# CFD Based Non-Dimensional Characterization of Energy Dissipation Due to Verticle Slosh
## 10 Conclusions  
This article presented the first ever volume of fluid (VoF) computational fluid dynamics (CFD) based non-dimensional analysis which characterises violent slosh induced energy dissipation of a tank under vertical excitation. This in the absence of significant phase change. The use of rigorously validated CFD for this purpose was essential as doing so via experimental means is not possible due limitations in available liquids. The work resulted in several new insights which are deemed of significant value to the field of liquid slosh modelling and liquid impact dynamics. Each of these key contributions are summarized next. The VoF CFD software was first validated via modelling a representative slosh experiment. A sophisticated two phase model was employed which accounted for surface tension, turbulence and gas compressibility (via a weakly compressible formulation). The validation study concluded that the slosh induced energy dissipation is predicted to within 2% of the experimental values. The CFD based mechanical energy budget also identified liquid impact as the major contributor to slosh induced energy dissipation. These constitute the first novel findings of this work. Next a non-dimensional analysis was detailed. The specific emphasis was on developing a functional relationship between energy dissipation and fluid physics. The latter was characterised by Reynolds number, Weber number, contact angle, gas-liquid density ratio and Froude number. The validated CFD software was then used to estimate the influence of each of these non-dimensional numbers on slosh induced energy dissipation. As would be expected, Rayleigh-Taylor instability was found key to inducing liquid impact due purely verticle excitation. Hence, an appropriate contact angle is key to inducing violent verticle slosh induced energy dissipation. Apart from Froude number, all other non-dimensional numbers were for the first time found to have a small (circa 10%) influence on slosh induced energy dissipation. Hence, the Froude number was concluded to be the most important non-dimensional number in characterising slosh induced damping. The validated CFD was then employed to characterise the change in slosh induced dissipation as a function of the most important non-dimensional numbers for the case of constant amplitude oscillatory tank excitation. Clear correlations (scaling laws) were  
Figure 10: Response surface of \(||\Delta E_{Disp}||\) as a function of \(\rho\) and \(Fr\). found for both liquid-gas density ratio and Froude number. The latter scaling laws are linear and quadratic, respectively, which is deemed a significant new finding. From this it was postulated for the first time that violent slosh induced energy dissipation may be expressed as a linear function of tank kinetic energy. The final novel contribution of the article entailed demonstrating the application of the developed scaling laws for Froude number and density ratio to estimate slosh induced energy dissipation for an ideally scaled experiment. Thus, using the developed scaling laws, an accuracy of 86% was achieved when compared to the CFD computed value. Conceptualization F.G., M.D.W., A.G.M. ; methodology M.D.W., F.G., A.G.M. ; software M.D.W., A.G.M. ; validation M.D.W. ; supervision A.G.M., F.G.; project administration A.G.M., F.G., funding acquisition A.G.M.. visualisation M.D.W. ; writing M.D.W., A.G.M., F.G.; All authors have read and agreed to the published version of the manuscript. This work is based on research supported by the National Research Foundation of South Africa (Grant Numbers: 89916). The opinions, findings and conclusions or recommendations expressed are that of the authors alone, and the NRF accepts no liability whatsoever in this regard. The research leading to these results has also received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 815044, the SLOshing Wing Dynamics (SLOWD) project.