Numerical Simulation of Three-Dimensional Dendritic Growth of Alloy: Part I—Model Development and Test

To improve the computational efficiency of the three-dimensional (3D) cellular-automaton–finite-volume-method (CA-FVM) model for describing the dendritic growth of alloy, the block-correction technique (BCT) and the parallel computation approach are introduced. Accordingly, a serial of investigations on the efficiency of the optimized codes in dealing with the designed cases for the melt flow and the heat transfer problems is carried out. Moreover, the accuracy of the present codes is evaluated by the comparisons between the solution to the melt flow and the heat transfer problems and the results from analytical equations and the commercial software. Additionally, the capability of the present CA model is evaluated by comparing the steady growth parameters of the equiaxed dendritic tip and the morphology and the secondary dendrite arm spacing (SDAS) of columnar dendrites with the LGK analytical model and the experimental results of the unidirectional solidification of high-carbon steels. The results show that with the introduction of the 3D BCT, the iteration process of the serial tri-diagonal matrix algorithm (TDMA) code changes from the fluctuation type to the smooth one, and thus, the computational cost is reduced significantly. Moreover, the parallel Jacobi code with one two-dimensional (2D) iteration in 3D BCT is proved to be the most efficient one among the codes compiled in the present work, and therefore, accordingly it is employed to simulate the 3D dendritic growth of alloys. The calculated velocity distribution and temperature variation agree well with the results from the analytical equations and the commercial software. The predicted steady tip velocities agree with the LGK analytical model as the undercooling is 6 K to 7 K. Moreover, the predicted columnar dendritic morphology and SDAS of high-carbon Fe-C alloys during the unidirectional solidification agree with the experimental results.