Modeling Liquid Motions in Spinning Spacecraft Tanks, 18-9946

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Principal Investigator
Franklin T. Dodge

Inclusive Dates:   04/01/96 - 10/6/99

Background - During the past decade, Southwest Research Institute has extended its world-wide reputation in the dynamics of liquids in spacecraft tanks to include the effects of liquids in spinning spacecraft. The kinetic energy of the spinning spacecraft is dissipated by the liquid motions, and this dissipation can destabilize the spacecraft and cause it to tumble. Thus, understanding the liquid motions is of critical importance.

Approach - This project builds on previous SwRI research and will develop analytic models that can predict energy dissipation rates and damping coefficients for liquids in partially full spinning tanks. The previously developed analytic models are capable of predicting the overall vortex-like motions, as shown in the left illustration, as well as the natural frequencies of the motions. However, the models are based on the assumption that the liquid is ideal (i.e., frictionless), so they cannot predict the rate of energy dissipation caused by viscous stresses in the liquid. The approach that will be used to predict energy-dissipation rates is to extend these previous models by incorporating into them the important viscous stresses near the tank walls by the well-known unsteady boundary layer approximation.

Accomplishments - The unsteady viscous boundary layer model has been developed and incorporated in the previous ideal-liquid vortex models. Predictions have been made of the damping of the vortex motions and the rate of energy dissipation caused by the vortex motions. The predictions were compared to results from the SwRI Liquid Motion Experiment conducted on shuttle flight STS-84 in May 1997 and from results from ground tests of spinning spacecraft. The illustration on the right shows the predictions for the Liquid Motion Experiment. The comparisons were generally close. The boundary layer model is concluded to be capable of predicting flight results with sufficient accuracy to constitute a design tool for spin-stabilized spacecraft.

The small arrows indicate the vortex-like liquid velocity in a partially full cylindrical tank spinning about an axis outside the tank. The shaded area represents the liquid. The vortex motion reverses direction at a frequency equal to the nutation frequency of the spinning tank.

The plot displays the variation of the vortex damping coefficient g and the rate dE/dt at which energy is dissipated by liquid motions in a small spinning cylindrical tank, as a function of the fill fraction of the tank.

Fluid and Machinery Dynamics Program
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