33 research outputs found
Optimizing the Source Distribution in Fluid Mixing
A passive scalar is advected by a velocity field, with a nonuniform spatial
source that maintains concentration inhomogeneities. For example, the scalar
could be temperature with a source consisting of hot and cold spots, such that
the mean temperature is constant. Which source distributions are best mixed by
this velocity field? This question has a straightforward yet rich answer that
is relevant to real mixing problems. We use a multiscale measure of
steady-state enhancement to mixing and optimize it by a variational approach.
We then solve the resulting Euler--Lagrange equation for a perturbed uniform
flow and for simple cellular flows. The optimal source distributions have many
broad features that are as expected: they avoid stagnation points, favor
regions of fast flow, and their contours are aligned such that the flow blows
hot spots onto cold and vice versa. However, the detailed structure varies
widely with diffusivity and other problem parameters. Though these are model
problems, the optimization procedure is simple enough to be adapted to more
complex situations.Comment: 19 pages, 23 figures. RevTeX4 with psfrag macro
Reduced models of chemical reaction in chaotic flows
A. Vikhansky and S. M. Co
Conditional moment closure for chemical reactions in laminar chaotic flows
We implement conditional moment closure (CMC) for simulation of chemical reactions in laminar chaotic flows. The CMC approach predicts the expected concentration of reactive species, conditional upon the concentration of a corresponding nonreactive scalar. Closure is obtained by neglecting the difference between the local concentration of the reactive scalar and its conditional average. We first use a Monte Carlo method to calculate the evolution of the moments of a conserved scalar; we then reconstruct the corresponding probability density function and dissipation rate. Finally, the concentrations of the reactive scalars are determined. The results are compared (and show excellent agreement) with full numerical simulations of the reaction processes in a chaotic laminar flow.
This is a preprint of an article published in AlChE Journal copyright (2007) American Institute of Chemical Engineers: http://www3.interscience.wiley.com
Granular flow in a rotating cylindrical drum

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Granular flow in a rotating cylindrical drum
Flow of granular material in a partially filled rotating cylinder is studied
using a boundary layer approach. Simple equations are derived to describe
granular dynamics in a transverse plane. A small parameter is recognized,
and the derived equations are solved analytically in the first-order approximation
of the small parameter. Cascading layer thickness, mean velocity along the
layer and profile of the free surface are determined in a closed analytical
form
Kinematics of the mixing of granular material in slowly rotating containers
The mixing of granular material in a two-dimensional slowly rotating container is studied
using a kinematic approach. A simple model is proposed to estimate the mixing capacity of a
mixer when the particles diffusivity is small. Different geometries of the container are examined
numerically. The mixing rate index for the case of a circular drum is derived analytically.
The optimum shape of the container and the optimum filling level are discussed
Granular flow in a rotating cylindrical drum
Abstract. { Flow of granular material in a partially lled rotating cylinder is studied using a boundary layer approach. Simple equations are derived to describe granular dynamics in a transverse plane. A small parameter is recognized, and the derived equations are solved analytically in the rst-order approximation of the small parameter. Cascading layer thickness, mean velocity along the layer and prole of the free surface are determined in a closed analytical form. Dynamics, mixing and separation of granular materials in a partially lled rotating cylin-drical drum have been the subject of numerous experimental and theoretical investigations (see, e.g., [1]-[3]). However only a few studies attempted to describe a continuous granular flow in a transverse plane of a rotating drum [1], [3]. In the present work a boundary value approximation is used to describe a two-dimensional granular flow. In the developed approach the transition from solid to liquid-like behavior is considered as a key process for specifying the granular dynamics. Let us consider a cylindrical drum of radius R which rotates with a constant angular velocity! ( g. 1). The drum is partially lled with a granular material of constant bulk density , and the length of the free surface is 2L. The free surface is inclined at an angle of internal frictio