Model for Predicting Solids Velocity Fluctuations in Sedimenting Suspensions

Effects of boundary walls on the properties of settling spheres

Numerical Simulations are performed, using Eulerian two fluid model (TFM) to investigate the effects of solid volume fraction and no-slip side walls on the settling particles. It is found that average settling velocity decreases with increasing volume fraction for both gas-solid (GS) and liquid-solid (LS) systems, in good agreement with the Richardson-Zaki 1 − ϕ n ${\left(1-\phi \right)}^{n}$ law. It was also noted that average velocity is independent of the boundary condition for both gas-solid (GS) and liquid-solid (LS) systems. The root mean square value of the solid volume fraction shows the increasing trend with volume fraction, caused by the many particle interactions. Furthermore, no-slip sidewalls were found to damp the velocity fluctuations quantitively, while following the well-known ϕ 1 / 2 ${\phi }^{1/2}$ scaling with volume fraction. Side walls were found to act as kinetic trap for the particles, damping the fluctuation near the walls and plateauing in the mid plane. These simulations showed that the GS system shows the higher solid fraction fluctuations that the LS system at the same Reynolds number, mainly because of the higher collision frequency (higher Stokes number) among the particles.