Auswahl der wissenschaftlichen Literatur zum Thema „Couette Plan Annulaire“

Experiments and numerical simulations have shown that turbulence in transitional wall-bounded shear flows frequently takes the form of long oblique bands if the domains are sufficiently large to accommodate them. These turbulent bands have been observed in plane Couette flow, plane Poiseuille flow, counter-rotating Taylor–Couette flow, torsional Couette flow, and annular pipe flow. At their upper Reynolds number threshold, laminar regions carve out gaps in otherwise uniform turbulence, ultimately forming regular turbulent–laminar patterns with a large spatial wavelength. At the lower threshold, isolated turbulent bands sparsely populate otherwise laminar domains, and complete laminarization takes place via their disappearance. We review results for plane Couette flow, plane Poiseuille flow, and free-slip Waleffe flow, focusing on thresholds, wavelengths, and mean flows, with many of the results coming from numerical simulations in tilted rectangular domains that form the minimal flow unit for the turbulent–laminar bands.

The onset of turbulence in subcritical shear flows is one of the most puzzling manifestations of critical phenomena in fluid dynamics. The present study focuses on the Couette flow inside an infinitely long annular geometry where the inner rod moves with constant velocity and entrains fluid, by means of direct numerical simulation. Although for a radius ratio close to unity the system is similar to plane Couette flow, a qualitatively novel regime is identified for small radius ratio, featuring no oblique bands. An analysis of finite-size effects is carried out based on an artificial increase of the perimeter. Statistics of the turbulent fraction and of the laminar gap distributions are shown both with and without such confinement effects. For the wider domains, they display a cross-over from exponential to algebraic scaling. The data suggest that the onset of the original regime is consistent with the dynamics of one-dimensional directed percolation at onset, yet with additional frustration due to azimuthal confinement effects.

The effect of an insoluble surfactant on the centrifugal and shear instability of a pair of radially stratified immiscible liquids in the annular gap between concentric two-fluid Taylor–Couette flow is investigated by a normal-mode linear analysis and complementary energy analysis. The interface is assumed to be concentric with the cylinders. The gravitational effects are ignored. Influences of density and viscosity stratification, surface tension, surfactant concentration distribution and Taylor–Couette shearing are considered comprehensively. The instability characteristics due to competition and interaction between various physical instability mechanisms are of principal concern. Neutral curves with upper and lower branches in the Reynolds number (Re1)/axial wavenumber (k) plane are obtained. A window of parameters is identified in which the flow is linearly stable. The Marangoni traction force caused by the gradient of surfactant concentration stabilizes the axisymmetric perturbations but initiates an instability corresponding to non-axisymmetric modes in the presence of basic Couette shearing flow. Co-rotation of the outer cylinder has a stabilizing effect in expanding the stable region, which dwindles in the counter-rotation situation.

Results of numerical simulations of a forced shear flow in an annular geometry are presented. The particular geometry used in this work reduces the effects of centrifugal and Coriolis forces. However, there are still a large number of system parameters (shear width, shear profile, radius of curvature, initial conditions, etc.) to characterize. This set of variables is limited after the code has been validated with experimental results (Rabaud & Couder 1983; Chomaz et al. 1988) and with the associated linear stability analysis. As part of the linear stability characterization, the pseudo-spectrum for the associated Orr–Sommerfeld operator for plane, circular Couette flow is calculated, and it is found to be insensitive to perturbations.The numerical simulation code is a highly accurate de-aliased spectral method which utilizes banded operators to increase the computational efficiency. Viscous dissipation terms enter the code directly from the equations of motion. The results from the simulation code at low Reynolds numbers are compared with the results from linear stability analysis and are used to give predictions for the coefficients of the Landau equation describing the saturation behaviour near the critical Reynolds number. Numerical results at higher Reynolds numbers demonstrate the effects of spin-up and spin-down, including the experimentally observed hysteresis. The properties of two- dimensional shears at high Reynolds numbers, at which temporal states are formed, are also addressed.

