Spacecraft use surface tension to transport liquid fuel and continuously provide gas-free propellants to engines. To ensure the normal operation of spacecraft

it is important to study the capillary flow behavior of liquid propellants. In this study

the capillary rise process was simulated using a single capillary tube

and the gas-liquid interface was captured using the phase-field method. A two-dimensional axisymmetric model of capillary rise was built and solved using the finite element method. To validate the model

numerical results were compared with those calculated using Jurin’s law and the Lucas-Washburn model. The relative errors were 4.44% and 5.21%

respectively

which confirmed the feasibility of the model for simulating the dynamic capillary rise process. Based on the verified model

the height and velocity of the capillary flow were investigated using different gravitational accelerations and cryogenic fluids. The results showed that when the effective gravity was small

the capillary rise process could be divided into three stages: purely inertial

inertial-viscous

and purely viscous. When the effective gravity is high

the capillary rise process can be divided into four stages

because the gravity of the liquid in the tube cannot be ignored. The four stages are purely inertial

inertial-viscous

viscous-gravitational

and purely gravitational. In addition

the height and velocity of the capillary flow decreased as the effective gravity increased. In the initial stage

the higher the surface tension of the cryogenic fluid

the greater the rising height and velocity. As the liquid level increases

the viscous force gradually increases. The velocity of the capillary flow with liquid hydrogen exceeded that with water

liquid nitrogen

and liquid oxygen.