Numerical study of the oscillations of axially excited liquid annuli with rotational symmetry enclosed in revolving circular cylindrical containers

Abstract

In this paper we investigate numerically the periodic, axisymmetric response of a liquid annulus enclosed in a revolving cylinder and subject to a periodic axial excitation within the range of the natural frequencies. We use a description which employs as solution variables the transverse component of the vorticity vector, the scalar stream function and the transverse velocity component, as well as the position of the free surface. The acceleration due to gravity is neglected, whereas friction and surface tension are taken into account. At the fixed walls the no-slip condition is fulfilled except at points on the contact line. At the contact line the slip condition is applied. The solution of this problem is achieved using the spectral method in the time direction and finite differences in the space direction, whereby surface-adapted coordinates are utilized. Far away from the walls the computational results show good agreement with results obtained from a linearized theory assuming an inviscid liquid, while at the walls boundary layers are generated.