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Understanding, predicting and controlling the motion of the solid particles in the square cavity with obstacles are important. This work performs a lattice Boltzmann study on the motion of a neutrally buoyant circular particle in a lid-driven square cavity with a semicircular obstacle, where the effects of Reynolds numbers and initial positions of the circular particle on the motion of the circular particle are investigated. The motion of the circular particle is affected significantly by the semicircular obstacle, which is quite different from the case without obstacles. With the increase of the Reynolds number, the motion of the circular particle is divided into three stages. At low Reynolds numbers (5 0 0 ≤ Re ≤ 8 0 0), similar to the case without obstacles, no matter where the initial position of the circular particle is, the limit cycle of the circular particle is the same. Beyond a critical Reynolds number (between 800 and 900), the limit cycle of the circular particle is dependent on the initial position of the circular particle obviously, which is attributed to the opposing centrifugal and wall-repulsion forces. [ABSTRACT FROM AUTHOR]

To understand, predict and control the motion of the solid particles, the motion of a neutrally buoyant circular particle with thermal convection in a square cavity is studied with the lattice Boltzmann method, where the effects of the initial position of the circular particle, Rayleigh number and particle size are investigated. Under the effect of thermal convection, the obvious feature of the motion of the circular particle in the square cavity is the existence of the limit cycle, which is created by the inertia of the circular particle, confinement of the boundaries of the square cavity and centrifugal force. Interestingly, the limit cycle is insensitive to the initial position of the circular particle. The effect of the Rayleigh number on the motion of the circular particle is obvious, with the increase of the Rayleigh number, the limit cycle expands toward the boundaries of the square cavity first, then shrinks and migrates toward the bottom left corner, which is caused by the combined effects of the centrifugal force and vortex behavior. The effect of the particle size on the motion of the circular particle is significant, with the increase of the particle size, the inertia of the circular particle becomes larger, which is more difficultly dragged by the fluid, thus, the limit cycle shrinks toward the bottom left corner of the square cavity. [ABSTRACT FROM AUTHOR]