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Feng L.,Chongqing University | Shi W.-Y.,Chongqing University | Shi W.-Y.,Key Laboratory of Low grade Energy Utilization Technologies and Systems
Metallurgical and Materials Transactions B: Process Metallurgy and Materials Processing Science | Year: 2015

In this work, the influence of eddy effect of coils on magnetic, flow, and temperature fields in an electromagnetically levitated molten droplet was investigated by a serial of axisymmetric numerical simulations. In an electromagnetic levitation device, both metal droplet and coils are conductive materials, therefore the distributions of current density in them should be non-uniform as a result of the eddy effect. However, in previous works, the eddy effect was considered alone in metal droplet but ignored in coils usually. As the distance of coils and metal droplet is several millimetres in general, the non-uniform distribution of current density in coils actually gives important influences on calculations of magnetic, flow, and temperature fields. Here, we consider the eddy effect both in metal droplet as well as that in coils simultaneously. Lifting force, absorbed power, fluid flow, and temperature field inside a 4-mm radius molten copper droplet as a typical example are then calculated and analyzed carefully under such condition. The results show that eddy effect leads to higher magnetic force, velocity, and temperature in both levitating and melting processes than those when the eddy effect is ignored. What is more, such influence increases as the distance of droplet and coils becomes closer, which corresponds to experimental measurement. Therefore, we suggest that eddy effect of coils should be considered in numerical simulation on this topic to obtain more reliable result. © 2015, The Minerals, Metals & Materials Society and ASM International.


Feng L.,Chongqing University | Shi W.-Y.,Chongqing University | Shi W.-Y.,Key Laboratory of Low grade Energy Utilization Technologies and Systems
ISIJ International | Year: 2016

This work presents a transient simulation of electromagnetically levitated deformed droplet based on Arbitrary Lagrangian-Eulerian method. The magnetic, flow, temperature fields as well as free surface deformation of a molten aluminum droplet are coupled to investigate the influence of coil angle arrangement on dynamic deformation and stability of the droplet under terrestrial conditions. Our results confirm that the Arbitrary Lagrangian-Eulerian method can trace the interface of molten droplet more precisely and the calculation of surface effect is more reliable than that of VOF method. Simulation results show that the electromagnetically levitated molten droplet tends to oscillate in vertical direction and the sphere shape deforms largely at the very beginning of simulation. The dynamic deformation of the molten droplet is small during vertical oscillations since the density of aluminum is small. With the increasing of coil angle, the maximum velocity inside droplet decreases gradually and an over 10% difference is observed comparing with 0 and 30 degree coil angles. At the same time, the temperature of droplet declines significantly with the increasing of coil angles, which is of potential interest for temperature control improvement and undercooling processes in electromagnetic device. The deformation of droplet is observed to be most serious with a coil angle of 12 degree, which should be avoided in future coil design for the purpose of stable levitation of massive materials. © 2016 ISIJ.


Tian X.-H.,Chongqing University | Shi W.-Y.,Chongqing University | Shi W.-Y.,Key Laboratory of Low grade Energy Utilization Technologies and Systems | Tang T.,Chongqing University | Feng L.,Chongqing University
ISIJ International | Year: 2016

In order to investigate the influence of static magnetic field on behavior of rising single bubble in conductive fluid, a series of axisymmetric numerical simulations are carried out. A uniform vertical magnetic field with intensities ranging from 0 to 0.4 T (Ha=0-16.97) is superposed and the bubble radii range from 2 mm to 6 mm (R∗=0.2-0.6). The rising velocity, instantaneous bubble shape and terminal height are discussed and whether the magnetic field restrains bubble rising simply or transits from positive effect to negative one with the increasing of magnetic field intensities is analyzed clearly. Besides, the discrepancy of bubble motion under magnetic field with weak or strong surface tension is compared. Numerical results show that vertical magnetic field elongates the bubble shape along vertical direction and a stronger magnetic field intensity contributes to a longer bubble shape. The imposed magnetic field has an inhibitory effect on the rising velocity for bubbles with strong surface tension as well as bubbles with weak surface tension but small sizes. However, for bubbles with weak surface tension but large sizes, the rising velocity is promoted by weak magnetic field intensities whereas inhibited by strong magnetic field intensities. The peak Hartmann number reaching the strongest positive effect and the critical Hartmann number turning from positive effect to negative effect are determined respectively. © 2016 ISIJ.


