Sloshing in 2-D Flows by the SPH Method

Sloshing is a violent resonant free surface flow with strong non-linear behavior in a partially filled tank. Resulting slamming loads are of main concern. It has become popular to use CFD to model sloshing, but the accuracy of the different methods is not always convincing. Our approach is based on the SPH method, introduced by Monaghan and coauthors (see Monaghan (1994)) and further developed by Tulin and Landrini (2000) and Colagrossi and Landrini (2003). Both single-phase and two-phase flow (gas and liquid) SPH models are used. The method is first verified for sloshing by comparing with theoretical results by the analytically oriented multi-modal method by Faltinsen and Timokha (2002) for 2D flows. This includes comparisons with model tests. The multi-modal method is robust and very time efficient, but cannot handle situations with run up-run down, overturning of the free surface and subsequent impact on the underlying free surface, with the occurrence of bubbly flows. This is a common phenomenon for intermediate and shallow depths. Further, the multi-modal method cannot handle breaking waves occurring in the middle of the tank and heavy tank roof impacts. The latter can be associated with strong two-phase flows, where the jet caused by the initial tank-roof impact shoots over to the opposite wall of the tank. We demonstrate the capabilitity of the SPH method to handle situations like this, and show that the impact can have an important effect on horizontal forces. However further studies are needed to validate slamming pressures.