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Vortex rings produced by non-parallel planar starting jets

Published online by Cambridge University Press:  21 September 2020

Ben Steinfurth Open the ORCID record for Ben Steinfurth [Opens in a new window]  and
Julien Weiss Open the ORCID record for Julien Weiss [Opens in a new window]
Ben Steinfurth*
Affiliation:
Institute of Aeronautics and Astronautics, Technische Universität Berlin, Marchstr. 12-14, 10587Berlin, Germany
Julien Weiss
Affiliation:
Institute of Aeronautics and Astronautics, Technische Universität Berlin, Marchstr. 12-14, 10587Berlin, Germany
*
†Email address for correspondence: [email protected]
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Abstract

Experimental methods are employed to investigate vortex rings generated by impulsively emitting pressurised air through a rectangular outlet of high aspect ratio into quiescent surroundings. The flow is characterised by a rapid transverse expansion as thick-cored, almost spherical vortex rings with a diameter more than 40 times the outlet width and entrainment rates of $\eta >0.9$ are generated. They continue to absorb vorticity far beyond the universal formation time of $t^*\approx 4$ applicable to axisymmetric parallel starting jets introduced by Gharib et al. (J. Fluid Mech., vol. 360, 1998, pp. 121–140). Here, the maximum circulation and the corresponding formation time depend on the magnitude of over-pressure in the outlet plane. After momentarily reaching a non-dimensional energy close to or even below a value of $\alpha =0.16$ associated with Hill's spherical vortex, vorticity is continuously shed into a trailing jet, and the vortex rings evolve into unsteady thinner-core states. No separation between the vortex ring and the trailing jet (pinch-off) is observed. The present study provides new insights into the flow physics of non-parallel planar starting jets that significantly differ from parallel starting flows investigated previously. The potential for active flow control applications is discussed.

JFM classification

Flow Control: Mixing enhancement Vortex Flows: Vortex dynamics Wakes/Jets: Jets
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 903 , 25 November 2020 , A16
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

