Numerical Investigation on the Wall Effect to the Motion of the Particle Sedimentation
Date Issued
2011
Date
2011
Author(s)
Tsai, Liang-Hsia
Abstract
Many researcher have studied the interaction between two particles in a Newtonian
fluid at the Reynolds number 30~100. Joseph et al. (1987) studied the basic mechanism
controlling the motion and interactions of spherical at this Reynolds number interval.
They described these motions as drafting, kissing and tumbling (DKT). When two particles settling in a viscoelastic non-Newtonian fluid, the drafting effect makes the trailing particle accelerate to kiss the leading one, as well as they chain together without tumbling or separating if the effect of elasticity is strong enough. In this thesis, our study focus on the abnormal settling of two particles system and long body, such as ellipse particle and dipole particle due to the gravity in Newtonian fluid in an infinite channel of different width L/D, including 3, 4, 5, 6, 7, respectively, where D is the characteristic length. For two-dimensional solid- fluid two-phase system, we consider the fluid as a viscous and incompressible Newtonian fluid, and the solid as rigid circular particle, elliptic particle, or dipole particle, whose density is slightly heavier than the fluid. In this study, we use Navier-Stokes equation to model the fluid flow and Euler-Newton equation to model the rigid body motion. Furthermore, we use the
distributed Lagrangian multiplier/ fictitious domain method(DLM/FDM), which was developed by Glowinski and Pan, to simulate the fluid flow and the particle motion
directly. In this thesis, we define a critical Reynolds number (Recr) as the max Reynolds number which can make two particles keep chaining and settling vertically for two
particle system. To compare with the settling of the
long body formed by two particles, we define the critical Reynolds number for ellipse and dipole as the max number which can make the long axis of the long body parallel to
the central line of the channel and settle vertically in the middle of infinite channel. Analyzing the critical Reynolds number of these three systems, we have gotten the
result that the critical Reynolds number decreases as the channel width increases. In addition, we found the relation between 1/Recr and L/D. The relation is linear for two
particle settling. For ellipse and dipole cases, the relations are linear in wider channel. The simulation results indicate that in the narrow channel, the wall effect is stronger so that with a lower viscous force and higher inertia effect, two disks can chained together and a long body can settle vertically in the middle of the channel with its long axis parallel to the central line of the channel. In wide channel, the wall effect gets weaker, and the inertia effect gets stronger. The particle won’t behave similarly as that in the narrow channel unless the viscous force is large. In comparison of critical Reynolds
number among different particle systems, in narrow channel, the three Reynolds numbers of the three systems are close; in wide channel, the inertia effect imposing on long body is larger so that the range of Reynolds number, which can make the particles settle vertically, is smaller.
Subjects
Wall effect
Dual-particle settling
Chain of disks
Low Reynolds number
Long body settling
Critical Reynolds number
Type
thesis
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