Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-28T09:37:41.928Z Has data issue: false hasContentIssue false
  • English
  • Français

Collision of vortex rings upon V-walls

Published online by Cambridge University Press:  14 July 2020

T. H. New Open the ORCID record for T. H. New [Opens in a new window] ,
J. Long ,
B. Zang  and
Shengxian Shi Open the ORCID record for Shengxian Shi [Opens in a new window]
T. H. New*
Affiliation:
School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore639798, Republic of Singapore
J. Long
Affiliation:
School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore639798, Republic of Singapore
B. Zang
Affiliation:
School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore639798, Republic of Singapore Department of Aerospace Engineering, University of Bristol, BristolBS8 1TR, UK
Shengxian Shi
Affiliation:
School of Mechanical Engineering, Shanghai Jiao Tong University, 800 Dong Chuan Road, 200240Shanghai, PR China
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

A study on ${Re} =2000$ and 4000 vortex rings colliding with V-walls with included angles of $\theta =30^{\circ }$ to 120$^{\circ }$ has been conducted. Along the valley plane, higher Reynolds numbers and/or included angles of $\theta \leqslant 60^{\circ }$ lead to secondary/tertiary vortex-ring cores leapfrogging past the primary vortex-ring cores. The boundary layers upstream of the latter separate and the secondary/tertiary vortex-ring cores pair up with these wall-separated vortices to form small daisy-chained vortex dipoles. Along the orthogonal plane, primary vortex-ring cores grow bulbous and incoherent after collisions, especially as the included angle reduces. Secondary and tertiary vortex-ring core formations along this plane also lag those along the valley plane, indicating that they form by propagating from the wall surfaces to the orthogonal plane as the primary vortex ring gradually comes into contact with the entire V-wall. Circulation results show significant variations between the valley and orthogonal plane, and reinforce the notion that the collision behaviour for $\theta \leqslant 60^{\circ }$ is distinctively different from those at larger included angles. Vortex-core trajectories are compared to those for inclined-wall collisions, and secondary vortex-ring cores are found to initiate earlier for the V-walls, postulated to be a result of the opposing circumferential flows caused by the simultaneous collisions of both primary vortex-ring cores with the V-wall surfaces. These circumferential flows produce a bi-helical flow mode (Lim, Exp. Fluids, vol. 7, issue 7, 1989, pp. 453–463) that sees higher vortex compression levels along the orthogonal plane, which limit vortex stretching along the wall surfaces and produce secondary vortex rings earlier. Lastly, vortex structures and behaviour of the present collisions are compared to those associated with flat/inclined walls and round-cylinder-based collisions for a more systematic understanding of their differences.

JFM classification

Vortex Flows: Vortex dynamics Vortex Flows: Vortex interactions Boundary Layers: Boundary layer separation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 899 , 25 September 2020 , A2
Copyright
© The Author(s), 2020. Published by 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

