Hostname: page-component-7479d7b7d-jwnkl Total loading time: 0 Render date: 2024-07-12T08:30:24.011Z Has data issue: false hasContentIssue false
  • English
  • Français

Head-on collisions of vortex rings upon round cylinders

Published online by Cambridge University Press:  08 November 2017

T. H. New Open the ORCID record for T. H. New [Opens in a new window]  and
B. Zang
T. H. New
Affiliation:
School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, 639798, Singapore
B. Zang
Affiliation:
School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, 639798, Singapore
Get access Rights & Permissions [Opens in a new window]

Abstract

Vortical structures and behaviour associated with vortex-ring collisions upon round cylinders with different cylinder-to-vortex-ring diameter ratios were studied using laser-induced fluorescence and time-resolved particle-image velocimetry techniques. Circular vortex rings of Reynolds number 4000 and three diameter ratios of $D/d=1$, 2 and 4 were considered in the present investigation. Results reveal that the collision behaviour is very different from that associated with flat surfaces, in which vortex disconnection and reconnection processes caused by the strong interactions between primary and secondary vortex rings produce small-scale vortex ringlets that eject away from the cylinders. For the cylinder with the largest diameter ratio used here, these vortex ringlets move towards each other along the collision axis, where they eventually collide to produce a vortex dipole that propagates upstream. However, as the diameter ratio decreases, these vortex ringlets are produced further away from the collision axis, which results in them ejecting away from the cylinder at increasingly larger angles relative to the collision axis. Trajectories of key vortex cores were extracted from the experimental results to demonstrate quantitatively the strong sensitivity of these vortical motions upon the diameter ratio. Furthermore, significant differences in the primary vortex-ring circulation along convex surfaces and straight edges after the collisions are observed. In particular, vortex flow models are presented here to better illustrate the highly three-dimensional flow dynamics of the collision behaviour, as well as highlighting the strong dependency of the secondary vortex-ring formation, vortex disconnection/reconnection processes, and ejection of the resulting vortex ringlets upon the diameter ratio. As such, these results are expected to shed more light on the more general scenario of vortex-ring collisions upon arbitrarily contoured solid boundaries.

JFM classification

Vortex Flows: Vortex dynamics Vortex Flows: Vortex Flows Vortex Flows: Vortex interactions
Type
Papers
Information
Journal of Fluid Mechanics , Volume 833 , 25 December 2017 , pp. 648 - 676
Copyright
© 2017 Cambridge University Press 

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.)

