Steady and Unsteady Vortex Flow Generated by Electromagnetic Forcing - Selected Topics of Computational and Experimental Fluid Mechanics - page 414

Fig. 4 Steady flow produced by an array of fourth magnets with alternating orientation and applied
current of 50mA that corresponds to a Reynolds number Re = 69. a Experimental flowvisualization
with dye. b Streamlines calculated numerically. c Lagrangian pathlines obtained by integration of
the advective equations using the numerical flow field

Fig. 5 Steady flow produced with an array of eight magnets with alternating orientation and
applied current of 50mA ( Re 77). a Experimental flow visualization. b Numerical streamlines.

c Lagrangian trajectories obtained by integration of the advective equations from the numerical
flow field

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tive scalar transport, which are neatly reproduced through the Lagrangian tracking.
Even the hyperbolic points created by the interaction of central vortices are clearly
observed. The lack of diffusion in the Lagrangian simulation is the main difference
with the experimental visualization. In fact, diffusion can be incorporated using the
Diffusion Strip Method (Figueroa et al. 2014 ). Figure 5 shows experimental and
numerical results for the steady flow obtained with an array of eight magnets with
alternating orientation and applied current of 50mA that corresponds to Re 77.

As in the previous case, the experimental visualization, numerical streamlines and
Lagrangian trajectories are presented in Fig. 5 a-c, respectively. Due to the shorter
distance between magnets, in this case vortex interactions are stronger but still the
Lagrangian numerical simulation reproduces themain qualitative features of the flow.
For any array of magnets, if the intensity of the current is sufficiently high the
resulting flowpresents a time-dependent behavior. For instance, with an array of eight

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