# Simulating Slosh Induced Damping, with Application to Aircraft Wing-like Structures
## 1 Introduction
[12] conducted experiments to measure systemic energy dissipation. By changing the liquid from a highly viscous liquid (glycerine), to a less viscous liquid (water), the oscillation amplitude of the pendulum-TSD system reduces. Here, water is clearly shown to counteract the effect of roll more quickly during the first several cycles, compared with glycerin. The idea of slosh-induced damping has also attracted the attention of civil aviation. [PERSON] and [PERSON] [13] conducted experiments on the dynamic effects of a cantilever beam with a fuel-sloshing tank subject to sudden bending oscillations. They observed substantial damping induced by the sloshing tank that varies notably according to the filling level, the density of liquid, and the transient cycle number. [PERSON] [14] experimentally studied the impact of a pylon-mounted tank with sloshing fluid on the flutter of a rigid wing supported by bending and torsional springs. Both frozen water and sloshing water were considered and slosh-induced damping was observed in the system with liquid water. [PERSON] [15] carried out analytical studies on wing models with an internal sloshing fuel tank under a bending-to-torsion frequency ratio that was close to one. Consistently, the highest flutter speeds were observed when the compartment emptying sequence proceeded from the front to the rear, due to the centre of mass of the system shifting. The EU Horizon 2020 SLOWD (**S**loshing **W**ing **D**ynamics) project aims to further investigate the physics of fuel sloshing in order to minimise aeroplane structural design loads and increase passenger comfort [16; 17]. The project also aims to integrate new software workflows into key areas of industry to support the use of the results. As a precursor to the SLOWD project, [PERSON] et al. [18] performed a number of liquid sloshing experiments at the Airbus Protospace Lab located in the United Kingdom. This utilised a scaled cantilever beam and attached water tank to study the impact of the liquid filling ratio on slosh-related structural damping. Complex behaviour with strong nonlinear phenomena was observed, both in terms of the fluid and the structure. The friction and nonlinear stiffness generated by the tank, even when dry, were found to have an impact on the dynamics of the cantilever beam, while the liquid sloshing phenomena when the tank contained fluid dominated the overall dynamics of the system. A filling level of 50% was found to provide the strongest damping effect. With the same experimental setup, [PERSON] et al. [19] studied the impacts of dry-roof/drop-impact-roof and different liquids, i.e., water and kerosene, on the behaviour of the sloshing tank-beam system. They found that the response of the system during the initial oscillation is dominated by an apparent Rayleigh-Taylor instability at the free surface. The system with both the dry-roof and drop-impact-roof showed similar responses in terms of the time histories from accelerometer and strain gauge data. As well as the experiments on the cantilever beam, [PERSON] and [PERSON] [20], [PERSON] et al. [5] and [PERSON] et al. [21] carried out experiments on the sloshing-induced damping of a harmonically vertically excited sloshing tank. The present study employs a CFD approach based on finite volumes and using the volume of fluid (VoF) method to capture the free surface. In [PERSON] et al. [22], a VoF-based curvature calculation method was proposed and validated for the modelling of surface tension in highly dynamic free-surface problems. A novel sweep-line algorithm was employed based on volume conservation and representing the free surface using a piecewise-linear representation. A number of test cases were carried out and showed second- and fourth-order accuracy, depending on the case. In [PERSON] et al. [23], the Harten-Lax-van Leer contact solver was then combined with a VoF-based compressive interface capturing scheme for arbitrary meshes.