Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-16T11:07:53.893Z Has data issue: false hasContentIssue false
  • English
  • Français

Numerical Simulations of Two Coaxial Vortex Rings Head-on Collision

Part of: Optics, electromagnetic theory - General

Published online by Cambridge University Press:  27 May 2016

Hui Guan ,
Zhi-Jun Wei ,
Elizabeth Rumenova Rasolkova  and
Chui-Jie Wu
Hui Guan
Affiliation:
College of Meteorology and Oceanography, PLA University of Science and Technology, Nanjing 211101, China
Zhi-Jun Wei
Affiliation:
State Key Laboratory of Structural Analysis for Industrial Equipment, School of Aeronautics and Astronautics, Dalian University of Technology, Dalian 116024, China
Elizabeth Rumenova Rasolkova
Affiliation:
State Key Laboratory of Structural Analysis for Industrial Equipment, School of Aeronautics and Astronautics, Dalian University of Technology, Dalian 116024, China
Chui-Jie Wu*
Affiliation:
State Key Laboratory of Structural Analysis for Industrial Equipment, School of Aeronautics and Astronautics, Dalian University of Technology, Dalian 116024, China
*
*Corresponding author. Email:cjwudut@dlut.edu.cn (C. J. Wu)
Get access

Abstract

Vortex rings have been a subject of interest in vortex dynamics due to a plethora of physical phenomena revealed by their motions and interactions within a boundary. The present paper is devoted to physics of a head-on collision of two vortex rings in three dimensional space, simulated with a second order finite volume scheme and compressible. The scheme combines non-iterative approximate Riemann-solver and piecewise-parabolic reconstruction used in inviscid flux evaluation procedure. The computational results of vortex ring collisions capture several distinctive phenomena. In the early stages of the simulation, the rings propagate under their own self-induced motion. As the rings approach each other, their radii increase, followed by stretching and merging during the collision. Later, the two rings have merged into a single doughnut-shaped structure. This structure continues to extend in the radial direction, leaving a web of particles around the centers. At a later time, the formation of ringlets propagate radially away from the center of collision, and then the effects of instability involved leads to a reconnection in which small-scale ringlets are generated. In addition, it is shown that the scheme captures several experimentally observed features of the ring collisions, including a turbulent breakdown into small-scale structures and the generation of small-scale radially propagating vortex rings, due to the modification of the vorticity distribution, as a result of the entrainment of background vorticity and helicity by the vortex core, and their subsequent interaction.

Keywords

Three dimensional numerical simulationvortex ringcollisionlarge eddy-simulation

MSC classification

Secondary: 78A48: Composite media; random media
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 8 , Issue 4 , August 2016 , pp. 616 - 647
Copyright
Copyright © Global-Science Press 2016 

