary obstacles protruding from an infinite wall are considered. The solution is similar to that of the vortex patch model; it depends on two free parameters that define the size of the hollow vortex and the location of the separation point. When a sharp edge constrains the separation point (Kutta condition), the solution depends on a single parameter. As with the vortex patch model, families of growing vortices exist, which represent the continuation of desingularized point vortices. Numerical results are presented for the flows past a semicircular bump, a Ringleb snow cornice and a normal flat plate. The differences from the previous results found in the literature are analysed and discussed with the present solutions for the flow past a normal flat plate.

JFM classification

Wakes/Jets: Separated flows Vortex Flows: Vortex dynamics Wakes/Jets: Wakes
Type
Papers
Information
Journal of Fluid Mechanics , Volume 669 , 25 February 2011 , pp. 214 - 224
Copyright
Copyright © Cambridge University Press 2011

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

REFERENCES

Batchelor, G. K. 1956 On steady laminar flows with closed streamlines at large Reynolds number. J. Fluid Mech. 1, 177–190.CrossRefGoogle Scholar
Birkoff, G. & Zarantonello, E. H. 1957 Jets, Wakes, and Cavities. Academic.Google Scholar
Chernyshenko, S. I. 1998 Asymptotic theory of global separation. Appl. Mech. Rev. 51, 523–536.CrossRefGoogle Scholar
Elcrat, A., Fornberg, B., Horn, M. & Miller, K. 2000 Some steady vortex flows past a circular cylinder. J. Fluid Mech. 409, 13–27.CrossRefGoogle Scholar
Gallizio, F. 2004 Modello di Prandtl–Batchelor per il flusso normale ad una placca piana posta all'interno di un canale: studio numerico dell'esistenza e unicità della soluzione. Dissertazione di Tesi Laurea, Ingegneria Aerospaziale, aa 2003/2004, Politecnico di Torino, Turin, Italy.Google Scholar
Gallizio, F., Iollo, A., Protas, B. & Zannetti, L. 2010 On continuation of inviscid vortex patches. Physica D 239, 190–201.CrossRefGoogle Scholar
Gilbarg, D. 1960 Jets and cavities. In Handbuch der Physik (ed. Truesdell, C.), vol. 9, pp. 311–445. Springer.Google Scholar
Gurevich, M. I. 1965 Theory of Jets in Ideal Fluids. Academic.Google Scholar
Hicks, W. M. 1883 On the steady motion of a hollow vortex. Proc. R. Soc. Lond. 35, 304–308.Google Scholar
Ives, D. C. 1976 A modern look at conformal mapping, including multiply connected regions. AIAA J. 14, 1006–1011.CrossRefGoogle Scholar
Lamb, H. 1932 Hydrodynamics. Cambridge University Press.Google Scholar
Lavrentiev, M. A. 1962 Variational Methods for Boundary Value Problems for Systems of Elliptic Functions. Noordhoff.Google Scholar
Levi-Civita, T. 1907 Scie e leggi di resistenza. Rend. Circ. Mat. Palermo 23, 1–37.CrossRefGoogle Scholar
Lin, A. & Landweber, L. 1977 On a solution of the Lavrentiev wake model and its cascade. J. Fluid Mech. 79, 801–823.CrossRefGoogle Scholar
Nehari, Z. 1975 Conformal Mapping. Dover.Google Scholar
Pocklington, H. C. 1895 The configuration of a pair of equal and opposite hollow straight vortices, of finite cross-section, moving steadily through fluid. Proc. Camb. Phil. Soc. 8, 178–187.Google Scholar
Ringleb, F. O. 1961 Separation control by trapped vortices. In Boundary Layer and Flow Control (ed. Lachman, G. V.), pp. 265–294. Pergamon.Google Scholar
Smith, J. H. B. & Clark, R. W. 1986 Nonexistence of stationary vortices behind a two-dimensional normal plate. AIAA J. 13 (8), 1114–1115.CrossRefGoogle Scholar
Tanveer, S. A. 1984 Topics in 2-D separated vortex flows. PhD thesis, California Institute of Technology.Google Scholar
Tanveer, S. A. 1986 A steadily translating pair of equal and opposite vortices with vortex sheets on their boundaries. Stud. Appl. Maths 74, 139–154.CrossRefGoogle Scholar
Tricomi, F. 1951 Funzioni Ellittiche. Zanichelli.Google Scholar
Turfus, C. 1993 Prandtl–Batchelor flow past a flat plate at normal incidence in a channel – inviscid analysis. J. Fluid Mech. 249, 59–72.CrossRefGoogle Scholar
Zannetti, L. 2006 Vortex equilibrium in the flow past bluff bodies. J. Fluid Mech. 562, 151–171.CrossRefGoogle Scholar