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The formation process of annular starting jets

Published online by Cambridge University Press:  06 October 2022

Jianwei Zhu Open the ORCID record for Jianwei Zhu [Opens in a new window] ,
Guoqing Zhang Open the ORCID record for Guoqing Zhang [Opens in a new window] ,
Lei Gao Open the ORCID record for Lei Gao [Opens in a new window]  and
S.C.M. Yu Open the ORCID record for S.C.M. Yu [Opens in a new window]
Jianwei Zhu
Affiliation:
Key Laboratory of Dynamics and Control of Flight Vehicle, School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, PR China
Guoqing Zhang*
Affiliation:
Key Laboratory of Dynamics and Control of Flight Vehicle, School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, PR China
Lei Gao
Affiliation:
School of Aeronautics and Astronautics, Sichuan University, Chengdu 610065, PR China
S.C.M. Yu
Affiliation:
Department of Aeronautical and Aviation Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong, PR China
*
†Email address for correspondence: zhanggq@bit.edu.cn
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Abstract

The formation and evolution process of the outer vortex ring (denoted as OV0) in annular starting jets has been studied numerically at stroke ratio $3\leqslant L_m/D\leqslant 8$, $\beta \leqslant 0.8$ and Reynolds number $400\leqslant Re_{\triangle R}\leqslant 1400$, where $D$ is the outer diameter of orifice, $L_m$ is the length of the fluid column, $\beta$ and $\triangle R$ are the ratio and difference between inner and outer radii of the annular orifice, respectively. The initial formation process of OV0 is found to be similar to that of the leading vortex ring in a circular starting jet, but the circulation strength is relatively lower and decreases gradually with increasing $\beta$. The pinch-off process will also appear after OV0 grows to a certain size but is different from that of the circular starting jet. On one hand, OV0 is stretched and deformed by the strain field generated by the trailing jet's instability, and vorticity would be shed. On the other hand, OV0 accelerates the irrotational fluids around it under viscous action so as to form the induced velocity field, which would consume energy causing it to shed vorticity further under the limit of the Kelvin–Benjamin variational principle. Furthermore, OV0 would eventually become a stable vortex ring whose non-dimensional circulation ($\varGamma /(U_{0max}D$)) is found to be between 0.59–0.62 and it would not change with different $L_m/D$ at $\beta =0.5$, which is much less than the 2–2.5 of circular starting jets.

JFM classification

Wakes/Jets: Jets Vortex Flows: Vortex interactions
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 949 , 25 October 2022 , A47
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

