Impact of a vortex ring on a density interface using a regularized inviscid vortex sheet method

Journal of Computational Physics

Volumn 227, Issue 21, 2008, Pages 9021-9043

  Stock, Mark J ^a   Dahm, Werner J A ^b   Tryggvason, Grétar ^c  

^a Applied Scientific Research   (United States)

^b The Department of Civil and Environmental Engineering   (United States)

^c Worcester Polytechnic Institute   (United States)

Author keywords

Density discontinuity; Stratified flow; Vortex methods; Vortex sheet dynamics; Vortex in cell

Indexed keywords

DENSITY DISCONTINUITY; DENSITY INTERFACE; STRATIFIED FLOWS; UNSTEADY MOTION; VORTEX IN CELL METHODS; VORTEX METHODS; VORTEX RINGS; VORTEX SHEET; VORTEX SHEET DYNAMIC; VORTEX-IN-CELL;

VORTEX FLOW;

EID: 51449090124     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2008.05.022     Document Type: Article

References (68)

1. Birkhoff G., and Fisher J. Do vortex sheets roll up?. Rend. Circ. Math. Palermo Ser. 2 8 (1959) 77-90
2. Moore D.W. The spontaneous appearance of a singularity in the shape of an evolving vortex sheet. Proc. Roy. Soc. Lond. Ser. A 365 (1979) 105
3. Krasny R. A study of singularity formation in a vortex sheet by the point-vortex approximation. J. Fluid Mech. 167 (1986) 65
4. Chorin A.J., and Bernard P.S. Discretization of a vortex sheet, with an example of roll-up. J. Comput. Phys. 13 3 (1973) 423-429
5. Krasny R. Desingularization of periodic vortex sheet roll-up. J. Comput. Phys. 65 (1986) 292-313
6. Tryggvason G., Dahm W.J.A., and Sbeih K. Fine structure of vortex sheet roll-up by viscous and inviscid simulation. J. Fluids Eng. 113 (1991) 31-36
7. Luchini P., and Tognaccini R. Comparisons of a viscous and inviscid numerical simulations of the start-up vortex issuing from a semi-infinite flat plate. ESAIM Proc. 7 (1999) 247-257
8. Christiansen J.P. Numerical simulation of hydrodynamics by the method of point vortices. J. Comput. Phys. 13 (1973) 363-379
9. Harabetian E., Osher S., and Shu C.-W. An Eulerian approach for vortex motion using a level set regularization procedure. J. Comput. Phys. 127 (1996) 15-26
10. Birdsall C.K., and Fuss D. Clouds-in-clouds, clouds-in-cells physics for many-body plasma simulations. J. Comput. Phys. 3 (1969) 494-511
11. Couët B., Buneman O., and Leonard A. Simulation of three-dimensional incompressible flows with a vortex-in-cell method. J. Comput. Phys. 39 2 (1981) 305-328
12. Cottet G.-H., Ould-Salihi M.L., and Hamraoui M.E. Multi-purpose regridding in vortex methods. ESAIM Proc. 7 (1999) 94-103
13. S. Mas-Gallic, Contribution à l'analyse numérique des méthodes particulaires, Ph.D. Thesis, Université Paris VI, 1987.
14. Shankar S., and van Dommelen L. A new diffusion procedure for vortex methods. J. Comput. Phys. 127 (1996) 88-109
15. G.S. Winckelmans, A. Leonard, Improved vortex methods for three-dimensional flows, in: R.E. Caflisch (Ed.), Proceedings of the Workshop on Mathematical Aspect of Vortex Dynamics, Leesburg, Virginia, April 25-27, 1988, 1989, pp. 25-35.
16. Leonard A. Numerical simulation of interacting, three-dimensional vortex filaments. Proceedings of the IV International Conference on Numerical Methods of Fluid Dynamics. Lecture Notes in Physics No. 35 (1975), Springer-Verlag 245-250
17. C. Rehbach, Numerical calculation of unsteady three-dimensional flows with vortex sheets, in: 16th AIAA Aerospace Sciences Meeting, 1978, aIAA-78-111.
