Real-Space Renormalization Estimates for Two-Phase Flow in Porous Media

We present a spatial renormalization group algorithm to handle immiscibletwo-phase flow in heterogeneous porous media. We call this algorithmFRACTAM-R, where FRACTAM is an acronym for Fast Renormalization Algorithmfor Correlated Transport in Anisotropic Media, and the R stands for relativepermeability. Originally, FRACTAM was an approximate iterative process thatreplaces the L × L lattice of grid blocks, representing the reservoir,by a (L/2) × (L/2) one. In fact, FRACTAM replaces the original L× L lattice by a hierarchical (fractal) lattice, in such a way thatfinding the solution of the two-phase flow equations becomes trivial. Thistriviality translates in practice into computer efficiency. For N=L ×L grid blocks we find that the computer time necessary to calculatefractional flow F(t) and pressure P(t) as a function of time scales as N^1.7 for FRACTAM-R. This should be contrasted with thecomputational time of a conventional grid simulator N^2.3. The solution we find in this way is an accurateapproximation to the direct solution of the original problem.     

A general model for the effective viscosity of pseudoplastic and dilatant fluids

Summary A new and very general expression is proposed for correlation of data for the effective viscosity of pseudoplastic and dilatant fluids as a function of the shear stress. Most of the models which have been proposed previously are shown to be special cases of this expression. A straightforward procedure is outlined for evaluation of the arbitrary constants.

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Zusammenfassung Eine neue und sehr allgemeine Formel wird für die Korrelation der Werte der effektiven Viskosität von strukturviskosen und dilatanten Flüssigkeiten in Abhängigkeit von der Schubspannung vorgeschlagen. Die meisten schon früher vorgeschlagenen Methoden werden hier als Spezialfälle dieser Gleichung gezeigt. Ein einfaches Verfahren für die Auswertung der willkürlichen Konstanten wird beschrieben.

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Nomenclature b arbitrary constant inSisko model (eq. [5]) - n arbitrary exponent in eq. [1] - x independent variable - y(x) dependent variable - y ₀(x) limiting behavior of dependent variable asx 0 - y(x) limiting behavior of dependent variable asx - z original dependent variable - arbitrary constant inSisko model (eq. [5]) andBird-Sisko model (eq. [6]) - arbitrary exponent in eqs. [2] and [8] - effective viscosity = shear stress/rate of shear - _A effective viscosity at = _A - _B empirical constant in eqs. [2] and [8] - ₀ limiting value of effective viscosity as 0 - ₀() limiting behavior of effective viscosity as 0 - limiting value of effective viscosity as - () limiting behavior of effective viscosity as - rate of shear - arbitrary constant inBird-Sisko model (eq.[6]) - shear stress - _A arbitrary constant in eqs. [2] and [8] - ₀ shear stress at inBingham model - _1/2 shear stress at = ( ₀ + )/2 With 8 figures     

Contrôle par rotation ou par aspiration de l'écoulement autour d'un cylindre calculé par Simulation des Grandes Échelles

Control of the flow around a circular cylinder is studied using Large Eddy Simulation. The influence of control by rotation and suction on the flow characteristics is considered for several Reynolds numbers. Comparisons with experiments were conducted at $\mathit{Re}={10}^5$ for the flow with and without control. A drag reduction up to 30% is obtained for an usual suction intensity. To cite this article: G. Fournier et al., C. R. Mecanique 333 (2005).     

Fully three-dimensional direct numerical simulation of a plunging breakerSimulation numérique directe tridimensionnelle du déferlement plongeant

The scope of this paper is to show the results obtained for simulating three-dimensional breaking waves by solving the Navier–Stokes equations in air and water. The interface tracking is achieved by a Lax–Wendroff TVD scheme (Total Variation Diminishing), which is able to handle interface reconnections. We first present the equations and the numerical methods used in this work. We then proceed to the study of a three-dimensional plunging breaking wave, using initial conditions corresponding to unstable periodic sinusoidal waves of large amplitudes. We compare the results obtained for two simulations, a longshore depth perturbation has been introduced in the solution of the flow equations in order to see the transition from a two-dimensional velocity field to a fully three-dimensional one after plunging. Breaking processes including overturning, splash-up and breaking induced vortex-like motion beneath the surface are presented and discussed. To cite this article: P. Lubin et al., C. R. Mecanique 331 (2003).     

