In this paper, an experimental model for the directional solidification of Pb-Sn alloy is built and the effects of five different initial concentrations on the solidification microstructure are investigated. In the experiment, the constant temperature gradient and growth rate are given by the designed control mechanism. These can lead to directional solidification, which can be seen in the macro and micro photos of the resulting microstructures. From the microstructure observation, the casting can be divided into three zones, the chill-affected, directional solidification and air-affected zones and the directional columnar structures can be obtained in the latter two zones. The non-lamellar eutectic structure is found in the case with the initial concentration closest to the eutectic one and it is also seen between the columnar structures, whose existence probability increases with the initial concentration. In the cases of low initial concentration, the columnar structures are cells, but in the cases of high concentration, they are dendrites. For either cellular or dendritic structure, the higher initial concentration has the smaller microstructure size. Due to the cooling effect of chill, as the location in the casting is farther from the chill, it has a slower cooling rate, which leads to larger microstructure size.
Rather than designated directly as solid if the micromesh (or cell) larger than a nucleus is
chosen as the nucleation site, the growth of a nucleus in the cell is considered in the application of
the modified cellular automaton model to simulate the evolution of dendritic microstructures in the
solidification of Al-Cu alloy. The growth velocity of a nucleus or a dendrite tip is calculated
according to the KGT (Kurz-Giovanola-Trivedi) model, which is the function of the undercooling.
In this study, the dendritic microstructures, such as the free dendritic growth in an undercooled melt
and the dendritic growth in the directional solidification, are simulated with the modified growth
algorithm in the nucleation cell. The simulated results for the temporal and final morphologies are
shown and are in agreement with the experimental ones.
Choosing appropriate time steps to model the transient and discontinuous characteristics of solidification processes is difficult. The current study develops a modified local time truncation error (LTE)-based strategy designed to adaptively adjust the size of the time step during the simulated solidification procedure in such a way that the time steps can be adapted in accordance with the local variations in latent heat released during phase change or the effects of pure conduction in a single solid or liquid phase. The computational accuracy, efficiency and convergence of the proposed method are demonstrated via the simulation of the one-dimensional and two-dimensional solidification problems and compared with those of other uniform time step and adaptive time step methods. Consequently, the effects of latent heat release are more accurately modeled, the precision and efficiency of the computational solutions is correspondingly improved, and the computational errors are minimized. Furthermore, in solving the 2-D problem, it is shown that the line Gauss-Seidel iteration method and the proposed nonlinear iteration method can be combined to construct a highly efficient and accurate solver.
SUMMARYAdaptive time step methods provide a computationally efficient means of simulating transient problems with a high degree of numerical accuracy. However, choosing appropriate time steps to model the transient characteristics of solidification processes is difficult. The Gresho-Lee-Sani predictor-corrector strategy, one of the most commonly applied adaptive time step methods, fails to accurately model the latent heat release associated with phase change due to its exaggerated time steps while the apparent heat capacity method is applied. Accordingly, the current study develops a modified local time truncation error-based strategy designed to adaptively adjust the size of the time step during the simulated solidification procedure in such a way that the effects of latent heat release are more accurately modeled and the precision of the computational solutions correspondingly improved. The computational accuracy and efficiency of the proposed method are demonstrated via the simulation of several one-dimensional and two-dimensional thermal problems characterized by different phase change phenomena and boundary conditions. The feasibility of the proposed method for the modeling of solidification processes is further verified via its applications to the enthalpy method.
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