Dynamics of Liquids in Moving Containers

Abstract

M interest in the behavior of liquids in various containers is undoubtedly very old. The phenomena of liquid motion within a containing vessel presented a challenge as a natural curiosity to the hydrodynamicist of the past centu^, and continues to present difficulties for the engineer today. Civil engineers and seismologists have been very active, particularly since the early 1930's, in studying earthquake effects on large dams, oil tanks, reservoirs and elevated tanks. More recently, particularly with the advent of the jet age, the effects of fuel motion in partially full tanks have, of necessity, been included in some aircraft dynamic stability studies. With the appearance of the large liquid propelled rocket, where at least 90 per cent of the gross weight at liftoff is contributed by the liquid propellants, the forces and moments produced by the movement of large masses of liquids within their containers take on added importance. The exponential increase in the number of reports and papers on the subject of sloshing/' during the past decade is a reflection of this trend. It will be noted that, with the obvious exception of the work on centrifugal slosh/' only those papers have been surveyed here which consider the liquid to be subject to a gravitational force. Problems of bubble formation and growth, the behavior of liquids in free fall, vortex formation in draining tanks, and other related problems have not, in general, been included. Moreover, attention has been mainly restricted to the American literature, although some British, Russian and a few references in Japanese journals are included. The French, German and Italian literature, probably very rich in this field, remains relatively untouched. An extensive bibliography pertaining to the general field of water waves (136) * and two sloshing literature surveys, containing many abstracts, are available (141,142). Attention is also directed to (45) for special studies pertaining to specific rocket vehicles. It should be mentioned that a very large percentage of the reports cited here were carried out under Government contract and are available through the ASTIA offices.