Falling balls in a viscous fluid with contact: Comparing numerical simulations with experimental data

TL;DR

This paper compares various finite element numerical methods for simulating falling particles in viscous fluids with experimental data, focusing on contact interactions and flow regimes between creeping and turbulent.

Contribution

It introduces a comprehensive comparison of ALE, CutFEM, and Eulerian approaches for fluid-structure contact problems, including fully Eulerian FSI with Nitsche's method and 3D simulations.

Findings

ALE and CutFEM effectively simulate particle trajectories.

Eulerian FSI with Nitsche's method handles contact well.

Symmetry-based 2D models improve computational efficiency.

Abstract

We evaluate a number of different finite element approaches for fluid-structure (contact) interaction problems against data from physical experiments. For this we take the data from experiments by Hagemeier [Mendeley Data, doi: 10.17632/mf27c92nc3.1]. This consists of trajectories of single particles falling through a highly viscous fluid and rebounding off the bottom fluid tank wall. The resulting flow is in the transitional regime between creeping and turbulent flows. This type of configuration is particularly challenging for numerical methods due to the large change of the fluid domain and the contact between the wall and particle. In the numerical simulations we consider both rigid body and linear elasticity models for the falling particles. In the first case, we compare results obtained with the well established Arbitrary Lagrangian Eulerian (ALE) approach and a moving domain CutFEM method together with a simple and common approach for contact avoidance. For the full fluid-structure interaction (FSI) problem with contact, we use a fully Eulerian approach in combination with a unified FSI-contact treatment using Nitsche's method. For higher computational efficiency we use the geometrical symmetry of the experimental set up to reformulate the FSI system into two spatial dimensions. Finally, we show full three dimensional ALE computations to study the effects of small perturbations in the initial state of the particle to investigate deviations from a perfectly vertical fall observed in the experiment. The methods are implemented in open-source finite element libraries and the results are made freely available to aide reproducibility.