Teichm\"uller polynomials of fibered alternating links

We give an algorithm for computing the Teichm\"uller polynomial for a certain class of fibered alternating links associated to trees. Furthermore, we exhibit a mutant pair of such links distinguished by the Teichm\"uller polynomial.Comment: 22 pages, 12 figure

Hydrodynamics and mass transfer in bubble column: Influence of liquid phase surface tension

According to literature, few experiments are performed in organic solvents which are mostly used in commercial gas–liquid reactors. However, it is commonly accepted that data obtained in aqueous solution allow to predict the surface tension effects, and to model the behaviour of organic solvents. In this work, we examine the validity of this approximation. In this objective, the flows observed in two pure media having similar viscosity but different surface tension—respectively, water (reference) and cyclohexane (solvent)—are successively compared at two scales: in a bubble column and in bubble plumes. In bubble plumes, as expected, the mean bubble size is smaller in the medium having the smallest surface tension (cyclohexane), but for this medium the destabilisation of flow is observed to occur at smaller gas velocity, due to break-up and coalescence phenomena. In bubble column, these phenomena induce the bubbling transition regime at lower gas velocity, whatever the operating conditions for liquid phase: batch or continuous. Consequently, when the two media are used at similar gas superficial velocity, but in different hydrodynamic regimes, greater gas hold-up and smaller bubble diameter can be observed in water; the interfacial area is then not always higher in cyclohexane. This result differs from the behaviour observed in the literature for aqueous solutions. The analysis of bubble plumes in aqueous solutions of butanol shows that this difference is due to a fundamental difference in coalescent behaviour between pure solvents and aqueous mixtures: the surface tension effect is less important in pure liquid than in aqueous solutions, because of the specific behaviour of surfactants. It is then still difficult to predict a priori the bubbling regime or the flow characteristics for a given medium, and all the more to choose an appropriate liquid as a model for industrial solvents

Pilot-Scale Laboratory Instruction for ChE: the specific case of the Pilot-unit leading group

This paper presents an original approach for Chemical Engineering laboratory teaching that is currently applied at INP-ENSIACET (France). This approach, referred to as "pilot-unit leading group" is based on a partial management of the laboratories by the students themselves who become temporarily in charge of one specific laboratory. In addition to meeting the classical pedagogic requirements of the laboratories, this teaching method allows the students to actively experience technical project management

Axial and Radial Investigation of Hydrodynamics in a Bubble Column;Influence of Fluids Flow Rates and Sparger Type

A detailed investigation of local hydrodynamics in a pilot plant bubble column has been performed using various techniques, exploring both axial and radial variations of the gas hold-up, bubble average diameter and frequency, surface area. A wide range of operating conditions has been explored up to large gas and liquid flow rates, with two sparger types. Two main complementary techniques were used: a quasi local measurement of gas hold-up via series of differential pressure sensors to get the axial variation and a double optic probe giving radial variations of gad hold-up, bubble average size and frequency and surface area. According to axial evolutions, three zones, where radial evolutions have been detailed,have been separated: at the bottom the gas injection zone, the large central region or column bulk and the disengagement zone at the column top. It was found that significant axial and radial variations of the two phase flow characteristics do exist even in the so called homogeneous regime. The normalized profiles of bubble frequency appear sparger and gas velocity independent contrary to bubble diameter, gas hold-up and interfacial area normalized profiles. In any case bubbles are larger in the sparger zone than elsewhere. The main result of this work is the very strong effect of liquid flow on bubble column hydrodynamics at low gas flow rate. First the flow regime map observed in batch mode is dramatically modified with a drastic reduction of the homogeneous regime region, up to a complete heterogeneous regime in the working conditions (uG> 0.02 m/s). On the contrary, liquid flow has limited effects at very high gas flow rates. A large data bank is provided to be used for example in detailed comparison with CFD calculations

Summary of an experimental investigation on the ground vortex

The results of an experimental investigation into the position and characteristics of the ground vortex are summarized. A 48-inch wind tunnel was modified to create a testing environment suitable for the ground vortex study. Flow visualization was used to document the jet-crossflow interaction and a two-component Laser Doppler Velocimeter (LDV) was used to survey the flowfield in detail. Measurements of the ground vortex characteristics and location as a function of freestream-to-jet velocity ratio, jet height, pressure gradient and upstream boundary layer thickness were obtained

Attenuation of the wake of a sphere in an intense incident turbulence with large length scales

