Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-23T03:05:53.521Z Has data issue: false hasContentIssue false
  • English
  • Français

Dynamics and Instability of a Vortex Ring Impinging on a Wall

Part of: Incompressible viscous fluids Turbulence

Published online by Cambridge University Press:  15 October 2015

Heng Ren  and
Xi-Yun Lu
Heng Ren
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, China
Xi-Yun Lu*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, China
*
*Corresponding author. Email address: [email protected] (X.-Y. Lu)
Get access

Abstract

Dynamics and instability of a vortex ring impinging on a wall were investigated by means of large eddy simulation for two vortex core thicknesses corresponding to thin and thick vortex rings. Various fundamental mechanisms dictating the flow behaviors, such as evolution of vortical structures, formation of vortices wrapping around vortex rings, instability and breakdown of vortex rings, and transition from laminar to turbulent state, have been studied systematically. The evolution of vortical structures is elucidated and the formation of the loop-like and hair-pin vortices wrapping around the vortex rings (called briefly wrapping vortices) is clarified. Analysis of the enstrophy of wrapping vortices and turbulent kinetic energy (TKE) in flow field indicates that the formation and evolution of wrapping vortices are closely associated with the flow transition to turbulent state. It is found that the temporal development of wrapping vortices and the growth rate of axial flow generated around the circumference of the core region for the thin ring are faster than those for the thick ring. The azimuthal instabilities of primary and secondary vortex rings are analyzed and the development of modal energies is investigated to reveal the flow transition to turbulent state. The modal energy decay follows a characteristic –5/3 power law, indicating that the vortical flow has become turbulence. Moreover, it is identified that the TKE with a major contribution of the azimuthal component is mainly distributed in the core region of vortex rings. The results obtained in this study provide physical insight of the mechanisms relevant to the vortical flow evolution from laminar to turbulent state.

Keywords

Large eddy simulationvortex ringvortical structureinstabilityturbulent state

MSC classification

Secondary: 76F65: Direct numerical and large eddy simulation of turbulence 76D17: Viscous vortex flows 76F06: Transition to turbulence
Type
Research Article
Information
Communications in Computational Physics , Volume 18 , Issue 4 , October 2015 , pp. 1122 - 1146
Copyright
Copyright © Global-Science Press 2015 

