Abstract
Spin-up from rest of a liquid metal having deformable free surface in the presence of a uniform axial magnetic field is numerically studied. Both liquid and gas phases in a vertically mounted cylinder are assumed to be an incompressible, immiscible, Newtonian fluid. Since the viscous dissipation and the Joule heating are neglected, thermal convection due to buoyancy and thermocapillary effects is not taken into account. The effects of Ekman number and Hartmann number were computed with fixing the Froude number of 1.5, the density ratio of 800, and the viscosity ratio of 50. The evolutions of the free surface, three-component velocity field, and electric current density are portrayed using the level-set method and HSMAC method. When a uniform axial magnetic field is imposed, the azimuthal momentum is transferred from the rotating bottom wall to the core region directly through the Hartmann layer. This is the most striking difference from spin-up of the nonmagnetic case.
Highlights
Rotating fluid flows are encountered in a wide variety of industrial occasions, in pumps, water turbines, compressors, wind turbines, and so on
Since since there is a meridional flow in the flow field, it is quite natural that the axisymmetric there a meridional flow in the flow due field, is quite natural that the axisymmetric flow flowisfield becomes three-dimensional to itcentrifugal force instability when the Ekman field becomes three-dimensional due to centrifugal force instability when the
The flow phenomenon with a free surface under the magnetic field depends on various dimensionless numbers and the geometry of the container
Summary
Rotating fluid flows are encountered in a wide variety of industrial occasions, in pumps, water turbines, compressors, wind turbines, and so on. In the study by Greenspan and Howard [1] or Wedemeyer [2], a theoretical method was implemented because the complete numerical calculation of the Navier–Stokes equation was difficult at that time due to the underdeveloped computer. The important parameter in spin-up is the Ekman number, whose time scale is E−0.5 Ω−1 (where E is the Ekman number and Ω is the angular velocity), while the time diffusion scale is E−1 Ω−1. This is due to the effect of the meridian flow due to the nonlinear term of the Navier–Stokes equation
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