Multiphysics modeling of the steel continuous casting process.

摘要

This work develops a macroscale, multiphysics model of the continuous casting of steel. The complete model accounts for the turbulent flow and nonuniform distribution of superheat in the molten steel, the elastic-viscoplastic thermal shrinkage of the solidifying shell, the heat transfer through the shell-mold interface with variable gap size, and the thermal distortion of the mold. These models are coupled together with carefully constructed boundary conditions with the aid of reduced-order models into a single tool to investigate behavior in the mold region, for practical applications such as predicting ideal tapers for a beam-blank mold.;The thermal and mechanical behaviors of the mold are explored as part of the overall modeling effort, for funnel molds and for beam-blank molds. These models include high geometric detail and reveal temperature variations on the mold-shell interface that may be responsible for cracks in the shell. Specifically, the funnel mold has a column of mold bolts in the middle of the inside-curve region of the funnel that disturbs the uniformity of the hot face temperatures, which combined with the bending effect of the mold on the shell, can lead to longitudinal facial cracks. The shoulder region of the beam-blank mold shows a local hot spot that can be reduced with additional cooling in this region. The distorted shape of the funnel mold narrow face is validated with recent inclinometer measurements from an operating caster. The calculated hot face temperatures and distorted shapes of the mold are transferred into the multiphysics model of the solidifying shell.;The boundary conditions for the first iteration of the multiphysics model come from reduced-order models of the process; one such model is derived in this work for mold heat transfer. The reduced-order model relies on the physics of the solution to the one-dimensional heat-conduction equation to maintain the relationships between inputs and outputs of the model. The geometric parameters in the model are calibrated such that the reduced-order model temperatures match a small, periodic subdomain of the mold. These parameters are demonstrated to be insensitive to the calibration conditions. The thermal behavior of the detailed, three-dimensional mold models used in this work can be approximated closely with a few arithmetic calculations after calibrating the reduced-order model of mold heat transfer.;The example application of the model includes the effects of the molten steel jet on the solidification front and the ferrostatic pressure. The model is demonstrated to match measurements of mold heat removal and the thickness of a breakout shell all the way around the perimeter of the mold, and gives insight to the cause of breakouts in a beam-blank caster. This multiphysics modeling approach redefines the state of the art of process modeling for continuous casting, and can be~used in future work to explore the formation and prevention of defects and other practical issues.;This work also explores the eigen-problem for an arbitrary 3x3 matrix. An explicit, algebraic formula for the eigenvectors is presented.