Inconsistency of the homogeneous vortex model for liquid slosh in spinning spherical tanks
The problem of liquid slosh in spinning containers represents an important factor in an analytical assessment of the destabilizing energy dissipation in dual spin spacecraft. The solution of the governing equations in this problem is involved due to the occurrence of the Coriolis term. Pfeiffer (1974) introduced the concept of homogeneous vorticity. Although the assumption is valid for completely filled ellipsoidal cavities, it is only an approximation for a partially filled cavity. On the basis of the results of a stability analysis, it appears that the assumption of homogeneous vorticity may be true for filling volumes more than 55%, while for lesser volumes this assumption cannot possibly be true, even approximately. Great care should then be taken in using Pfeiffer's model in flow problems involving intrinsic resonances.