Acheson, D.J. 1991 Elementary fluid dynamics. J. Acoust. Sco. Am. 89, 3020–3020.CrossRefGoogle Scholar
Alben, S. 2021 Collective locomotion of two-dimensional lattices of flapping plates. Part 1. Numerical method, single-plate case and lattice input power. J. Fluid Mech. 915, A20.CrossRefGoogle Scholar
Bi, X. & Zhu, Q. 2019 Fluid-structure investigation of a squid-inspired swimmer. Phys. Fluids 31 (10), 101901.CrossRefGoogle Scholar
Crow, S.C.. & Champagne, F.H.. 1971 Orderly structure in jet turbulence. J. Fluid Mech. 48 (3), 547–591.CrossRefGoogle Scholar
Cummins, C., Seale, M., Macente, A., Certini, D., Mastropaolo, E., Viola, I.M. & Nakayama, N. 2018 A separated vortex ring underlies the flight of the dandelion. Nature 562 (7727), 414–418.CrossRefGoogle ScholarPubMed
Didden, N. 1979 On the formation of vortex rings: rolling-up and production of circulation. Z. Angew. Math. Phys. 30 (1), 101–116.CrossRefGoogle Scholar
Gao, L., Wang, X., Yu, S.C.M. & Chyu, M.K. 2020 Development of the impulse and thrust for laminar starting jets with finite discharged volume. J. Fluid Mech. 902, A27.CrossRefGoogle Scholar
Gao, L. & Yu, S.C.M. 2010 A model for the pinch-off process of the leading vortex ring in a starting jet. J. Fluid Mech. 656, 205–222.CrossRefGoogle Scholar
Gao, L. & Yu, S.C.M. 2012 Development of the trailing shear layer in a starting jet during pinch-off. J. Fluid Mech. 700, 382–405.CrossRefGoogle Scholar
Gao, L. & Yu, S.C.M. 2016 Vortex ring formation in starting forced plumes with negative and positive buoyancy. Phys. Fluids 28 (11), 113601.CrossRefGoogle Scholar
Gao, L., Yu, S.C.M., Ai, J.J. & Law, A.W.K. 2008 Circulation and energy of the leading vortex ring in a gravity-driven starting jet. Phys. Fluids 20 (9), 093604.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. 1988 The formation of vortex rings. Phys. Fluids 31 (12), 3532–3542.CrossRefGoogle Scholar
James, S. & Madnia, C.K. 1996 Direct numerical simulation of a laminar vortex ring. Phys. Fluids 8 (9), 2400–2414.CrossRefGoogle Scholar
Kambe, T. & Takao, T. 1971 Motion of distorted vortex rings. J. Phys. Soc. Japan 31 (2), 591–599.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. 2021 A new kinematic criterion for vortex ring pinch-off. Phys. Fluids 33 (3), 037120.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
Lim, T.T. & Nickels, T.B. 1995 Vortex rings. In Fluid Vortices (ed. S.I. Green), pp. 95–153. Springer.CrossRefGoogle Scholar
Limbourg, R. & Nedić, J. 2021 a An extended model for orifice starting jets. Phys. Fluids 33 (6), 067109.CrossRefGoogle Scholar
Limbourg, R. & Nedić, J. 2021 b Formation of an orifice-generated vortex ring. J. Fluid Mech. 913, A29.CrossRefGoogle Scholar
Marugán-Cruz, C., Rodríguez-Rodríguez, J. & Martínez-Bazán, C. 2013 Formation regimes of vortex rings in negatively buoyant starting jets. J. Fluid Mech. 716, 470–486.CrossRefGoogle Scholar
Meleshko, V.V. 2010 Coaxial axisymmetric vortex rings: 150 years after Helmholtz. Theor. Comput. Fluid Dyn. 24 (1), 403–431.CrossRefGoogle Scholar
Mohseni, K., Ran, H. & Colonius, T. 2001 Numerical experiments on vortex ring formation. J. Fluid Mech. 430, 267–282.CrossRefGoogle Scholar
Nitsche, M. 2001 Self-similar shedding of vortex rings. J. Fluid Mech. 435, 397–407.CrossRefGoogle Scholar
Norbury, J. 1973 A family of steady vortex rings. J. Fluid Mech. 57 (3), 417–431.CrossRefGoogle Scholar
Orlandi, P. & Verzicco, R. 1993 Vortex rings impinging on walls: axisymmetric and three-dimensional simulations. J. Fluid Mech. 256, 615–646.CrossRefGoogle Scholar
Pullin, D.I. 1979 Vortex ring formation at tube and orifice openings. Phys. Fluids 22 (3), 401–403.CrossRefGoogle Scholar
Riley, N. 1993 On the behavior of pairs of vortex rings. Q. J. Mech. Appl. Maths 46, 521–539.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
Sadri, V. & Krueger, P.S. 2017 Formation and behavior of counter-rotating vortex rings. Theor. Comput. Fluid Dyn. 31 (4), 369–390.CrossRefGoogle Scholar
Saffman, P.G. 1975 On the formation of vortex rings. Stud. Appl. Maths 54 (3), 261–268.CrossRefGoogle Scholar
Shariff, K. & Leonard, A. 1992 Vortex rings. Annu. Rev. Fluid Mech. 24 (1), 235–279.CrossRefGoogle Scholar
Shusser, M. & Gharib, M. 2000 Energy and velocity of a forming vortex ring. Phys. Fluids 12 (3), 618–621.CrossRefGoogle Scholar
Shusser, M., Rosenfeld, M., Dabiri, J.O. & Gharib, M. 2006 Effect of time-dependent piston velocity program on vortex ring formation in a piston/cylinder arrangement. Phys. Fluids 18 (3), 033601.CrossRefGoogle Scholar
Trieling, R.R., Beckers, M. & Van Heijst, G.J.F. 1997 Dynamics of monopolar vortices in a strain flow. J. Fluid Mech. 345, 165–201.CrossRefGoogle Scholar
Wakelin, S.L. & Riley, N. 1997 On the formation and propagation of vortex rings and pairs of vortex rings. J. Fluid Mech. 332, 121–139.CrossRefGoogle Scholar
Weidman, P.D. & Riley, N. 1993 Vortex ring pairs: numerical simulation and experiment. J. Fluid Mech. 257, 311–337.CrossRefGoogle Scholar
Weigand, A. & Gharib, M. 1997 On the evolution of laminar vortex rings. Exp. Fluids 22 (6), 447–457.CrossRefGoogle Scholar
Widnall, S.E., Bliss, D.B. & Tsai, C.Y. 1974 The instability of short waves on a vortex ring. J. Fluid Mech. 66 (1), 35–47.CrossRefGoogle Scholar
Yamada, H. & Matsui, T. 1978 Preliminary study of mutual slip-through of a pair of vortices. Phys. Fluids 21 (2), 292–294.CrossRefGoogle Scholar
Yamada, H. & Matsui, T. 1979 Mutual slip-through of a pair of vortex rings. Phys. Fluids 22 (7), 1245–1249.CrossRefGoogle Scholar