A review of earlier studies in the area of sloshing shows that, although there are extensive studies on the main flow analysis, theoretical investigations of viscous damping are scarce, especially for arbitrary axisymmetric tanks. In this paper, an analytical method for calculating the viscous damping ratio of low-gravity sloshing in arbitrary axisymmetric tanks is presented, and its dependence on the Bond number and the filling level is examined. Using two systems of spherical coordinates, an analytical expression of bidirectional flow in the boundary layer is derived. By substituting this expression into the virtual work expression of the Navier–Stokes equations’ viscous terms, the modal damping term is determined. It is shown that as the Bond number decreases the damping ratio increases, due to prolongation of the natural period rather than to increase in the damping coefficient. A notable finding is that for high filling levels the damping coefficient decreases with decreasing Bond number, unlike the damping ratio. The reason for this is explained by introducing a correlation parameter whose Bond number dependence is similar to that of the damping coefficient. The analysis is verified by comparing with earlier experimental results.
Viscous Damping Ratio of Low-Gravity Sloshing in Arbitrary Axisymmetric Tanks
Journal of Spacecraft and Rockets ; 50 , 4 ; 807-815
2013-07-01
Article (Journal)
Electronic Resource
English
Viscous Damping Ratio of Low-Gravity Sloshing in Arbitrary Axisymmetric Tanks
Online Contents | 2013
|Sloshing of liquids in axisymmetric ellipsoidal tanks
AIAA | 1965
|Low-gravity sloshing in rectangular tanks
NTRS | 1970
|Sloshing damping in cylindrical liquid storage tanks with baffles
Tema Archive | 2008
|