The large-scale laminar/turbulent spiral patterns that appear in the linearly unstable regime of counter-rotating Taylor–Couette flow are investigated from a statistical perspective by means of direct numerical simulation. Unlike the vast majority of previous numerical studies, we analyse the flow in periodic parallelogram-annular domains, following a coordinate change that aligns one of the parallelogram sides with the spiral pattern. The domain size, shape and spatial resolution have been varied and the results compared with those in a sufficiently large computational orthogonal domain with natural axial and azimuthal periodicity. We find that a minimal parallelogram of the right tilt significantly reduces the computational cost without notably compromising the statistical properties of the supercritical turbulent spiral. Its mean structure, obtained from extremely long time integrations in a co-rotating reference frame using the method of slices, bears remarkable similarity with the turbulent stripes observed in plane Couette flow, the centrifugal instability playing only a secondary role. This article is part of the theme issue ‘Taylor–Couette and related flows on the centennial of Taylor’s seminal Philosophical transactions paper (Part 2)’.

AbstractIn this paper, we investigate the stability of the 2-dimensional (2D) Taylor–Couette (TC) flow for the incompressible Navier–Stokes equations. The explicit form of velocity for 2D TC flow is given by $$u=(Ar+\frac{B}{r})(-\sin \theta , \cos \theta )^T$$ u = ( A r + B r ) ( - sin θ , cos θ ) T with $$(r, \theta )\in [1, R]\times \mathbb {S}^1$$ ( r , θ ) ∈ [ 1 , R ] × S 1 being an annulus and A, B being constants. Here, A, B encode the rotational effect and R is the ratio of the outer and inner radii of the annular region. Our focus is the long-term behavior of solutions around the steady 2D TC flow. While the laminar solution is known to be a global attractor for 2D channel flows and plane flows, it is unclear whether this is still true for rotating flows with curved geometries. In this article, we prove that the 2D Taylor–Couette flow is asymptotically stable, even at high Reynolds number ($$Re\sim \nu ^{-1}$$ R e ∼ ν - 1 ), with a sharp exponential decay rate of $$\exp (-\nu ^{\frac{1}{3}}|B|^{\frac{2}{3}}R^{-2}t)$$ exp ( - ν 1 3 | B | 2 3 R - 2 t ) as long as the initial perturbation is less than or equal to $$\nu ^\frac{1}{2} |B|^{\frac{1}{2}}R^{-2}$$ ν 1 2 | B | 1 2 R - 2 in Sobolev space. The powers of $$\nu $$ ν and B in this decay estimate are optimal. It is derived using the method of resolvent estimates and is commonly recognized as the enhanced dissipative effect. Compared to the Couette flow, the enhanced dissipation of the rotating Taylor–Couette flow not only depends on the Reynolds number but also reflects the rotational aspect via the rotational coefficient B. The larger the |B|, the faster the long-time dissipation takes effect. We also conduct space-time estimates describing inviscid-damping mechanism in our proof. To obtain these inviscid-damping estimates, we find and construct a new set of explicit orthonormal basis of the weighted eigenfunctions for the Laplace operators corresponding to the circular flows. These provide new insights into the mathematical understanding of the 2D Taylor–Couette flows.

