A new continuum-based liquid sloshing approach that accounts for the effect of complex fluid and tank-car geometry on railroad vehicle dynamics is developed in this investigation. A unified geometry/analysis mesh is used from the outset to examine the effect of liquid sloshing on railroad vehicle dynamics during curve negotiation and during the application of electronically controlled pneumatic (ECP) brakes that produce braking forces uniformly and simultaneously across all cars. Using a non-modal approach, the geometry of the tank-car and fluid is accurately defined, a continuum-based fluid constitutive model is employed, and a fluid-tank contact algorithm is developed. The liquid sloshing model is integrated with a three-dimensional multibody system (MBS) railroad vehicle algorithm which accounts for the nonlinear wheel/rail contact. The three-dimensional wheel/rail contact force formulation used in this study accounts for the longitudinal, lateral, and spin creep forces that influence the vehicle stability. In order to examine the effect of the liquid sloshing on the railroad vehicle dynamics during curve negotiation, a general and precise definition of the outward inertia force is defined, and in order to correctly capture the fluid and tank-car geometry, the absolute nodal coordinate formulation (ANCF) is used. The balance speed and centrifugal effects in the case of tank-car partially filled with liquid are studied and compared with the equivalent rigid body model in curve negotiation and braking scenarios. In particular, the results obtained in the case of the ECP brake application of two freight car model are compared with the results obtained when using conventional braking. The traction analysis shows that liquid sloshing has a significant effect on the load distribution between the front and rear trucks. A larger coupler force develops when using conventional braking compared with ECP braking, and the liquid sloshing contributes to amplifying the coupler force in the ECP braking case compared to the equivalent rigid body model which does not capture the fluid nonlinear inertia effects. Furthermore, the results obtained in this study show that liquid sloshing can exacerbate the unbalance effects when the rail vehicle negotiates a curve at a velocity higher than the balance speed.

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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.