Dynamics of particle sedimentation in a vertical channel: Period-doubling bifurcation and chaotic state

Abstract

The dynamics and interaction of two circular cylinders settling in an infinitely long narrow channel (width equal to four times the cylinder diameter) is explained by direct computational analysis. The results show that at relatively low Reynolds numbers (based on the average particle velocity and diameter), the particles undergo complex transitions to reach a low-dimensional chaotic state represented by a strange attractor. As the Reynolds number increases, the initial periodic state goes through a turning point and a subcritical transition to another periodic branch. Further increase in the Reynolds number results in a cascade of period-doubling bifurcations to a chaotic state represented by a low dimensional chaotic attractor. The entire sequence of transitions takes place in a relatively narrow range of Reynolds number between 2 and 6. The physical reason for the period-doubling transitions is explained based on the interaction of the particles with each other and the channel walls. The particles undergo near contact interactions as settling in the channel. To accurately capture the dynamics, the computational method requires accurate resolution of the particle interactions. The computational results are obtained with our lattice-Boltzmann method developed for suspended particles near contact. The results show that even in the most simple and ideal multiparticle sedimentation, the system undergoes transition to complex dynamics at relatively low Reynolds number.