Coalescence of fluid particles with deformable interfaces in non-Newtonian media

The role of wave-induced separated flow in solute transport above a rippled bed is studied from numerical solutions to the two-dimensional Navier–Strokes equations and the advection-diffusion equation. A horizontal ambient flow that varies sinusoidally in time is imposed far above the bed, and a constant concentration difference between the upper and lower boundaries of computation is assumed. The computed flow field is the sum of an oscillatory rectilinear flow and a vortical flow which is periodic both in time and in the horizontal. Poincaré sections of this flow suggest chaotic mixing. Vertical lines of fluid particles above the crest and above the trough deform into whorls and tendrils, respectively, in just one wave period. Horizontal lines near the bottom deform into Smale horseshoe patterns. The combination of high shear and vortex-induced normal velocity close to the sediment surface results in large net displacements of fluid particles in a period. The resulting advective transport normal to the bed can be higher than molecular diffusion from well within the viscous boundary layer up to a few ripple heights above the bed. When this flow field is applied to the transport equation of a passive scalar, two distinct features – regular temporal oscillations in concentration and a linear time-averaged vertical concentration profile – are found immediately above the bed. These features have also been observed previously in field measurements on oxygen concentration. Advective transport is shown to be dominant even in the region where the time-averaged concentration profile is linear, a region where vertical solute transport has often been estimated using diffusion-type models in many field studies.

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Coupled systems of two-dimensional turbulence

Journal of Fluid Mechanics ◽

10.1017/jfm.2013.422 ◽

2013 ◽

Vol 732 ◽

Author(s):

Rick Salmon

Keyword(s):

Hamiltonian System ◽

Energy Conservation ◽

Strong Correlation ◽

Conservation Law ◽

Hamiltonian Dynamics ◽

Coupled Systems ◽

The Other ◽

Two Dimensional ◽

Coherent Vortices ◽

Fluid Particles

AbstractOrdinary two-dimensional turbulence corresponds to a Hamiltonian dynamics that conserves energy and the vorticity on fluid particles. This paper considers coupled systems of two-dimensional turbulence with three distinct governing dynamics. One is a Hamiltonian dynamics that conserves the vorticity on fluid particles and a quantity analogous to the energy that causes the system members to develop a strong correlation in velocity. The other two dynamics considered are non-Hamiltonian. One conserves the vorticity on particles but has no conservation law analogous to energy conservation; the other conserves energy and enstrophy but it does not conserve the vorticity on fluid particles. The coupled Hamiltonian system behaves like two-dimensional turbulence, even to the extent of forming isolated coherent vortices. The other two dynamics behave very differently, but the behaviours of all four dynamics are accurately predicted by the methods of equilibrium statistical mechanics.

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Multisymplectic formulation of fluid dynamics using the inverse map

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2007.1892 ◽

2007 ◽

Vol 463 (2086) ◽

pp. 2671-2687 ◽

Cited By ~ 35

Author(s):

C.J Cotter ◽

D.D Holm ◽

P.E Hydon

Keyword(s):

Fluid Dynamics ◽

Conservation Laws ◽

Fluid Particle ◽

Hamilton’S Principle ◽

Hamilton's Principle ◽

Numerical Integrators ◽

Fluid Particles ◽

Infinite Set ◽

Circulation Theorem

We construct multisymplectic formulations of fluid dynamics using the inverse of the Lagrangian path map. This inverse map, the ‘back-to-labels’ map, gives the initial Lagrangian label of the fluid particle that currently occupies each Eulerian position. Explicitly enforcing the condition that the fluid particles carry their labels with the flow in Hamilton's principle leads to our multisymplectic formulation. We use the multisymplectic one-form to obtain conservation laws for energy, momentum and an infinite set of conservation laws arising from the particle relabelling symmetry and leading to Kelvin's circulation theorem. We discuss how multisymplectic numerical integrators naturally arise in this approach.

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Fluid-Particles Flows: A Thin Spray Model with Energy Exchanges

ESAIM Proceedings ◽

10.1051/proc/2009047 ◽

2009 ◽

Vol 28 ◽

pp. 195-210 ◽

Cited By ~ 4

Author(s):

Laurent Boudin ◽

Benjamin Boutin ◽

Bruno Fornet ◽

Thierry Goudon ◽

Pauline Lafitte ◽

...

Keyword(s):

Energy Exchanges ◽

Fluid Particles

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Mathematical Aspects of Using Electrostatic Filters in Food Industry

Bulletin of University of Agricultural Sciences and Veterinary Medicine Cluj-Napoca Agriculture ◽

10.15835/buasvmcn-agr:6581 ◽

2011 ◽

Vol 68 (2) ◽

Author(s):

Mircea Valentin MUNTEAN ◽

Ioan DROCAS ◽

Ovidiu MARIAN ◽

V BARBIERU ◽

C. TOPAN

Keyword(s):

Cost Effectiveness ◽

Food Industry ◽

Naked Eye ◽

Conventional Microscope ◽

Air Suspension ◽

Fluid Particles

Purifying processes on gas or liquid streams are often required to treat such large volumes of fluid. Particles in air suspension will range downwards from 100 m. Down to 20 m they will be visible to naked eye, while on down to 0,1...0,2 m they can be observed with a conventional microscope. Electrostatic filters are used in food industry to purify pollute emission and climate the precincts. Characteristic of electrostatic separate operation is: efficiency, level of filtration needed, dust storage capability, cost effectiveness, temperature of suspension, velocities in still air.

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Secondary Flow in Cascades: Two Simple Derivations for the Components of Vorticity

Journal of Mechanical Engineering Science ◽

10.1243/jmes_jour_1974_016_073_02 ◽

1974 ◽

Vol 16 (6) ◽

pp. 391-401 ◽

Cited By ~ 13

Author(s):

P. M. Came ◽

H. Marsh

Keyword(s):

Secondary Flow ◽

Secondary Circulation ◽

Governing Equations ◽

New Approach ◽

Simple Theories ◽

Fluid Particles ◽

The Difference ◽

Downstream Flow ◽

Three Components

By considering a many-bladed cascade, two simple theories are developed for secondary flow in cascades. Following the work of Hawthorne (1)†, three components of vorticity are identified at exit from the cascade. An expression is obtained for the difference in the time taken for fluid particles to travel over the two surfaces of the blade, and this is used to derive the governing equations for the distributed secondary, trailing filament and trailing shed vorticities. It is shown that, for a many-bladed cascade, the total secondary circulation in the downstream flow is zero. The calculation of secondary flow for a real cascade is discussed, and it is shown that earlier calculations of secondary flow at exit from cascades are consistent with this new approach.

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