REFERENCES

Afanasyev, Y. D. 2006 Formation of vortex dipoles. Phys. Fluids 18 (3), 037103.CrossRefGoogle Scholar
Akima, H. 1970 A new method of interpolation and smooth curve fitting based on local procedures. J. ACM 17 (4), 589–602.CrossRefGoogle Scholar
Arakeri, J. H., Das, D., Krothapalli, A. & Lourenco, L. 2004 Vortex ring formation at the open end of a shock tube: a particle image velocimetry study. Phys. Fluids 16 (4), 1008–1019.CrossRefGoogle Scholar
Béra, J. C., Michard, M., Grosjean, N. & Comte-Bellot, G. 2014 Flow analysis of two-dimensional pulsed jets by particle image velocimetry. Exp. Fluids 31 (5), 519–532.Google Scholar
Bradbury, L. J. S. 1963 An investigation into the structure of a turbulent plane jet. PhD thesis, Queen Mary University of London.Google Scholar
Choutapalli, I., Krothapalli, A. & Arakeri, J. H. 2009 An experimental study of an axisymmetric turbulent pulsed air jet. J. Fluid Mech. 631, 23–63.CrossRefGoogle Scholar
Dabiri, J. O. & Gharib, M. 2004 Fluid entrainment by isolated vortex rings. J. Fluid Mech. 511, 311–331.CrossRefGoogle Scholar
Das, P., Govardhan, R. N. & Arakeri, J. H. 2013 Effect of hinged leaflets on vortex pair generation. J. Fluid Mech. 730, 626–658.CrossRefGoogle Scholar
Didden, N. 1979 On the formation of vortex rings: rolling-up and production of circulation. Z. Angew. Math. Phys. 30, 101–116.CrossRefGoogle Scholar
Gharib, M., Rambod, E. & Shariff, K. 1998 A universal time scale for vortex ring formation. J. Fluid Mech. 360, 121–140.CrossRefGoogle Scholar
Glezer, A. 1998 The formation of vortex rings. Phys. Fluids 31, 3532–3542.CrossRefGoogle Scholar
Greenblatt, D. & Wygnanski, I. J. 2000 The control of flow separation by periodic excitation. AIAA J. 36, 487–545.Google Scholar
Gutmark, E. & Wygnanski, I. 1976 The turbulent planar jet. J. Fluid Mech. 73 (3), 465–495.CrossRefGoogle Scholar
Haller, G. 2001 Distinguished material surfaces and coherent structures in three-dimensional fluid flows. Physica D 149, 248–277.CrossRefGoogle Scholar
Hussain, F. & Husain, H. S. 1989 Elliptic jets. Part 1. Characteristics of unexcited and excited jets. J. Fluid Mech. 208, 257–320.CrossRefGoogle Scholar
James, S. & Madnia, C. K. 1996 Direct numerical simulation of a laminar vortex ring. Phys. Fluids 8, 2400–2414.CrossRefGoogle Scholar
Knystautas, R. 1964 The turbulent jet from a series of holes in line. Aeronaut. Q. 15 (1), 1–28.CrossRefGoogle Scholar
Krieg, M. & Mohseni, K. 2013 Modelling circulation, impulse and kinetic energy of starting jets with non-zero radial velocity. J. Fluid Mech. 719, 488–526.CrossRefGoogle Scholar
Krieg, M. & Mohseni, K. 2015 Pressure and work analysis of unsteady, deformable, axisymmetric, jet producing cavity bodies. J. Fluid Mech. 769, 337–368.CrossRefGoogle Scholar
Krueger, P. S. 2005 An over-pressure correction to the slug model for vortex ring circulation. J. Fluid Mech. 545, 427–443.CrossRefGoogle Scholar
Krueger, P. S., Dabiri, J. O. & Gharib, M. 2006 The formation number of vortex rings in uniform background coflow. J. Fluid Mech. 556, 1271–1281.CrossRefGoogle Scholar
Lim, T. T. & Nickels, T. B. 1995 Vortex rings. In Fluid Vortices. Fluid Mechanics and its Applications (ed. Green, S. I.), vol. 30. Springer.Google Scholar
Maxworthy, T. 1972 The structure and stability of vortex rings. J. Fluid Mech. 51 (1), 15–32.CrossRefGoogle Scholar
Mei, R. 1996 Velocity fidelity of flow tracer particles. Exp. Fluids 22 (1), 1–13.CrossRefGoogle Scholar
Müller, E. A. & Didden, N. 2004 Zur Erzeugung der Zirkulation bei der Bildung eines Ringwirbels an einer Düsenmündung. Stroj. Casop. 31, 363–372.Google Scholar
Moffatt, H. K. & Moore, D. W. 1978 The response of hill's spherical vortex to a small axisymmetric disturbance. J. Fluid Mech. 87, 749–760.CrossRefGoogle Scholar
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. & Colonius, T. 2000 Numerical experiments on vortex ring formation. J. Fluid Mech. 430, 267–282.CrossRefGoogle Scholar
Musculus, M. P. B. 2009 Entrainment wave in decelerating transient turbulent jets. J. Fluid Mech. 638, 117–140.CrossRefGoogle Scholar
Nitsche, M. & Krasny, R. 1994 A numerical study of vortex ring formation at the edge of a circular tube. J. Fluid Mech. 276, 139–161.CrossRefGoogle Scholar
Norbury, J. 1973 A family of steady vortex rings. J. Fluid Mech. 57 (3), 417–431.CrossRefGoogle Scholar
O'Farrell, C. & Dabiri, J. O. 2014 Pinch-off of non-axisymmetric vortex rings. J. Fluid Mech. 740, 61–96.CrossRefGoogle Scholar
Pawlak, G., Cruz, C. M., Bazan, C. M. & Hrdyi, P. G. 2007 Experimental characterization of starting jet dynamics. Fluid Dyn. Res. 39, 711–730.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
Pozrikidis, C. 1986 The nonlinear instability of Hill's vortex. J. Fluid Mech. 168, 337–367.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
Sau, R. & Mahesh, K. 2007 Passive scalar mixing in vortex rings. J. Fluid Mech. 582, 449–461.CrossRefGoogle Scholar
Shariff, K. & Leonard, A. 1992 Vortex rings. Annu. Rev. Fluid Mech. 24, 235–279.CrossRefGoogle Scholar
Shin, D., Aspden, A. J. & Richardson, E. S. 2017 Self-similar properties of decelerating turbulent jets. J. Fluid Mech. 833, R1.CrossRefGoogle Scholar
Smith, B. L. & Glezer, A. 1998 The formation and evolution of synthetic jets. Phys. Fluids 10 (9), 2281–2297.CrossRefGoogle Scholar
Weigand, A. & Gharib, M. 1997 On the evolution of laminar vortex rings. Exp. Fluids 22, 447–457.CrossRefGoogle Scholar
Witze, P. O. 1983 Hot-film anemometer measurements in a starting turbulent jet. AIAA J. 21 (2), 308–309.CrossRefGoogle Scholar
Zhao, W., Fraenkel, S. H. & Mongeau, L. G. 2000 Effects of trailing jet instability on vortex ring formation. Phys. Fluids 12, 589–596.CrossRefGoogle Scholar

Steinfurth and Weiss supplementary movie 1

Flow visualisation of vortex rings generated with circular outlet

Download Steinfurth and Weiss supplementary movie 1(Video)
Video 8.4 MB

Steinfurth and Weiss supplementary movie 2

Flow visualisation of vortex rings generated with square outlet

Download Steinfurth and Weiss supplementary movie 2(Video)
Video 10.1 MB

Steinfurth and Weiss supplementary movie 3

Flow visualisation of vortex tubes generated with slit-shaped outlet

Download Steinfurth and Weiss supplementary movie 3(Video)
Video 8.8 MB

Steinfurth and Weiss supplementary movie 4

Flow visualisation of vortex tubes generated with slit-shaped outlet; cross section at $x = 20\,\mathrm{mm}$ is shown

Download Steinfurth and Weiss supplementary movie 4(Video)
Video 363.6 KB