# CFD Based Non-Dimensional Characterization of Energy Dissipation Due to Verticle Slosh
###### Abstract  
We present the CFD based non-dimensional characterization of violent slosh induced energy dissipation due a tank under vertical excitation. Experimentally validated CFD is used for this purpose as an ideally suited and versatile tool. It is thus first demonstrated that a weakly compressible VoF based CFD scheme is capable of computing violent slosh induced energy dissipation with high accuracy. The resulting CFD based energy analysis further informs that the main source of energy dissipation during violent slosh is due liquid impact. Next, a functional relationship characterising slosh induced energy dissipation is formulated in terms of fluid physics based non-dimensional numbers. These comprised contact angle and liquid-gas density ratio as well as Reynolds, Weber and Froude numbers. The Froude number is found the most significant in characterising verticle violent slosh induced energy dissipation (in the absence of significant phase change). The validated CFD is consequently employed to develop scaling laws (curve fits) which quantify energy dissipation as a function of the most important fluid physics non-dimensional numbers. These newly developed scaling laws show for the first time that slosh induced energy dissipation may be expressed as a quadratic function of Froude number and as a linear function of liquid-gas density ratio. Based on the aforementioned it is postulated that violent slosh induced energy dissipation may be expressed as a linear function of tank kinetic energy. The article is concluded by demonstrating the practical use of the novel CFD derived non-dimensional scaling laws to infer slosh induced energy dissipation for ideal experiments (with exact fluid physics similarity to the full scale Aircraft) from (non-ideal) slosh experiments. multi-phase flows; non-dimensional analysis; violent slosh induced energy dissipation; volume of fluid (VoF) method; computational fluid dynamics (CFD)  
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vertical tank motion at a fixed frequency \(\omega\). The tank motion is therefore prescribed as a single-degree-of-freedom (SDOF) system. Further, it is assumed that the liquid density is orders of magnitude larger than that of the gas while the liquid may be assumed as incompressible while the gas is modelled via a weakly compressible formulation. Finally, the flow physics does not involve significant phase change. Due to the laboratory scale of the cited experiments [2; 3], increased understanding of the bias introduced by such geometric scaling is a key objective of this article. To this end we develop suitable similarity parameters to account for the effects introduced by non-ideal (practical) scaling such that the influence of sloshing on the structural dynamics of full scale aircraft wings may be quantified. Once validated, the use of CFD is key in such studies, as it allows for quantification of the influence of a wide range of parameters and their combinations on slosh induced damping. This is not possible experimentally if limited to available fluid properties. In this work, all CFD calculations are conducted with the multi-physics CFD code Elemental(r)[4; 5; 6; 7; 8]. It is widely accepted that non-dimensional analysis provides a powerful technique to characterise a complex physical system. This enables the study and quantification of the relative importance of various physical parameters/phenomena on such systems [9]. Despite the insights that non-dimensional analyses provide, limited studies of violent slosh through such techniques exist in literature. [PERSON] and [PERSON] [10] successfully employed dimensional analysis as a method to predict the pressurisation requirements for space vehicles at launch. [PERSON] [11] developed a generalisation of slosh force subject to several excitation frequency parameters for various tank geometries. The above cited work did not deal specifically with slosh induced energy dissipation. Past work into the application and tuning of liquid damping systems has centred on structural design and civil engineering applications [12; 13].