MHD solidification calculation in Darcy flow

Summary form only given. In a steel making plant, most of the steel quality is decided in the casting process, because most of the surface cracks or non-metallic inclusions cannot be removed in the rolling process. To remove the non-metallic inclusion, electromagnetic stirring (EMS) is used in the initial solidification position of casting to give some velocity to the molten steel. Magnetohydrodynamic (MHD) calculations including heat transfer and a solidification physical model have an important roll to make clear the fundamental characteristics of casting process by EMS. In an MHD calculation model, a coexistence region of liquid and solid is important because it has a great influence on the velocity distribution including the free surface velocity and wall velocity distribution. The steel quality depends upon the velocity distribution. Here, the coexistence is modeled by the Darcy flow model. In the Darcy flow model, a friction coefficient is expressed as a Darcy flow coefficient and a function of the solid fraction The friction force is inserted into the Navier-Stokes equation as a disturbance force. Electromagnetic force is derived from the Maxwell equations by way of the I-V method. I calculate rotating velocity distribution as a parameter of the Darcy flow coefficient. The rotating velocity distribution and the free surface deformation are quite different when the coefficient changes from 0.01 to 1000. I obtain the free surface deformation by means of an oscillation mark at the surface of solidified steel. The oscillation mark is generated when the mold is oscillated at the initial solidification point in order to obtain the lubricant characteristics and to avoid mold burn out. According to the operating data, the oscillation mark height is 8mm. Then the Darcy flow coefficient is decided as 0.7. The free surface velocity distribution by the MHD calculation at that Darcy flow coefficient is the same as the operating velocity.