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

[1]Shariff, K. and Leonard, A., rings, Vortex, Annu. Rev. Fluid Mech., 24 (1992), 235–279.Google Scholar
[2]Walker, J. D. A., Smith, C. R., Cerra, A. W. and Doligalski, T. L., The impact of a vortex ring on a wall, J. Fluid Mech., 181 (1987), 99–140.Google Scholar
[3]Orlandi, P. and Verzicco, R., Vortex rings impinging on walls: axisymmetric and three-dimensional simulations, J. Fluid Mech., 256 (1993), 615–646.Google Scholar
[4]Archer, P. J., Thomas, T. G. and Coleman, G. N., The instability of a vortex ring impinging on a free surface, J. Fluid Mech., 642 (2010), 79–94.Google Scholar
[5]Boldes, U. and Ferreri, J. C., Behavior of vortex rings in the vicinity of a wall, Phys. Fluids, 16 (1973), 2005–2006.Google Scholar
[6]Orlandi, P., Vortex dipole rebound from a wall, Phys. Fluids A, 2 (1990), 1429–1436.CrossRefGoogle Scholar
[7]Lim, T. T., Nickels, T. B. and Chong, M. S., A note on the cause of rebound in the head-on collision of a vortex ring with a wall, Exp. Fluids, 12 (1991), 41–48.Google Scholar
[8]Chu, C. C., Wang, C. T. and Hsieh, C. S., An experimental investigation of vortex motions near surfaces, Phys. Fluids A, 5 (1993), 662–676.CrossRefGoogle Scholar
[9]Chu, C. C., Wang, C. T. and Chang, C. C., A vortex ring impinging on a solid plane surface-vortex structure and surface force, Phys. Fluids, 7 (1995), 1391–1401.Google Scholar
[10]Fabris, D., Liepmann, D. and Marcus, D., Quantitative experimental and numerical investigation of a vortex ring impinging on a wall, Phys. Fluids, 8 (1996), 2640–2649.CrossRefGoogle Scholar
[11]Cheng, M., Lou, J. and Luo, L. S., Numerical study of a vortex ring impacting a flat wall, J. Fluid Mech., 660 (2010), 430–455.Google Scholar
[12]Couch, L. D. and Krueger, P. S., Experimental investigation of vortex rings impinging on inclined surfaces, Exp. Fluids, 51 (2011), 1123–1138.Google Scholar
[13]Krutzsch, C., Uber eine experimentell beobachtete erscheining an werbelringen bei ehrer translatorischen beivegung in weklechin, flussigheiter, Annln Phys., 5 (1939), 497–523.CrossRefGoogle Scholar
[14]Crow, S. C., Stability theory for a pair of trailing vortices, AIAA J., 8 (1970), 2172–2179.CrossRefGoogle Scholar
[15]Widnall, S. E., Bliss, D. B. and Tsai, C. Y., The instability of short waves on a vortex ring, J. Fluid Mech., 66 (1974), 35–47.Google Scholar
[16]Widnall, S. E. and Tsai, C. Y., The instability of the thin vortex ring of constant vorticity, Phil. Trans. R. Soc. Lond. A, 287 (1977), 273–305.Google Scholar
[17]Maxworthy, T., The structure and stability of vortex rings, J. Fluid Mech., 51 (1972), 15–32.CrossRefGoogle Scholar
[18]Maxworthy, T., Turbulent vortex rings, J. Fluid Mech., 64 (1974), 227–239.Google Scholar
[19]Maxworthy, T., Some experimental studies of vortex rings, J. Fluid Mech., 81 (1977), 465–495.Google Scholar
[20]Widnall, S. E. and Sullivan, J. P., On the stability of vortex rings, Proc. R. Soc. Lond. A, 332 (1973), 335–353.Google Scholar
[21]Dazin, A., Dupont, P. and Stanislas, M., Experimental characterization of the instability of the vortex ring. Part I: Linear phase, Exp. Fluids, 40 (2006a), 383–399.Google Scholar
[22]Dazin, A., Dupont, P. and Stanislas, M., Experimental characterization of the instability of the vortex ring. Part II: Non-linear phase, Exp. Fluids, 41 (2006b), 401–413.Google Scholar
[23]Gan, L., Nickels, T. B. and Dawson, J. R., An experimental study of a turbulent vortex ring: a three-dimensional representation, Exp. Fluids, 51 (2011), 1493–1507.Google Scholar
[24]Orlandi, P. and Verzicco, R., Identification of zones in a free evolving vortex ring, Appl. Sci. Res., 53 (1994), 387–399.Google Scholar
[25]Shariff, K., Verzicco, R. and Orlandi, P., A numerical study of three-dimensional vortex ring instabilities: viscous corrections and early nonlinear stage, J. Fluid Mech., 279 (1994), 351–375.Google Scholar
