Liquid sloshing in partly-filled laterally-excited circular tanks equipped with baffles

Linear potential theory in conjunction with the conformal mapping technique are employed to develop rigorous mathematical models for two-dimensional transient sloshing in non-deformable baffled horizontal circular cylindrical vessels, filled with inviscid incompressible fluids to arbitrary depths, and subjected to arbitrary time-dependent lateral accelerations. Three common baffle configurations are considered, namely, a pair of free surface-touching horizontal side baffles, and a central surface-piercing or bottom-mounted vertical baffle of arbitrary extension. The first few normalized antisymmetric/symmetric sloshing frequencies of the partially-filled tanks are tabulated for selected baffle extension and fill depth ratios. Also, the effects of liquid fill depth or baffle length parameter on the impulsive, total and modal convective mass ratios are examined. A ramp-step function is used to replicate the lateral acceleration excitation encountered in an idealized turning maneuver. Durbin's numerical Laplace transform inversion scheme was applied to solve the resulting truncated linear sets of ordinary differential equations in the time-domain. The effects of excitation input time, fill level, and baffle configuration/extension on the force and moment amplification factors are illustrated through appropriate design charts. Furthermore, the transient hydrodynamic responses to a real seismic event are calculated and the effectiveness of baffle configuration/length on suppression of the induced destabilizing lateral forces are examined. Limiting cases are considered and rigorous verifications are made by comparison with the available data as well as with the numerical simulations performed by using a commercial CFD software package.