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The flow in the square cavity with internal obstacles exists widely; thus, investigating the effect of the existence of the obstacles on the flow and the motion of the solid particles is important. To understand, predict, and control the motion of the solid particles, the motion of a neutrally buoyant circular particle in a lid-driven square cavity with an internal circular obstacle is studied with the lattice Boltzmann method, where the effects of the obstacle size, obstacle location, initial position of the circular particle, and Reynolds number are investigated. Under the effect of the obstacle, the flow and the motion of the particle are quite different. Especially, under some cases, no limit cycle is observed, and the particle is captured by the secondary vortex at the lower layer of the square cavity, which is insensitive to the initial position of the circular particle. The effect of the Reynolds number on the motion of the particle is significant, with the increase in the Reynolds number, and the motion of the particle is different obviously. At low Reynolds numbers, the motion of the particle is confined by the primary vortex, which moves along the limit cycle at the upper layer of the square cavity. With the increase in the Reynolds number, the effect of the inertia of the particle becomes stronger, and the particle moves from the primary vortex to the secondary vortex until it is captured by the secondary vortex. At relatively high Reynolds numbers, the primary vortex develops, and the particle is confined by the primary vortex again, forming another limit cycle. [ABSTRACT FROM AUTHOR]

The motion of the solid particles in the enclosed cavity is important, to investigate the interaction between the motion of the solid particles and the fluid flow, the motion of a neutrally buoyant elliptical particle in a lid-driven square cavity is studied with the lattice Boltzmann method. To understand, predict and control the motion of the elliptical particle, the effects of the aspect ratio, initial orientation, initial position, particle size and Reynolds number are studied. The obvious characteristic of the motion of the elliptical particle in the square cavity is the existence of the limit cycle, which is created by the inertia of the elliptical particle, confinement of the boundaries of the square cavity and vortex behavior. Compared with the circular particle, with the increase of the aspect ratio, the roundness of the limit cycle decreases, namely, the limit cycle becomes flatter. Especially, the limit cycle is insensitive to the initial orientation and position, namely, the limit cycle is the same no matter where the elliptical particle is placed initially. With the increase of the particle size, the confinement of the boundaries becomes stronger, and the limit cycle is squeezed toward the center of the square cavity. Finally, with the increase of the Reynolds number, the vortex at the top left corner develops, and the limit cycle is pushed toward the bottom right corner of the square cavity. • A global limit cycle for the motion of the elliptic particle is observed. • The limit cycle is insensitive to the initial position of the elliptic particle. • The limit cycle shrinks toward the center of the square cavity with the increase of the particle size. • The limit cycle migrates toward the bottom right corner of the square cavity with the increase of Re. [ABSTRACT FROM AUTHOR]