Meshless Method for Nonuniform Heat-Transfer/Solidification Behavior of Continuous Casting Round Billet
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the continuous casting (CC) process, the quality defects are closely related to the complex thermomechanical and flow behaviors in the mold. In order to compute the accurate temperature variable and shell distribution, numerous efforts focus on the precise heat-transfer solution of the billet. In most cases, the nonuniform growth, shrinkage, and thermal stress of the shell caused by the uneven heat transfer between the billet and mold will lead to surface and internal cracks eventually. However, it is extremely expensive to conduct a full-scale physical simulation on this problem,
LAIQIANG CAI, XUDONG WANG, NING WANG, and MAN YAO are with the School of Materials Science and Engineering, Dalian University of Technology, Dalian 116024, P.R. China and also with the Key Laboratory of Solidification Control and Digital Preparation Technology (Liaoning Province), Dalian University of Technology, Dalian 116024, P.R. China. Contact email: [email protected] Manuscript submitted April 2, 2019.
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and the high-temperature conditions also impose significant obstacles on temperature and stress measurement. Therefore, the methods of numerical simulation, such as the finite element method (FEM), finite difference method (FDM), and finite volume method (FVM),[1–3] are widely employed in a conventional CC process. The discretization techniques of the mesh-based methods mentioned previously rely on the mesh information, which increases the pretreatment of mesh generation, and the grid quality has a great influence on the calculation accuracy. Besides, the numerical integration could be difficult if a single mesh is filled with different phases. One possible solution for the problem is to refine the grid, which means an increase in computational cost. Furthermore, finding or tracking the location of new boundaries and interfaces over time is very challenging when faced with moving boundary problems such as phase transition. In general, it is difficult or even impossible to apply the mesh-based simulation method to deal with the phase transformation, crack formation, large deformation, and other discontinuity issues. Regarding this, the rapid development of meshless methods in recent years provides an alternative solution
to the preceding problems. The approximate solution of meshless methods is constructed entirely in terms of scattered nodes, avoiding the meshing process and connectivity concept between elements. To date, the meshless method has been employed in solving transmission, solid mechanics, and coupled problems and has achieved several favorable results.[4–6] However, only a few studies can be found, to our knowledge, on solving the heat transfer, stress behavior, and flow behavior for the CC process. Zhang et al.[7,8] employed the finite point method (FPM) and meshless local Petrov–Galerkin method to develop a meshless solidification model and a thermoelastic-plastic analysis model and solved the heat transfer and thermal stress of the CC billet, respectively. Considering the thermal properties as
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