Modeling of solid-air multi-dendrite growth evolution driven by coupled thermal-solute using non-isothermal quantitative phase field method

The safety hazard posed by residual or infiltrated air condensing into external oxygen-rich solid-air (SA) particles in the liquid hydrogen container deserves attention. In this study, the patterns of morphological evolution, oxygen solute distribution, and growth rate of SA single- and multi-dendrite under various thermal environments are investigated using a non-isothermal quantitative phase field model for the first time. The lattice anisotropy problem of six-fold symmetric dendrites is effectively avoided. The results show that the Type II boundary condition is more suitable for the simulation of dendrite growth, which can avoid the influence of boundary conditions on dendrite growth. In addition, the suitability of the isotropic difference method for simulating the growth of SA multi-dendrites with six-fold symmetry is verified in this paper. The maximum values of solid fraction and oxygen solute concentration within the simulated domain are 0.62 and 0.435, respectively, for an initial subcooling degree of 4 K. The temperature distribution is significantly altered by the application of boundary heat flux and affects the growth pattern of SA dendrites. Compared to the scenario with no boundary heat flux, unilateral heat input and heat extraction decreased the solid fraction of SA dendrites by 31% and increased it by 43%, respectively, while the maximum concentration of oxygen solute was reduced to 144.8% and 97.3%, respectively. When boundary heat flux was applied to all quadrilateral boundaries, the solid fraction under heat extraction and heat input conditions is reduced by 82% and enhanced by 138%, respectively, compared to the scenario with no boundary heat flux. Additionally, the maximum concentration of oxygen solute is found to be 197.6% and 69.5% of that without boundary heat flux, respectively. This study improves the understanding of the evolution of solid-air dendrite growth and can provide theoretical guidance for the safe use of liquid hydrogen systems.