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On the formation of vortex pairs near orifices

Published online by Cambridge University Press:  20 April 2006

P. Blondeaux  and
B. De Bernardinis
P. Blondeaux
Affiliation:
Istituto di Idraulica, Università di Genova
B. De Bernardinis
Affiliation:
Istituto di Idraulica, Università di Genova
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Abstract

A two-dimensional vortex pair is commonly generated by pushing fluid down a semi-infinite channel by means of an impulsively started piston. The strength and separation of the two fully developed vortices strongly depend upon the time history of the piston motion. When the piston is impulsively stopped, two secondary vortices are formed downstream of the channel ends and interact with the primary pair in a fairly complicated way.

In the present work we attempt to provide a discrete-vortex model of the process of pair formation. The effects of viscosity are assumed to affect only the separation process, having negligible influence on the overall flow. In the limit of infinite Reynolds number, the problem becomes one of inviscid flow, and the separation at the sharp edges is approximated by a Kutta–Joukowski condition, large vortex regions being replaced by simple concentrated vortices. The growing vortex sheets shed from the edge are represented by a simplified model due to Brown and Michael.

Present results are able to account for the failure of the ‘puffing’ technique as well as the success of Barker and Crow's ‘downwash’ technique in producing vortex pairs.

Flow-visualization experiments are also reported, and good qualitative agreement is found between numerical and experimental results.

The present model also shows that the presence of secondary vortices drastically modifies the trajectories of free vortices as obtained in a previous work due to Sheffield.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 135 , October 1983 , pp. 111 - 122
Copyright
© 1983 Cambridge University Press

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References

Barker, S. J. & Crow, S. C. 1977 The motion of two-dimensional vortex pairs in a ground effect J. Fluid Mech. 82, 659.Google Scholar
Brown, C. E. & Michael, W. H. 1954 Effect of leading edge separation on the lift of a delta wing J. Aero. Sci. 21, 690.Google Scholar
Brown, G. L. & Roshko, A. 1974 On density effects and large structure in turbulent mixing layers J. Fluid Mech. 64, 775.Google Scholar
Crow, S. C. 1975 The stability of vortex cores. Poseidon Res. Note 4Google Scholar
Dhanak, M. R. 1981 The stability of an expanding circular vortex layer Proc. R. Soc. Lond. A375, 443.Google Scholar
Didden, N. 1979 On the formation of vortex rings Z. angew. Math. Phys. 30, 101.Google Scholar
Graham, J. M. R. 1977 Vortex shedding from sharp edges. Imperial College Aero. Rep. 77.06.Google Scholar
Graham, J. M. R. 1980 The forces on sharp-edged cylinders in oscillatory flow at low Keulegan-Carpenter numbers J. Fluid Mech. 97, 331.Google Scholar
Hama, F. R. 1964 Streaklines in a perturbed shear flow Phys. Fluids 5, 664.Google Scholar
Harvey, J. K. & Perry, F. J. 1971 Flow field produced by trailing vortices in the vicinity of the ground AIAA J. 9, 1659.Google Scholar
Maxworthy, T. 1977 Some experimental studies of vortex rings J. Fluid Mech. 81, 465.Google Scholar
Moore, D. W. 1976 The stability of an evolving two-dimensional vortex sheet Mathematika 23, 35.Google Scholar
Pierce, D. 1961 Photographic evidence of the formation and growth of vorticity behind plates accelerated from rest in still air J. Fluid Mech. 11, 460.Google Scholar
Pullin, D. I. 1978 The large-scale structure of unsteady self-similar rolled-up vortex sheets J. Fluid Mech. 88, 401.Google Scholar
Pullin, D. I. & Perry, A. E. 1980 Some flow visualization experiments on the starting vortex J. Fluid Mech. 97, 239.Google Scholar
Rott, N. 1956 Diffraction of a weak shock with vortex generation J. Fluid Mech. 1, 111.Google Scholar
Saffman, P. G. 1979 The approach of a vortex pair to a plane surface in inviscid fluid J. Fluid Mech. 92, 497.Google Scholar
Sheffield, J. S. 1977 Trajectories of an ideal vortex pair near an orifice Phys. Fluids 20, 543.Google Scholar
Walker, J. D. A. 1978 The boundary layer due to a rectilinear vortex Proc. R. Soc. Lond. A359, 167.Google Scholar