Effects Of Static Magnetic Field On Oscillation And Deformation Of Levitated Droplet By Phase Field Simulation

The phenomena of the phase flow with free surface play significant roles in theindustrial processes such as the measurement of thermal properties by electromagneticlevitation experiment. The gas-liquid free interface of molten levitated metal dropletinvolves deformation and oscillation, and the internal convection is very complex due tothe effect of surface tension, Lorentz force and viscous force. The motion of droplet hasan important influence on the accurate measurement of the physical parameters inexperiments. Therefore, a detailed understanding of the characteristics of dropletdeformation and internal flow is benefit for measurement of physical parameters ofmolten droplet.This paper introduces us the oscillation process in a silicon melt droplet with theinitial shape of the second-order and fourth-order Legendre function by phase-fieldmethod. Taking account of the influence of static magnetic field, we get the result ofoscillation deformation process of melt droplet with different magnetic field strength.The simulated object has the characteristics of high-density ratio, which results in agreat gradient at the interface. In order to ensure the numerical stability, an algorithmcombining Newton iteration and semi-implicit scheme is adopted to solve Cahn-Hilliardequation. The shape deformation, motion and oscillation period of the droplet wereobtained as well as the influences of parameters, such as Ha, We, Re number and theinitial shape. The main conclusions are as follows:By analyzing and comparing the characteristics of droplet oscillation with differentRe and We，we found that the droplet oscillation period increases with the increase ofviscous force, and decreases with the surface tension. In the process of dropletoscillation, the surface tension prevent the droplet extension, so slow down the dropletextension and promote droplet retraction. The direction of the viscous force is alwaysopposite to movement of the droplet, the resistance force of the flow increases, makingthe period of the droplet oscillation increases. With the We increases and the surfacetension decreases, the pressure in the droplet significantly decreases. With the decreasesof the pressure in the droplet, its pressure difference inside the droplets decreases, so theflow of droplet is weakened. When the Reynolds number increases, the viscous forcedecreases and the amplitude of the droplet increases. The curvature of the dropletincreases and the pressure increases, so the pressure difference increases. The flow in the droplet is enhanced with increase of Reynolds number.Through simulation results of the droplet oscillation under different magnetic fieldstrength, we analyze the influence of magnetic field on the internal flow of droplet. Wefound that at the initial moment of the droplet movement impact of static magnetic fieldis not obvious because the flow in the droplet is weak. As the flow in the dropletenhances the magnetic force increases and the inhibitory effect of the magnetic field onconvective inside the droplet significantly increases. The magnetic force has moreprominent effect on the droplet flow with the increase of magnetic field strength. Theadditional static magnetic field can stabilize the internal convection and restrain theoscillation of the droplet. As a result, the progress of the droplet varying to be sphericalis accelerated under the function of static magnetic field.