Particle imaging velocimetry experiments and lattice-Boltzmann simulations on a single sphere settling under gravity

Abstract

A comparison is made between experiments and simulations on a single sphere settling in silicon oil in a box. Cross-correlation particle imaging velocimetry measurements were carried out at particle Reynolds numbers ranging from 1.5 to 31.9. The particle Stokes number varied from 0.2 to 4 and at bottom impact no rebound was observed. Detailed data of the flow field induced by the settling sphere were obtained, along with time series of the sphere's trajectory and velocity during acceleration, steady fall and deceleration at bottom approach. Lattice-Boltzmann simulations prove to capture the full transient behavior of both the sphere motion and the fluid motion. The experimental data were used to assess the effect of spatial resolution in the simulations over a range of 2-8 grid nodes per sphere radius. The quality of the flow field predictions depends on the Reynolds number. When the sphere is very close to the bottom of the container, lubrication theory has been applied to compensate for the lack of spatial resolution in the simulations.

A contact model for normal immersed collisions between a particle and a wall

“…The trajectory and the velocity profiles are compared in figure 1. The circles in the figure are digitized from figure 8 in TenCate et al (2002). The comparison shows that the simulation coupling the evolution of the flow field and the motion of the sphere predicts the same motion of the sphere as found in the experiment.…”

“…In the current simulations, similar results were computed with two different grid sizes in order to establish convergence. Figure 2 compares the flow field at the moment when the sphere is a halfdiameter from the wall with the particle image velocimetry (PIV) measurement of TenCate et al (2002). The velocity contours above the sphere are not included in the experimental result.…”

“…For the case of a moving sphere, the time-marching scheme of the original IB projection method was also modified to treat the two-way coupled system where the motion of the Lagrangian points on the surface are found by integrating an equation of motion for the sphere; the details are discussed in § 2.2, and validations for the two-way coupled system are presented in § 2.3, where we compare with corresponding experiments and simulations of TenCate et al (2002).…”

“…To validate the coupled algorithm, the simulation results are compared with the experimental results by TenCate et al (2002). In the experiment, the trajectory and associated flow field of a settling sphere are measured from the moment of release until rest at the bottom of a vessel.…”

“…The sphere was stopped at a distance of 0.005 times the particle diameter from the wall to avoid the development of a mesh singularity as the particle impacted the surface; the particle was not allowed to rebound. TenCate et al (2002) simulated a sphere settling toward a solid wall without rebound and compared with experiment results. Both the spatial structure and the temporal behaviour of the flow field were obtained.…”