Evaluation of breaking wave effects in liquid sloshing problems: ANCF/SPH comparative study

Abstract

This paper is focused on evaluating the effect of breaking waves in liquid sloshing problems. Two fundamentally different approaches, namely the smoothed particle hydrodynamics (SPH) and the finite element (FE) absolute nodal coordinate formulation (ANCF), are used to describe the liquid sloshing response in several sloshing scenarios. The SPH method is a mesh-free numerical technique often used to capture very large displacements in fluid and solid mechanics problems. ANCF finite elements, on the other hand, can be used to develop a non-incremental solution procedure, suited for the nonlinear analysis of flexible bodies undergoing large rotation and large deformation. The fundamental differences between the two approaches and the advantages and limitations of each are discussed. Two benchmark problems, the dam break and sloshing tank, are used to perform a detailed SPH/ANCF quantitative comparative study in different sloshing scenarios. While a good agreement is found between the ANCF and SPH converged solutions for the dam break problem, in the sloshing tank problem the SPH solution underpredicts the amplitude of oscillation of the fluid center of mass and the wave height at a selected probe point. Because one ANCF element can capture complex shapes, nearly 40 times fewer degrees of freedom than the SPH model are needed in both problems. The use of the ANCF models leads to a CPU saving of 70% and 25% in the broken dam and sloshing tank problems, respectively. In the case of the tank problem, the effect of light, moderate, and severe turbulence is examined. The position of the fluid center of mass is computed using the two approaches, and the results obtained are verified using a reference analytical solution. The power spectral density of the center of mass is evaluated using the fast Fourier transform (FFT) to study the effect of breaking waves. The results show that in the case of light and moderate turbulence, the ANCF model allows for accurately averaging the fluid inertia properties, and the obtained solutions are in good agreement with the SPH solutions. In the case of severe turbulence, on the other hand, the mechanical energy dissipation due to fluid mixing and wave breaking, which can only be captured using the SPH method, damps out the sloshing oscillations.