Mixture modeling to simulate helium boiling: Helium gas bubble trapped in high magnetic field

Abstract

Multi-phase flow hydrodynamics is an essential theoretical foundation for modernizing engineering and is important in guiding and developing modernizing engineering. In the realm of superconducting power technology, it is imperative to submerge and cool high-field superconducting magnets and superconducting cables, constructed from superconducting materials, in cryogenic fluids in order to maintain a superconducting state. Even minor thermal disturbances can induce boiling of the cryogenic fluid, leading to a two-phase flow regime. In the case of high-field superconducting magnets, the presence of liquid helium as the cooling medium gives rise to a diamagnetic effect. Consequently, the formation of a bubble resulting from boiling is confined in close proximity to the central aperture of the magnet owing to the influence of the magnetic field force. This confinement adversely affects the heat transmission properties of the magnet. This work presents a comprehensive analysis of the flow state during the boiling process of liquid helium, using the finite element approach and the mixture model. The heat transfer in a two-phase flow is analyzed by treating the system as a single pseudo-fluid. The model is consistent with empirical formulations of liquid helium boiling in large vessels and is also suitable for modeling the effect of heating surface orientation on the critical heat flux. Consequently, the analysis of the retention of helium bubbles generated by boiling in a high-field magnet has been further examined, using this particular model. The results of numerical hydrodynamic studies show that the width of the helium bubble stagnation zone is larger compared to the results of hydrostatic calculations. This poses a major challenge for superconducting magnets operating at high magnetic fields and high temperatures. The paper further analyses the effect of supercooled liquid helium on helium bubble stagnation, thus providing valuable insight into the construction of superconducting magnets with high magnetic fields.