Wall-induced forces on a rigid sphere at finite Reynolds number

Abstract

We perform direct numerical simulations of a rigid sphere translating parallel to a flat wall in an otherwise quiescent ambient fluid. A spectral element method is employed to perform the simulations with high accuracy. For $Re\,{<}\,100$, we observe the lift coefficient to decrease with both Reynolds number and distance from the wall. In this regime the present results are in good agreement with the low-Reynolds-number theory of Vasseur & Cox (1977), with the recent experiments of Takemura & Magnaudet (2003) and with the simulations of Kim et al. (1993). The most surprising result from the present simulations is that the wall-induced lift coefficient increases dramatically with increasing $Re$ above about 100. Detailed analysis of the flow field around the sphere suggests that this increase is due to an imperfect bifurcation resulting in the formation of a double-threaded wake vortical structure. In addition to a non-rotating sphere, we also simulate a freely rotating sphere in order to assess the importance of free rotation on the translational motion of the sphere. We observe the effect of sphere rotation on lift and drag forces to be small. We also explore the effect of the wall on the onset of unsteadiness.

Dynamics of particle migration in channel flow of viscoelastic fluids

“…Dynamics of particle migration (Asmolov 1999), and (ii) the wall repulsion force arising from the asymmetry of the corresponding wake vorticity distribution which pushes the particles away from the walls (Zeng et al 2005).…”

“…Inertia is necessary for this phenomenon. The balance of two competing effects, the shear-gradient lift force (Asmolov 1999) and the wall repulsive force (Zeng et al 2005), determines the equilibrium position of the particles. These two forces scale differently but both depend on the Reynolds number (Matas et al 2004) and blockage ratio Gossett et al 2012).…”

Numerical study of a sphere descending along an inclined slope in a liquid

“…Apart from the bottom wall that represents a slope, the other five walls, especially the upper wall, have an effect on the movement of the sphere as discussed by many researchers [6,10,12,26]. In order to estimate the impact of the upper and side walls on the results, several simulations with different domain sizes were conducted.…”

“…According to Zeng et al [12,13] who conducted simulations of a sphere settling down close to a vertical wall, there are three primary contributions to the lift force: (i) shearinduced lift, (ii) rotation-induced lift, and (iii) wall-induced lift. The lift force of the sphere originates from the vorticity Fig.…”

“…Cox and Hsu [10] and Vasseur and Cox [11] proposed an analytical expression of the lateral inertial motion of a sphere near a wall at low particle Reynolds numbers (Re < 0.3). Zeng et al [12,13] performed numerical simulations of a rigid sphere translating parallel to a flat wall using the spectral element method. Both lift and drag forces were studied and the relationship between the drag and lift coefficients with the Reynolds number (from 2 to 300) at different distances from the wall were obtained.…”