Sloshing in microgravity

The International Space Station provides a low gravity environment for experiments that require very low acceleration. The steady component of acceleration due to the gravity gradient is in the microgravity range. It is possible to achieve microgravity levels for the variable component by using isolation racks. For experiments cooled by liquid cryogens sloshing may increase the variable acceleration at the experiment beyond acceptable levels. Sloshing of cryogens in microgravity can be predicted using a surface wave model. The model should include: a calculation of the shape of the unperturbed liquid–gas interface; a listing of the normal modes and resonant frequencies for the container; a prediction of the amplitude of the modes in response to the motion of the container; and a test to detect the breakdown of linear theory. A model is presented that contains these components. The shape of the interface is calculated and it is found that for most anticipated applications the interface is nearly cylindrical or spherical. Since gravity is not aligned with the symmetry of the container, the depth of the liquid is variable. Examples are presented to show how to estimate the extent of variable depth and curved interface on the normal modes and resonant frequencies. Equations are derived for the dynamic interaction of the isolation rack, the dewar and the sloshing motion. Damping is introduced by using boundary layer theory. Random vibration theory is applied to the incoherent component of the driving spectrum while standard resonance formalism is used for the coherent component. The model cannot be used if the wave amplitude becomes so large that linear theory does not apply. A procedure is developed to check for nonlinear difficulties.