# On the Efficacy of Turbulence Modelling for Sloshing
## 5 Conclusions  
Simulations of sloshing-induced damping of partially filled water tanks under a harmonic oscillation motion are performed in this study. The simulations are conducted  
Figure 8: Snapshots of the liquid volume ration \(\alpha>=0.5\) obtained by different turbulent models, (**a**) no-model, (**b**) \(k\)-\(\omega\) SST(**c**) \(k\)-\(\epsilon\), and (**d**) RNG \(k\)-\(\epsilon\). The left figures are three-dimensional snapshots, and the right figures are two-dimensional slices in the middle plane of the left figures. The colouring scheme is the turbulent viscosity, and the opacity is reduced to 50% to show the internal voids.  
via the Volume of Fluid approach using the interFoam solver from the OpenFOAM v8 suite and using different turbulence models. The aim of the study is to investigate the efficacy of the most widely used turbulence models in providing an accurate representation of the flow under a range of sloshing conditions. The standard \(k\)-\(\epsilon\), RNG \(k\)-\(\epsilon\), \(k\)-\(\omega\) SST and no-model are used in the simulation and compared against the experimental data of [59]. A range of excitation amplitudes are considered, starting from a Froude number of 0.7 and reaching 1.85. This corresponds to different sloshing patterns, ranging from single and symmetric mode of sloshing to a violent and turbulent sloshing. Therefore, this work can form the basis of future decision making on what modelling approaches are best suited for the sloshing problems at hand, with the understanding that no one approach is likely to work for all sloshing regimes.  
It is found that the two-dimensional simulation fails to capture the complex dynamics in all cases, and hence the subsequent study is established using three-dimensional simulations. Comparison between the models is based on the estimated dissipated energy induced by the sloshing and a hysteresis of the damping force. In the case of weak and moderate sloshing, all of the turbulence models, except the standard \(k\)-\(\epsilon\), can accurately predict the damping force hysteresis and the energy dissipation. When the sloshing becomes more violent, the quality of the results obtained using any turbulence model degrades, especially in the prediction of the peak damping force. For the tested range of the excitation, the no-model simulations are found to have the best representation of the sloshing dynamics.  
Analysing the added turbulent viscosity, it was found that the standard \(k\)-\(\epsilon\) is the most dissipative, followed by \(k\)-\(\omega\) SST and then RNG \(k\)-\(\epsilon\). This suggests that the use of turbulence models, without an interface treatment, results in numerical damping that limits the strength of the sloshing that can be simulated and hence the modelled damping effect is reduced and not accurately captured compared to the no-model simulations. Another issue with the standard models is the non-physical and excessive dissipation near the interface, which can lower the efficacy of the model [30; 68; 50]. In future work, the effect of the treatment of turbulent viscosity at the interface will be addressed in order to improve the capability of the employed VoF approach to address complex sloshing flows as presented. Additionally, understanding the underlying cause of the differences between models and why some models are more dissipative at the interface than others presents an interesting topic for future work.  
Investigation, O.A.M.; Project administration, S.M.L. and D.R.E.; Writing-original draft, O.A.M.; Writing-review & editing, W.L., S.M.L., A.S. and D.R.E. All authors have read and agreed to the published version of the manuscript. The research leading to these results was undertaken as part of the SLOWD project which has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No. 815044. The data presented in this study are available on request from the corresponding author. The authors declare no conflict of interest.