Advertisement

Steady and Unsteady Vortex Flow Generated by Electromagnetic Forcing

  • C. G. Lara
  • A. Figueroa
  • S. CuevasEmail author
Conference paper
Part of the Environmental Science and Engineering book series (ESE)

Abstract

In this paper, we present a numerical and experimental study of the laminar flow that results from the interaction of vortices driven electromagnetically in a thin layer of an electrolyte. The fluid motion is generated by a Lorentz force due to a uniform D.C. current and a non-uniform magnetic field produced by different symmetric arrays of small permanent magnets placed on the perimeter of a circle. Depending on the number of magnets and the intensity of the electric current, we find that steady or unsteady vortex flow patterns may arise. We developed a quasi-two-dimensional numerical model that accounts for the effect of the boundary layer adhered to the bottom wall. Once the velocity field is obtained, we perform a Lagrangian tracking that shows a good qualitative comparison with the experimental flow visualization. From numerical and experimental results, a map of stability that defines regions of steady and unsteady flow, according to the electric current intensity and magnet arrays, is built. We find that the larger the number of magnets, the less intense the applied current required to transit from steady to unsteady flow patterns.

Keywords

Lorentz Force Unsteady Flow Point Vortex Experimental Visualization Vortex Interaction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

Financial support from CONACYT, Mexico, through Project 131399 is gratefully acknowledged. C.G. Lara and A. Figueroa thank, respectively, a grant and a posdoctoral fellowship from CONACYT.

References

  1. Aref H (2007) J Math Phys 48:065401CrossRefGoogle Scholar
  2. Aref H (2009) Phys Fluids 21:094101CrossRefGoogle Scholar
  3. Clercx HJH, Van Heijst GJF, Zoeteweij (2003) Phys Rev E 67:066303CrossRefGoogle Scholar
  4. Dirksen T (2012) Masters thesis, Technical University of DenmarkGoogle Scholar
  5. Durán-Matute M, Kamp LPJ, Clercx HJH, van Heijst GJF (2010) Phys Rev E 82:026314Google Scholar
  6. Figueroa A, Cuevas S, Ramos E (2011) Phys Fluids 23:013601CrossRefGoogle Scholar
  7. Figueroa A, Demiaux F, Cuevas S, Ramos E (2009) J Fluid Mech 641:245–261CrossRefGoogle Scholar
  8. Figueroa A, Meunier P, Cuevas S, Villermaux E, Ramos E (2014) Phys Fluids 26:013601CrossRefGoogle Scholar
  9. Helmholtz HV (1858) J für die reine und angewandte Mathematik 55:25–55CrossRefGoogle Scholar
  10. Kelvin L (1867) Proc R Soc Edinb VI:94–105Google Scholar
  11. Lara CG (2013) Theoretical and experimental study of electromagnetic stirring in shallow fluid flows. MSc Thesis, National Autonomous University of Mexico (in Spanish)Google Scholar
  12. McCaig M (1977) WileyGoogle Scholar
  13. Meunier P, Leweke T (2005) J Fluid Mech 533:125–159CrossRefGoogle Scholar
  14. Ottino JM (1990) Annu Rev Fluid Mech 22:207–253CrossRefGoogle Scholar
  15. Rossi L, Lardeau S (2011) J Turbul 12:1–31CrossRefGoogle Scholar
  16. Rossi L, Vassilicos JC, Hardalupas Y (2006) Phys Rev Lett 97(14):144501CrossRefGoogle Scholar
  17. Satijn MP, Cense AW, Verzicco R, Clercx HJH, Van Heijist GJF (2001) Phys Fluids 13(7):1932–1945CrossRefGoogle Scholar
  18. Sommeria J (1988) J Fluid Mech 189:553–569CrossRefGoogle Scholar
  19. Versteeg HK, Malalasekera W (1995) Longman Scientific & TechnicalGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Instituto de Energías RenovablesUniversidad Nacional Autónoma de MéxicoTemixcoMexico
  2. 2.Facultad de CienciasUniversidad Autónoma del Estado de MorelosCuernavacaMexico

Personalised recommendations