Modeling the Flow of Settling Suspensions

Abstract

Flow of settling particles differs substantially from the flow of nonsettling particles in three basic aspects: need for averaging, flow pattern formation, and extension of the concept of interface. Since the particles tend to settle during transport through the pipe, different packing densities exist in the radial direction of the pipe in horizontal flow. Averaging techniques have to be developed to be able to use Navier-Stokes equations to model the flow behavior. Variation of compaction densities of the particles in the radial direction causes the formation of different flow behaviors of particles to arise within the same cross-sectional area. The segregation of particles into different sections necessitates an extension of the concept of the interface. Along with the solid-liquid interfaces on the surface of the particles, interfaces also exist between layers of different compactions in the pipe. The variations in these interfaces should also be taken into account in the momentum balance equation. The mathematical methods and models used in describing two-phase flow will be taken up in this chapter. BASIC CONCEPTS IN MODELING OF TWO-PHASE FLOWWhatever the flow pattern that exists in solid-liquid two-phase flow an interface between the solid particles and the liquid is always present. Besides the phase interface between the solids and the liquid, another type of interface is defined between layers of a flowing suspension with different compaction levels.There are two main approaches used in flow models, the Lagrangian and Eulerian approaches. These approaches are initially explained for a single-phase (fluid) flow and then for homogeneous solid-liquid suspension flow. Eulerian and Lagrangian approaches for single-phase flowIn the Eulerian approach, a control volume is fixed in space (constant x, y, and z) through which the fluid flows. However, the control volume moves with the fluid in the Lagrangian approach with a velocity equal to that of the fluid stream V.The difference in the Eulerian and Lagrangian approaches can best be illustrated with the continuity equation. The continuity equation in Eulerian form is derived by using a 291