Numerical modelling of axisymmetric electromagnetically driven flows in thin layers

Sergey A. Suslov, Sergio Cuevas

Abstract


We present the results of the numerical modelling of deceptively simple steady axisymmetric electromagnetically driven flows in thin disk-like layers of a weakly conducting electrolyte. The fluid motion is caused by an azimuthally acting Lorentz force appearing when a radial current flows in the electrolyte layer placed on top of a magnet with a vertical polarisation. The small layer thickness and the circumferential direction of the driving force suggest that the flow in such a system should be essentially uni-directional. However, it was found that not only is the flow fully three-dimensional, but multiple solutions can exist for the same set of governing parameters.

References
  • R. M. Digilov, Making a fluid rotate: circular flow of a weakly conducting fluid induced by Lorentz force. Am. J. Phys., 75(4):361–367, 2007. doi:10.1119/1.2372472
  • F.V. Dolzhanskii, V. A. Krymov and D. Y. Manin, Stability and vortex structures of quasi-two-dimensional shear flows. Sov. Phys. Usp., 33(7):495–520, 1990. doi:10.3367/UFNr.0160.199007a.0001
  • V. A. Dovzhenko, V. A. Krymov and V. M. Ponomarev, Experimental and theoretical study of a shear flow driven by an axisymmetric force. Izv. Akad. Nauk SSSR Fiz. Atm. Okeana (in Russian), 20(8):693–704, 1984.
  • D. Hatziavramidis and H. C. Ku, An integral Chebyshev expansion method for boundary-value problems of O.D.E. type. Comput. Math. Appl., 11(6):581–586, 1985. doi:10.1016/0898-1221(85)90040-9
  • H. C. Ku and D. Hatziavramidis, Chebyshev expansion methods for the solution of the extended Graetz problem. J. Comput. Phys., 56:495–512, 1984. doi:10.1016/0021-9991(84)90109-8
  • J. Perez-Barrera, J. E. Ortiz, E. Ramos and S. Cuevas, Instability of electrolyte flow driven by an azimuthal Lorentz force. Magnetohydrodynamics, 51(2):203–213, 2015. http://mhd.sal.lv/contents/2015/2/MG.51.2.4.R.html
  • S. A. Suslov and S. Paolucci, Stability of mixed-convection flow in a tall vertical channel under non-Boussinesq conditions. J. Fluid. Mech. 302:91–115, 1995. doi:10.1017/S0022112095004022
  • S. A. Suslov and S. Paolucci, Stability of natural convection flow in a tall vertical enclosure under non-Boussinesq conditions. Int. J. Heat Mass Transfer, 38:2143–2157, 1995. doi:10.1016/0017-9310(94)00348-Y
  • S. A. Suslov, J. Perez-Barrera and S. Cuevas, Electromagnetically driven flow of electrolyte in a thin annular layer: axisymmetric solutions. J. Fluid Mech., to appear, 2017.

Keywords


electrolyte flow, rotating flow

Full Text:

PDF BibTeX


DOI: http://dx.doi.org/10.21914/anziamj.v58i0.11602



Remember, for most actions you have to record/upload into this online system
and then inform the editor/author via clicking on an email icon or Completion button.
ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.