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]Lim, T. T. and Nickels, T. B., Instability and reconnection in the head-on collision of two vortex rings, Nature, 357 (1992), pp. 225–227.Google Scholar
[2]Akhmetov, and Gazizovich, D., Vortex Rings, Springer Science and Business Media, Berlin Heidelberg, 2009.Google Scholar
[3]Oshima, Y., Head-on collision of two vortex rings, J. Phys. Soc. Japan, 44 (1978), pp. 328–331.CrossRefGoogle Scholar
[4]Kambe, T. and Minota, T., Acoustic wave radiated by head-on collision of two vortex rings, P. Roy. Soc. A Math. Phy., 386 (1983), pp. 277–308.Google Scholar
[5]Kambe, T. and Mya oo, U., An axisymmetric viscous vortex motion and its acoustic emission, J. Phys. Soc. Japan, 53 (1984), pp. 2263–2273.Google Scholar
[6]Chu, C., Wang, C., Chang, C., Chang, R. and Chang, W., Head-on collision of two coaxial vortex rings: experiment and computation, J. Fluid Mech., 296 (1995), pp. 39–71.CrossRefGoogle Scholar
[7]Chorin, A. J., Hairpin removal in vortex interactions, J. Comput. Phys., 91 (1990), pp. 1–21.CrossRefGoogle Scholar
[8]Chorin, A. J., Vorticity and Turbulence, Springer Science and Business Media, 1994.CrossRefGoogle Scholar
[9]Bernard, P. S., A vortex method for wall bounded turbulent flows, EDP Sci., (1996), pp. 15–31.Google Scholar
[10]Saghbini, J. C., Simulation of Vorticity Dynamics in Swirling Flows, Mixing and Vortex Breakdown, PH.D thesis, 1996.Google Scholar
[11]Fernandez, V. M., Zabusky, N. J., Liu, P., Bhatt, S. and Gerasoulis, A., Filament surgery and temporal grid adaptivity extensions to a parallel tree code for simulation and diagnosis in 3D vortex dynamics, EDP Sci., (1996), pp. 197–211.Google Scholar
[12]Chorin, A. J. and Hald, O. H., Vortex renormalization in three space dimensions, Phys. Rev. B, 51 (1995), pp. 11–969.CrossRefGoogle ScholarPubMed
[13]Chorin, A. J., Microstructure, renormalization, and more efficient vortex methods, EDP Sci., (1996), pp. 1–14.Google Scholar
[14]Chorin, A. J. and Hald, O. H., Analysis of Kosterlitz-Thouless transition models, Phys. D Nonlinear Phenomena, 99 (1997), pp. 442–470.CrossRefGoogle Scholar
[15]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
[16]Bui, T. T., A parallel, finite-volume algorithm for large-eddy simulation of turbulent flows, Comput. Fluids, 29 (2000), pp. 877–915.Google Scholar
[17]Vreman, B., Geurts, B. and Kuerten, H., Subgrid modeling in LES of compressible flow, Appl. Sci. Res., 51 (1995), pp. 191–203.Google Scholar
[18]Chernousov, A. A., LES of mixing layer and flow in square duct by the second-order explicit scheme, (2001).Google Scholar
[19]Smagorinsky, J., General circulation experiments with the primitive equations: I. the basic experiment, Mon. Weather Rev., 91 (1963), pp. 99–164.Google Scholar
[20]Chakravarthy, S. R. and Osher, S., A new class of high accuracy TVD schemes for hyperbolic conservation laws, AIAA Paper No. 85-0363 (1985).Google Scholar
[21]Chernousov, A. A., A characteristic-based approximate Riemann solver, Technical report, Ufa State Aviation Technical University, (2001).Google Scholar
[22]Gottlieb, S. and Shu, C., Total variation diminishing Runge-Kutta schemes, Math. Comput. American Math. Society, 67 (1998), pp. 73–85.CrossRefGoogle Scholar
[23]Jackiewicz, Z., Renaut, R. and Feldstein, A., Two-step Runge-Kutta methods, SIAM J. Numer. Anal., 28 (1991), pp. 1165–1182.Google Scholar
[24]Brown, G. L. and Roshko, A., On density effects and large structure in turbulent mixing layers, J. Fluid Mech., 64 (1974), pp. 775–816.Google Scholar
[25]Menon, S. and Soo, J. H., Simulation of vortex dynamics in three-dimensional synthetic and free jets using the large-eddy lattice Boltzmann method, J. Turbul., 5 (2004), pp. 1–4.Google Scholar
[26]Reynolds, O., On the resistance encountered by vortex rings and the relation between vortex rings and the stream-lines of a disc, Nature, 14 (1876), pp. 477–479.Google Scholar
[27]Maxworthy, T., The structure and stability of vortex rings, J. Fluid Mech, 51 (1972), pp. 15–32.Google Scholar
[28]Knio, O. M. and Ghoniem, A. F., Numerical study of a three-dimensional vortex method, J. Comput. Phys., 86 (1990), pp. 75–106.CrossRefGoogle Scholar
[29]Widnall, S. E. and Tsai, C., The instability of the thin vortex ring of constant vorticity, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 287(1977), 273–305.Google Scholar
[30]Shu, C. and Osher, S., Efficient implementation of essentially non-oscillatory shock-capturing schemes, J. Comput. Phys., 77 (1988), pp. 439–471.CrossRefGoogle Scholar
[31]Cockburn, B. and Shu, C., TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. II. General framework, Math. Comput., 52 (1989), pp. 411–435.Google Scholar
[32]Harten, A., High resolution schemes for hyperbolic conservation laws, J. Comput. Phys., 49 (1983), pp. 357–393.Google Scholar
[33]Osher, S. and Chakravarthy, S., High resolution schemes and the entropy condition, SIAM J. Numer. Anal., 21 (1984), pp. 955–984.Google Scholar
[34]Sweby, P. K., High resolution schemes using flux limitersfor hyperbolic conservation laws, SIAM J. Numer. Anal., 21 (1984), pp. 995–1011.CrossRefGoogle Scholar
[35]Shu, C., TVB uniformly high-order schemes for conservation laws, Math. Comput., 49 (1987), pp. 105–121.CrossRefGoogle Scholar
[36]Harten, A., Engquist, B., Osher, S. and Chakravarthy, S. R., Uniformly high order accurate essentially non-oscillatory schemes, III, J. Comput. Phys., 71 (1987), pp. 231–303.Google Scholar
[37]Cockburn, B., Hou, S. and Shu, C., The Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. IV, The multidimensional case, Math. Comput., 54 (1990), pp. 545–581.Google Scholar
[38]Williamson, J. H., Low-storage Runge-Kutta schemes, J. Comput. Phys., 35 (1980), pp. 48–56.Google Scholar
[39]Carpenter, M. H. and Kennedy, C. A., Fourth-order 2N-storage Runge-Kutta schemes, NASA Langley Research Center, (1994).Google Scholar
[40]Van Leer, B., Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method, J. Comput. Phys., 32 (1979), pp. 101–136.CrossRefGoogle Scholar