Numerical simulations on the motion of a heavy sphere in upward Poiseuille flow

Abstract

A “heavy” sphere moving in upward Poiseuille flow is numerically investigated using direct numerical simulations (DNS). The overset mesh and the moving computation domain are utilized for simulating the long-distance motion of the sphere. The path trajectory, slip velocity and radial equilibrium position of the “heavy” sphere are analyzed. The pressure and shear stress distributions on the sphere surface are presented. The hydrodynamic forces on the sphere are further discussed by constraining various degrees-of-freedom (DOFs) of sphere motion. The effects of tube Reynolds numbers (Ret) and sphere-to-fluid density ratios (ρr) on the sphere motion are evaluated. As the increase of Ret, five types of path trajectories of the sphere are observed at ρr=2: helical falling, oscillating falling, vertical falling, vertical rising, and chaotic rising. The slip Reynolds number (Res) corresponding to the density ratio plays a crucial role in the dynamic responses of the sphere. Three types of path trajectories are revealed with the variation of ρr at Ret=1106: steady, periodic oscillating, and chaotic.