18. Chorin A.J. Vortex models and boundary layer instability. SIAM J. Sci. Stat. Comput. 1 (1980) 1-21
19. Feynman R.P. Application of quantum dynamics to liquid helium. Prog. Low Temp Phys. I (1957) 16-53
20. Chorin A.J. Hairpin removal in vortex interactions. J. Comput. Phys. 91 (1990) 1-21
21. Lindsay K., and Krasny R. A particle method and adaptive treecode for vortex sheet motion in three-dimensional flow. J. Comput. Phys. 172 (2001) 879-907
22. B. Couët, Evolution of turbulence by three-dimensional numerical particle-vortex tracing, Ph.D. Thesis, Stanford University Institute for Plasma Research, 1979.
23. Leonard A. Vortex methods for flow simulation. J. Comput. Phys. 37 (1980) 289-335
24. W.T. Ashurst, Large eddy simulation via vortex dynamics, in: Presented at the AIAA Computational Fluid Dynamics Conference, 6th, 1983, AIAA Pap. No. 83-1879-CP.
25. Lozano A., García-Olivares A., and Dopazo C. The instability growth leading to a liquid sheet breakup. Phys. Fluids 10 9 (1998) 2188-2197
26. Haroldsen D.J., and Meiron D.I. Numerical calculation of three-dimensional interfacial potential flows using the point vortex method. SIAM J. Sci. Comput. 20 (1998) 648-683
27. Pozrikidis C. Theoretical and computational aspects of the self-induced motion of three-dimensional vortex sheets. J. Fluid Mech. 425 (2000) 335-366
28. J.T. Beale, Methods for computing singular and nearly singular integrals, J. Turb. 3 (041).
29. Brady M., Leonard A., and Pullin D.I. Regularized vortex sheet evolution in three dimensions. J. Comput. Phys. 146 (1998) 520-545
30. Knio O.M., and Ghoniem A.F. Three-dimensional vortex simulation of rollup and entrainment in a shear layer. J. Comput. Phys. 97 (1991) 172-223
31. Knio O.M., and Ghoniem A.F. The three-dimensional structure of periodic vorticity layers under non-symmetric conditions. J. Fluid Mech. 243 (1992) 353-392
32. Knio O.M., and Ghoniem A.F. Vortex simulation of a three-dimensional reacting shear layer with infinite-rate kinetics. AIAA J. 30 1 (1992) 105-116
33. L. Kaganovskiy, Hierarchical panel method for vortex sheet motion in three-dimensional flow, Ph.D. Thesis, University of Michigan, 2006.
34. Unverdi S.O., and Tryggvason G. A front-tracking method for viscous, incompressible, multi-fluid flows. J. Comput. Phys. 100 (1992) 25-37
35. Wu J.-Z. A theory of three-dimensional interfacial vorticity dynamics. Phys. Fluids 7 10 (1995) 2375-2395
36. Peskin C.S. Numerical analysis of blood flow in the heart. J. Comput. Phys. 25 (1977) 220-252
37. M.J. Stock, A regularized inviscid vortex sheet method for three-dimensional flows with density interfaces, Ph.D.Thesis, University of Michigan, 2006.
38. P. Swarztrauber, R. Sweet, Efficient FORTRAN subprograms for the solution of elliptic partial differential equations, Tech. Rep. NCAR Technical Note-TN/IA-109, NCAR, , July 1975.
39. Linden P.F. The interaction of a vortex ring with a sharp density interface: a model for turbulent entrainment. J. Fluid Mech. 60 (1973) 467-480
40. Dahm W.J.A., Scheil C.M., and Tryggvason G. Dynamics of vortex interaction with a density interface. J. Fluid Mech. 205 (1989) 1-43
41. G. Tryggvason, Vortex dynamics of stratified flows, in: R.E. Caflisch (Ed.), Proceedings of the Workshop on Mathematical Aspect of Vortex Dynamics, Leesburg, Virginia, April 25-27, 1988, 1989, pp. 160-170.
42. Tryggvason G., Unverdi S.O., Song M., and Abdollahi-Alibeik J. Interaction of vortices with a free surface and density interfaces. In: Anderson C., and Greengard C. (Eds). Vortex Dynamics and Vortex Methods. Lectures in Applied Mathematics No. 28 (1991), American Mathematical Society 679-699
