Suspension mechanics at finite inertia

Title

Identifier

d_2009_2013:d200bb49a0e4:10188

identifier

10455

Creator

Kulkarni, Pandurang Manohar,

Contributor

Jeffrey F. Morris

Date

2009

Language

English

Publisher

City University of New York.

Subject

Abstract

This work addresses the influence of microscale inertia on the motion of rigid particles freely suspended in a Newtonian fluid via lattice-Boltzmann numerical simulations. The suspended particles are non-Brownian, neutrally-buoyant and spherical in shape to consider inertial effects exclusively.;First, the relative trajectories of two spheres immersed in finite-inertia simple-shear flow are described. The inertia is characterized by the shear flow Reynolds number Re = rho g&d2; alpha2/mu, where mu and rho are the viscosity and density of the fluid respectively, g&d2; is the shear rate and alpha is radius of the particle. Reynolds numbers of 0 ≤ Re ≤ 1 are considered with a focus on inertia at Re = O(0.1). At finite inertia, the topology of the pair trajectories is altered from that predicted at Re = 0, as closed trajectories found in Stokes flow vanish and two new forms of trajectories are observed. These include spiraling and reversing trajectories in addition to largely undisturbed open trajectories. For Re = O(0.1), the limits of the various regions in pair space yielding open, reversing and spiraling trajectories are roughly defined.;In a pressure-driven pipe flow at finite Reynolds number, suspended particles are known to undergo lateral migration to a specific position off the centerline. We investigate the inertia-driven lateral migration of a single particle in a rectangular conduit flow. The parameters that affect the cross-stream motion are particle size relative to the channel (W/d), aspect ratio of the channel (H/W) and the shear rate based Reynolds number on the particle scale, Rep. The particle equilibrium positions in rectangular cross-section are obtained by the trajectory analysis with various starting positions of the particle. In a 2:1 channel with particle of size one-third of the channel width, it is found that the particle migrates to the center of the longer edge and the rate of approach scales linearly with Rep. Upon changing the particle size and the aspect ratio, we find a bifurcation in the form of multiple equilibrium locations. In case of a dilute suspension, the existence of particle ordering in the axial direction and the underlying physical mechanism are also discussed.;Furthermore, we examine the effect of particle-scale inertia on the rheology of a dense suspension subjected to simple-shear flow. The dimensionless parameters governing the bulk rheology are the solid-volume fraction &phis; and the Reynolds number Re = rho g&d2; alpha2/mu. Using the lattice Boltzmann simulations in a wall-bounded shear flow, the time averaged particle stress is computed. The relative viscosity, normal stress differences and particle pressure are reported for 0.01 ≤ Re < 5 and 0.05 ≤ &phis; ≤ 0.3. The anisotropy in microstructure at finite Re is also studied through the pair distribution function g( r).;The suspension balance approach is then used to perform "computational suspension dynamics". Specifically we develop continuum modeling of suspension flows with inertia to predict the velocity and particle concentration profiles in a pressure-driven pipe flow. The particle-scale inertia is taken into account by modifying the model for particle stress and introducing the lateral force associated with inertial migration to the particle phase momentum balance. Case studies on cross-stream migration are provided and it is found that the predicted profiles show the influence of inertia in a manner consistent with the limited experimental data.

Type

dissertation

Source

2009_2013.csv

degree

Ph.D.

Program

Engineering

Item