Hostname: page-component-848d4c4894-4hhp2 Total loading time: 0 Render date: 2024-05-06T23:05:09.701Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  17 October 2012

N. M. Nouri ,
S. Yekani Motlagh ,
M. Navidbakhsh  and
E. Yasari
N. M. Nouri*
Affiliation:
Department of Mechanical Engineering, Iran University of Science and Technology, Tehran 16844, Iran
S. Yekani Motlagh
Affiliation:
Department of Mechanical Engineering, Iran University of Science and Technology, Tehran 16844, Iran
M. Navidbakhsh
Affiliation:
Department of Mechanical Engineering, Iran University of Science and Technology, Tehran 16844, Iran
E. Yasari
Affiliation:
Department of Mechanical Engineering, Iran University of Science and Technology, Tehran 16844, Iran
*
* Corresponding author (mnouri@iust.ac.ir)
Get access

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.

Keywords

Ring vortexNon-conservative forceInterpolation schemesNumerical diffusionBubble drag reduction
Type
Technical Note
Information
Journal of Mechanics , Volume 28 , Issue 4 , December 2012 , pp. N13 - N21
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2012

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

REFERENCES

1.Didden, N., “Formation of Vortex Rings Rolling-Up and Production of Circulation,” Zeitschrift für angewandte Mathematik und Physik, 30, pp. 101–116 (1979).CrossRefGoogle Scholar
2.Shariff, K. and Leonard, A., “Vortex Rings,” Annual Review of Fluid Mechanics, 24, pp. 235–279 (1992).Google Scholar
3.Gharib, M., Rambod, E. and Shariff, K., “A Universal Time Scale for Vortex Ring Formation,” Journal of Fluid Mechanics, 360, pp. 121–140 (1998).Google Scholar
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. 1271–1281 (2003).Google Scholar
5.Dabiri, J. O. and Gharib, M., “Fluid Entrainment by Isolated Vortex Rings,” Journal of Fluid Mechanics, 511, pp. 311–331 (2004).Google Scholar
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. 147–166 (2006).CrossRefGoogle Scholar
7.Pullin, D. I., “Vortex Ring Formation at Tube and Orifice Openings,” Physics of Fluids, 22, pp. 401–403 (1979).CrossRefGoogle Scholar
8.Zhao, W., Frankel, S. H. and Mongeau, L. G., “Effects of Trailing Jetinstability on Vortex Ring Formation,” Physics of Fluids, 12, pp. 589–596 (2000).CrossRefGoogle Scholar
9.Mohseni, K., Ran, H. Y. and Colonius, T., “Numerical Experiments on Vortex Ring Formation,” Journal of Fluid Mechanics, 430, pp. 267–282 (2001).Google Scholar
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).Google Scholar
11.Wegener, P. P. and Parlange, J., “Spherical-Cap Bubbles,” Annual Review of Fluid Mechanics, 5, p. 79 (1973).Google Scholar
12.Savic, P., “Internal Circulation Inside Drops,” Natural Resources Defense Council, MT-22 (1953).Google Scholar
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. 1–17 (1984).Google Scholar
14.Hill, M. J. M., “On a Spherical Vortex,” Philosophical transactions of the Royal Society of London, 185, pp. 213–245 (1894).Google Scholar
15.Saffman, P. G., “Vortex Models of Isotropic Turbulence,” Philosophical transactions of the Royal Society of London, 355. pp. 1949–1956 (1997).CrossRefGoogle Scholar
16.Aivazis, A. and Pullin, D. I., “On Velocity Structure Functions and the Spherical Vortex Model for Isotropic Turbulence,” Physics of Fluids, 13, pp. 2019–2029 (2001).CrossRefGoogle Scholar
17.Stanaway, S. and Cantwell, B., “A Numerical Study of Viscous Vortex Rings Using a Spectral Method,” NASA TM 101041 (1988).Google Scholar
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. 139–161 (1994).Google Scholar
19.James, S. and Madnia, C., “Direct Numerical Simulation of a Laminar Vortex Ring,” Physics of Fluids, 8, pp. 2400–2414 (1996).Google Scholar
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. 215–239 (1996).Google Scholar
21.Panton, L., Incompressible Flow, Third Edition, Wiley (2005).Google Scholar
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. 505–512 (2011).Google Scholar
23.Moriguchi, Y. and Kato, H., “Influence of Microbubble Diameter and Distribution on Frictional Resistance Reduction,” Journal of Marine Science and Technology, 7, pp. 79–85 (2002).Google Scholar