REFERENCES

Adhikari, D. & Lim, T. T. 2009 The impact of a vortex ring on a porous screen. Fluid Dyn. Res. 41 (5), 051404.CrossRefGoogle Scholar
Amitay, M., Smith, D. R., Kibens, V., Parekh, D. E. & Glezer, A. 2001 Aerodynamic flow control over an unconventional airfoil using synthetic jet actuators. AIAA J. 39 (3), 361–370.CrossRefGoogle Scholar
An, D., Warning, A., Yancey, K. G., Chang, C.-T., Kern, V. R., Datta, A. K., Steen, P. H., Luo, D. & Ma, M. 2016 Mass production of shaped particles through vortex ring freezing. Nat. Commun. 7, 12401.CrossRefGoogle ScholarPubMed
Arévalo, G., Hernández, R. H., Nicot, C. & Plaza, F. 2007 Vortex ring head-on collision with a heated vertical plate. Phys. Fluids 19 (8), 083603.CrossRefGoogle Scholar
Cheng, M., Lou, J. & Lim, T. T. 2014 A numerical study of a vortex ring impacting a permeable wall. Phys. Fluids 26 (10), 103602.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
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
Feng, H., Kaganovskiy, L. & Krasny, R. 2009 Azimuthal instability of a vortex ring computed by a vortex sheet panel method. Fluid Dyn. Res. 41 (5), 051405.CrossRefGoogle Scholar
Gan, L., Dawson, J. R. & Nickels, T. B. 2012 On the drag of turbulent vortex rings. J. Fluid Mech. 709, 85–105.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
Gharib, M., Rambod, E. & Shariff, K. 1998 A universal time scale for vortex ring formation. J. Fluid Mech. 360, 121–140.CrossRefGoogle Scholar
Gilarranz, J. L., Traub, L. W. & Rediniotis, O. K. 2005 A new class of synthetic jet actuators. Part 2. application to flow separation control. J. Fluids Engng 127 (2), 377–387.CrossRefGoogle Scholar
Glezer, A. 1988 The formation of vortex rings. Phys. Fluids 31 (12), 3532–3542.CrossRefGoogle Scholar
Glezer, A. & Coles, D. 1990 An experimental study of a turbulent vortex ring. J. Fluid Mech. 211, 243–283.CrossRefGoogle Scholar
Goldstein, R. J. & Franchett, M. E. 1988 Heat transfer from a flat surface to an oblique impinging jet. J. Heat Transfer 110 (1), 84–90.CrossRefGoogle Scholar
Hadžiabdić, M. & Hanjalić, K. 2008 Vortical structures and heat transfer in a round impinging jet. J. Fluid Mech. 596, 221–260.CrossRefGoogle Scholar
Heeg, R. S. & Riley, N. 1997 Simulations of the formation of an axisymmetric vortex ring. J. Fluid Mech. 339, 199–211.CrossRefGoogle Scholar
Hrynuk, J. T., Van Luipen, J. & Bohl, D. 2012 Flow visualization of a vortex ring interaction with porous surfaces. Phys. Fluids 24 (3), 037103.CrossRefGoogle Scholar
Hu, J. & Peterson, S. D. 2018 Vortex ring impingement on a wall with a coaxial aperture. Phys. Rev. Fluids 3 (8), 084701.CrossRefGoogle Scholar
Johnson, W. 2005 Model for vortex ring state influence on rotorcraft flight dynamics. Tech. Rep. NASA/TP-2005-213477.Google 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
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
Krueger, P. S., Paul, 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
Leishman, J. G.ordon, Bhagwat, Mahendra J & Ananthan, Shreyas 2004 The vortex ring state as a spatially and temporally developing wake instability. J. Am. Helicopter Soc. 49 (2), 160–175.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., 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
Mao, Xuerui & Hussain, F. 2017 Optimal transient growth on a vortex ring and its transition via cascade of ringlets. J. Fluid Mech. 832, 269–286.CrossRefGoogle Scholar
Mariani, R., Quinn, M. K., Kontis, K. & Marraffa, L. 2013 Shock-free compressible vortex rings impinging on a stationary surface: effects of surface angle variation. Exp. Therm Fluid Sci. 47, 126–142.CrossRefGoogle Scholar
Martin, H. 1977 Heat and mass transfer between impinging gas jets and solid surfaces. Adv. Heat Transfer 13, 1–60.CrossRefGoogle Scholar
Maxworthy, T. 1972 The structure and stability of vortex rings. J. Fluid Mech. 51 (1), 15–32.CrossRefGoogle Scholar
Minota, T., Nishida, M. & Lee, M. G. 1997 Shock formation by compressible vortex ring impinging on a wall. Fluid Dyn. Res. 21 (3), 139–157.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. 2001 Numerical experiments on vortex ring formation. J. Fluid Mech. 430, 267–282.CrossRefGoogle Scholar
Naaktgeboren, C., Krueger, P. S. & Lage, J. 2012 Interaction of a laminar vortex ring with a thin permeable screen. J. Fluid Mech. 707, 260–286.CrossRefGoogle Scholar
Naitoh, T., Banno, O. & Yamada, H. 2001 Longitudinal vortex structure in the flow field produced by a vortex ring impinging on a flat plate. Fluid Dyn. Res. 28 (1), 61.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. & Long, J. 2015 Dynamics of laminar circular jet impingement upon convex cylinders. Phys. Fluids 27 (2), 024109.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. & Zang, B. 2017 Head-on collisions of vortex rings upon round cylinders. J. Fluid Mech. 833, 648–676.CrossRefGoogle Scholar
New, T. H., Zang, B., Shi, S. & Long, J. 2018 Impact of vortex-rings upon v-walls. In 19th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics.Google Scholar
Newman, S., Brown, R., Perry, J., Lewis, S., Orchard, M. & Modha, A. 2001 Comparative numerical and experimental investigations of the vortex ring phenomenon in rotorcraft. In 57th Annual Forum of American Helicopter Society, pp. 242–262.Google 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
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
Ponitz, B., Sastuba, M. & Brücker, C. 2016 4D visualization study of a vortex ring life cycle using modal analyses. J. Vis. 19 (2), 237–259.CrossRefGoogle Scholar
Pullin, D. I. 1979 Vortex ring formation at tube and orifice openings. Phys. Fluids 22 (3), 401–403.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
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
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. & 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
Xu, Y. & Wang, J.-J. 2016 Flow structure evolution for laminar vortex rings impinging onto a fixed solid wall. Exp. Therm. Fluid Sci. 75, 211–219.CrossRefGoogle Scholar
Xu, Y., Wang, J.-J., Feng, L.-H., He, G.-S. & Wang, Z.-Y. 2018 Laminar vortex rings impinging onto porous walls with a constant porosity. J. Fluid Mech. 837, 729–764.CrossRefGoogle Scholar
You, D. & Moin, P. 2008 Active control of flow separation over an airfoil using synthetic jets. J. Fluids Struct. 24 (8), 1349–1357.CrossRefGoogle Scholar
Zhan, Y., Yan, N., Li, Y., Meng, Y., Wang, J., Zhang, N., Yu, Q. & Xia, H. 2017 Fabrication of graphene millimeter-vortex ring with excellent absorption via solution dripping and in-situ reduction method. Chem. Engng J. 327, 142–149.CrossRefGoogle Scholar

New et al. supplementary movie 1

Re=2000, θ=120°, valley-plane, 15FPS

Download New et al. supplementary movie 1(Video)
Video 9.9 MB

New et al. supplementary movie 2

Re=2000, θ=90°, valley-plane, 15FPS

Download New et al. supplementary movie 2(Video)
Video 11.7 MB

New et al. supplementary movie 3

Re=2000, θ=60°, valley-plane, 15FPS

Download New et al. supplementary movie 3(Video)
Video 11.9 MB

New et al. supplementary movie 4

Re=2000, θ=30°, valley-plane, 15FPS

Download New et al. supplementary movie 4(Video)
Video 5.7 MB

New et al. supplementary movie 5

Re=2000, θ=120°, orthogonal-plane, 15FPS

Download New et al. supplementary movie 5(Video)
Video 2.1 MB

New et al. supplementary movie 6

Re=2000, θ=90°, orthogonal-plane, 15FPS

Download New et al. supplementary movie 6(Video)
Video 2.5 MB

New et al. supplementary movie 7

Re=2000, θ=60°, orthogonal-plane, 15FPS

Download New et al. supplementary movie 7(Video)
Video 4.3 MB

New et al. supplementary movie 8

Re=2000, θ=30°, orthogonal-plane, 15FPS

Download New et al. supplementary movie 8(Video)
Video 7.6 MB