Skip to main content Accessibility help
×
Home

Investigation of the Convection Term Discretization Schemes for a Force-Generated Ring-Vortex

  • N. M. Nouri (a1), S. Yekani Motlagh (a1), M. Navidbakhsh (a1) and E. Yasari (a1)

Abstract

In this paper, a model has been presented for generating a special ring vortex by applying a nonconservative force with specific distribution through the Navier-Stokes equations. Moreover, the ring's vortical pattern has been compared with the analytical and experimental results. In continuation, the diffusion, dissipation, and dispersion errors of four basic convection term interpolation schemes for the velocity and vorticity field of the vortex ring have been investigated. The simulations are performed for both the small and large time steps. Next, an appropriate discretization scheme for the convection term, and a proper order of time steps for simulating flows that contain ring vortices have been proposed. Finally, the ring vortexes generated by non-conservative force are added to the turbulent channel flow as a bubble induced vortex on carrier flow in two-phase flows, and the drag reduction due to the interaction between ring vortexes and flow vorticity field is observed.

Copyright

Corresponding author

* Corresponding author (mnouri@iust.ac.ir)

References

Hide All
1.Didden, N., “Formation of Vortex Rings Rolling-Up and Production of Circulation,” Zeitschrift für angewandte Mathematik und Physik, 30, pp. 101116 (1979).
2.Shariff, K. and Leonard, A., “Vortex Rings,” Annual Review of Fluid Mechanics, 24, pp. 235279 (1992).
3.Gharib, M., Rambod, E. and Shariff, K., “A Universal Time Scale for Vortex Ring Formation,” Journal of Fluid Mechanics, 360, pp. 121140 (1998).
4.Krueger, P. S. and Gharib, M., “The Significance of Vortex Ring Formation to the Impulse and Thrust of a Starting Jet,” Physics of Fluids, 15, pp. 12711281 (2003).
5.Dabiri, J. O. and Gharib, M., “Fluid Entrainment by Isolated Vortex Rings,” Journal of Fluid Mechanics, 511, pp. 311331 (2004).
6.Krueger, P. S., Dabiri, J. O. and Gharib, M., “The Formation Number of Vortex Rings Formed in Uniform Background Co-Flow,” Journal of Fluid Mechanics, 556, pp. 147166 (2006).
7.Pullin, D. I., “Vortex Ring Formation at Tube and Orifice Openings,” Physics of Fluids, 22, pp. 401403 (1979).
8.Zhao, W., Frankel, S. H. and Mongeau, L. G., “Effects of Trailing Jetinstability on Vortex Ring Formation,” Physics of Fluids, 12, pp. 589596 (2000).
9.Mohseni, K., Ran, H. Y. and Colonius, T., “Numerical Experiments on Vortex Ring Formation,” Journal of Fluid Mechanics, 430, pp. 267282 (2001).
10.Rosenfeld, M., Katija, K. and Dabiri, J. O., “Circulation Generation and Vortex Ring Formation by Conic Nozzles,” Journal of Fluids Engineering, 131, pp. 091204, 1-8 (2009).
11.Wegener, P. P. and Parlange, J., “Spherical-Cap Bubbles,” Annual Review of Fluid Mechanics, 5, p. 79 (1973).
12.Savic, P., “Internal Circulation Inside Drops,” Natural Resources Defense Council, MT-22 (1953).
13.Ryskin, G. and Leal, L. G., “Numerical Solution of Free-Boundary Problems in Fluid Mechanics. Part 1. the Finite-Difference Technique,” Journal of Fluid Mechanics, 148, pp. 117 (1984).
14.Hill, M. J. M., “On a Spherical Vortex,” Philosophical transactions of the Royal Society of London, 185, pp. 213245 (1894).
15.Saffman, P. G., “Vortex Models of Isotropic Turbulence,” Philosophical transactions of the Royal Society of London, 355. pp. 19491956 (1997).
16.Aivazis, A. and Pullin, D. I., “On Velocity Structure Functions and the Spherical Vortex Model for Isotropic Turbulence,” Physics of Fluids, 13, pp. 20192029 (2001).
17.Stanaway, S. and Cantwell, B., “A Numerical Study of Viscous Vortex Rings Using a Spectral Method,” NASA TM 101041 (1988).
18.Nitsche, M. and Krasny, R., “A Numerical Study of Vortex Ring Formation at the Edge of a Circular Tube,” Journal of Fluid Mechanics, 276, pp. 139161 (1994).
19.James, S. and Madnia, C., “Direct Numerical Simulation of a Laminar Vortex Ring,” Physics of Fluids, 8, pp. 24002414 (1996).
20.Verzicco, R., Orlandi, P., Eisenga, A., Heijst, G., van and Carnevale, G., “Dynamics of a Vortex Ring in a Rotating Fluid,” Journal of Fluid Mechanics, 317, pp. 215239 (1996).
21.Panton, L., Incompressible Flow, Third Edition, Wiley (2005).
22.Nouri, N. M., Yekani, Motlagh S., Yasari, E. and Navidbakhsh, M., “Comparison Between Explicit Filtering with Smooth and Cutoff Filters in the Large Eddy Simulation of Turbulent Channel Flows,” European Journal of Mechanics - B/Fluids, 30, pp. 505512 (2011).
23.Moriguchi, Y. and Kato, H., “Influence of Microbubble Diameter and Distribution on Frictional Resistance Reduction,” Journal of Marine Science and Technology, 7, pp. 7985 (2002).

Keywords

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed