Wall Effects on the Flow Dynamics of a Rigid Sphere in Motion

Abstract

The presence of a wall near a rigid sphere in motion is known to disturb the particle fore and aft flow-field symmetry and to affect the hydrodynamic force. An immersed boundary direct numerical simulation (IB-DNS) is used in this study to determine the wall effects on the dynamics of a free-falling sphere and the drag of a sphere moving at a constant velocity. The numerical results are validated by comparison to the published experimental, numerical, and analytical data. The pressure and velocity fields are numerically computed when the particle is in the vicinity of the wall; the transverse (lift) and longitudinal (drag) parts of the hydrodynamic force are calculated; its rotational velocity is investigated in the case of a free-falling sphere. The flow asymmetry also causes the particle to rotate. The wall effect is shown to be significant when the dimensionless ratio of the wall distance to the particle diameter, L/D, is less than 3. The wall effects are more pronounced and when the particle Reynolds number, Re, is less than 10. Based on the computational results, a useful correlation for the wall effects on the drag coefficients of spheres is derived in the range 0.75 < L/D < 3 and 0.18 < Re < 10.