Vortex breakdown in time-dependent electromagnetically driven flow between concentric spheres

Abstract

The electromagnetically driven flow in the wide gap of a concentric spheres system is studied experimentally and numerically in the laminar regime ($Re \leq 1540$). The mainly azimuthal driving Lorentz force is promoted by the interaction of a direct current and a dipolar magnetic field. The current is injected through two ring-shaped copper electrodes located at the equatorial zone of each sphere and the magnetic field is produced by a permanent magnet located inside the inner sphere. Velocity profiles for the azimuthal component in the equatorial plane were obtained with Particle Image Velocimetry and the radial velocity component of the flow was recorded using Ultrasonic Doppler Velocimetry. Laser-fluorescein technique was used for flow visualization. It was found that for a critical electric current ($Re=1140$), an instability occurs and the flow becomes time-dependent. We found, theoretically and experimentally a vortex breakdown structure at each of the polar zones of the spherical gap, which to the best knowledge of the authors, this is the first time it is reported with electromagnetic forcing. A full three-dimensional numerical simulation reproduces the experimental observations qualitatively and quantitatively.

Electromagnetically driven anticyclonic rotation in spherical Couette flow

“…2022; Piedra et al. 2022). The numerical solution considers no-slip conditions on the spheres, whereas the initial conditions consider a quiescent fluid () with no electric current ( ).…”

“…2022; Piedra et al. 2022) allow modelling electromagnetically driven flows of weak electrolytes. In this case, the low magnetic Reynolds number or quasi-static approximation is valid (Figueroa et al.…”

“…Close to the electrode rings, there also exists a component in the polar direction with the same order of magnitude as the radial one, (Piedra et al. 2022). However, the electric current behaves mainly as , which allowed a good comparison with experimental velocity fields, as in previous studies (Figueroa et al.…”

“…If , then we can obtain a previous dimensionless model where the spheres are at rest and the only forcing is the electromagnetic one (Piedra et al. 2022). In the present work, the rotation velocity is larger than the diffusive velocity ; the difference is three orders of magnitude, thus .…”

“…This time-dependent flow is investigated in Piedra et al. (2022). The authors reported a vortex breakdown structure in the polar regions, validated by experiments and theoretical results.…”