493 research outputs found
Critical jamming of frictional grains in the generalized isostaticity picture
While frictionless spheres at jamming are isostatic, frictional spheres at
jamming are not. As a result, frictional spheres near jamming do not
necessarily exhibit an excess of soft modes. However, a generalized form of
isostaticity can be introduced if fully mobilized contacts at the Coulomb
friction threshold are considered as slipping contacts. We show here that, in
this framework, the vibrational density of states (DOS) of frictional discs
exhibits a plateau when the generalized isostaticity line is approached. The
crossover frequency to elastic behavior scales linearly with the distance from
this line. Moreover, we show that the frictionless limit, which appears
singular when fully mobilized contacts are treated elastically, becomes smooth
when fully mobilized contacts are allowed to slip.Comment: 4 pages, 4 figures, submitted to PR
Simulation of slug propagation for by-pass pigging in two-phase stratified pipe flow
The present paper is focused on the development of an accurate 1D numerical model for pig motion in two-phase flow. The focus will be on the liquid slug that is accumulated in front of the pig, the so-called pig-generated slug. Under the assumption of a stratified flow, we first discuss the academic case of liquid slug accumulation where we neglect the viscosity of the fluids. The size of the liquid slug will then effectively be determined by the speed of the hydrostatic wave which runs ahead of the pig. We also consider the more realistic case which includes the viscosity of the fluid. Finally, we discuss the effect of the presence of a by-pass in the pig on the accumulated liquid slug
Energy-stable discretization of the one-dimensional two-fluid model
In this paper we present a complete framework for the energy-stable
simulation of stratified incompressible flow in channels, using the
one-dimensional two-fluid model. Building on earlier energy-conserving work on
the basic two-fluid model, our new framework includes diffusion, friction, and
surface tension. We show that surface tension can be added in an
energy-conserving manner, and that diffusion and friction have a strictly
dissipative effect on the energy.
We then propose spatial discretizations for these terms such that a
semi-discrete model is obtained that has the same conservation properties as
the continuous model. Additionally, we propose a new energy-stable advective
flux scheme that is energy-conserving in smooth regions of the flow and
strictly dissipative where sharp gradients appear. This is obtained by
combining, using flux limiters, a previously developed energy-conserving
advective flux with a novel first-order upwind scheme that is shown to be
strictly dissipative.
The complete framework, with diffusion, surface tension, and a bounded
energy, is linearly stable to short wavelength perturbations, and exhibits
nonlinear damping near shocks. The model yields smoothly converging numerical
solutions, even under conditions for which the basic two-fluid model is
ill-posed. With our explicit expressions for the dissipation rates, we are able
to attribute the nonlinear damping to the different dissipation mechanisms, and
compare their effects
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