Numerical analysis of sloshing dynamics in a horizontal circular tank under horizontal and vertical excitations

This study numerically investigated the global sloshing flows in a partially filled horizontal circular tank subjected to harmonic excitations. The computational model adopted the geometry specified in the fifth Collaborative Computational Project in Wave Structure Interaction blind test, considering horizontal and vertical excitations. Commercial computational fluid dynamics software employing the volume-of-fluid method was used to resolve complex free-surface deformations. Furthermore, the grid uncertainty was assessed to ensure numerical reliability. The numerical results were validated against experimental data by comparing the wave elevations measured at the left and right sidewalls. Comprehensive analyses were conducted at various excitation frequencies and amplitudes using time-series data, phase-space trajectories, Poincaré sections, and a fast Fourier transform to characterize the dynamical responses of the sloshing flows. Under horizontal excitations, distinct nonlinear characteristics, including softening and jump phenomena, were observed. The phase-space analysis and frequency-sweep simulations revealed path-dependent hysteresis and coexistence of multiple stable states, thereby confirming the presence of subcritical bifurcations. Under vertical excitations, the flows exhibited typical Faraday wave patterns, thereby showing nonlinear characteristics driven by parametric resonance. The instabilities were identified using the Mathieu equation and Strutt stability diagrams, which established the boundaries between the stable and unstable sloshing motions.