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produced by solid obstacles. It has been shown that localized magnetic forces in
flows of electrically conducting fluids act as obstacles for the flow. When the con-
ducting fluid is a liquid metal, the relative motion of the fluid and a localized magnetic
field induces electric currents that interact with the same field to produce a Lorentz
force braking the liquid (Cuevas et al.
2006
; Votyakov et al.
2007
). In the case of an
electrolyte, due to the low conductivity of the fluid, induced currents are negligible
but an opposing Lorentz force can still be created if an electric current is externally
applied (Honji
1991
; Honji and Haraguchi
1995
; Afanasyev and Korabel
2006
).
In both cases, experimental and theoretical studies have shown the appearance of
different flow regimes such as steady vortices, vortex shedding, and even turbulent
wakes (Honji and Haraguchi
1995
; Afanasyev and Korabel
2006
; Votyakov et al.
2008
; Kenjeres et al.
2011
). In fact, the term
magnetic obstacle
was coined (Cuevas
et al.
2006
) to emphasize that localized Lorentz forces produce flow behaviors that
in some aspects resemble flows past solid obstacles, although very important differ-
ences exist.
So far, investigations of flows past magnetic obstacles have mainly addressed the
problem of a single obstacle in liquid metal flows (see, for instance, Votyakov et al.
2008
; Kenjeres et al.
2011
; Tympel et al.
2013
). Recently, the flow in an array of three
magnetic obstacles has been simulated numerically (Kenjeres
2012
), a situation that
may have relevance for heat transfer applications (Zhang and Huang
2013
). Flows
of electrolytes past magnetic obstacles have been less explored. Honji (
1991
) and
Honji and Haraguchi (
1995
) performed experiments in a shallow layer of salt water
contained in a long tank, where a D.C. current was applied transversally to the tank's
long axis, while a permanent magnet located externally was dragged at a constant
velocity along the center line of the water tank. Similarly, more extensive experiments
were performed by Afanasyev and Korabel (
2006
). These authors considered flows
produced by a single magnet as well as by two magnets with opposite orientations,
aligned with the direction of motion and separated by a short distance. However, to
the best of our knowledge, the electrolytic flow created by a pair of magnetic obstacles
side by side has not been previously considered. This problem is interesting, since
the analogous flow with solid obstacles has been investigated extensively so that
flow regimes are well characterized (Zdravkovich
1985
; Peschard and Gal
1996
;
Sumner et al.
1999
). In the present paper, we explore numerically the flow past a
pair of magnetic obstacles side by side and compare the flow regimes with those
corresponding to the flow past solid cylinders.
2 Formulation of the Problem
We consider the flow of a shallow layer of an electrolyte in a rectangular container
affected by localized Lorentz forces, i.e. magnetic obstacles. The forces are produced
by the interaction of magnetic fields generated by two permanent magnets and a D.C.
electrical current applied transversally to the main flow through electrodes located in
the lateral walls and connected to a power source. Square magnets whose side length
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