NUMERICAL STUDY OF THE OSCILLATIONS OF AXIALLY EXCITED LIQUID ANNULI WITH ROTATIONAL SYMMETRY ENCLOSED IN REVOLVING CIRCULAR CYLINDRICAL CONTAINERS

In this paper we investigate numerically the periodic, axisymmetric re sponse of a liquid annulus enclosed in a revolving cylinder and subjec t to a periodic axial excitation within the range of the natural frequ encies. We use a description which employs as solution variables the t ransverse component of the vorticity vector, the scalar stream functio n and the transverse velocity component, as well as the position of th e free surface. The acceleration due to gravity is neglected, whereas friction and surface tension are taken into account. At the fixed wall s the no-slip condition is fulfilled except at points on the contact l ine. At the contact line the slip condition is applied. The solution o f this problem is achieved using the spectral method in the time direc tion and finite differences in the space direction, whereby surface-ad apted coordinates are utilized. Far away from the walls the computatio nal results show good agreement with results obtained from a linearize d theory assuming an inviscid liquid, while at the walls boundary laye rs are generated.