Thermocapillary-driven dynamics of a free surface in microgravity: Control of sloshing

Abstract

Numerical simulations are used to analyze the dynamics of a free surface excited by thermal modulations at the lateral boundaries that generate a time-dependent thermocapillary flow. Fluid parameters are selected to be representative of 5 cSt silicone oil. Following the work of Gligor et al. [“Thermocapillary-driven dynamics of a free surface in microgravity: Response to steady and oscillatory thermal excitation,” Phys. Fluids 34, 042116 (2022)], the response of the free surface to oscillatory thermal excitation is characterized by the displacement of the contact points, and a frequency sweep is used to obtain a Bode-type diagram that reveals a resonance peak in the vicinity of the first sloshing mode. The ability of the thermocapillary flow to excite this sloshing mode suggests a control strategy that uses thermal modulations to dampen sloshing motion. After the response of the isothermal surface to a generic pulse-like inertial perturbation is measured, a classical proportional integral derivative control is implemented and the effect of its gains is considered separately. The efficacy of the controller is characterized by the decay time of the contact point oscillations and by a cost function. The effect of possible delays in the control loop is accounted for. Finally, a controller with a derivative gain is selected and used to dampen the motion induced by a reboosting maneuver of the International Space Station.