A coupled multimodal and boundary-element method for analysis of anti-slosh effectiveness of partial baffles in a partly-filled container

The liquid slosh within a partially-filled moving horizontal cylindrical container with different designs of longitudinal baffles is analyzed for predicting transient lateral slosh force and overturning moment, assuming inviscid, incompressible and irrotational flows. A boundary element method is initially formulated to solve the spectral problem of free liquid slosh using the zoning method involving the velocity potentials alone of the half free-surface length, which significantly increases the computational efficiency. The resulting natural slosh frequencies and modes are subsequently implemented in a linear multimodal method to obtain generalized coordinates of the free-surface under a lateral acceleration excitation. Damping due to baffles, estimated from the energy dissipated per cycle, is also implemented into the multimodal equation. The validity of the model is illustrated through comparisons with available analytical solutions. The results are presented for the tank with bottom-mounted, top-mounted and center-mounted partial baffles of different lengths. The effects of baffle design and length on the natural slosh frequencies/modes, damping ratios and hydrodynamic coefficients are further investigated. The lateral force and overturning moment due to liquid motion within the container are derived in terms of generalized coordinates and the natural slosh modes. It is shown that the multimodal method yields computationally efficient solutions of liquid slosh within moving baffled containers. The results suggest that top-mounted baffles are most effective in suppressing the fluid slosh force under more likely fill height conditions in road tankers (well above 50% of diameter), when the baffle is partly submerged in the liquid domain. The center-mounted baffle was effective under intermediate fill levels in the vicinity of 50%, while the bottom mounted baffle was effective only under very low fill heights.