Numerical Simulation of Coupled Liquid-Solid Dynamics

Under micro-gravity conditions, fluid behaviour is — at least from a computational point of view — more complicated than under terrestrial conditions. Since capillary forces at the free surface dominate the flow, the location and shape of the free surface have to be computed accurately. Moreover, in an extra-terrestrial environment, fluid has the tendency to undergo large topological changes requiring an accurate and robust method for free-surface advection. Further, the fluid is often contained in a cavity (e.g. satellite) that itself is moving; not only because of external forces (e.g. manoeuvring thrusters on a satellite), but also under influence of the fluid motion: the dynamics of the solid body motion and the liquid motion are coupled. In this paper we present a method for simulating coupled liquid-solid dynamics. For the liquid dynamics (the first part of this paper) we solve the Navier-Stokes equations on a Cartesian grid; complex geometries are handled using a cut-cell approach. Transportation of the free surface is based on the VOF-method, but is adapted with a local height function in order to avoid ‘flotsam’ and ‘jetsam’. In the second part of this paper we discuss the coupling between the liquid- and solid body motion. Care has to be taken in integrating the coupled equations in order to keep the numerical method stable for arbitrary liquid/solid mass ratios. Finally, the free-flying satellite SloshSat will be introduced. SloshSat is scheduled for launch in the year 2001 and is designed to investigate liquid dynamics and the coupled liquid-solid dynamics under micro-gravity conditions. The results of this mission promise to provide valuable validation material for Computational Fluid Dynamics methods.