Mathematical and computational studies of the stability of axisymmetric annular capillary free surfaces
Abstract
Of principal interest is the stability of a perfectly wetting liquid in an inverted, vertical, right circularcylindrical container having a concave spheroidal bottom. The mathematical conditions that the contained liquid be in stable static equilibrium are derived, including those for the limiting case of zero contact angle. Based on these results, a computational investigation is carried out for a particular container that is used for the storage of liquid fuels in NASA Centaur space vehicles, for which the axial ratio of the container bottom is 0.724. It is found that for perfectly wetting liquids the qualitative nature of the onset of instability changes at a critical liquid volume, which for the Centaur fuel tank corresponds to a mean fill level of approximately 0.503 times the tank's radius. Smallamplitude periodic sloshing modes for this tank were calculated; oscillation frequencies or growth rates are given for several Bond numbers and liquid volumes, for normal modes having up to six angular nodes.
 Publication:

California Univ., Berkeley Report
 Pub Date:
 November 1977
 Bibcode:
 1977ucb..reptR....A
 Keywords:

 Interface Stability;
 Liquid Sloshing;
 LiquidVapor Interfaces;
 Static Stability;
 Centaur Launch Vehicle;
 Differential Equations;
 Dynamic Stability;
 Numerical Analysis;
 Propellant Tanks;
 Reduced Gravity;
 Fluid Mechanics and Heat Transfer