References

Afanasyev, Y. D. 2006 Formation of vortex dipoles. Phys. Fluids 18 (3), 037103.CrossRefGoogle Scholar
Chan, T. L., Leung, C. W., Jambunathan, K., Ashforth-Frost, S., Zhou, Y. & Liu, M. H. 2002 Heat transfer characteristics of a slot jet impinging on a semi-circular convex surface. Intl J. Heat Mass Trans. 45 (5), 993–1006.CrossRefGoogle Scholar
Cheng, M., Lou, J. & Lim, T. T. 2016 Evolution of an elliptic vortex ring in a viscous fluid. Phys. Fluids 28 (3), 037104.CrossRefGoogle Scholar
Cheng, M., Lou, J. & Luo, L.-S. 2010 Numerical study of a vortex ring impacting a flat wall. J. Fluid Mech. 660, 430–455.CrossRefGoogle Scholar
Chu, C.-C., Wang, C.-T. & Chang, C.-C. 1995 A vortex ring impinging on a solid plane surface vortex structure and surface force. Phys. Fluids 7 (6), 1391–1401.CrossRefGoogle Scholar
Cornaro, C., Fleischer, A. S., Rounds, M. & Goldstein, R. J. 2001 Jet impingement cooling of a convex semi-cylindrical surface. Intl J. Therm. Sci. 40 (10), 890–898.CrossRefGoogle Scholar
Couch, L. D. & Krueger, P. S. 2011 Experimental investigation of vortex rings impinging on inclined surfaces. Exp. Fluids 51 (4), 1123–1138.CrossRefGoogle Scholar
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
Fabris, D., Liepmann, D. & Marcus, D. 1996 Quantitative experimental and numerical investigation of a vortex ring impinging on a wall. Phys. Fluids 8 (10), 2640–2649.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
Gau, C. & Chung, C. M. 1991 Surface curvature effect on slot-air-jet impingement cooling flow and heat transfer process. Trans. ASME J. Heat Transfer 113 (4), 858–864.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
Gharib, M. & Weigand, A. 1996 Experimental studies of vortex disconnection and connection at a free surface. J. Fluid Mech. 321, 59–86.CrossRefGoogle Scholar
Glezer, A. 1988 The formation of vortex rings. Phys. Fluids 31 (12), 3532–3542.CrossRefGoogle Scholar
Harris, D. M. & Williamson, C. H. K. 2012 Instability of secondary vortices generated by a vortex pair in ground effect. J. Fluid Mech. 700, 148–186.CrossRefGoogle Scholar
Homa, J., Lucas, M. & Rockwell, D. 1988 Interaction of impulsively generated vortex pairs with bodies. J. Fluid Mech. 197, 571–594.CrossRefGoogle Scholar
Kaplanski, F., Sazhin, S. S., Fukumoto, Y., Steven, B. & Heikal, M. 2009 A generalized vortex ring model. J. Fluid Mech. 622, 233–258.CrossRefGoogle Scholar
Kida, S. & Takaoka, M. 1994 Vortex reconnection. Annu. Rev. Fluid Mech. 26 (1), 169–177.CrossRefGoogle Scholar
Krueger, P. S., Dabiri, J. O. & Gharib, M. 2006 The formation number of vortex rings formed in uniform background co-flow. J. Fluid Mech. 556, 147–166.CrossRefGoogle Scholar
Leweke, T., Le Dizés, S. & Williamson, C. H. K. 2016 Dynamics and instablilities of vortex-pairs. Annu. Rev. Fluid Mech. 48, 507–541.CrossRefGoogle Scholar
Lim, T. T. 1989 An experimental study of a vortex ring interacting with an inclined wall. Exp. Fluids 7 (7), 453–463.CrossRefGoogle Scholar
Lim, T. T. 2012 Dye and smoke visualization. In Flow Visualization: Techniques and Examples (ed. Smits, A. J. & Lim, T. T.), chap. 3, pp. 47–78. Imperial College Press.CrossRefGoogle Scholar
Lim, T. T., New, T. H. & Luo, S. C. 2001 On the development of large-scale structures of a jet normal to a cross flow. Phys. Fluids 13 (3), 770–775.CrossRefGoogle Scholar
Lim, T. T., Nickels, T. B. & Chong, M. S. 1991 A note on the cause of rebound in the head-on collision of a vortex ring with a wall. Exp. Fluids 12 (1–2), 41–48.CrossRefGoogle Scholar
Long, J. & New, T. H. 2015 A DPIV study on the effects of separation distance upon the vortical behaviour of jet cylinder impingements. Exp. Fluids 56, 153.CrossRefGoogle Scholar
Maxworthy, T. 1972 The structure and stability of vortex rings. J. Fluid Mech. 51 (1), 15–32.CrossRefGoogle Scholar
McDaniel, C. S. & Webb, B. W. 2000 Slot jet impingement heat transfer from circular cylinders. Intl J. Heat Mass Transfer 43 (11), 1975–1985.CrossRefGoogle Scholar
Mohseni, K., Ran, H. & Colonius, T. 2001 Numerical experiments on vortex ring formation. J. Fluid Mech. 430, 267–282.CrossRefGoogle Scholar
Naitoh, T., Sun, B. & Yamada, H. 1995 A vortex ring travelling across a thin circular cylinder. Fluid Dyn. Res. 15 (1), 43.CrossRefGoogle Scholar
