# On the Efficacy of Turbulence Modelling for Sloshing
###### Abstract
Therefore, a less expensive simulation can be conducted via turbulence modelling. [PERSON] et al. [40] produced a very accurate representation of the dynamics of violent vertical sloshing via large eddy simulation (LES). However, full-scale studies via LES can also be very expensive, especially for wall-bounded flows where the boundary layer has to be resolved [41]. Reynolds-averaged Navier-Stokes simulation (RANS) represents a potential and less computationally demanding alternative. However, there is a lack of consensus regarding whether commonly employed turbulence models should be used for free surface problems, while sloshing simulation without a turbulence model has been widely used with good accuracy [29; 42; 43; 44]. [PERSON] et al. [45], [PERSON] and [PERSON] [46] illustrated that the sloshing load is insensitive to the use of turbulence modelling. [PERSON] et al. [47] also showed that RANS simulation using \(k\)-\(\omega\) was less accurate than its no-model flow counterpart. Recently, [PERSON] et al. [48] compared between different free surface capturing approaches (VoF, SPH, ALE) and they also compared the prediction accuracy of unsteady \(k\)-\(\epsilon\), LES-WALE and DES, and no-model. They found that the no-model and the LES model provided the best correlation to the experimental results, which is in line with our general findings but is not a complete answer as we know that the no-model approach is sub-optimal for complex sloshing flows while a full LES simulation is often excessively computationally intensive, especially in an industrial context. [PERSON] et al. [30] demonstrated that the RANS model can suffer an over-production of turbulence at the interface due to the large velocity gradient that can be evident. [PERSON] and [PERSON] [49] and [PERSON] and [PERSON] [50] proved that most two-equation closed problems suffer an unstable exponential growth of turbulent kinetic energy. To overcome this issue, several treatments for the models near the interface are proposed [30; 49; 50]. Conversely, several studies have shown the importance of turbulence models in the simulation of free surface flows. Realising the lack of consensus on the importance of turbulence modelling in sloshing simulations, [51; 52] assumed sloshing is a turbulent phenomenon, and standard turbulence models were used. [PERSON] [53] showed that a lack of turbulence modelling can lead to non-physical irregularities and instabilities in the no-model solution. The sensitivity study of [PERSON] et al. [54] also suggested that a laminar assumption is not appropriate in a sloshing flow and that turbulence modelling has to be employed to obtain accurate representation. Additionally, [PERSON] et al. [55] compared between RANS, LES and very large eddy simulations and concluded that an adequate energy dissipation via turbulence modelling is key in the predictions of plunging wave breaking. [PERSON] et al. [30] argued that \(k\)-\(\omega\) is more suitable and stable for the simulation of unsteady two-phase flow due to the linear relationship between the turbulent kinetic energy and the specific turbulent dissipation rate, while a reliable simulation of rolling response of a ship with an internal tank was conducted with \(k\)-\(\omega\) SST [8]. [PERSON] and [PERSON] [56] computed the impact pressure of sloshing using the standard \(k\)-\(e\), realizable \(k\)-\(e\) and Wilcox \(k\)-\(\omega\) models, and they found that predictions of standard \(k\)-\(e\) and Wilcox \(k\)-\(\omega\) models were very close and accurate. [PERSON] et al. [57] tested eight turbulence models for simulating transverse sloshing in a rectangular tank. They found that RNG \(k\)-\(e\) and \(k\)-\(\omega\) SST performed best in predicting the free surface behaviour. Thus, a proper selection of the turbulence model is clearly key for providing an accurate representation of fluid-sloshing dynamics. [PERSON] et al. [58] evaluated a library of turbulence models in predicting different characteristics of spilling and plunging wave breakers.