Experiments and simulations of settling cylinders over a wide range of Archimedes numbers

Abstract

Quantitative visualization experiments and particle‐resolved simulations of rigid cylindrical particles settling in a Newtonian liquid have been conducted. By varying the viscosity of the liquid—a glycerol‐water mixture—as well as the density of the cylinders, we were able to cover an Archimedes number range that spans almost six orders of magnitude in the experiments. The length over diameter aspect ratio of the cylinders ranged from 2.5 to 20. Cylinders were released vertically and rotated to a stable horizontal orientation in most of the lower viscosity solutions. The time required for reaching a horizontal orientation, as well as the Reynolds number at that stage, scale with the Archimedes number and only weakly depend on the aspect ratio. Particle‐resolved numerical simulations based on the lattice‐Boltzmann method complement the experimental study and illustrate the relevance of the experimental data as a benchmark for numerical approaches to solid–liquid flow with non‐spherical particles.

Experiments on and Simulations of Hollow Cylinders Falling through Quiescent Liquids

“…The initial slight inclination angle means that if the cylinder rotates it will do so around the y ‐axis so that the domain size in the y ‐direction can be made relatively small, which is helpful for limiting computational time. In our previous work on solid cylinders 17 we have shown that the release angle has only limited effect on the settling process of the cylinder.…”

“…This paper builds upon our previous experimental and numerical work on the settling of solid cylinders [17], where it was shown that the Archimedes number is the principal parameter that determines the sedimentation process, both in terms of settling speed and the evolution of the cylinder's orientation. The current paper extends this work by adding the inner diameter as an additional degree of freedom.…”

“…The timescales over which this happens and whether it happens in a monotonic or a wobbling way depend on the Archimedes number and the aspect ratio(s) 12. As in our previous paper 17, we characterize this process by measuring two dimensionless parameters. The first is the dimensionless time t m at which the cylinder reaches a horizontal orientation (i.e., θ = 0) for the first time: with t h the dimensional, measured time (in seconds); the relative uncertainty of t h for repeated experiments is about 5.6 %.…”

“…The simulation domain is periodic in all three coordinate directions. This is because it is computationally not feasible to simulate the entire experimental column (see also the discussion on this topic in 17). The default domain size in the three Cartesian coordinate directions is nx · ny · nz = 12.5 d o · 5 d o · 150 d o .…”

“…If a cylinder-at least a solid one-is vertically released in a Newtonian fluid it will eventually change its orientation to horizontal [17]. The timescales over which this happens and whether it happens in a monotonic or a wobbling way depend on the Archimedes number and the aspect ratio(s) [12].…”