Nonlinear fluid slosh coupled to the dynamics of a spacecraft

Abstract

The dynamics of a linear spacecraft mode coupled to the nonlinear low-gravity slosh of a fluid in a cylindrical tank is investigated. Coupled, nonlinear equations of motion for the fluid-spacecraft system are derived through an assumed mode Lagrangian method. Unlike a linear model, this nonlinear model retains two fundamental slosh modes and three secondary slosh modes. An approximate perturbation solution of the equations of motion indicates that the nonlinear coupled system response involves fluid-spacecraft modal resonances not predicted by either a linear, or a nonlinear, uncoupled slosh analysis. An experiment was developed to verify and complement this analysis. Scale model fluid tanks were coupled to an electromechanical analog for the second-order oscillatory spacecraft mode. Moderate and low gravity were simulated in 1 g using capillary scale models, and zero gravity was simulated in parabolic flight tests on the NASA KC-135 Reduced Gravity Test Facility. The experimental results substantiated the analytical predictions. The dependence of the coupled nonlinear response on the coupled system parameters and the gravity level is illustrated and discussed.