14,192 research outputs found
A Multiscale Diffuse-Interface Model for Two-Phase Flow in Porous Media
In this paper we consider a multiscale phase-field model for
capillarity-driven flows in porous media. The presented model constitutes a
reduction of the conventional Navier-Stokes-Cahn-Hilliard phase-field model,
valid in situations where interest is restricted to dynamical and equilibrium
behavior in an aggregated sense, rather than a precise description of
microscale flow phenomena. The model is based on averaging of the equation of
motion, thereby yielding a significant reduction in the complexity of the
underlying Navier-Stokes-Cahn-Hilliard equations, while retaining its
macroscopic dynamical and equilibrium properties. Numerical results are
presented for the representative 2-dimensional capillary-rise problem
pertaining to two closely spaced vertical plates with both identical and
disparate wetting properties. Comparison with analytical solutions for these
test cases corroborates the accuracy of the presented multiscale model. In
addition, we present results for a capillary-rise problem with a non-trivial
geometry corresponding to a porous medium
Optimization algorithms for the solution of the frictionless normal contact between rough surfaces
This paper revisits the fundamental equations for the solution of the
frictionless unilateral normal contact problem between a rough rigid surface
and a linear elastic half-plane using the boundary element method (BEM). After
recasting the resulting Linear Complementarity Problem (LCP) as a convex
quadratic program (QP) with nonnegative constraints, different optimization
algorithms are compared for its solution: (i) a Greedy method, based on
different solvers for the unconstrained linear system (Conjugate Gradient CG,
Gauss-Seidel, Cholesky factorization), (ii) a constrained CG algorithm, (iii)
the Alternating Direction Method of Multipliers (ADMM), and () the
Non-Negative Least Squares (NNLS) algorithm, possibly warm-started by
accelerated gradient projection steps or taking advantage of a loading history.
The latter method is two orders of magnitude faster than the Greedy CG method
and one order of magnitude faster than the constrained CG algorithm. Finally,
we propose another type of warm start based on a refined criterion for the
identification of the initial trial contact domain that can be used in
conjunction with all the previous optimization algorithms. This method, called
Cascade Multi-Resolution (CMR), takes advantage of physical considerations
regarding the scaling of the contact predictions by changing the surface
resolution. The method is very efficient and accurate when applied to real or
numerically generated rough surfaces, provided that their power spectral
density function is of power-law type, as in case of self-similar fractal
surfaces.Comment: 38 pages, 11 figure
Two-dimensional flows of foam: drag exerted on circular obstacles and dissipation
A Stokes experiment for foams is proposed. It consists in a two-dimensional
flow of a foam, confined between a water subphase and a top plate, around a
fixed circular obstacle. We present systematic measurements of the drag exerted
by the flowing foam on the obstacle, \emph{versus} various separately
controlled parameters: flow rate, bubble volume, solution viscosity, obstacle
size and boundary conditions. We separate the drag into two contributions, an
elastic one (yield drag) at vanishing flow rate, and a fluid one (viscous
coefficient) increasing with flow rate. We quantify the influence of each
control parameter on the drag. The results exhibit in particular a power-law
dependence of the drag as a function of the solution viscosity and the flow
rate with two different exponents. Moreover, we show that the drag decreases
with bubble size, increases with obstacle size, and that the effect of boundary
conditions is small. Measurements of the streamwise pressure gradient,
associated to the dissipation along the flow of foam, are also presented: they
show no dependence on the presence of an obstacle, and pressure gradient
depends on flow rate, bubble volume and solution viscosity with three
independent power laws.Comment: 23 pages, 13 figures, proceeding of Eufoam 2004 conferenc
Surface flow profiles for dry and wet granular materials by Particle Tracking Velocimetry; the effect of wall roughness
Two-dimensional Particle Tracking Velocimetry (PTV) is a promising technique
to study the behaviour of granular flows. The aim is to experimentally
determine the free surface width and position of the shear band from the
velocity profile to validate simulations in a split-bottom shear cell geometry.
The position and velocities of scattered tracer particles are tracked as they
move with the bulk flow by analyzing images. We then use a new technique to
extract the continuum velocity field, applying coarse-graining with the
postprocessing toolbox MercuryCG on the discrete experimental PTV data. For
intermediate filling heights, the dependence of the shear (or angular) velocity
on the radial coordinate at the free surface is well fitted by an error
function. From the error function, we get the width and the centre position of
the shear band. We investigate the dependence of these shear band properties on
filling height and rotation frequencies of the shear cell for dry glass beads
for rough and smooth wall surfaces. For rough surfaces, the data agrees with
the existing experimental results and theoretical scaling predictions. For
smooth surfaces, particle-wall slippage is significant and the data deviates
from the predictions. We further study the effect of cohesion on the shear band
properties by using small amount of silicon oil and glycerol as interstitial
liquids with the glass beads. While silicon oil does not lead to big changes,
glycerol changes the shear band properties considerably. The shear band gets
wider and is situated further inward with increasing liquid saturation, due to
the correspondingly increasing trend of particles to stick together
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