Forces on a finite-sized particle located close to a wall in a linear shear flow

Abstract

To understand and better model the hydrodynamic force acting on a finite-sized particle moving in a wall-bounded linear shear flow, here we consider the two limiting cases of (a) a rigid stationary spherical particle in a linear wall-bounded shear flow and (b) a rigid spherical particle in rectilinear motion parallel to a wall in a quiescent ambient flow. In the present computations, the particle Reynolds number ranges from 2 to 250 at separation distances to the wall from nearly sitting on the wall to far away from the wall. First we characterize the structure of the wake for a stationary particle in a linear shear flow and compare with those for a particle moving parallel to a wall in a quiescent ambient [see L. Zeng, S. Balachandar, and P. Fischer, J. Fluid Mech. 536, 1 (2005)]. For both these cases we present drag and lift results and obtain composite drag and lift correlations that are valid for a wide range of Re and distance from the wall. These correlations have been developed to be consistent with all available low Reynolds number theories and approach the appropriate uniform flow results at large distance from the wall. Particular attention is paid to the case of particle in contact with the wall and the computational results are compared with those from experiments.

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

“…The asymmetry of the vorticity distribution in the wake of the sphere contributes to an asymmetric induced flow. This generates a lift force on the particle directed away from the slope [13]. When Re is smaller than 100, the vortex in the wake behind the sphere is stable, as shown in Figs.…”

“…Thus, in our cases, C l = C l,W − C l,M . Zeng et al [13] obtained an empirical relation, 0.313 + 0.812e (−0.125Re 0.77 ) , for the translation-induced lift coefficient when the particle is in contact with a vertical wall but without contact forces. In our case with contact forces, C l,W = 0.41 + 1.2e (−0.17Re 0.64 ) gave a good fit.…”

“…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.…”