On the experimental scaling and power dissipation of violent sloshing flows

Abstract

Violent and vertical sloshing flows appear when the fuel tanks of aircraft wings are shaken by air gusts or turbulence. The liquid slosh inside of the tank significantly damps the wing vibrations and its behaviour is still not fully understood. In this paper a simplified version of the problem is tackled, presenting the results obtained in an experimental campaign that investigates the scaling effects and the influence of the most relevant non-dimensional numbers of the problem. Single degree of freedom (SDOF) Froude scaled decay tests are devised in order to study the vertical sloshing problem in an aerospace context establishing relations between the slosh induced damping ratio and three of the most relevant non-dimensional numbers, namely the filling level, density ratio and initial amplitude. The experimental results indicate a maximum damping for a 50% fill level and a positive relationship between the damping ratio with the density ratio. The initial amplitude also increases with the damping ratio up until a threshold amplitude after which the damping starts to decrease. A clear explanation of the liquid induced damping ratio behaviour, confirmed for the three selected scales, is given in terms of two magnitudes: the sloshing force intensity and the phase-shift between this force and the tank motion. These two magnitudes are the key elements behind the physical interpretation of the liquid dissipation in the problem.Finally, the power dissipated by the liquid is calculated and correlated with the liquid slosh damping ratio, the sloshing force intensity and the phase-shift. This correlation shows an equivalency of the damping ratio with the dissipated power.