Sedimentation of two circular particles with different sizes in a vertical channel at low Reynolds numbers

Abstract

In this study, the generalized finite-difference with singular value decomposition method for fluid–structure interaction problems is used to simulate the sedimentation of the two circular particles with different sizes in a vertical channel. The effects of the Reynolds number (8 ≤ Re ≤ 70) and the size difference (0 ≤ β ≤ 0.1) on the final motions of the two particles are analyzed. Over the ranges of the parameters investigated, three modes in the final state of the two-particle system are identified, i.e., the steady state, the periodic oscillation state, and the period-doubling bifurcation (PDB) state. Depending on the importance of the inertial force, the steady state can be classified as the steady state I and the steady state II. Similarly, the periodic oscillation state can be categorized into the periodic motion I (PMI) and the periodic motion II (PMII) based on the influence of the wake between the two particles. The directions of the limit cycles corresponding to PMI and PMII are counterclockwise and clockwise, respectively. In PMI, the limit cycle at 8 ≤ Re ≤ 9 decreases in size with increasing β, while the limit cycle at 12 ≤ Re < 70 behaves oppositely. The limit cycle in PMII always increases in size with β. PDB, characterized by the limit cycle with two branches, mainly appears at 14 ≤ Re ≤ 30.