Sloshing waves induced by the rotational motion of the tank have been simulated using the mixed Euler-Lagrangian formulation. The fully nonlinear wave model is solved using the finite element method with the cubic spline and finite difference approximations of velocity recovery to minimize the need for smoothing and re-gridding. In the present model, the rotational motion is built into the kinematic and dynamic boundary condition and the problem is solved in the fixed coordinate system without moving the tank. The results are compared with Nakayama et al.(1980) in the time domain and with experimental measurements of Nasar et al.(2008) in the frequency domain. A good agreement with results is achieved and also, it is shown that the present model predicts the different sloshing harmonics well. Further, harmonics present in a tank with 25% fill liquid level, is explored for two roll amplitudes(1˚ and 2˚) for a range of frequencies. Similar harmonics are observed for both the roll amplitudes. The variation of sloshing response is highly sensitive near the sloshing frequencies and is less sensitive at off-resonance frequencies.
Sloshing is of great importance in problems like large storage tanks filled with liquid subjected to earthquake, liquid fuel in aircrafts and spacecrafts, liquid storage tank in ships. Free liquid surface oscillation inside the cargo tank of seagoing ships poses a threat to the stability of the vessel by influencing the sea-keeping characteristics, in particular roll motion. In some cases, excessive roll motion can lead to cargo damage or cargo loss, passenger injury and, in extreme cases, ship capsize. Since past few decades, several studies have been carried out on the physical and numerical modeling of sloshing oscillation in tanks. However, studies on the sloshing due to rotational tank motion are rather limited.