Sloshing reduced-order model trained with Smoothed Particle Hydrodynamics simulations

Abstract

The main goal of this paper is to provide a Reduced Order Model (ROM) able to predict the liquid induced dissipation of the violent and vertical sloshing problem for a wide range of liquid viscosities, surface tensions and tank filling levels. For that purpose, the Delta Smoothed Particle Hydrodynamics (δ-SPH) formulation is used to build a database of simulation cases where the physical parameters of the liquid are varied. For each simulation case, a bouncing ball-based equivalent mechanical model is identified to emulate sloshing dynamics. Then, an interpolating hypersurface-based ROM is defined to establish a mapping between the considered physical parameters of the liquid and the identified ball models. The resulting hypersurface effectively estimates the bouncing ball design parameters while considering various types of liquids, producing results consistent with SPH test simulations. Additionally, it is observed that the estimated bouncing ball model not only matches the liquid induced dissipation but also follows the liquid center of mass and presents the same sloshing force and phase-shift trends when varying the tank filling level. These findings provide compelling evidence that the identified ROM is a practical tool for accurately predicting critical aspects of the vertical sloshing problem while requiring minimal computational resources.

Rapid sloshing-free transport of liquids in arbitrarily shaped containers

“…Sloshing dynamics are described by the fluid field equations, which can be solved numerically, e.g. by the finite element method [2,3] or smooth particle hydrodynamics [4][5][6][7][8] which are prticularly suitable for modelling large free surface displacments and splashing. While numerical methods are applicable to containers of arbitrary shapes, the resulting models are often unsuitable for model-based control tasks due to their high computational demand.…”

“…Different sloshing phenomena require adapted equivalent models, e.g. highly non-linear vertical sloshing phenomena have been successfully represented by bouncing-ball models [8] or neural-network models [12,13], moderately non-linear horizontal sloshing has been described by a linear mechanical oscillator with an internal cubic mass-spring system [14], and lowamplitude horizontal sloshing is commonly modeled by mechanical equivalent pendulum models. Existing approaches for designing equivalent (pendulum) models often rely on closed-form solutions for the governing equations [15].…”