New AGILD EMS Electromagnetic Field Modeling

Abstract

The Electromagnetic Stirring (EMS) technology has wide applications in the metal continuous casting. Stirring consists of exciting variable magnetic field in metal liquid, the magnetic field generates induction current. The induction current in the metal flow interacts with magnetic filed to generate EM force, which makes perfect motion to improve casting. The EM force strength is proportional with square of the magnetic field strength. The key of the optimized control of EMS is to adjust several parameters for best EM force and deep magnetic penetration. In this paper, we present a new AGILD EMS modeling. We use Maxwell magnetic field differential equation to replace the reduced magnetic field equation. We present new volume magnetic differential integral equation and new boundary strip magnetic field differential integral equation which are proposed by XIe and Li in GLGEO. According to the new AGILD EM modeling in [1], we developed 3D AGILD EMS modeling. Our AGILD EMS modeling does not need any complex boundary condition. The matrix equations are decomposed by GILD parallel processes. Therefore, our AGILD EMS modeling is fast and accurate without any boundary error. Our AGILD EMS modeling can simulate multiple strands and EMSs together. The simulation shows that the AGILD EMS modeling is very powerful tool for the design of excellent EMS system in Billent/Bloom and metal continuous casting system. The simulation is performed by using GLGEO’s new GL[2-4] and AGILD EMS modeling software. The EMS is an established technology and installed in Billet, Bloom and metal casters. The stirring consists of exciting variable magnetic field which is penetrating in the steel, iron, and metal liquid. The magnetic field generates induction electric current in the metal liquid. The induction current in the metal liquid interacts with the magnetic field to generate EM force which drives the metal liquid flow motion such that the casting is perfectly performing. The casting quality is improved by reduced segregation and porosity through transformation to an equiaxed solidification structure. The steel and iron productions are increasing due to the increased casting speeds. The temperature and carbon component are key factors for high quality steel. The magnetic field penetrating distribution depends on the material properties and high temperature. Moreover, the electromagnetic properties depend on the temperature. The temperature difference between outer and insider of the caster mold is very large. We consider the magnetic conductivity be space variable. The reduced magnetic field equation is no longer to govern this case. In this paper, we use the magnetic field Maxwell equation to replace the reduced magnetic equation. Moreover, we present a new strip magnetic field differential integral equation which is proposed by Xie and Li in [1]. We use the new strip integral equation on the double layered boundary and the magnetic field Garlekin equation in the internal domain to construct the AGILD EMS modeling for the metal continuous casting. It has more advantages over FEM and FD modeling. The AGILD and GL EMS modeling, GL and AGILD nondestructive testing, GL and AGILD heating modeling, and GL and AGILD heavier viscosity flow modeling for the continuous casting are developed by Xie and Li in GLGEO. Many EM research works on motor need the condition that the magnetic resistivity monotone increasedly depends on the magnetic induction. It is very strong and unpractical condition. In practice, magnetic resistivity is not monotone increasing but has a minimum point at B = B0. Our nonlinear FEM EM modeling [10-12] are available for the above practical condition, i.e. the magnetic resistivity is not monotone increasing. We prove that if H(B) monotone increasedly depends on B, the nonlinear FEM is convergent. Because H(B) = υ(B)B, so, we only need that υ(B)B monotone increasedly depends on the B, which is widely generalized. Moreover, the H(B)’s monotone property is the practical physical property. Our nonlinear FEM magnetic DC modeling is briefly described in this paper. The organization of the paper is as follows. We present the new strip differential integral equation in the section 2 which is proposed in [1]. The double layered collocation FEM equation for the magnetic field is