Steady and Unsteady Vortex Flow Generated by Electromagnetic Forcing - Selected Topics of Computational and Experimental Fluid Mechanics - page 417

Fig. 8 Stability map of electrically driven flows with the different arrays of permanent magnets
placed on the perimeter of a circle . The interpolated solid line divides the regions of steady and
unsteady flow
5 Conclusions
In this work, we performed an experimental and numerical study of the spatio-
temporal behavior of laminar flows generated in a thin electrolyte layer through the
interaction of a D.C. current and a magnetic field produced by different arrays of
magnets placed on the perimeter of a circle. Flows were experimentally visualized
using dye and recorded for comparison with numerical simulations. We used a Q2D
numerical model that includes both the detailed Lorentz driving force produced by
the electromagnetic interaction and the friction effects of boundary layers at the
bottom of the container. The comparison of numerical simulations with available
experiments show a satisfactory agreement for both steady and unsteady flows. In
fact, Lagrangian trajectories calculated numerically suitably capture the motion and
elongation of the vortical structures caused by the Lorentz force. For steady flows,
well-defined spatial symmetries that depend on the magnet arrays can be identified.
For all the explored arrays of magnets, we found either experimentally or numeri-
cally the applied current for which the flow transits from steady to unsteady state.
With this information, we built a stability map that collects all the available experi-
mental and numerical results. It was found that the larger the number of magnets, the
lower the intensity of the applied current required to transit from steady to unsteady
state which could favour the fluid mixing. The characterization of time-dependent
flows and the possible appearance of a chaotic behavior remains as a future topic of
study.
Acknowledgments Financial support from CONACYT, Mexico, through Project 131399 is grate-
fully acknowledged. C.G. Lara and A. Figueroa thank, respectively, a grant and a posdoctoral
fellowship from CONACYT.