We investigate the coupling effect of buoyancy and shear based on an annular centrifugal Rayleigh–Bénard convection (ACRBC) system in which two cylinders rotate with an angular velocity difference. Direct numerical simulations are performed in a Rayleigh number range $10^6\leq Ra\leq 10^8$ , at fixed Prandtl number $Pr=4.3$ , inverse Rossby number $Ro^{-1}=20$ , and radius ratio $\eta =0.5$ . The shear, represented by the non-dimensional rotational speed difference $\varOmega$ , varies from $0$ to $10$ , corresponding to an ACRBC without shear and a radially heated Taylor–Couette flow with only the inner cylinder rotating, respectively. A stable regime is found in the middle part of the interval for $\varOmega$ , and divides the whole parameter space into three regimes: buoyancy-dominated, stable and shear-dominated. Clear boundaries between the regimes are given by linear stability analysis, meaning the marginal state of the flow. In the buoyancy-dominated regime, the flow is a quasi-two-dimensional flow on the $r\varphi$ plane; as shear increases, both the growth rate of instability and the heat transfer are depressed. In the shear-dominated regime, the flow is mainly on the $rz$ plane. The shear is so strong that the temperature acts as a passive scalar, and the heat transfer is greatly enhanced. The study shows that shear can stabilize buoyancy-driven convection, makes a detailed analysis of the flow characteristics in different regimes, and reveals the complex coupling mechanism of shear and buoyancy, which may have implications for fundamental studies and industrial designs.

