Numerical investigation of the damping rates of free oscillations in fluid energy acquired due to sloshing in rectangular tanks

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Abstract
Enhancing the dissipation of fluid energy generated due to sloshing is necessary to eliminate the undesirable hydrodynamic forces it produces on the walls of a mobile container. With this goal, this work investigates the fluid motion due to sloshing in three rectangular tanks (A, B, and C) that undergo sinusoidal displacements from their mean positions for a short duration of time, Ts. Tank A is partially filled with water; tank B is partially filled with water and contains a bottom-mounted baffle at a distance of xb from the left wall; and tank C consists of an oil-layer of thickness, d, floating on a water layer. Three-dimensional simulations are performed to obtain the flow field and temporal evolution of fluid kinetic energy in several cases. The period of evolution includes the initial transient regime; the periodic forced-oscillation regime; and the free-oscillation regime, which comprises the nonlinear and linear damping sub-regimes. In each case, nonlinear and linear damping rates are obtained and analyzed to estimate the timescales for energy dissipation in the respective sub-regimes. Results of detailed parametric studies reveal that damping rates increase significantly due to the baffle (tank B) and oil-layer (tank C), so both are effective in mitigating sloshing. For flow in tank B, nonlinear damping rates are consistently higher than corresponding linear damping rates, and both are non-monotonic functions of xb and Ts. For flow in tank C, the nonlinear (linear) damping rate is a monotonic (non-monotonic) function of d. Reasons for variations in damping rates due to the baffle and the oil-layer are highlighted, and discussions of the physics causing these changes are also presented.

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