Simulation of Attachment, Rolling, and Detachment of a Single Settling Particle over a Stationary Cylinder by Homogenized Lattice Boltzmann Method

The particle motion and settling especially over obstacles encounter in many industrial and natural phenomena such as water, wastewater treatment, and mining industries. When a particle settles over an obstacle, such as a cylinder, simultaneously with settling it has rolled. Rolling is a combination of rotating and sliding. In this research, the settling and rolling of a particle over a stationary cylinder in a chamber was simulated by the homogenized lattice Boltzmann method. For validation, the vertical particle velocity of a single settling particle was compared with previous work, and a good agreement between them was observed. It is seen, that when a particle starts to settle from rest condition over a cylinder, it rotates in a counterclockwise direction under the effect of the chamber wall until it attaches to the cylinder. For heavier particles, the rotation is larger. Also, the attachment angle for heavier particles is higher. After attachment, the particle rolls in reverse direction (clockwise direction). It is observed that the attachment angle increases with increasing particle density. Next, the particle detached from the cylinder and continued its rotation in the clockwise direction at some time due to its moment of inertia. When the particle rolls around the cylinder, the rotating angle and angle between attachment and detachment were obtained. It is seen that these two angles are not identical. Moreover, the linear velocity of the particle rotating and the velocity of the particle mass center are not equal. This inequality approves that when the particle moves around the cylinder, it has both rotating and sliding. It is shown that with increasing the particle density these velocities and also those differences increase. By determining the lengths of the rolling and rotating paths of the particle, we acquired the percentages of rotation and subsequent sliding between attachment and detachment. For instance, at particle densities of ۱۰۳۰ and ۱۱۲۰ ۱۰۳۰ kg/m^۳, the particle covers ۱۷% and ۵% of its path through rotation before detaching, with the remainder of its travels completed through sliding. It is concluded that when a particle settles over an obstacle it has both sliding and rotating during its travel. Also, its attachment and detachment angles to the obstacle depend on its density. During the rolling of particles over the obstacle wall it has both rotating and sliding.

Keywords:

Particle settling , homogenized lattice Boltzmann method , Rolling , sliding , rotating