43. Tryggvason G. Deformation of a free surface as a result of vortical flows. Phys. Fluids 31 (1988) 955-957
44. Willmarth W.W., Tryggvason G., Hirsa A., and Yu D. Vortex pair generation and interaction with a free surface. Phys. Fluids A 1 1 (1989) 170-172
45. Tryggvason G., Abdollahi-Alibeik J., Willmarth W.W., and Hirsa A. Collision of a vortex pair with a contaminated free surface. Phys. Fluids A 4 6 (1992) 1215-1229
46. Marcus D.L., and Bell J.B. Numerical simulation of a viscous vortex ring interaction with a density interface. Phys. Fluids 6 4 (1994) 1505-1514
47. Liu C.H. A three-dimensional vortex particle-in-cell method for vortex motions in the vicinity of a wall. Intl. J. Num. Meth. Fluids 37 5 (2001) 501-523
48. Liu C.H. Vortex simulation of unsteady shear flow induced by a vortex ring. Comput. Fluids 31 2 (2002) 183-207
49. 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
50. Orlandi P., and Verzicco R. Vortex rings impinging on walls: axisymmetric and three-dimensional simulations. J. Fluid Mech. 256 (1993) 615-646
51. 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
52. Naitoh T., Banno O., and Yamada H. Longitudinal vortex structure in the flow field produced by a vortex ring impinging on a flat plate. Fluid Dynam. Res. 28 1 (2001) 1-74
53. Leweke T., Thompson M.C., and Hourigan K. Vortex dynamics associated with the collision of a sphere with a wall. Phys. Fluids 16 9 (2004) L74-L77
54. Tung C., and Ting L. Motion and decay of a vortex ring. Phys. Fluids 10 5 (1967) 901-910
55. Saffman P.G. Approach of a vortex pair to a rigid free surface in viscous fluid. Stud. Appl. Math. 49 4 (1970) 371-380
56. Fraenkel L.E. Examples of steady vortex rings of small cross-section in an ideal fluid. J. Fluid Mech. 51 (1972) 119-135
57. Norbury J. A family of steady vortex rings. J. Fluid Mech. 57 (1973) 417-431
58. Nitsche M. Evolution of a cylindrical and a spherical vortex sheet. ESAIM Proc. 1 (1996) 401-414
59. Krasny R., and Nitsche M. The onset of chaos in vortex sheet flow. J. Fluid Mech. 454 (2002) 47-69
60. Orlandi P. Vortex dipole rebound from a wall. Phys. Fluids A 2 8 (1990) 1429-1436
61. Luton J.A., and Ragab S.A. The three-dimensional interaction of a vortex pair with a wall. Phys. Fluids 9 10 (1997) 2967-2980
62. Lim T.T. On the role of Kelvin-Helmholtz-like instability in the formation of turbulent vortex rings. Fluid Dynam. Res. 21 1 (1997) 47-56
63. Eames I., and Dalziel S.B. Dust resuspension by the flow around an impacting sphere. J. Fluid Mech. 403 (2000) 305-328
64. Han J., and Tryggvason G. Secondary breakup of liquid drops in axisymmetric geometry Part I, constant acceleration. Phys. Fluids 11 (1999) 3650-3667
65. Han J., and Tryggvason G. Secondary breakup of liquid drops in axisymmetric geometry Part II, impulsive acceleration. Phys. Fluids 13 (2001) 1554-1565
66. Ghoniem A.F., Heidarinejad G., and Krishnan A. Numerical simulation of a thermally stratified shear layer using the vortex element method. J. Comput. Phys. 79 (1988) 135-166
67. Reinaud J., Joly L., and Chassaing P. Numerical simulation of a variable-density mixing-layer. ESAIM Proc. 7 (1999) 359-368
68. Anderson C.R. A method of local corrections for computing the velocity field due to a distribution of vortex blobs. J. Comput. Phys. 62 (1986) 111-123