Multiphysics Model of Metal Solidification on the Continuum Level

Abstract

Separate three-dimensional (3-D) models of thermomechanical behavior of the solidifying shell, turbulent fluid flow in the liquid pool, and thermal distortion of the mold are combined to create an accurate multiphysics model of metal solidification at the continuum level. The new system is applied to simulate continuous casting of steel in a commercial beam-blank caster with complex geometry. A transient coupled elastic-viscoplastic model [1 S. Koric and B. G. Thomas , Efficient Thermo-Mechanical Model for Solidification Processes , Int. J. Numer. Meth. Eng. , vol. 66 , pp. 1955 – 1989 , 2006 .[Crossref], [Web of Science ®] , [Google Scholar]] computes temperature and stress in a transverse slice through the mushy and solid regions of the solidifying metal. This Lagrangian model features an efficient numerical procedure to integrate the constitutive equations of the delta-ferrite and austenite phases of solidifying steel shell using a fixed-grid finite-element approach. The Navier-Stokes equations are solved in the liquid pool using the standard K–ϵ turbulent flow model with standard wall laws at the mushy zone edges that define the domain boundaries. The superheat delivered to the shell is incorporated into the thermalmechanical model of the shell using the enhanced latent heat method [2 S. Koric , B. G. Thomas , and V. R. Voller , Enhanced Latent Heat Method to Incorporate Superheat Effects into Fixed-Grid Multiphysics Simulations , Numer. Heat Transfer B , vol. 57 , pp. 396 – 413 , 2010 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]]. Temperature and thermal distortion modeling of the complete complex-shaped mold includes the tapered copper plates, water cooling slots, backing plates, and nonlinear contact between the different components. Heat transfer across the interfacial gaps between the shell and the mold is fully coupled with the stress model to include the effect of shell shrinkage and gap formation on lowering the heat flux. The model is validated by comparison with analytical solutions of benchmark problems of conduction with phase change [3 J. A. Dantzig and C. L. Tucker III , Modeling in Materials Processing , pp. 282 – 321 , Cambridge University Press , Cambridge , UK , 2001 .[Crossref] , [Google Scholar]], and thermal stress in an unconstrained solidifying plate [4 J. H. Weiner and B. A. Boley , Elasto-Plastic Thermal Stresses in a Solidifying Body , J. Mech. Phys. Solids , vol. 11 , pp. 145 – 154 , 1963 .[Crossref], [Web of Science ®] , [Google Scholar]]. Finally, results from the complete system compare favorably with plant measurements of shell thickness.