Semi-analytical characterization of a sloshing fluid mass with the smoothed particle hydrodynamic based method

Sloshing phenomena regard the dynamic excitation of a partially filled tank which leads to the motion of the fluid within. The dynamic effects, especially if the excitation frequency approaches the natural frequency of the tank (near resonance), may compromise the structure stability. Amplification of motion may be either pursued or avoided, depending on the design purposes; regardless, it is important to predict the coupled effects generated by the tank interacting with the contained liquid. The present study aims to offer a simplified approach along with valid parameters that link the filling level of the tank to the sloshing mode of vibration. The parameterization procedure is numerically supported by a Computational Fluid Dynamics (CFD) solver based upon the Smoothed Particles Hydrodynamics (SPH) meshless method. Within the proposed framework, a parametric sloshing tank is simulated and validated using experimental data as a test-rig, therefore used to perform a wide sensitivity study by changing the filling ratio. The numerical results interpretation leads to a method which can synthetically predict the characterizing frequency of the phenomenon using a semi-analytical fitting, with improved accuracy over previous literature methods. This procedure is established within the open-source SPH-based DualSPHysics, and provides a reliable alternative to traditional approaches, proving that validated numerical methods can directly support the design of sloshing tanks, with all the advantages related: quickness, affordability and reproducibility.