[26]Bergdorf, M., Koumoutsakos, P. and Leonard, A., Direct numerical simulation of vortex rings at Re Γ =7500, J. Fluid Mech., 581 (2007), 495–505.CrossRefGoogle Scholar
[27]Archer, P. J., Thomas, T. G. and Coleman, G. N., Direct numerical simulation of vortex ring evolution from the laminar to the early turbulent regime, J. Fluid Mech., 598 (2008), 201–226.Google Scholar
[28]Swearingen, J. D., Crouch, J. D. and Handler, R. A., Dynamics and stability of a vortex ring impacting a solid boundary, J. Fluid Mech., 297 (1995), 1–28.Google Scholar
[29]Masuda, N., Yoshida, J., Ito, B., Furuya, T. and Sana, O., Collision of a vortex ring on granular material. Part I. Interaction of the vortex ring with the granular layer, Fluid Dyn. Res., 44 (2012), 015501.Google Scholar
[30]Yoshida, J., Masuda, N., Ito, B., Furuya, T. and Sana, O., Collision of a vortex ring on granular material. Part II. Erosion of the granular layer, Fluid Dyn. Res., 44 (2012), 015502.CrossRefGoogle Scholar
[31]Sreedhar, M. and Ragab, S., Large eddy simulation of longitudinal stationary vortices, Phys. Fluids, 6 (1994), 2501–2514.Google Scholar
[32]Mansfield, J. R., Knio, O. M. and Meneveau, C., Dynamic LES of colliding vortex rings using a 3D vortex method, J. Comput. Phys., 152 (1999), pp. 305–345.Google Scholar
[33]Faddy, J. M. and Pullin, D. I., Flow structure in a model of aircraft trailing vortices, Phys. Fluids, 17 (2005), 085106.Google Scholar
[34]Ragab, S. and Sreedhar, M., Numerical simulation of vortices with axial velocity deficits, Phys. Fluids, 7 (1995), 549–558.Google Scholar
[35]Lu, X.-Y., Wang, S.-W., Sung, H.-G., Hsieh, S.-Y. and Yang, V., Large-eddy simulations of turbulent swirling flows injected into a dump chamber, J. Fluid Mech., 527 (2005), 171–195.Google Scholar
[36]Xu, C.-Y., Chen, L.-W. and Lu, X.-Y., Large eddy simulation of the compressible flow past a wavy cylinder, J. Fluid Mech., 665 (2010), 238–273.Google Scholar
[37]Chen, L.-W., Xu, C.-Y. and Lu, X.-Y., Numerical investigation of the compressible flow past an aerofoil, J. Fluid Mech., 643 (2010), 97–126.Google Scholar
[38]Chen, L.-W., Wang, G.-L. and Lu, X.-Y., Numerical investigation of a jet from a blunt body opposing a supersonic flow, J. Fluid Mech., 684 (2011), 85–110.CrossRefGoogle Scholar
[39]Saffman, P. G., The number of waves on unstable vortex rings, J. Fluid Mech., 84 (1978), 625–639.Google Scholar
[40]Krishnamoorthy, S. and Marshall, J. S., Three-dimensional blade-vortex interaction in the strong vortex regime, Phys. Fluids, 10 (1998), 2828–2845.Google Scholar
[41]Krishnamoorthy, S., Gossler, A. A. and Marshall, J. S., Normal vortex interaction with a circular cylinder, AAIA J, 37 (1999), 50–57.Google Scholar
[42]Gossler, A. A. and Marshall, J. S., Simulation of normal vortex-cylinder interaction in a viscous fluid, J. Fluid Mech., 431 (2001), 371–405.CrossRefGoogle Scholar
[43]Hon, T. L. and Walker, J. D. A., Evolution of hairpin vortices in a shear flow, Comput. Fluids, 20 (1991), 343–358.Google Scholar
[44]Adrian, R. J., Hairpin vortex organization in wall turbulence, Phys. Fluids, 19 (2007), 041301.Google Scholar
[45]Liu, C. Q. and Chen, L., Parallel DNS for vortex structure of late stages of flow transition, Comput. Fluids, 45 (2011), 129–137.Google Scholar
[46]Wu, J. Z., Ma, H. Y. and Zhou, M. D., Vorticity and Vortex Dynamics, Springer, 2006.Google Scholar
[47]Naitoh, T., Fukuda, N., Gotoh, T., Yamada, H. and Nakajima, K., Experimental study of axial flow in a vortex ring, Phys. Fluids, 14 (2002), 143–149.Google Scholar
[48]Laporte, F. and Corjon, A., Direct numerical simulations of the elliptic instability of a vortex pair, Phys. Fluids, 12 (2000), 1016–1031.Google Scholar
[49]de Sousa, P. J. F., Three-dimensional instability on the interaction between a vortex and a stationary sphere, Theor. Comput. Fluid Dyn., 26 (2012), 391–399.Google Scholar
[50]Rees, W. M., Hussain, F. and Koumoutsakos, P., Vortex tube reconnection at Re =104, Phys. Fluids, 24 (2012), 075105.Google Scholar