Integration of Geometry and Analysis for the Study of Liquid Sloshing in Vehicle System Dynamics

Commonly-used sloshing models are either unable to capture changes in the continuous distribution of the fluid free surface, or are not suited for the integration with high fidelity computational multibody system (MBS) algorithms. The objective of this investigation is to address this deficiency by developing a new continuum-based liquid sloshing approach that accounts for the effect of complex fluid and tank geometry and can be systematically integrated with MBS algorithms in order to allow for studying complex motion scenarios. A unified geometry/analysis mesh is used from the outset to examine the effect of liquid sloshing on railroad and highway vehicle dynamics during various maneuvers including braking and curve negotiation [1,2]. Using a non-modal approach, the geometry of the tank and fluid is accurately defined, a continuum-based fluid constitutive model is developed, and a fluid-tank contact algorithm using the penalty approach is employed. In order to examine the effect of liquid sloshing on vehicle dynamics during curve negotiation, a general and precise definition of the outward inertia force is defined, which for flexible bodies does not take the simple form used in rigid body dynamics. During maneuvers, the liquid may experience large displacements and significant changes in shape that can be captured effectively using absolute nodal coordinate formulation (ANCF) finite elements. For rail systems, the liquid sloshing model is integrated with a three-dimensional MBS vehicle algorithm, in which the three-dimensional wheel/rail contact force formulation is used to account for the longitudinal, lateral, and spin creep forces that influence vehicle stability. The effects of fluid sloshing on vehicle dynamics in the case of a tank partially filled with liquid are studied and compared with the equivalent rigid body model in braking and curve negotiation. The results obtained in the study of the rail vehicle model show that liquid sloshing can exacerbate the unbalance effects when the rail vehicle negotiates a curve at a velocity higher than the balance speed, and can significantly increase coupler forces during braking. Analysis of the highway vehicle model shows that the liquid sloshing changes the contact forces between the tires and the ground — increasing the forces on certain wheels and decreasing the forces on other wheels — which in cases of extreme sloshing, can negatively impact the vehicle stability by increasing the possibility of wheel lift and vehicle rollover.