| Summary: | 碩士 === 臺灣大學 === 應用力學研究所 === 98 === In this thesis, we have studied the Boycott effect for heavy particles and bidisperse suspension that contains light and heavy particles. In these two-dimensional solid-liquid two-phase systems, the fluid is a viscous incompressible Newtonian fluid and the particles are rigid disks. We have applied a distributed Lagrange multiplier/fictitious domain method, developed by Glowinski, Pan, Chang, et al., to simulate the motion of particles during the sedimentation process in an inclined closed channel. We have considered the particle-particle, particle-wall and particle-fluid interactions, and calculated all particle positions, settling velocities, and angular velocities via the direct numerical simulation.
In the most of study related to the Boycott effect, continuum theory and the PNK model have been used to predict the interface between the clear fluid and the suspension. In this thesis, we have computed the fluid velocity field and the trajectories of particles with different solid fractions (10%, 15%, 20%) and tilted angles (0°, 10°, 20°, 30°, 40°, 50° and 60°). The global convection and local secondary vortexes are observed in our simulation results (in an inclined channel). We have compared our results with the PNK model, and found that the local vortexes affect the interface settling velocity in a low tilted channel.
For the bidisperse suspension problem, we have considered a suspension of light and heavy particles of equal size in a tilted channel with the total solid fraction of 20% and the angle of 0°, 20°, 30°, 40° and 50°, respectively. We have calculated the light and heavy particle trajectories and the fluid velocity field via the direct numerical simulation. We have found that smaller local vortexes merge and form a clockwise rotation of a global convection in time. The simulation results have been compared with the prediction of the interfaces of the light and heavy particles, respectively, based on a modified PNK model when both types of particles are either fully mixed or completely separated.
In conclusion, although the continuum theory can explain global convection associated with the sedimentation in a tilted channel, it still couldn''t describe the local vortex occurrence. In this thesis, we have shown how the local smaller vortexes have a strong effect on the interface settling velocity in a low tilted channel.
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