Modeling of solid-air dendrite growth solidification in liquid hydrogen by using isotropic quantitative phase field method

Abstract

The safety hazards caused by solid-air accumulation in liquid hydrogen need attention. This paper is dedicated to the numerical reproduction of the microstructural evolution of solid-air dendrites in liquid hydrogen and the investigation of the oxygen solute distribution pattern. A quantitative phase field model for the growth of six-fold symmetric solid-air dendrites is developed to investigate the growth behavior of solid-air single and multiple dendrites under different subcooling and continuous cooling conditions to address the quantitative deficiencies of previous studies. The results show that the current model can maintain the rotational invariance of solid-air dendrites. With the escalation of subcooling, the dendritic morphology undergoes heightened complexity, and the development of secondary dendrite arms becomes more pronounced. Three characteristic position curves were chosen to quantify the oxygen solute distribution within the solid-air dendrites and in the liquid phase, with the highest oxygen solute concentration near the solid–liquid interface and increasing with subcooling. The distribution of oxygen solute concentration shows the same qualitative characteristics under constant subcooling and continuous cooling conditions, but the oxygen concentration at the solid–liquid interface is higher under continuous cooling compared to constant subcooling. The interaction of multiple dendrites changes the dendrite growth pattern. At constant subcooling, solid-air dendrite growth gradually tends to stagnate, whereas under continuous cooling conditions, solid-air dendrites can achieve greater solid phase fraction. The gaps formed between the dendrites impede the diffusion of oxygen solutes, and the concentration of oxygen solutes is higher at the grain boundaries of the dendrites compared to single dendrite.