Influence du gradient de seuil sur des essais de remontée de pression et d'écoulement dans les puits.

2017

Transp Porous Med

The Buckingham-Reiner models for the one-dimensional flow of a Bingham fluid along a uniform pipe or channel are well-known, but are modified here to cover much more general one-dimensional configurations. These include selections of channels with different widths, and five different probability density functions describing distributions of channel widths. It is found that the manner in which breakthrough occurs at the threshold pressure gradient depends very strongly on the type of distribution of pores and that a pseudo-threshold pressure gradient, which might be inferred from measurements of flow at relatively high pressure gradients, may be more than twice the magnitude of the true threshold gradient.

Section: Introductionmentioning

confidence: 99%

The Effect of Microstructure on Models for the Flow of a Bingham Fluid in Porous Media: One-Dimensional Flows

Nash

2017

Transp Porous Med

“…In the present paper we shall adopt Pascal's model (Pascal [1,2] to describe how a Bingham fluid flows within a homogeneous and isotropic porous medium. This is a piecewise linear relationship between the fluid velocity and the applied pressure gradient and it may be expressed as follows,…”

Section: Governing Equationsmentioning

confidence: 99%

“…This correction needs to be found because T c was chosen to be the reference temperature and therefore the corresponding hydrostatic pressure gradient is incorrect if an overall zero mean flux is to be maintained. To illustrate this, if we choose to consider a Newtonian fluid (Rb = 0) in a channel with external heating only (Ra i = 0), then p z = 1 2 Ra corresponds to a zero mean flow, and w = Ra(x − 1 2 ). A similar analysis for solely internal heating yields p z = 1 12 Ra i .…”

Section: Numerical Solutionsmentioning

confidence: 99%

“…Within the context of a porous medium the natural yield threshold is expressed in terms of a pressure gradient and, in the context of convective flows, this includes the buoyancy force. Pascal's piecewise-linear law (Pascal [1,2]) is itself the simplest relationship, and in this model there is no flow (as opposed to zero shear) when the threshold has not been met.…”

Section: Introductionmentioning

confidence: 99%

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The Effect of Internal and External Heating on the Free Convective Flow of a Bingham Fluid in a Vertical Porous Channel

Bassom

2019

Fluids

We study the steady free convective flow of a Bingham fluid in a porous channel where heat is supplied by both differential heating of the sidewalls and by means of a uniform internal heat generation. The detailed temperature profile is governing by an external and an internal Darcy-Rayleigh number. The presence of the Bingham fluid is characterised by means of a body force threshold as given by the Rees-Bingham number. The resulting flow field may then exhibit between two and four yield surfaces depending on the balance of magnitudes of the three nondimensional parameters. Some indication is given of how the locations of the yield surfaces evolve with the relative strength of the Darcy-Rayleigh numbers and the Rees-Bingham number. Finally, parameter space is delimited into those regions within which the different types of flow and stagnation patterns arise.

“…Just as the Navier-Stokes equations, which apply for a clear Newtonian fluid, are replaced by Darcy's law, which applies in a porous medium, so it is that the usual yield-stress form of the Navier-Stokes equations, which gives zero shear when stresses are less than the yield stress, needs to be replaced by a Darcy-Bingham law. The first papers which presented such a law were those by Pascal (1979Pascal ( , 1981. This law appears later, see Eq.…”

Section: Introductionmentioning

confidence: 96%

Unsteady Free Convection Boundary Layer Flows of a Bingham Fluid in Cylindrical Porous Cavities

Bassom

2018

Transp Porous Med

We consider two unsteady free convection flows of a Bingham fluid when it saturates a porous medium contained within a vertical circular cylinder. The cylinder is initially at a uniform temperature, and such flows are then induced by suddenly applying either a new constant temperature or a nonzero heat flux to the exterior surface. As time progresses, heat conducts inwards and this may or may not overcome the yield threshold for flow. For the constant temperature case, flow begins immediately should the parameter, Rb, which is a nondimensional yield parameter, be sufficiently large. The ultimate fate, though, is full immobility as the cylinder eventually tends towards a new constant temperature. For the constant heat flux case, the fluid remains immobile but will begin to flow eventually should Rb be sufficiently large. The two cases have different critical values for Rb.