Arbitrary Lagrangian-Eulerian finite element method for liquid sloshing with contact angle hysteresis in microgravity

Abstract

Liquid sloshing in microgravity environment remains a focus of attention in space engineering. In this paper, an arbitrary Lagrangian-Eulerian finite element method is proposed to simulate the liquid sloshing dynamics with contact angle hysteresis, in which an infinitely small contact free-surface mesh method is used to implement the contact angle boundary condition. The contact angle hysteresis is accounted for by the relation between the contact angle and the advancing contact angle or the receding contact angle. This method not only guarantees the conformity between the numerical treatment and the actual liquid sloshing behavior, but also improves the accuracy of the numerical method. The numerical results of the free surface configurations, including the height of the contact line along the tank wall and the height of the free surface along the centerline, which are obtained by simulating the partially wetted liquid reorientation show good agreements with the correspongding experimental results. Then, the liquid sloshing in a spherical tank under microgravity is simulated, and the influences of the contact angle hysteresis on the free surface evolution are analyzed. The results show that it is of great significance to consider the contact angle hysteresis in microgravity environment.