Abstract
The vortex particle method has been applied to the axisymmetric swirling flow of a viscous fluid. The formulation used yields two transport equations which have been solved within the lagrangian framework of particle method. The diffusion operator for both equations has been approximated by means of a Particle Strength Exchange scheme. Applications to the cases of one isolated vortex ring and two co-rotating vortex rings illustrate the interest of this new method. Special attention has been devoted to the vorticity production resulting from the interaction between the azimuthal components of vorticity and velocity. The generation of small eddies at the boundary of the vortex ring cross-section has been particularly investigated.
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References
Acton, E., A modeling of large eddies in an axisymmetric jet. J.Fluid Mech. 98 (1980) 1.
Beaudoin, A., Huberson, S. and Rivoalen, E., Simulation of anisotropic diffusion by means of a diffusion velocity method. J.Comput.Phys. 186 (2003) 122–135.
Cottet, G.H. and Koumoutsakos, P., Vortex Methods – Theory and Practice. Cambridge University Press (2000) p. 313.
Chorin A.J., Numerical study of slightly viscous flow, J.Fluid Mech. 57 (1973) 785.
Giovannini, A. and Gagnon, Y., Vortex simulation of axisymetrical flows in cylindrical coordinates, Part 1: Numerical algorithm. Internat.J.Thermal Fluid Sci. 4 (1996) 213–220.
Hill, M., On a spherical vortex. Philos.Trans.Roy.Soc.London A 185 (1894) 219–223.
Huberson, S. and Jolles, A., Correction de l'erreur de projection dans les méthodes particules/ maillage. Rech.Aérosp. 4 (1990) 1–6.
Lifschitz, A., Suters, W.H. and Beale, J.T., The onset of instability in exact vortex ring with swirl. J.Comput.Phys. 129 (1996) 8–29.
Marshall, J.S., The flow induced by periodic vortex rings wrapped around a columnar vortex core. J.Fluid Mech. 345 (1997) 1–30.
Marshall, J.S. and Krishnamoorthy, S., On the instantaneous cutting of a columnar vortex with non-zero axial flow. J.Fluid Mech. 351 (1997) 41–74.
Martins, L.F. and Ghoniem, A., Simulation of the nonreacting flow in bluff-body burner; Effect of the diameter ratio. J.Fluids Engrg. 115 (1993) 413.
Melander, M.V. and Hussain, F., Topological vortex dynamics in axisymmetric vortex flows. J. Fluid Mech. 260 (1994) 57–80.
Nitsche, M., Axisymmetric vortex sheet roll-up. Ph.D. Thesis, University of Michigan (1992).
Nitsche, M. and Krasny, R., A numerical study of vortex ring formation at the edge of circular tube. J.Fluid Mech. 276 (1994) 139–161.
Moffatt, K., Generalized vortex rings with and without swirl. Fluid Dynam.Res. 3 (1988 22–30.
Norbury J., A family of steady vortex ring. J.Fluid Mech. 57 (1973) 417–431.
Pozrikidis, C., The nonlinear instability of Hill's vortex. J.Fluid Mech. 168 (1986) 337–367.
Rivoalen, E. and Huberson, S., Numerical simulation of axisymmetric viscous flows by means of a particle method. J.Comput.Phys. 52 (1999) 1–31.
Rivoalen, E. and Huberson, S., The particle strength exchange method applied to axisymmetric viscous flows. J.Comput.Phys. 168 (2001) 519–526.
Saffman, P.G., Vortex Dynamics. Cambridge University Press (1992) p. 311.
Shariff, K. and Leonard, A., Vortex ring. Annual Rev.Fluid Mech. 24 (1992) 235–279.
Tung, C. and Ting, L., Motion and decay of a vortex ring, Phys.Fluids 10 (1967) 901.
Turkington, B., Vortex rings with swirl: Axisymmetric solutions of the Euler equations with non-zero helicity. SIAM J.Math.Anal. 20 (1989) 57–73.
Stanaway, S.K., Cantwell, B.J. and Spalart, P.R., Navier–Stokes simulations of axisymmetric vortex rings AIAA J. 318 (1988) 1–14.
Verzicco, R., Iafrati, A., Riccardo, G. and Fatica, M., Analysis of the sound generated by the pairing of two axisymmetric co-rotating vortex rings. J.Sound Vibration 200 (1997) 347–358.
Virk, D., Melander, M.V. and Hussain, F., Dynamics of a polarized vortex ring, J.Fluid Mech. 260 (1994) 23–55.
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Rivoalen, E., Huberson, S. & Bratec, H. Particle Simulation of Swirling Flows. Flow, Turbulence and Combustion 72, 69–90 (2004). https://doi.org/10.1023/B:APPL.0000014986.94393.e9
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DOI: https://doi.org/10.1023/B:APPL.0000014986.94393.e9