Modelling of electromagnetic breaking and electromagnetic stirring in the process of continuous casting of steel

More than 95 % of crude steel is nowadays processed by Continuous Casting (CC) [1]. To further advance the quality of the products and efficiency of the process, electromagnetic (EM) field, which affects the fluid flow as well as the temperature and segregation is added to the CC process. In general, there are two types of electromagnetic devices applicable to the CC process; the electromagnetic breakers (EMBR) which employ the direct current, and the electromagnetic stirrers (EMS), which employ the alternating current. Which of the devices is employed depends on what are the desired effects. Both of the processes are modelled by implementing the Lorentz force into the momentum equation, and if necessary, the Joule heating term into the energy equation. However, the way how these two terms are modelled, depends on the type of the implemented device. In case of EMBRs, the assumption of low magnetic Reynolds number Rem is made, and consequently, the current density is calculated by solving the Poisson’s equation for the electric potential. The EMSs on the other hand, require a low-frequency approximation and the solution of induction equation. The complete set of governing equations for CC process [2] under the influence of magnetic field includes mass, momentum, energy, and species transfer equations, and Maxwell’s equations together with Ohm’s law and charge conservation equation. Additionally, the turbulent kinetic energy and dissipation rate equations together with Abe-Kondoh-Nagano closures are used to account for the turbulence, the lever rule model is used to model the microsegregation, the mixture continuum model is used to model the macrosegregation, fractional step method is used to model pressure-velocity coupling and the enthalpy-temperature relation is used to calculate the temperature from the enthalpy. The solution is sought for on a five-nodded local subdomains by constructing an approximation with multiquadric radial basis functions as a basis and collocation to find the expansion coefficients [3,4]. Present paper presents the discretization of governing equations, together with boundary conditions for both EMBR and EMS devices with meshless Local Radial Basis Function Collocation Method (LRBFCM) [5]

Meshless modelling of microstructure evolution in the continuous casting of steel

A two-dimensional two-scale slice model has been developed to predict the microstructure evolution in the solidifying strand with an arbitrary cross section geometry during continuous casting of steel. The enthalpy equation is solved at the macro level by using meshless local radial basis function collocation method (LRBFCM) based on multiquadrics for spatial discretization and explicit Euler scheme for temporal discretization. The temperature and the solid fraction in computational nodes are calculated by using a continuum model formulation while the lever rule is used as the supplementary microsegregation relation. The temperature field is interpolated to the micro level by using LRBFCM. At the micro level, the normal distribution and Kurz-Giovanola-Trivedi model are proposed to determine temperature dependent nucleation rate and grain growth velocity, respectively. Meshless point-automata algorithm is applied to implement nucleation and grain growth equations. Several examples of computations of the strand with different cross-sections are shown

A numerical benchmark test for continuous casting of steel - II

Abstract. There is a continuously developing need for benchmarking of solidification simulations-from the theoretical [1] as well as from the applied [2] points of view. The history of related benchmarking shows differences of the results between different numerical methods, and differences in comparison with the experiments when solving even quite simple solidification situations. The present benchmark test proposes macrosegregation [3] upgrades to the verification benchmark for continuous casting of steel, first presented in [2]. The paper represents guidelines for the presentation of the numerical method, discretisation and results and shows a reasonable comparison between a commercial finite volume based code and our in-house developed meshless method based code

Modelling of electromagnetic breaking and electromagnetic stirring in the process of continuous casting of steel

More than 95 % of crude steel is nowadays processed by Continuous Casting (CC) [1]. To further advance the quality of the products and efficiency of the process, electromagnetic (EM) field, which affects the fluid flow as well as the temperature and segregation is added to the CC process. In general, there are two types of electromagnetic devices applicable to the CC process; the electromagnetic breakers (EMBR) which employ the direct current, and the electromagnetic stirrers (EMS), which employ the alternating current. Which of the devices is employed depends on what are the desired effects. Both of the processes are modelled by implementing the Lorentz force into the momentum equation, and if necessary, the Joule heating term into the energy equation. However, the way how these two terms are modelled, depends on the type of the implemented device. In case of EMBRs, the assumption of low magnetic Reynolds number Rem is made, and consequently, the current density is calculated by solving the Poisson’s equation for the electric potential. The EMSs on the other hand, require a low-frequency approximation and the solution of induction equation. The complete set of governing equations for CC process [2] under the influence of magnetic field includes mass, momentum, energy, and species transfer equations, and Maxwell’s equations together with Ohm’s law and charge conservation equation. Additionally, the turbulent kinetic energy and dissipation rate equations together with Abe-Kondoh-Nagano closures are used to account for the turbulence, the lever rule model is used to model the microsegregation, the mixture continuum model is used to model the macrosegregation, fractional step method is used to model pressure-velocity coupling and the enthalpy-temperature relation is used to calculate the temperature from the enthalpy. The solution is sought for on a five-nodded local subdomains by constructing an approximation with multiquadric radial basis functions as a basis and collocation to find the expansion coefficients [3,4]. Present paper presents the discretization of governing equations, together with boundary conditions for both EMBR and EMS devices with meshless Local Radial Basis Function Collocation Method (LRBFCM) [5]

The role of hydrogel structure and dynamic loading on chondrocyte gene expression and matrix formation

The purpose of this paper is a multiphysics simulation of 3D temperature and velocity fields in continuous casting of steel under the influence of electromagnetic stirring by a combined meshless - finite element method approach. The transport phenomena are calculated by a meshless local radial basis function collocation technique and the magnetic force by the finite element method solver Elmer. The electromagnetic stirring increases the mixing in the molten steel. The thermal gradient is sharper and solidification is faster along the strand. The results are similar to other publications in the field. The local radial basis function collocation method is for the first time applied to 3D continuous casting problem with mold electromagnetic stirring

Meshless approach to the large-eddy simulation of the continuous casting process

The paper discusses the numerical solution of the large-eddy formulation for modelling the turbulent fluid flow with solidification in the continuous casting of steel. This industrially relevant problem is solved by a meshless method for the first time. The solid-liquid system is formulated within the continuum mixture formulation of the governing, mass momentum and energy equations. The Darcy porous media model describes the mushy region. The large-eddy formulation is based on the Smagorinsky model for sub-grid scale viscosity and the van Driest damping function. The synthetic turbulence is prescribed at the molten steel inlet. The generated turbulent fluctuations are isotopic and correlated in time through an asymmetric time filter. Explicit time discretisation, combined with meshless local radial basis function collocation method, is employed. Five-noded subdomains, non-uniform node arrangement and multiquadrics shape functions are used for solving a two-dimensional model. The sensitivity to different node arrangements, time steps, inlet temperature, and velocity boundary conditions is elaborated and successfully verified by comparison with our previously published meshless k − ε turbulence model of the same process