Radial integral boundary element method for simulating phase change problem with mushy zone

A radial integral boundary element method (BEM) is used to simulate the phase change problem with a mushy zone in this paper. Three phases, including the solid phase, the liquid phase, and the mushy zone, are considered in the phase change problem. First, according to the continuity conditions of temperature and its gradient on the liquid-mushy interface, the mushy zone and the liquid phase in the simulation can be considered as a whole part, namely, the non-solid phase, and the change of latent heat is approximated by heat source which is dependent on temperature. Then, the precise integration BEM is used to obtain the differential equations in the solid phase zone and the non-solid phase zone, respectively. Moreover, an iterative predictor-corrector precise integration method (PIM) is needed to solve the differential equations and obtain the temperature field and the heat flux on the boundary. According to an energy balance equation and the velocity of the interface between the solid phase and the mushy zone, the front-tracking method is used to track the move of the interface. The interface between the liquid phase and the mushy zone is obtained by interpolation of the temperature field. Finally, four numerical examples are provided to assess the performance of the proposed numerical method.

Directional Solidification of AlSi7Fe1 Alloy Under Forced Flow Conditions: Effect of Intermetallic Phase Precipitation and Dendrite Coarsening

A forced flow was experimentally shown to influence the solidification microstructure of metal alloys by modifying the coarsening/ripening law. In some technical alloys (AlSi7Fe1), this flow effect can also be significantly suppressed due to the formation of intermetallic precipitates (β-Al5FeSi) that can block the flow in the mushy region. The forced flow was induced by a rotating magnetic field (RMF). Herein, a three-phase volume-average-based solidification model is introduced to reproduce the above experiment. The three phases are the melt, the primary solid phase of columnar dendrites, and the second solid phase of intermetallic precipitates. The dynamic precipitation of the intermetallic phase is modelled, and its blocking effect on the flow is considered by a modified permeability. Dendrite coarsening, which influences the permeability, is also considered. The RMF induces a strong azimuthal flow and a relatively weak meridional flow (Ekman effect) at the front of the mushy zone during unidirectional solidification. This forced flow reduces the mushy zone thickness, induces the central segregation channel, affects the distribution of the intermetallic precipitates, and influences dendrite coarsening, which in turn modifies the interdendritic flow. Both interdendritic flow and the microstructure formation are strongly coupled. The modelling results support the explanation of Steinbach and Ratke—the formed intermetallic precipitates (β-Al5FeSi) can block the interdendritic flow, and hence influence the coarsening law. The distribution of β-Al5FeSi is dominantly influenced by the flow-induced macrosegregation. The simulation results of the Si and Fe distribution across the sample section are compared with the experimental results, showing good simulation–experiment agreement. Graphic Abstract During alloy solidifications the flow can influence the mushy zone by inducing macrosegregation, modifying the solidification microstructure, and influencing the formation of intermetallic precipitates. The resulting microstructural features can in turn affect the melt flow by changing the flow intensity and flow pattern. A three-phase volume-average-based solidification model is introduced to study the flow-solidification interaction, and hence to improve the knowledge on the formation mechanism of intermetallics and their effect on solidification. (a) Schematic for the flow pattern and formation of different phases; (b) experiment–simulation comparison of macrosegregation (Fe) across the diameter of as-solidified sample.

Effects of aspect ratio and mushy-zone parameter on melting performance of a thermal energy storage unit filled with phase change material

An intermittent supply of energy from renewable or unconventional resources has resulted in the use of phase change materials (PCM) in thermal energy storage (TES) systems. In this work, melting and heat transfer characteristics in a rectangular enclosure of different aspect ratios (width to height) filled with a phase change material (PCM) have been studied numerically. The n-octadecane has been selected as the PCM (melting temp = 301.35 K, Prandtl number ∼ 60). We considered five different aspect ratios (AR) of the enclosure to delineate the effects of 9-fold variation in the aspect ratio. The simulations were carried out using ANSYS Fluent 19.2. In particular, extensive results have been presented and discussed in terms of the temperature contours, rate of melting and energy storage, and total time required to reach the fully melt condition. Additionally, the effect of the mushy zone parameter (A mush ) on the melting performance has also been investigated. Low values of the A mush were seen to predict the higher rate of melting. At a fixed value of A mush , ∼ 3 times faster melting rate was observed as the value of AR was reduced from 3 to 1/3. Finally, it can be concluded that melting and energy storage rate largely depends on the aspect ratio of the enclosure and the optimal choice of the value of the A mush .