Li Y.-R.,Chongqing University | Li Y.-R.,Key Laboratory of Low grade Energy Utilization Technologies and Systems | Yuan X.-F.,Chongqing University | Wu C.-M.,Chongqing University | Hu Y.-P.,Chongqing University
International Journal of Heat and Mass Transfer | Year: 2011

In order to understand the characteristics of natural convection of cold water near its density maximum between horizontal cylinders, a series of unsteady two-dimensional numerical simulations were conducted by using finite volume method. The radius ratio of horizontal cylinders ranged from 1.2 to 2.0, density inversion parameter from 0 to 1, and the vertical eccentricity from 0 to 1.0 for eccentric annulus. The results show that the flow pattern mainly depends on the density inversion parameter and Rayleigh number. The formation of small cell at the top or bottom of annulus corresponds to the Rayleigh-Bénard instability within the converse density gradient layer. The width of annulus has slightly influence on the flow structure. However, the number of Bénard cells decreases with the increase of the radius ratio. For the oscillatory flow at a large Rayleigh number, the vertical converse density gradient in the top of annulus or the horizontal density gradient in the middle of annulus plays an important role for the formation of oscillatory flow when the density inversion parameter is in a small or moderate range. But the vertical density gradient in the bottom of annulus and the horizontal density gradient in the middle of annulus work together for oscillatory flow when the density inversion parameter is high. Average Nusselt number on the inner wall increases with the increase of Rayleigh number and radius ratio. However, there exists the minimum value of average Nusselt number at a moderate density inversion parameter. The flow pattern in eccentric annulus has the characteristics of coupling flows in the narrow-gap at the bottom with in the large-gap at the top of annulus. With the increase of the eccentricity, heat transfer is enhanced and the average Nusselt number increases slightly. Based on the simulation results, the new heat transfer correlation has been proposed according to the multiple linear regression technique. © 2011 Elsevier Ltd. All rights reserved.


Feng L.,Chongqing University | Shi W.-Y.,Chongqing University | Shi W.-Y.,Key Laboratory of Low grade Energy Utilization Technologies and Systems
International Journal of Heat and Mass Transfer | Year: 2016

The influence of Marangoni effect on electromagnetically levitated molten droplet under a static magnetic field is investigated by a series of numerical simulations based on Arbitrary Lagrangian-Eulerian method. Firstly the motions and dynamic deformation as well as flow and temperature fields of droplet without Marangoni effect are calculated under various static magnetic fields, then Marangoni effect is introduced and clear comparisons are conducted. The results show that the static magnetic field could dynamically suppress the oscillation and enhance the levitation stability of molten droplet. With the increase of magnetic field intensity, the oscillation amplitude of droplet is decreased and the dynamic deformation during the oscillation is reduced. When the droplet eventually achieves the equilibrium position, the deformation can also be reduced by static magnetic field. Meanwhile the convection inside molten droplet is suppressed and the temperature difference grows, creating a suiting situation for Marangoni effect. The influence of Marangoni effect on behaviors of molten droplet can be divided into two aspects. On one hand, when the static magnetic field is less than 2T, considering of Marangoni effect will dynamically enlarge the deformation due to the linear decrease of surface tension. But further increasing of magnetic field, the shape difference between cases with and without Marangoni effect gets minished gradually because of the strong suppression effect of magnetic field on droplet deformation. On the other hand, when static magnetic field is over 2T, the Marangoni effect would produce a new vortex near the equatorial surface of droplet. With the increasing of magnetic field, firstly the maximum velocity area shifts into zones near the free surface due to the competition between electromagnetic force and thermocapillary force. Then it returns to the free surface and on this occasion, the flow near the equatorial areas is totally dominated by thermocapillary force. Undoubtedly, the Marangoni effect plays an important role in electromagnetic levitation process and it is necessary to take the Marangoni effect into consideration in future numerical simulations for precise prediction of droplet behavior. © 2016 Elsevier Ltd.

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