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Three-dimensional impulsive vortex formation from slender orifices

Published online by Cambridge University Press:  06 January 2011

F. DOMENICHINI
F. DOMENICHINI*
Affiliation:
Dipartimento di Ingegneria Civile e Ambientale, Università di Firenze, Via S. Marta 3, 50139 Firenze, Italy
*
†Email address for correspondence: [email protected]
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Abstract

The vortex formation behind an orifice is a widely investigated phenomenon, which has been recently studied in several problems of biological relevance. In the case of a circular opening, several works in the literature have shown the existence of a limiting process for vortex ring formation that leads to the concept of critical formation time. In the different geometric arrangement of a planar flow, which corresponds to an opening with straight edges, it has been recently outlined that such a concept does not apply. This discrepancy opens the question about the presence of limiting conditions when apertures with irregular shape are considered. In this paper, the three-dimensional vortex formation due to the impulsively started flow through slender openings is studied with the numerical solution of the Navier–Stokes equations, at values of the Reynolds number that allow the comparison with previous two-dimensional findings. The analysis of the three-dimensional results reveals the two-dimensional nature of the early vortex formation phase. During an intermediate phase, the flow evolution appears to be driven by the local curvature of the orifice edge, and the time scale of the phenomena exhibits a surprisingly good agreement with those found in axisymmetric problems with the same curvature. The long-time evolution shows the complete development of the three-dimensional vorticity dynamics, which does not allow the definition of further unifying concepts.

JFM classification

Vortex Flows: Vortex dynamics Wakes/Jets: Wakes/Jets
Type
Papers
Information
Journal of Fluid Mechanics , Volume 666 , 10 January 2011 , pp. 506 - 520
Copyright
Copyright © Cambridge University Press 2011

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References

REFERENCES

Afanasyev, Y. D. 2006 Formation of vortex dipoles. Phys. Fluids 18, 037103.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. Ann. Rev. Fluid Mech. 41, 17–33.CrossRefGoogle Scholar
Dabiri, J. O. & Gharib, M. 2005 a Starting flow through nozzles with temporally variable exit diameter. J. Fluid Mech. 538, 111–136.CrossRefGoogle Scholar
Dabiri, J. O. & Gharib, M. 2005 b The role of optimal vortex formation in biological fluid transport. Proc. R. Soc. B 272, 1557–1560.CrossRefGoogle ScholarPubMed
Domenichini, F. 2008 On the consistency of the direct forcing method in the fractional step solution of the Navier–Stokes equations. J. Comput. Phys. 227 (12), 6372–6384.CrossRefGoogle Scholar
Domenichini, F., Pedrizzetti, G. & Baccani, B. 2005 Three-dimensional filling flow into a model left ventricle. J. Fluid Mech. 539, 179–198.CrossRefGoogle Scholar
Domenichini, F., Querzoli, G., Cenedese, A. & Pedrizzetti, G. 2007 Combined experimental and numerical analysis of the flow structure into the left ventricle. J. Biomech. 40, 1988–1994.CrossRefGoogle ScholarPubMed
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. 103, 6305–6308.CrossRefGoogle ScholarPubMed
Gharib, M., Rambod, E. & Shariff, K. 1998 A universal time scale for vortex ring formation. J. Fluid Mech. 360, 121–140.CrossRefGoogle Scholar
Graham, J. M. R. 1977 Vortex shedding from sharp edges. I.C. Aero. Rep. 77-06, Department of Aeronautics, Imperial College, London, UK.Google Scholar
Grinstein, F. F. 2001 Vortex dynamics and entrainment in rectangular free jets. J. Fluid Mech. 437, 69–101.CrossRefGoogle Scholar
Hofmans, G. C. J. 1998 Vortex Sound in Confined Flows. Technische Universiteit Eindhoven. Available at: 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
Jeong, F. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 69–94.CrossRefGoogle Scholar
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
Krueger, P. S. 2008 Circulation and trajectories of vortex rings formed from tube and orifice openings. Physica D 237, 2218–2222.CrossRefGoogle Scholar
Krueger, P. S. & Gharib, M. 2003 The significance of vortex ring formation to the impulse and thrust of a starting jet. Phys. Fluids 15 (5), 1271–1281.CrossRefGoogle Scholar
Linden, P. F. & Turner, J. S. 2001 The formation of optimal vortex rings, and the efficiency of propulsion devices. J. Fluid Mech. 427, 61–72.CrossRefGoogle Scholar
Linden, P. F. & Turner, J. S. 2004 Optimal vortex rings and aquatic propulsion mechanisms. Proc. R. Soc. B 271, 647–653.CrossRefGoogle ScholarPubMed
Mohseni, K. & Gharib, M. 1998 A model for universal time scale of vortex ring formation. Phys. Fluids 10 (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. 2010 Vortex formation out of two-dimensional orifices. J. Fluid Mech. 655, 198–216.CrossRefGoogle Scholar
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. & Tonti, G. 2010 On the left ventricular vortex reversal after mitral valve replacement. Ann. Biomed. Engng 38 (3), 769–773.CrossRefGoogle ScholarPubMed
Rosenfeld, M., Katija, K. & Dabiri, J. O. 2009 Circulation generation and vortex ring formation by conic nozzles. J. Fluids Engng 131, 091204.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
Saffmann, P. G. 1992 Vortex Dynamics. Cambridge University Press.Google Scholar
Shusser, M. & Gharib, M. 2000 Energy and velocity of a forming vortex ring. Phys. Fluids 12 (3), 618–621.CrossRefGoogle Scholar
Verzicco, R. & Orlandi, P. 1996 A finite-difference scheme for 3D incompressible flow in cylindrical coordinates. J. Comput. Phys. 123, 402–414.CrossRefGoogle Scholar