Study on Efficient and High-Precision Modeling of 3D Temperature Field in Continuous Casting Round Billets Based on Hybrid Coordinate System and Equal-Area Grid

Aiming at the challenging issue of nonlinear coupling control between cooling intensity and solidification rate in the secondary cooling zone of round billet continuous casting, this study proposes an efficient 3D temperature field modeling method that integrates hybrid coordinate systems with equal-area meshing. The model is applicable to the temperature range of 800–1520 °C during the continuous casting process. With the modeling strategies of constructing an r-θ-z hybrid coordinate system and designing a dynamic equal-area meshing method, and combined with a topological structure optimization algorithm, the geometric adaptability and numerical stability of the model are significantly improved. Based on this, an explicit-semi-implicit dual-mode finite difference solution model is developed, where the explicit scheme meets real-time online calculation requirements, and the semi-implicit scheme combined with preconditioned Gauss–Seidel iteration enables high-precision offline simulation. Furthermore, a boundary condition model incorporating adaptive mold heat flux correction and multi-mechanism heat transfer in the secondary cooling zone is established. Based on Microsoft Visual Studio 2019 (Version 16.11) C++ development, SIMD vectorization and temperature gradient threshold optimization technologies are employed, resulting in a 35% improvement in computational efficiency. Industrial validation results show that, taking 42CrMo steel with a casting speed of 0.24 m/min and a cross-section of φ600 mm as an example, the deviation between the calculated surface temperature (887 °C) and the measured value (876 °C) of the round billet in the straightening zone is only 11 °C, and the calculation error of the cold billet diameter is only 0.325% (with a calculated value of 597.548 mm and a measured average value of 599.5 mm), both meeting the accuracy requirements for engineering applications. The model breaks through the limitations of traditional empirical formulas and provides theoretical support for digital control of continuous casting processes and quality optimization of high-alloy steels.