Two phase analysis of sloshing in a rectangular container with Volume of Fluid (VOF) methods

Free surface oscillations of a liquid confined in a closed container (sloshing phenomenon) are an important issue when big amounts of liquid are industrially transported. The phenomenon involves two fluids that share a free surface boundary separating them, normally the density of the upper fluid is several orders of magnitude less than the bottom one. Due to this density difference, this phenomena has widely been studied considering only one phase fluid and using different assumptions in the physical fluid modeling. In a recent paper, Ansari et al. (2011) simulated the sloshing in containers considering two liquid phases with different densities using a multimodal method. In this work, all the results obtained by Ansari have been tested, using different densities for the phase set at the top. Despite observing a good agreement in the cases where Ansari used a zero density assumption for the higher phase, serious discrepancies in the free-surface amplitudes have been found in those cases where the experiment involves two phase fluids. In order to make sure that the results computed for comparison are correct, three different codes were used as reference: one multimodal single phase code for those cases where the upper fluid was much less dense that the bottom one and two different Navier-Stokes/VOF codes for all cases. Although these reference codes use different physical and numerical hypotheses, we obtained a remarkable agreement among them. In those cases where a second phase was set at the top of the container, the computed amplitudes were clearly lower compared to the ones obtained by Ansari.