110 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
IHTC14-22470 EFFECT OF RAIN ON EVOLUTION OF DISTRIBUTION OF SOLUBLE GASEOUS POLLUTANTS IN THE ATMOSPHERE
ABSTRACT We suggest a model of rain scavenging of soluble gaseous pollutants in the atmosphere. It is shown that below-cloud gas scavenging is determined by non-stationary convective diffusion equation with the effective Peclet number. The obtained equation was analyzed numerically in the case of lognormal droplet size distribution. Calculations of scavenging coefficient and the rates of precipitation scavenging are performed for wet removal of ammonia (NH 3 ) and sulfur dioxide (SO 2 ) from the atmosphere. It is shown that scavenging coefficient is non-stationary and height-dependent. It is found also that the scavenging coefficient strongly depends on initial concentration distribution of soluble gaseous pollutants in the atmosphere. It is shown that in the case of linear distribution of the initial concentration of gaseous pollutants whereby the initial concentration of gaseous pollutants decreases with altitude, the scavenging coefficient increases with height in the beginning of rainfall. At the later stage of the rain scavenging coefficient decreases with height in the upper below-cloud layers of the atmosphere
Topological Chaos in Spatially Periodic Mixers
Topologically chaotic fluid advection is examined in two-dimensional flows
with either or both directions spatially periodic. Topological chaos is created
by driving flow with moving stirrers whose trajectories are chosen to form
various braids. For spatially periodic flows, in addition to the usual
stirrer-exchange braiding motions, there are additional
topologically-nontrivial motions corresponding to stirrers traversing the
periodic directions. This leads to a study of the braid group on the cylinder
and the torus. Methods for finding topological entropy lower bounds for such
flows are examined. These bounds are then compared to numerical stirring
simulations of Stokes flow to evaluate their sharpness. The sine flow is also
examined from a topological perspective.Comment: 18 pages, 14 figures. RevTeX4 style with psfrag macros. Final versio
Reduced models of chemical reaction in chaotic flows
A. Vikhansky and S. M. Co
Single-Phase Flow of Non-Newtonian Fluids in Porous Media
The study of flow of non-Newtonian fluids in porous media is very important
and serves a wide variety of practical applications in processes such as
enhanced oil recovery from underground reservoirs, filtration of polymer
solutions and soil remediation through the removal of liquid pollutants. These
fluids occur in diverse natural and synthetic forms and can be regarded as the
rule rather than the exception. They show very complex strain and time
dependent behavior and may have initial yield-stress. Their common feature is
that they do not obey the simple Newtonian relation of proportionality between
stress and rate of deformation. Non-Newtonian fluids are generally classified
into three main categories: time-independent whose strain rate solely depends
on the instantaneous stress, time-dependent whose strain rate is a function of
both magnitude and duration of the applied stress and viscoelastic which shows
partial elastic recovery on removal of the deforming stress and usually
demonstrates both time and strain dependency. In this article the key aspects
of these fluids are reviewed with particular emphasis on single-phase flow
through porous media. The four main approaches for describing the flow in
porous media are examined and assessed. These are: continuum models, bundle of
tubes models, numerical methods and pore-scale network modeling.Comment: 94 pages, 12 figures, 1 tabl
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