Modeling solid air dendrite growth solidification with thermosolutal diffusion using non-isothermal quantitative phase field method

Exposure of air to liquid hydrogen may result in the formation of external oxygen-enriched solid air particles, posing significant safety hazards to the liquid hydrogen system. This study involves the development of a nonisothermal growth model for solid air (air of solid state) dendrites, which is driven by the coupling of thermosolutal diffusion, and is implemented using the quantitative phase field method. The primary aim is to investigate the morphological evolution, growth rate, and solute distribution in solid air dendrites under various thermal conditions. The findings indicate that non-isothermal simulations, considering the latent heat of solidification, offer a more realistic representation of solid air dendrite growth compared to isothermal simulations. Specifically, the non-isothermal simulations show a significant reduction in dendrite tip growth rate by 34.14 % and a peak oxygen concentration decrease of 14.6 % compared to isothermal simulations. When the initial subcooling is set at 4 K, the solid-liquid mushy zone exhibits a maximum oxygen concentration of 0.403. Boundary heat transfer drastically alters the temperature distribution in the computational domain, thereby affecting the growth pattern of solid air dendrites. Boundary heat transfer significantly alters the lengths of dendritic arms near that boundary. Specifically, heating causes a reduction in arm lengths by 30.74 %, while cooling induces an increase of 143.29 % compared to the case without any boundary heat flux. Under heating conditions, the diffusion capacity of the oxygen solute increases with temperature. However, simultaneously, the growth of dendrite arms is inhibited, causing less oxygen solute to be released into the liquid phase. As a result, there is a significant decrease in oxygen concentration in the calculated domain. This effect becomes more pronounced as the boundary heat flux increases, with a 33.26 % reduction in dendrite arm length and a 10.64 % reduction in oxygen concentration for a heating with 162 kW/m2. The opposite effect is observed during cooling.