Dynamic of one and two elliptical particles settling in oscillatory flow: Period bifurcation and resonance state

The inertial migrations of one and two elliptical particles in a two-dimensional channel under oscillatory pressure driven flow are investigated by a finite element arbitrary Lagrangian-Eulerian (ALE) method. The effects of oscillation frequency on rotation behavior, vortex structure, pressure distribution and relative displacement during sedimentation have been studied. The results show that the oscillation can accelerate the eddy formation and shedding behind the particle, and cause a strong modification of the turning couples on the ellipse with lateral displacement. As the frequency increases, the initial ‘zigzag migration’ at the channel side goes through a period bifurcation transition to the resonance state with ‘anomalous rotation’ near the wall, and further induces ‘rotation shift’ near the channel center. The angular velocity increases before the resonance state, while the average vertical velocity decreases with the rising frequency. Moreover, the hydrodynamic interaction between the particles has a close association with the oscillatory effect. In the period bifurcation regions, the higher the oscillation frequency, the bigger the horizontal distance of the opposite rotation particles, and the particles separate fastest at the resonance state. In contrast, an attractor is formed between the pairs in the high frequency, and the two particles are exchanging the lead as settling forward. The final configuration of the pairs is shown to be caused by the Magnus type of lift balancing the wall repulsion and the interplay between particles, and is sensitive to the dynamic drag statistically corresponding to the oscillation in the wake and the periodic discharge of vorticity.