Axisymmetric surface oscillations in a cylindrical container with compensated gravity.

In this study the first mode of axisymmetric surface oscillations of a free liquid interface in a partly filled right circular cylinder under compensated gravity is investigated numerically. The situation is similar to a spacecraft that enters a ballistic flight at the end of thrust. A reorientation of the liquid of the free liquid surface toward the new equilibrium position takes place. The characteristics of this flow, such as the frequency and the damping, are governed by the behavior of the contact line. The investigations focus on the dependence on the contact line boundary condition, including contact angle variation, and on viscous effects. The effect on the natural frequency and the damping is considered. An analytical approximation for the frequency behavior for a frictionless liquid for a free and a fixed contact line condition is given. Further analytical approximations for the damping behavior in dependence on the contact angle and the Ohnesorge number are determined. The numerical results show very good agreement with experimental data.