L'extraction sous-marine du pétrole inclut le transport d'émulsions eau-dans-huile (E/H) concentrées, stabilisées par des tensioactifs naturellement solubles dans le pétrole, et transporté dans des pipelines horizontaux sur de longues distances, jusqu'à 50 km. En raison de ces longs séjours, les configurations d'écoulement sont susceptibles de passer d'un état entièrement stratifié à un état entièrement dispersé ou vice-versa. Ces transitions sont induites par des processus tels que la sédimentation, la migration induite par le cisaillement et la coalescence. Ces processus sont influencés par les propriétés du liquide et de l'interface, la concentration de la phase dispersée, les régimes d'écoulement et la taille des gouttes. Cette thèse porte sur les écoulements horizontaux d'émulsions E/H concentrées.Des méthodes et des appareils expérimentaux uniques sont conçus pour visualiser localement l'écoulement de ces émulsions. En introduisant divers composants dans l'eau et dans une huile alcane, l’indice de réfraction entre les deux phases est ajusté, tout en contrôlant la différence de densité. Ce contrôle permet d'étudier l'interaction entre les forces de flottabilité et hydrodynamiques, ce qui est primordial pour étudier la migration des particules dans ces écoulements. Les profils de vitesse sont obtenus par Particle Image Velocimetry (PIV) en introduisant des particules fluorescentes dans la phase huile, tandis que la topologie des phases est obtenue en ajoutant un fluorophore à l'intérieur de la phase huile également. Des expériences en lit statique sont faites, fournissant des résultats concernant la métastabilité des émulsions E/H sur de longues périodes, où seule la gravité contrôle le processus de coalescence. Les expériences en écoulement cisaillés sont réalisées dans un Couette Plan Annulaire représentant un écoulement Couette plan courbé sur lui-même. Cette géométrie est choisie pour sa périodicité et sa capacité à présenter un plan de cisaillement vertical dans la même direction que la gravité.L'étude de la transition entre les écoulements stratifiés-dispersés et les écoulements pleinement dispersés a permis de mettre en évidence différents régimes. Ces régimes sont : le régime d’expansion, à vagues, d’éjections et pleinement dispersé. A partir d'un lit d'émulsion au repos, la vitesse de rotation du rotor est augmentée jusqu’à atteindre l’écoulement pleinement dispersé. A faible cisaillement, le lit s’expand jusqu'à atteindre une hauteur d'équilibre. Aux cisaillements moyens, le lit est déstabilisé et des vagues d'émulsion se forment dans la direction azimutale. À cisaillement élevés, les vagues sont fortement déformées, isolant les gouttelettes d'eau de leur amas d'émulsion à viscosité élevée. Cela conduit à leur éjection dans les vagues déferlantes, vidant progressivement le lit d'émulsion. Enfin, le régime de dispersion totale est atteint lorsque le lit d'émulsion a entièrement disparu. Dans ce régime, la migration des gouttelettes est contrôlée par la diffusion induite par cisaillement. Il est démontré que les transitions entre chaque régime dépendent d'un seul nombre de Froude critique.La métastabilité de ces émulsions E/H concentrées est également étudiée en comparant les résultats des expériences en statique aux écoulement cisaillés. Ces résultats ont montré que dans des conditions statiques, l'émulsion E/H est hautement métastable, alors que dans des écoulements cisaillés, la même couche E/H a coalescé jusqu'à la formation d'une couche entièrement continue de phase aqueuse. Cela peut s'expliquer par les caractéristiques uniques de ces émulsions, qui sont stabilisées par des multicouches de micelles de tensioactifs, et ces multicouches sont percées par le taux de cisaillement.Ces connaissances permettront de construire de nouveaux modèles de transport pour le dimensionnement précis d’appareils industriels traitant des écoulements multiphasiques (pompes, mélangeurs, séparateurs de phase...)
The subsea extraction of petroleum encompasses the transport of concentrated water-in-oil (W/O) emulsions, stabilized by natural oil-soluble surfactants, like asphaltenes, acids and alcohols, in horizontal pipelines over long distances, up to 50 km. Due to these long residence times, flow configurations are liable to change from fully-stratified to fully-dispersed or vice-versa, including an intermediate stratified-dispersed state. These transitions are driven by processes such as sedimentation, shear-induced migration and coalescence. These processes are influenced by liquid and interface properties, dispersed-phase concentration, flow regimes, and drop size. This Phd focuses on horizontal flows of concentrated W/O emulsions.Unique experimental methods and apparatuses are designed in order to locally visualize the flow of such emulsions. By introducing various components in water and in an alkane oil, refractive index matching is achieved between both phases, while controlling the density difference. The control of density difference allows for the study of the interplay between buoyancy and hydrodynamic forces, which is primordial to study particle migration in dispersed-phase flows. Velocity profiles are obtained with Particle Image Velocimetry by introducing fluorescent particles in the oil phase while phase topologies are obtained with adding a fluorophore inside the oil phase as well.Static-bed experiments are carried out in a static-bed apparatus, providing results regarding the metastability of W/O emulsions over long-time periods, where only gravity controls the coalescence process. Shear-flow experiments are performed in an Annular Plane Couette device, representing a plane Couette curved around itself. This geometry is selected for its periodicity and its ability to present a vertical plane of shear in the same direction as gravity.By studying the transition from stratified-dispersed to fully-dispersed flows, different regimes have been highlighted. These regimes are : the bed-expansion, the wavy, the drop-ejection and the fully-dispersed regime. Starting from an emulsion bed left at rest at the bottom of the APC channel, the rotation speed of the top annular lid is increase, up until the fully-dispersed regime. At low shear rates, the emulsion bed expands until it reaches an equilibrium height. At medium shear rates, the emulsion bed is destabilized and emulsion waves are formed along the azimuthal direction, which statistics have been computed with a wave detection algorithm. At high shear rates, the waves are highly deformed, isolating water droplets, surfing atop of waves, from their emulsion cluster and its high viscosity. This leads to their ejection in breaking waves, which gradually depletes the emulsion bed. Finally, the fully-dispersed regime is reached when the emulsion bed has dissapeared and the entire channel is filled with water droplets. In this regime, the migration of droplets is controlled by shear-induced diffusion. The transitions between each regime are shown to be dependent on a single critical Froude number, from low values to high values of this dimensionless parameter.The metastability of these concentrated W/O emulsions are also studied by comparing the results between static-flow and shear-flow experiments. These results showed that in static conditions, the W/O emulsion is highly metastable (no coalescence over few months of observations), while in shear flows, the same W/O layer coalesced up until a fully-continuous layer of water phase is formed. This may be explained by the unique characteristics of such emulsions, which are stabilized by multilayer of surfactant micelles, and these multilayers are pierced by the shear rate.This knowledge will help to build new transport models for accurate sizing of industrial devices dealing with two-phase flow of emulsions (pumps, mixers, phase separators …)