A numerical model is developed on the basis of SIMPLER algorithm to study the ammonothermal Gallium Nitride (GaN) crystal growth. The model, in general, is applicable to transient fluid flows, heat transfer and species transport including a solid/fluid moving boundary, chemical reaction kinetics, porous media and natural convection. The model, in particular, is used to analyze the bulk GaN crystal growth as a function of the most important parameters in ammonothermal crystallization process in supercritical ammonia and potassium amide mineralizer systems, i.e. KNH2-NH3, resulting in a retrograde solubility. The numerical model is developed by volume averaging of the conservation equations over a localized control volume to include the porous medium effects. Darcy-Brinkman-Forchheimer extensions are employed along with Boussinesq approximation for free convection. One set of governing equation is solved for the entire domain. The solid/fluid interface reconstruction was performed with Piecewise Linear Interface Calculation (PLIC) method in which sloped line segments in computational cells are used to approximate the actual crystal surface.;Numerical model predictions are validated with the available experimental and numerical results for natural convection in side heated porous medium and crystal growth in the ammonothermal systems. Simulations were then performed for a typical, but common, research autoclave for the retrograde KNH 2-NH3 ammonothermal system. It was shown that the presence of a narrow gap between the nutrient basket and the autoclave walls, which has been neglected repeatedly in the literature, is central for the correct modeling of the autoclave geometry specially when dealing with mass transfer and overall crystal growth rate. For the considered base case in this study, flow oscillations were observed in the fluid flow which has adverse effects on the crystal quality. Effects of the geometry design on these oscillations and overall crystal growth are studied.;Previous simulations mostly provided information on the flow field and temperature distribution in the hydrothermal crystal growth processes but neglected the critical effects of the mass transfer, chemical reaction kinetics and the crystal growth mechanism. This work addresses the shortcomings of the previous efforts with special attention to the crystallization zone near the seed and provides the tool for the design and optimization of the hydrothermal crystal growth processes.
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