Computational Evaluation of Stability in Slosh Dynamics of Tank Vehicles Using Zero Moment Point

Abstract

Sloshing characterized by inertial waves has an adverse effect on the directional dynamics and safety of partially filled tank vehicles, limiting their stability and controllability during steering, accelerating or braking maneuvers. A mathematical description of the transient fluid slosh in a horizontal cylindrical tank should consider the simultaneous lateral, vertical and roll excitations assuming potential flows and a linearized free-surface boundary condition. While the determination of vehicle stability would require coupling this model to a dynamic roll plane model of a tank vehicle resulting in a computationally expensive analysis. Considering the need for a simpler method to predict roll stability for partially filled tank vehicles, we explore the Zero Moment Point of a liquid domain as a novel solution to this challenge. Numerical investigations are carried out in a three-dimensional partially filled tanks while tracking the movement of the liquid-air interface by employing the volume of fluid method in OpenFOAM. The center of Mass and Zero Moment Point were calculated from the computational results using analytical expressions. The movement of free surface is found to be in good agreement with available literature. The center of mass of the liquid domain was traced as a practical means to quantify the slosh in the tanker. The analyses are performed for different fluid fill heights at varying speeds. The results suggest that the roll stability of tank vehicles can be efficiently analyzed using the zero moment point with significantly lower computational effort.