Experimental, theoretical, and numerical investigation on sloshing behavior in annular sectored containers

Annular sectored containers are widely used in nuclear engineering, aerospace, marine, and civil engineering. It is crucial for the safety assessment of such containers to accurately describe their sloshing behavior under external disturbances and seismic conditions. Many studies have been conducted on the sloshing behavior in regular-shaped containers (rectangular, circular, and annular cross sections); however, the studies on the sloshing in annular sectored containers are relatively limited. Specifically, there is a lack of studies on sloshing damping and nonlinear behaviors under large-amplitude resonance conditions and earthquakes. This paper examines the effects of excitations and geometry (curvatures and sizes) on the dynamic sloshing characteristics and transient response of annular sectored containers through shaking table experiments. Experimental results show significant nonlinear sloshing, including breaking waves, at sharp inner corners of annular sectored containers under large harmonic and seismic excitations. It also shows that curvature has a small effect on the frequency and sloshing damping; however, it significantly influences wave heights and hydrodynamic pressures on the outer curved surface. Based on potential flow theory, we derived a wave height formula with damping for the annular sectored container under arbitrary ground motion excitation. Through experiments, we also determined a correction factor for wave height under large-amplitude excitation. The results were compared with experimental data, volume-of-fluid (VOF) results, and the corrected wave height formula for rectangular containers. The comparison shows that under large-amplitude excitation, both the VOF method and potential flow theory show significant errors compared to experimental results, while the corrected formula for the annular sectored container agrees well with the experimental results.