Slosh Damping Caused by Friction Work Due to Contact Angle Hysteresis

The damping ratio of low-gravity sloshing induced by the friction work due to contact angle hysteresis is calculated using a newly developed semianalytical sloshing analysis method for arbitrary axisymmetric tanks. The damping ratio is estimated for the first mode for the case with small contact angle and its variation, as a fundamental study for propellant sloshing. First, the relation between the friction force and the change in the contact angle caused by contact angle hysteresis is derived from the equilibrium among the friction force and the three surface tensions. Next, the virtual work done by the friction force is calculated to determine the nonlinear damping term to be introduced into the modal equation for sloshing. Physical considerations are made for the dependencies of the damping ratio on the Bond number and filling level. Although the damping term arises from the second-order small term in the friction force, the damping ratio can reach the same order as the viscous damping ratio for low Bond numbers because, due to the hysteresis nonlinearity, the friction damping ratio increases with decreasing Bond number more markedly than the viscous ratio.