Principles of Fluid Dynamic Similarity Analysis for Slosh Experiments

Most tank slosh test programs are not conducted with flight hardware in a flight-like environment due to cost and schedule constraints. Instead, subscale tanks are typically tested on the ground. If the “real”, flight liquid in the tank is a cryogenic propellant, sometimes a cryogen is used during testing, but more often a simulant liquid is used. Fluid dynamic similarity analysis, or “scaling analysis” as it is sometimes called, for slosh examines nondimensional numbers to determine which fluid dynamic regime(s) a tank is operating in. If the relevant nondimensional numbers of a scale tank test are similar enough to the real tank’s nondimensional numbers, then it is likely that the scale test data will be similar to what would be obtained with the real tank. This type of analysis is useful for guiding experiment design, test liquid selection, and for understanding the physical relevance of prior test data to a specific application. The authors have performed scaling analyses for many slosh test programs conducted in ground, parabolic flight, suborbital, and in-orbit environments. Basics of how to perform the analysis, along with select examples from ground and microgravity environments, are presented. Suggestions for various assumptions and compromises to make are discussed. Limitations and challenges are also discussed.