Nonlinear free surface effects in tank draining at low gravity

Abstract

Solutions are developed for the low-gravity draining problem, retaining all of the nonlinear terms in the free surface boundary conditions. The resultant free surface shapes are compared to published experimental data, linearized solutions, and solutions from the Marker and Cell method (finite difference solutions of the Navier-Stokes equations). Linearized analyses are shown to fail at both large and small Weber number (based on mean velocity). Domains of validity for the linearized and nonlinear analyses are found by comparison of theory and experiment. Bond number is shown to have little effect on the pull-through height for the range of Bond number of interest to orbiting spacecraft. Weber number is shown to be a better choice for correlating experimental data than Froude number.