Meshless Method for Non-Uniform Heat Transfer/Solidification Behavior of Continuous Casting Round Billet

CAI Laiqiang^{1}^{,}^{2}, WANG Xudong^{1}^{,}^{2}(), YAO Man^{1}^{,}^{2}, LIU Yu^{3}

1 School of Materials Science and Engineering, Dalian University of Technology, Dalian 116024, China 2 Key Laboratory of Solidification Control and Digital Preparation Technology (Liaoning Province), Dalian University of Technology, Dalian 116024, China 3 School of Mechanical Engineering, Northeast Electric Power University, Jilin 132012, China

Compared with the mesh-based numerical calculation method, the meshless methods avoid the problems caused by geometric topology, nodal numbering and information transmission of discrete meshes or nodes, which shows significant advantages in solving the problems of complex computing domain boundaries, phase transformation, interface tracking, and crack propagation. Based on the moving least squares approximation and variational principles, a two-dimensional element-free Galerkin (EFG) model for heat transfer/solidification behavior of continuous casting round billets is derived and established in this work. Taking the measured heat flux as the boundary conditions, the non-uniform solidification behavior of the round billet is calculated and analyzed. The essential issues that affect the suitability and calculation accuracy of the meshless model are discussed, such as the nodal arrangement and the size of the supporting domain. The "concentric circle" nodal arrangement scheme in rectangular coordinate system is proposed, and the results show this scheme can conveniently deal with the problem of curve boundary and the solidified shell movement of round billet, showing great flexibility in node arrangement. When the supporting domain size is adopted to be 1.7 times of the average nodal spacing, the calculation accuracy is high under the regular and random nodal arrangement schemes. The results verify the feasibility and accuracy of EFG meshless model in the calculation of non-uniform heat transfer and solidification of billet. It shows a significant advantage in the phase transformation interface tracking, and provides a theoretical foundation for subsequent research on thermo-mechanical coupling and crack prediction analysis.

Fund: National Natural Science Foundation of China(51974056);National Natural Science Foundation of China(51474047);National Natural Science Foundation of China(51704073)

Corresponding Authors:
WANG Xudong
E-mail: hler@dlut.edu.cn

CAI Laiqiang, WANG Xudong, YAO Man, LIU Yu. Meshless Method for Non-Uniform Heat Transfer/Solidification Behavior of Continuous Casting Round Billet. Acta Metall Sin, 2020, 56(8): 1165-1174.

Fig.1 Schematic of background cells, nodes and supporting domains around integration points adopted in the element-free Galerkin (EFG) method (${\mathit{X}}_{I}$ and ${\mathit{X}}_{J}$ are generic integration points in the calculation domain)

Fig.2 Schematics of the mold assembly (a) and structure of heat flux sensor (b) (${T}_{\mathrm{1}}$ and ${T}_{\mathrm{2}}$ are the temperatures measured by two thermocouples; ${R}_{\mathrm{1}}$ and ${R}_{\mathrm{2}}$ are the distances from the two thermocouples to the hot surface of the mold)

Temperature

Latent heat

Density

Thermal conductivity

Specific heat

J·kg^{-1}

kg·m^{-3}

W·m^{-1}·℃^{-1}

J·kg^{-1}·℃^{-1}

T>T_{L}

7102-1.2(T-T_{L})

k_{effl}

466+0.17T

T_{S}≤T≤T_{L}

272000

7102+3.1(T_{L}-T)

k_{eff}

c_{eff}

T<T_{S}

7299+0.3(T_{S}-T)

14.73+0.0125T

466+0.17T

Table 1 Thermophysical properties of steel^{[31]}

Fig.3 Profiles of measured heat flux along the circumference at various mold heights Color online

Fig.4 The regular nodal arrangement (a) and random nodal arrangement (b) adopted in EFG model

Fig.5 Comparison of EFG surface temperature calculated by regular and random nodal arrangements with finite element method (FEM) results Color online

Fig.6 The comparisons of shell surface temperatures of different supporting domain sizes along the casting direction (α—scaling parameter) Color online (a) 120° from the inner arc(b) 180° from the inner arc

Fig.7 Effects of the supporting domain size on error

Fig.8 Temperature contours at the mold outlet Color online

Fig.9 Position identification of liquid and solid phase interface at different heights under meniscus Color online

Fig.10 Heat flux (a), predicted shell surface temperature (b) and shell thickness (c) along the casting direction at different angles

Fig.11 Comparisons of the circumferential heat flux with the shell thickness at mold height of 75 mm (a) and 285 mm (b), and mold outlet (c), and the comparison of averaged heat flux along the casting direction with the shell thickness (d)

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