Fast computation of the Lorentz force induced by longitudinal electromagnetic stirring

In this work, we revisit a recent transient three-dimensional (3D) model for longitudinal electromagnetic stirring in the continuous casting of rectangular steel blooms. Whereas the earlier work was able to demonstrate accurate approximations to the solutions in two asymptotic limits, both of which gave economical alternatives to time-consuming 3D computations, here we show that the original governing equations can be manipulated to a form that allows for rapid computation even outside of these asymptotic limits. The resulting formulation requires the numerical solution of two steady-state complex Helmholtz-like equations in two dimensions that are coupled via a non-standard internal interface condition that is reminiscent of that occurring in the study of Marangoni convection; these equations are then solved numerically using the finite-element software Comsol Multiphysics. With this formulation, it is possible to compute the time-averaged Lorentz force components in a way that requires around four orders of magnitude less computational time than the fully 3D approach. (c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Automated summary

This work revisits a recent model for longitudinal electromagnetic stirring in the continuous casting process. By manipulating the governing equations, a rapid computation method is proposed, which requires significantly less computational time compared to traditional 3D methods. Numerical solutions and finite-element software are used to simulate the process and calculate the time-averaged Lorentz force components.