A mathematical model has been developed to analyze the mass transfer in the sequence continuous casting process with the static magnetic field. The induced electromagnetic force is obtained by solving simultaneous equations for the momentum and the electromagnetic field. The application of static magnetic field affects the mass transfer by changing the flow field in the strand. The results of numerical calculation show a reasonable agreement of the calculated relative concentration of mixed steel with the measured one. The mixing of molten steel in the low part of the mold is significantly suppressed by the static magnetic field, and composition of new grade steel along the slab length in the transition zone increases significantly. The distribution of relative concentration averaged at cross section changes from parabolic to integral symbolic-like along the slab length, and the transition length is reduced about 50% by applying the magnetic field of 0.5 T.

Rotating magnetic field is applied in up-leg of RH vessel to promote the removal of non- metallic inclusions of molten steel and to prolong the life of RH equipment. Physical and mathematical models have been developed to understand the two-phase turbulent flow considering the effect of the rotating magnetic field in the RH vacuum degassing vessel. Water model experiments verified that the gas bubbles can be moved toward the central zone of up-leg of RH vessel as the result of density difference between gas bubbles and liquid in the swirling flow. The larger circulation flow rate can be obtained in RH degassing vessel with the effect of swirling flow. A penetrating velocity, which does not change the equation characteristics but changes solution distribution, is proposed to revise the gas volume fraction conservation equation. A revised gas volume fraction conservation equation is successfully used to solve the gas distribution in RH vessel. If there is no swirling flow, the larger upward velocities and maximum of the gas volume fraction appear near wall of up-leg. If the rotating magnetic field is applied in up-leg, the larger upward velocities occur in the central zone of up-leg. These phenomena agree with the experimental observation. When the rotating electromagnetic force is applied, the numerical results showed that a swirling flow may be produced and extended into the vacuum chamber. As the occurrence of swirling flow in upper part of up-leg, the maximum of gas volume fraction moves toward the center zone of up-leg and the upward parabolic velocity distribution is also formed.

A mathematical model has been developed to analyze molten metal flow, considering the effects of argon gas injection and static magnetic-field application in the continuous casting process. The k-« turbulence model is used to calculate the turbulent variables. A homogeneous fluid model with variable density is employed to tackle the molten metal-argon gas flow. The electromagnetic force is incorporated into the Navier–Stokes equation, and the effects of boundary conditions of the magnetic field on the velocity distribution near the mold wall are included. A good agreement between the numerically obtained flow-field results and measurements is obtained. The argon gas injection changes the molten metal flow pattern, mainly in the upper portion of the mold. By applying the magnetic field, values of the averaged velocity field in the bulk decrease significantly, and, especially at the top free surface, they become very small, which can cause meniscus freezing. When magnetic-field application and argon gas injection are used together, the external flow field out of the gas plume is significantly suppressed; nevertheless, flotation of gas bubbles is still active and is not affected directly by the magnetic field. Although the penetrating length of the gas plume is shortened, the argon gas bubbles in molten steel still cause fluctuation at the top free surface, which prevents the occurrence of freezing.

Biased flow occurs frequently in the slab continuous casting process and leads to downgraded steel quality. A mathematical model has been developed to analyze the three-dimensional biased flow phenomena associated with the effects of static magnetic-field application and argon gas injection in the slab continuous casting process. By moving the submerged entry nozzle (SEN) from center to off-center, the biased flow and vortexing flow in the mold can be reproduced in the numerical simulation. The existence of a vortexing flow is shown to result from three-dimensional biased flow in the mold. A vortex is located at the low-velocity side adjacent to the SEN. The vortex strength depends on the local horizontal velocity of molten steel and decreases gradually with distance from the free surface. The vortexing-zone size depends on the biased distance of the SEN, and the intensity of the vortexing flow depends on the casting speed of the continuous caster. Only when the location and strength of the magnetic field are properly chosen, can the vortexing flow be suppressed by a static magnetic-field application. The effect of argon gas injection on the vortexing flow is not remarkable. The combination of magnetic-field application and argon gas injection can correct the biased flow and suppress the vortexing flow by suppressing the surface velocity and removing the downward velocity near the SEN in the mold.

A mathematical model has been developed to analyze the circulating flow characteristics in RH Degassing vessel designed for two-and multi-legs system. The homogeneous model with the spatially variable density was used to simulate gas-liquid flow in up-legs. The difference of density between pure liquid and gas-liquid was considered to be a driving force of circulation flow. The volume fraction of gas was obtained by modifying the gas plume model of the stirred ladle. The complicated geometry including ladle, vacuum, up-legs, and down-leg was considered by incorporation of blockage technique. Numerical calculations of the circulating flow have been conducted for the water model of RH degassing vessel with twoand multi-legs with changing the air flowrates from 5 to 35 l/min. Computed velocities at the exit of downleg agree well with the observed data available in the literature. The momentum transport in RH degassing vessel with multi-legs will be larger than that with two-legs. This is justified based on fact that the velocities in RH degassing vessel with multi- legs tend to be uniform, i.e. the mean velocity of bulk in a ladle is remarkably larger than that in two-legs. Simulated transient concentration profile of the tracer from top surface to interior shows clearly the difference of flow characteristics between two-and multi-legs RH degassing vessels.