Hostname: page-component-7dd5485656-glrdx Total loading time: 0 Render date: 2025-10-31T16:26:41.586Z Has data issue: false hasContentIssue false
  • English
  • Français

Vortex formation out of two-dimensional orifices

Published online by Cambridge University Press:  05 May 2010

GIANNI PEDRIZZETTI
GIANNI PEDRIZZETTI*
Affiliation:
D.I.C.A., Università di Trieste, P. le Europa 1, 34127 Trieste, Italy
*
†Email address for correspondence: giannip@dica.units.it
Get access Rights & Permissions [Opens in a new window]

Abstract

The understanding of the vortex formation process is currently driving a novel attempt to evaluate the performance of fluid dynamics in biological systems. The concept of formation time, developed for axially symmetric orifices, is here studied in two-dimensional flows for the generation of vortex pairs. The early stage of the formation process is studied with the single vortex model in the inviscid limit. Within this framework, the equation can be written in a universal form in terms of the formation time. The single vortex model properly represents the initial circular spiralling vortex sheet and its acceleration for self-induced motion. Then, an analysis is performed by numerical simulation of the two-dimensional Navier–Stokes equations to cope with the spatially extended vortex structure. The results do not show the pinch-off phenomenon previously reported for vortex rings. The two-dimensional vortex pair tends to a stably growing structure such that, while it translates and extends longitudinally, it remains connected to the sharp edge by a shear layer whose velocity is always about twice that of the leading vortex. At larger values of the Reynolds number the instability of the shear layer develops small-scale vortices capable of destabilizing the coherent vortex growth. The absence of a critical formation number for two-dimensional vortex pairs suggests further considerations for the development of concepts of optimal vortex formation from orifices with variable curvature or of a tapered shape.

Information

Type
Papers
Information
Journal of Fluid Mechanics , Volume 655 , 25 July 2010 , pp. 198 - 216
Copyright
Copyright © Cambridge University Press 2010

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

Afanasyev, Y. D. 2006 Formation of vortex dipoles. Phys. Fluids 18, 037103.CrossRefGoogle Scholar
Blondeaux, P. & De Bernardinis, B. 1983 On the formation of vortex pairs near orifices. J. Fluid Mech. 135, 111–122.CrossRefGoogle Scholar
Brown, C. E. & Michael, W. H. 1954 Effect of leading edge separation on the lift of a delta wing. J. Aeronaut. Sci. 21 (10), 690–694, 706.CrossRefGoogle Scholar
Dabiri, J. O. 2009 Optimal vortex formation as a unifying principle in biological propulsion. Annu. Rev. Fluid Mech. 41, 17–33.CrossRefGoogle Scholar
Dabiri, J. O. & Gharib, M. 2005 Starting flow through nozzles with temporally variable exit diameter. J. Fluid Mech. 538, 111–136.CrossRefGoogle Scholar
Gharib, M., Rambod, E., Kheradvar, A., Sahn, D. J. & Dabiri, J. O. 2006 Optimal vortex formation as an index of cardiac health. Proc. Natl Acad. Sci. 109, 6205–6308.Google Scholar
Gharib, M., Rambod, E. & Shariff, K. 1998 A universal time scale for vortex ring formation. J. Fluid Mech. 360, 121–140.CrossRefGoogle Scholar
Hofmans, G. C. J. 1998 Vortex Sound in Confined Flows. Technische Universiteit Eindhoven. ISBN 90-386-0697-4. http://alexandria.tue.nl/extra2/9802719.pdf.Google Scholar
Hong, G. R., Pedrizzetti, G., Tonti, G., Li, P., Wei, P., Kim, J. K., Bawela, A., Liu, S., Chung, N., Houle, H., Narula, J. & Vannan, M. A. 2008 Characterization and quantification of vortex flow in the human left ventricle. J. Am. Coll. Cardiol. Img. 1, 705–717.CrossRefGoogle ScholarPubMed
Kheradvar, A. & Gharib, M. 2007 Influence of ventricular pressure drop on mitral annulus dynamics through the process of vortex ring formation. Ann. Biomed. Engng 35, 2050–2064.CrossRefGoogle ScholarPubMed
Kheradvar, A. & Gharib, M. 2009 On mitral valve dynamics and its connection to early diastolic flow. Ann. Biomed. Engng 37, 1–13.CrossRefGoogle ScholarPubMed
Kilner, P. J., Yang, G. Z., Wilkes, A. J., Mohiaddin, R. H., Firmin, D. N. & Yacoub, M. H. 2000 Asymmetric redirection of flow through the heart. Nature 404, 759–761.CrossRefGoogle ScholarPubMed
Korakianitis, T. & Shi, Y. 2006 Numerical simulation of cardiovascular dynamics with healthy and diseased heart valves. J. Biomech. 39, 1964–1982.CrossRefGoogle ScholarPubMed
Krueger, P. S. 2008 Circulation and trajectories of vortex rings formed from tube and orifice openings. Physica D 237, 2218–2222.CrossRefGoogle Scholar
Lamb, H. 1932. Hydrodynamics, 6th edn. Cambridge University Press.Google Scholar
Luchini, P. & Tognaccini, R. 2002 The start-up vortex issuing from a semi-infinite flat plate. J. Fluid Mech. 455, 175–193.CrossRefGoogle Scholar
Mohseni, K. & Gharib, M. 1998 A model for universal time scale of vortex ring formation. Phys. Fluids 10, 2436–2438.CrossRefGoogle Scholar
Mohseni, K., Ran, H. Y. & Colonius, T. 2001 Numerical experiments on vortex ring formation. J. Fluid Mech. 430, 267–282.CrossRefGoogle Scholar
Pedrizzetti, G. 2005 Kinematic characterization of valvular opening. Phys. Rev. Lett. 94, 194–502.CrossRefGoogle ScholarPubMed
Pedrizzetti, G. & Domenichini, F. 2005 Nature optimizes the swirling flow in the human left ventricle. Phys. Rev. Lett. 95, 1080101.CrossRefGoogle ScholarPubMed
Pedrizzetti, G. & Domenichini, F. 2006 Flow-driven opening of a valvular leaflet. J. Fluid Mech. 569, 321–330.CrossRefGoogle Scholar
Pedrizzetti, G. & Domenichini, F. 2007 Asymmetric opening of a simple bi-leaflet valve. Phys. Rev. Lett. 98, 214–503.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
Rosenfeld, M., Rambod, E. & Gharib, M. 1998 Circulation and formation number of laminar vortex rings. J. Fluid Mech. 376, 297–318.CrossRefGoogle Scholar
Rott, N. 1956 Diffraction of a weak shock with vortex generation. J. Fluid Mech. 1, 111–128.CrossRefGoogle Scholar
Routh, E. J. 1881 Some applications of conjugate functions Proc. Lond. Math. Soc. 12, 73–89.Google Scholar
Shusser, M. & Gharib, M. 2000 Energy and velocity of a forming vortex ring. Phys. Fluids 12, 618–621.CrossRefGoogle Scholar