SIMULATING THE SEDIMENTATION OF A DILUTE SUSPENSION D. J. E. Harvie * , K. Nandakumar and J. H. Masliyah Department of Chemical and Materials Engineering University of Alberta, Edmonton, AB, Canada November 2002 Abstract The results of simulations of dilute suspensions of mono- disperse Stokesian spheres are reported and validated against available experimental data. The equations and method of solution appear to be capable of capturing the often unstable suspension/clear fluid interface present in these systems. Keywords: Suspensions, CFD, Sedimentation, Inclinded Settlers 1 INTRODUCTION Sedimentation describes a process whereby solid parti- cles are separated from a fluid, usually under the action of gravitational forces. In industrial processes sedimenta- tion is often performed in arrays of inclinded settlers. As shown in Figure 1, an inclinded settler is a simple ves- sel which has its longest dimension inclined slightly away from vertical. Such vessels are popular as the production rate of clarified fluid is generally higher than the produc- tion rate of fluid from equivalently sized vertically orien- tated settlers, primarily because the particles have less dis- tance to travel before impacting a wall. For the past eight decades the performance of inclined settlers has been described using the Ponder-Nakamura- Kuroda (PNK) theory (see Davis and Acrivos, 1985). The PNK theory is a kinematic theory which gives the rate of production of clear fluid per unit depth of a rectangular vessel as S = v o B [cos θ +(H/B) tan θ] , (1) where the geometric variables are as shown in Figure 1, and v o is the hindered settling velocity of a single particle within the suspension region. In practice the PNK theory often overestimates the effi- ciency of an inclined settler as it does not consider the kinetics of the fluid motion. When a settler is inclined, a thin layer of clear fluid forms along the underside of the longer downward facing vessel wall. As the density of this fluid is smaller than that of the nearby suspension, it experiences a large buoyancy force, causing it to acceler- ate upwards. Resisting this upward movement are viscous ∗ daltonh@ualberta.ca and inertial forces that act between the Clear Fluid Layer (CFL) and the adjacent wall and suspension regions. If the velocities within the CFL are large enough, waves can form along the interface that separates the CFL and sus- pension regions. These waves may grow and break as they ascend the vessel, entraining suspension into the CFL and decreasing the efficiency of the settler. Thus, to predict the performance of an inclined settler, we must be able to describe the formation and subsequent growth of these instabilities. Past papers concerned the operation of inclinded settlers can be loosely classified as either analytical or numerical in nature. Studies published prior to 1985 are reviewed in Davis and Acrivos (1985) while more recent theoretical developments are outlined in Ungarish (1993). Current analytical theories to describe the operation of in- clinded settlers are generally based on the analysis pre- sented by Acrivos and Herbolzheimer (1979) who exam- ined the process using a simplified set of ‘mixture’ equa- tions. A set of mixture equations consists of a continuity equation for each phase (ie, one for the solid and one for the fluid), a mixture averaged momentum equation to de- scribe the movement of the suspension as a whole, and a relationship between the velocities of each phase. By neglecting inertial effects and assuming that the suspen- x y d q B H Figure 1: Sketch of an inclinded settler.