Influence of higher harmonics of the undulator in X‐ray polarimetry and crystal monochromator design

The spectrum of the undulator radiation of beamline P01 at Petra III has been measured after passing a multiple reflection channel‐cut polarimeter. Odd and even harmonics up to the 15th order, as well as Compton peaks which were produced by the high harmonics in the spectrum, could been measured. These additional contributions can have a tremendous influence on the performance of the polarimeter and have to be taken into account for further polarimeter designs.     

A crack perpendicular to and terminating at a bimaterial interface

Using dislocation simulation approach, the basic equation for a finite crack perpendicular to and terminating at a bimaterial interface is formulated. A novel expansion method is proposed for solving the problem. The complete solution to the problem, including the explicit formulae for theT stresses ahead of the crack tip and the stress intensity factors are presented. The stress field characteristics are analysed in detail. It is found that normal stresses {ie27-1} and {ie27-2} ahead of the crack tip, are characterised byQ fields if the crack is within a stiff material and the parameters |p _T | and |q _T | are very small, whereQ is a generalised stress intensity factor for a crack normal to and terminating at the interface. If the crack is within a weak material, the normal stresses {ie27-3} and {ie27-4} are dominated by theQ field plusT stress. This work was supported by the Swedish Research Council for Engineering Sciences.     

An iterative method of evaluation of elastic-plastic deflections of hyperstatic framed structures

Summary The concept of substitutive concentrated elastic-plastic rotations, replacing actual elasticplastic zones is used, together with an iterative method of determination of the bending moment distribution to simplify the evaluation of elastic-plastic deflections of hyperstatic beams and frames.

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Eine iterative Methode der Auswertung von elastisch-plastischen Verschiebungen für statisch unbestimmte Rahmen

Übersicht Die Idee von fiktiven Ersatzrotationen, welche die tatsächlichen elastisch-plastischen Zonen modelliert, wird mit einer iterativen Methode kombiniert, um eine relativ einfache Bestimmung von Biegemomentenfeldern in statisch unbestimmten Balken und Rahmen zu ermöglichen. Die resultierenden Verschiebungen, ergeben sich mit ausreichender Genauigkeit.

     

Motion of a viscoplastic liquid in a porous inhomogeneous medium

Equations of motion are derived for a viscoplastic liquid in a nonuniform medium of type 2 (piecewise uniform) or type 3 (with a variable filtration coefficient) [1] on the assumption that the motion is of steady-state type. Solutions are presented for a parallel flow and a flow with axial symmetry.     

Use of a sliding plate rheometer to measure the first normal stress difference at high shear rates

The use of a sliding plate rheometer (SPR) to determine the first normal stress difference of molten polymers and elastomers at high shear rates is demonstrated. The simple shear flow in this instrument is not subject to the flow instabilities that limit the use of rotational rheometers to shear rates often below 1 s⁻¹. However, issues of secondary flow and wall slip must be addressed to obtain reliable data using an SPR. A highly entangled, monodisperse polybutadiene and a commercial polystyrene were the polymers studied. The inclusion of the polystyrene made it possible to compare data with those obtained by Lodge using a stressmeter, which is an instrument based on the measurement of the hole pressure. The data from the two instruments are in good agreement and are also close to the predictions of an empirical equation of Laun based on the storage and loss moduli.     

Spectroscopies and Electron Microscopies Unravel the Origin of the First Colour Photographs

The first colour photographs were created by a process introduced by Edmond Becquerel in 1848. The nature of these photochromatic images colours motivated a debate between scientists during the XIX^th century, which is still not settled. We present the results of chemical analysis (EDX, HAXPES and EXAFS) and morphology studies (SEM, STEM) aiming at explaining the optical properties of the photochromatic images (UV-visible spectroscopy and low loss EELS). We rule out the two hypotheses (pigment and interferences) that have prevailed since 1848, respectively based on variations in the oxidation degree of the compound forming the sensitized layer and periodically spaced photolytic silver planes. A study of the silver nanoparticles dispersions contained in the coloured layers showed specific localizations and sizes distributions of the nanoparticles for each colour. These results allow us to formulate a plasmonic hypothesis on the origin of the photochromatic images colours.