### Aspects of Particle Sedimentation in Dilute Flows at Finite Reynolds numbers

The purpose of these studies is to examine dilute two-phase flows at finite Reynolds numbers along two main themes. First, to investigate the sedimentation of solid particles arranged in a regular periodic lattice and to determine both sedimentation rates and flow characteristics over a range of finite Reynolds numbers and particle concentrations up to 20%. This is a canonical problem in sedimentation theory and should provide useful insights into the dynamics of two-phase flow. Second, to investigate a simplified, approximate method for calculating dispersed two-phase flow using a force-coupling model that employs the fluid force on the individual particles to represent the particulate phase as a distributed body force action on the fluid phase. This makes the equations of motion for finite Reynolds number flows suitable to be solved numerically, and to be independent of the choice of algorithms. A spectral/hp element direct numerical method is also used to solve the time dependent Navier-Stokes equations for flow through periodic arrays of cylindrical and spherical particles. The DNS calculations more accurately model the flow dynamics and is used to validate the results of the force-coupling model.

The two dimensional problem was used as a test of the DNS and the results agree well with those of other numerical simulations. Analyzing the three dimensional problem proved to be informative. Determining the relationships between the superficial velocity or sedimentation velocity, the external force on the particles and flow structure as the volume fraction and Reynolds number are varied were the main goals. For Stokes flow conditions the sedimentation velocity decreases as the volume fraction is increased. At finite Reynolds numbers, this is countered by an interaction between the particles and the wakes when the system is dilute. As the volume fraction increases, the velocity is hindered by the particles and the settling rate decreases so that the flow experiences a blocking effect. Flow separation is delayed till higher Reynolds numbers. Comparing the force-coupling model for spherical particle motion in dilute flows to the DNS show that it successfully captures the flow dynamics and reproduces observed flow characteristics from experimental data as well. As a first approximation method it proves to be efficient and consistent.