Investigation to establish modelling and predictive methods for microstructure formation during freeze casting
Final Report Abstract
Gibbs energy curves approximating the bentonite-water phase diagram dependent on the particle size were derived for the first time. These were then utilized to conduct phase-field simulations of freeze-casting to investigate the effects of solidification conditions and the suspension particle size. The transition velocity from a planar front to a cellular or dendritic morphology was determined and found to be in the same order of magnitude as the experiments. An initially roughly linear dependence of the critical velocity on the solids loading, similar to experiments, was found. Variation of the temperature gradient showed an unexpected dependence of vc ∼ G1/4 in contrast to classical theory, which may be feature of freeze-casting itself. Simulations conducted in the unstable regime showed dendritic morphologies. The primary arm spacing, ice trunk diameter and suspension channel diameter were measured and correlated to the solidification conditions for two different suspension particle sizes. The influence of the velocity on the microstructural lengths was found to be largely similar to that found in experiments, though generally a slightly smaller dependence than in experiments was observed. Furthermore, the simulations showed that the temperature gradient has a significant influence on the observed lengths, which has been largely ignored in the experimental literature. Comparison with the experiments showed similar scaling behavior and the same order of magnitude in the wavelength. Closer accordance could be reached by determining appropriate kinetic parameters based on the experiments. Finally, the influence of convection was investigated by continuing an exemplary simulation with either forced convection or natural convection enabled. Forced convection perpendicular to the growth direction was found to have little influence on the morphology. Body forces antiparallel to the growth direction resulted in a coarsening of the microstructure, with larger body forces showing greater coarsening. Large plumes of concentration were observed for sufficiently high values of body forces parallel to the growth direction (g > 0.019 62 m2 /s) which then interacted with the boundary. For sufficiently small values of g to avoid these plumes, no refinment was observed but the interface temperature was decreased substantially. As in the case of antiparallel body forces the interface temperature was increased, it is likely that for g > 0 refinement would be evident if the simulation would have been conducted with convection from the initial conditions. Further studies into the effect of gravity parallel to the growth direction need to determine a sufficient domain height or boundary condition such that the boundary does not affect the growth in this case.
Publications
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Bad nodes considered harmful: How to Find and Fix the Problem, accepted for Springer International Publishing ,,Sustained Simulation Performance 2018 and 2019”, eds. M. Resch, Y. Kovalenko, W. Bez, E. Focht, E., H. Kobayashi, ISBN 978-3-030-39181-2
Marco Seiz, Johannes Hötzer, Henrik Hierl, S. Andersson, Britta Nestler
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High Performance Computing in Science & Engineering - 23rd Results and Review Workshop of the HLRS
Marco Seiz, Paul Hoffrogge, Henrik Hierl, Andreas Reiter, Daniel Schneider and Britta Nestler
