Sloshing is the motion of a free-surface liquid in a partially filled vessel, experienced in marine, automotive, rail, and aerospace industries. During sloshing, the liquid exerts a dynamic force on the surrounding vessel, which may cause leakage or damage to the vessel or its supporting structure. The sloshing motion is a highly nonlinear and random process depending on vessel motion, liquid depth, liquid properties, and vessel geometry.
Resonance also plays a role when the external forcing frequency is close to a natural frequency of the liquid volume. Existing analytical models for predicting the effects of sloshing sometimes offer a reasonable approximation, but their basic assumptions make them invalid for a wide range of applications.
Veryst evaluated several computational methods that can predict liquid sloshing and its effect on the deformation and stresses in the vessel. Multiphase CFD (computational fluid dynamics) methods (such as volume of fluid or phase field) are expensive for this type of application. Single phase CFD methods with free surface modeling are faster, but cannot handle wave breaking and the large deformations. We instead used a mesh-free smoothed particle hydrodynamics (SPH) method, which is a good compromise between accuracy and speed for this application. The model also accounts for the effect of contact between the liquid and the vessel.
We set up a simulation of a partially filled vessel using SPH in Abaqus/Explicit solver. The tank, which is supported at two locations, is initially moving and undergoes a deceleration that brings it to a stop in 0.1 seconds.
The animation above shows the resulting liquid motion. The graph below shows the horizontal reaction at the tank support due to sloshing. The reaction force is normalized by the maximum horizontal load from a similar simulation without an internal liquid mass. The results show the increased forces resulting from the liquid. Note that for this problem the mass of the liquid is 7.3 times that of the tank.
Although the liquid mass absolutely increases reaction forces, simply adding the weight of the liquid to a tank structural analysis would dramatically overestimate the resulting reaction force. The modeling approach we demonstrated therefore provides a much more accurate design tool for baffles and other wave-breaking designs to control the effect of liquid sloshing.
Baffles are commonly used to suppress the sloshing effect in containers and also enhance the integrity of containers. We also considered the effect of alternating and conventional baffles on sloshing.