New, T. H. 2009 An experimental study on jets issuing from elliptic inclined nozzles. Exp. Fluids 46 (6), 1139–1157.CrossRefGoogle Scholar
New, T. H. & Long, J. 2015 Dynamics of laminar circular jet impingement upon convex cylinders. Phys. Fluids 27 (2), 024109.CrossRefGoogle Scholar
New, T. H., Shi, S. & Liu, Y. 2013 Cylinder-wall interference effects on finite-length wavy cylinders at subcritical Reynolds number flows. Exp. Fluids 54 (10), 1–24.CrossRefGoogle Scholar
New, T. H., Shi, S. & Liu, Y. 2015 On the flow behaviour of confined finite-length wavy cylinders. J. Fluids Struct. 54, 281–296.CrossRefGoogle Scholar
New, T. H., Shi, S. & Zang, B. 2016 Some observations on vortex-ring collisions upon inclined surfaces. Exp. Fluids 57 (6), 1–18.CrossRefGoogle Scholar
New, T. H. & Tsovolos, D. 2009 Influence of nozzle sharpness on the flow fields of V-notched nozzle jets. Phys. Fluids 21 (8), 084107.CrossRefGoogle Scholar
New, T. H. & Tsovolos, D. 2011 On the vortical structures and behaviour of inclined elliptic jets. Eur. J. Mech. (B/Fluids) 30 (4), 437–450.CrossRefGoogle Scholar
Orlandi, P. 1990 Vortex dipole rebound from a wall. Phys. Fluids A 2 (8), 1429–1436.CrossRefGoogle Scholar
Orlandi, P. 1993 Vortex dipoles impinging on circular cylinders. Phys. Fluids A 5 (9), 2196–2206.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
Öztekin, E., Aydin, O. & Avcı, M. 2013 Heat transfer in a turbulent slot jet flow impinging on concave surfaces. Intl Commun. Heat Mass Transfer 44, 77–82.CrossRefGoogle Scholar
Ren, H., Zhang, G. & Guan, H. 2015 Three-dimensional numerical simulation of a vortex ring impinging on a circular cylinder. Fluid Dyn. Res. 47 (2), 025507.CrossRefGoogle Scholar
Saffman, P. G. 1970 The velocity of viscous vortex rings. Stud. Appl. Maths 49 (4), 371–380.CrossRefGoogle Scholar
Sharif, M. A. R. & Mothe, K. K. 2010 Parametric study of turbulent slot-jet impingement heat transfer from concave cylindrical surfaces. Intl J. Therm. Sci. 49 (2), 428–442.CrossRefGoogle Scholar
Shi, S. & New, T. H. 2013 Some observations in the vortex-turning behaviour of noncircular inclined jets. Exp. Fluids 54 (11), 1–11.CrossRefGoogle Scholar
Singh, D., Premachandran, B. & Kohli, S. 2013 Experimental and numerical investigation of jet impingement cooling of a circular cylinder. Intl J. Heat Mass Transfer 60, 672–688.CrossRefGoogle Scholar
Sullivan, I. S., Niemela, J. J., Hershberger, R. E., Bolster, D. & Donnelly, R. J. 2008 Dynamics of thin vortex rings. J. Fluid Mech. 609, 319–347.CrossRefGoogle Scholar
Swearingen, J. D., Crouch, J. D. & Handler, R. A. 1995 Dynamics and stability of a vortex ring impacting a solid boundary. J. Fluid Mech. 297, 1–28.CrossRefGoogle Scholar
Verzicco, R., Flor, J. B., Van Heijst, G. J. F. & Orlandi, P. 1995 Numerical and experimental study of the interaction between a vortex dipole and a circular cylinder. Exp. Fluids 18 (3), 153–163.CrossRefGoogle Scholar
Verzicco, R. & Orlandi, P. 1994 Normal and oblique collisions of a vortex ring with a wall. Meccanica 29 (4), 383–391.CrossRefGoogle Scholar
Walker, J. D. A., Smith, C. R., Cerra, A. W. & Doligalski, T. L. 1987 The impact of a vortex ring on a wall. J. Fluid Mech. 181, 99–140.CrossRefGoogle Scholar
Weigand, A. & Gharib, M. 1997 On the evolution of laminar vortex rings. Exp. Fluids 22, 447–457.CrossRefGoogle Scholar
Yang, Y.-Z., Wei, T.-C. & Wang, Y.-H. 2011 Numerical study of turbulent slot jet impingement cooling on a semi-circular concave surface. Intl J. Heat Mass Transfer 54 (1), 482–489.CrossRefGoogle Scholar
Yu, S. C. M., Ai, J. J., Gao, L. & Law, A. C. K. 2008 Vortex formation process of a starting square jet. AIAA J. 46 (1), 223–231.CrossRefGoogle Scholar

New et al. supplementary movie 1

Vortex-ring collision with D=4d round cylinder convex surface

Download New et al. supplementary movie 1(Video)
Video 3.4 MB

New et al. supplementary movie 2

Vortex-ring collision with D=2d round cylinder convex surface

Download New et al. supplementary movie 2(Video)
Video 3.2 MB

New et al. supplementary movie 3

Vortex-ring collision with D=1d round cylinder convex surface

Download New et al. supplementary movie 3(Video)
Video 3.7 MB