Effects Of Static Magnetic Field On Oscillation And Deformation As Well As Thermophysical Property Measurements Of An Electromagnetically Levitated Droplet

The electromagnetic levitation(EML)is a widely used containerless processing technology which enables materials to get rid of the restraint of containers and eliminates the potential pollution and heterogeneous nucleation.In addition,since materials can reach a high degree of overheating and supercooling easily,EML is also an important way for measuring the thermophysical properties of molten melts over a wide range of temperature,such as surface tension,thermal conductivity,emissivity,density,heat capacity,etc.In numerical simulations,these parameters play crucial roles in accurately predicting the behaviors of melt,so as to better preparation of high quality semiconductor monocrystalline materials and high performance alloys.In present work,the electromagnetically levitated droplet is taken as the research object,the movement and oscillation behaviors during levitation process are analysized systematically.In addition,the effects of static magnetic field on oscillation,deformation and thermophysical property measurements of molten droplet are investigated throughly.Firstly,the influence of eddy effect on electromagnetic force and levitation position of droplet is investigated.The arbitrary Lagrangian Euler method is adopted to track the free surface of droplet.The eddy effect on flow,temperature field and deformations of droplet under various currents and radii are analysized.The results show that the eddy effect declines the electromagnetic force and Joule heat,which leads to a lower levitation position.However,the flow and temperature field is barely affected with relative error of 1%.When the levitation position is relatively low,the eddy effect decreases the pinch force effectively resulting to a smaller deformation.When the droplet is suspended in a high height,the eddy effect decreases the levitation height and leading to a higher pinch force and larger deformation.On terrestrial condition,strong electromagnetic force is essential for stable levitatation of droplet,which is often accompanied by severe convection and oscillation.In present work,the effects of current intensity and droplet radius on lifting force and equilibrium position of silicon melt are investigated firstly.The effects of current intensity and droplet radius on flow,temperature,oscillation as well as deformation are investigated and analyzed throughly.Comparisons of convection and temperature distribution between deformed and undeformed droplets are given.With the increase of current intensity,the levitation position increases gradually,and the convection,temperature and deformation rate of droplet decrease accordingly,which indicates that the increase of current intensity can effectively improve the levitation stability of droplet.With the increase of droplet radius,the levitation position of droplet increases first and then declines,and the convection intensity,deformation rate and maximum temperature in droplet decreases rapidly at first and then increases gradually.Besides,the flow and temperature of an undeformed droplet is lower than that of deformed ones.The discrepancy shows a decline with the increase of current intensity and droplet radius.The effects of vertical magnetic field on oscillation and deformation of an electromagnetically levitated is analysized.The results show that with the increase of magnetic field intensity,the oscillation amplitude and dynamic deformation of droplet decreases,while the suspension position increases and the MHD convection is restrained obviously.Besides the temperature difference is increasing,leading to more suitable condition for the Marangoni convection.For a weak magnetic field,the inhibition effect on deformation and convection of droplet is small.In such case,the deformation of droplet is enlarged due to Marangoni effect.However,due to the strong convection inside droplet,the temperature difference is small and thermocapillary convection is hard to occur.With the increase of magnetic field intensity,the deformation of droplets is obviously inhibited.In addition,due to the suppression effect on MHD convection and increasing temperature difference,thermocapillary convection occurs near the equatorial surface of droplet.In order to validate the suppression effect of vertical magnetic field on deformation and oscillation of an electromagnetically levitated droplet,we observed and analyzed the droplet oscillation and deformation process experimentally under vertical static magnetic field of 0-3T.The characteristic parameters of longer axis length,Area,sum of longer and shorter axes,difference of longer and shorter axes and rotation angle during oscillations were extracted,and the oscillation mode of droplet was identified under various static magnetic fields.With the increase of the magnetic field intensity,the oscillation amplitude of the droplet decreased gradually,but anomalies appreared around 0.3T and 1.0T during wihch the amplitude increases slightly.When the static magnetic field intensity is less than 0.3T,the m=0,±1,±2 oscillation modes of droplets are easy to distinguish,while with the increase of static magnetic field intensity,only m=±2 oscillation mode continues to exist.The surface tension of the droplet was calculated according to Rayleigh theory using the oscillation frequency of droplet.The results show that when the static magnetic field increases from 0 to 0.3T,the surface tension increases rapidly,and when the static magnetic field intensity was greater than 0.3T,the surface tension decreases gradually and eventually achieves a stable value.By fitting the numerically obtained laser frequency and phase lag curve to conduction models,the effective thermal conductivity of material,including the conduction and convection,is determined.It is found that the main factors affecting the frequency-phaselag curve includes thermal conductivity,emissivity,droplet size and convection intensity as well as deformation of droplet.The higher the frequency is,the smaller the influence of emissivity will be,and the greater the influence of thermal conductivity gets.The radius also has an apparent influence on the frequency-phaselag curve.As the droplet radius increases,the phaselag increases continuously.With the increase of the magnetic field intensity,the convection inside the droplet declines gradually,and the frequency-phaselag curve gets more coincident.Under present model and operating conditions,under magnetic field intensity of 4T,the effective thermal conductivity is almost the same as the real thermal conductivity.The deformation of droplet will enlarge the convection inside droplet and resulting to a longer heat transfer distance.Under strong magnetic field,the former one is totally suppressed while the latter one still exists.The results show that for a droplet with deformation rate of 15.81%,the effective thermal conductivity is about 20% smaller than inherent value.Therefore,the deformation of droplet should be taken into account carefully both in simulations and experiments.Finally,a series of three-dimensional numerical simulations were conducted to investigate and compare the convection inside droplet under vertical,horizontal and rotational magnetic fields.The results show that the flow is totally axisymmetric and two counter-circulating vortexes appear in the droplet with an inner-outer distribution under vertical magnetic fields.The inner vortex brings fluids from the top area to bottom area directly,which is potentially responsible for the requirement of quite strong vertical magnetic fields in the experimental measurement of thermal conductivity of molten silicon.With horizontal magnetic fields,the vortexes inside the droplet turn to an up-down distribution,which is more beneficial in the thermal conductivity measurement since it prevents the direct convective heat transfer effectively.However,the horizontal magnetic field fails to suppress the convection effectively and the flow is intense and spatially imbalanced,leading to a less stable flow state.The rotational magnetic field combines the advantages of the formers,suppressing the convection along z-axis apparently and creating an up-down distribution of vortexes simultaneously.It suggests that the rotational magnetic field provides an alternative or even more suitable way for the thermal conductivity measurement of materials.Besides,the rotational magnetic field would evoke forced convection in azimuthal direction,which can be better controlled by varying rotating frequency.The azimuthal flow is expected to balance the rotation of melts induced by helicity of coils in experiments and shows potential advantages in melt stirring and solidification from undercooled melts.