We report an investigation of the wake of a sphere immersed in a uniform turbulent flow for sphere Reynolds numbers ranging from 100 to 1000. An original experimental setup has been designed to generate a uniform flow convecting an isotropic turbulence. At variance with previous works, the integral length scale of the turbulence is of the same order as the sphere diameter and the turbulence intensity is large. In consequence, the most intense turbulent eddies are capable of influencing the flow in the close vicinity of the sphere. Except in the attached region downstream of the sphere where the perturbation of the mean velocity is larger than the standard deviation of the incident turbulence, the flow is controlled by the incident turbulence. The distortion of the turbulence while the flow goes round the sphere leads to an increase in the longitudinal fluctuation and a decrease in the transversal one. The attenuation of the transversal fluctuations is still significant at 30 radii downstream of the sphere whereas the longitudinal fluctuations relax more rapidly toward the incident value. The more striking result however concerns the evolution of the mean velocity defect with the distance x from the sphere. It decays as x−2 and scales with the standard deviation of the incident turbulence instead of scaling with the mean incident velocity

Dynamique d'un nuage de bulles homogène confiné

De nombreuses applications industrielles mettent en jeu des écoulements à bulles dans des échangeurs de masse et de chaleur ou des réacteurs. Les mouvements des bulles génèrent de l'agitation dans le liquide qui, en retour, influence la distribution spatiale des bulles et leur vitesse. La compréhension générique de ce problème de couplage inverse total est fondamentale mais délicate. Des travaux expérimentaux dédiés dans des configurations d'écoulements bien définies sont donc nécessaires pour atteindre cet objectif. Ce travail explore la dynamique d'un nuage de bulles en ascension à grand nombre de Reynolds dans une cellule de Hele-Shaw ([1]). Cette configuration apporte une contribution à une compréhension générale car elle permet d'étudier l'agitation générée par des bulles à grand nombre de Reynolds possédant des sillages instables tout en empêchant, par les effets de confinement, la production de turbulence. La comparaison avec la dynamique de nuages de bulles non confinés ([2]) est également éclairante. Par ailleurs, la détection des interfaces est considérablement facilitée par le confinement: une description complète et précise de la répartition spatiale et de la dynamique des bulles peut être ici obtenue directement par ombroscopie avec une seule caméra. De même, la mesure par PIV du champ de vitesse du liquide intégré dans l'épaisseur de la cellule permet de caractériser de manière pertinente la dynamique du liquide ([3]) (Fig.1-a). La dynamique des deux phases a ainsi été explorée pour des fractions volumiques de gaz α comprises entre 1% et 14% dans un régime où l'inertie est importante (Re≈500). Les bulles étudiées possèdent un sillage instable avec des lâchers tourbillonnaires réguliers et suivent une trajectoire ascendante oscillante tout en gardant une forme elliptique constante. Le frottement aux parois impose néanmoins une décroissance très forte des sillages ([4]). Les résultats montrent que l'on peut expliquer les statistiques associées au mouvement des bulles dans le nuage à partir de deux mécanismes élémentaires: (i) les oscillations induites par le sillage associées aux lâchers tourbillonnaires et (ii) la forte perturbation de vitesse localisée à l'arrière des bulles. Le mécanisme dominant dans la direction verticale est l'entrainement dans le sillage alors que celui qui régit la dynamique des bulles dans la direction horizontale est associé aux oscillations générées par les sillages dont l'intensité est indépendante de α (Fig.1-b). L'auto-dispersion des bulles a également été étudiée. Elle peut être caractérisée par des coefficients de dispersion qui évoluent linéairement avec α. En ce qui concerne l'agitation dans le liquide, comme en écoulement non confiné, les deux composantes des fluctuations de vitesse évoluent proportionnellement à αn avec ici αn=0.38 et 0.46 dans les directions horizontales et verticales respectivement. Le spectre spatial des fluctuations de vitesse évolue, sur une gamme de nombres d'ondes k bien définie, proportionnellement à k-³. Dans cette configuration où la turbulence ne peut se développer, cette évolution s'explique très clairement par la superposition linéaire de perturbations de vitesses aléatoires ([5]), il s'agit donc d'un effet statistique associé aux passages de perturbations convectées par les bulles

Dynamics of a high-Reynolds-number bubble rising within a thin gap

We report an experimental analysis of path and shape oscillations of an air bubble of diameter d rising in water at high Reynolds number in a vertical Hele-Shaw cell of width h. Liquid velocity perturbations induced by the relative movement have also been investigated to analyze the coupling between the bubble motion and the wake dynamics. The confinement ratio h/d is lower than unity so that the bubble is flattened in between the walls of the cell. As the bubble diameter is increased, the Archimedes and the Bond numbers increase within 10 6 Ar 6 104 and 6 × 10−3 6 Bo 6 140. Mean shapes become more and more elongated. They first evolve from in-plane circles to ellipses, then to complicated shapes without fore-aft symmetry and finally to semi-circular capped bubbles. The scaling law Re = 0.5Ar is however valid for a large range of Ar, indicating that the liquid films between the bubble and the walls do no contribute significantly to the drag force exerted on the bubble. The coupling between wake dynamics, bubble path and shape oscillations evolves and a succession of contrasted regimes of oscillations is observed. The rectilinear bubble motion becomes unstable from a critical value Ar1 through an Hopf bifurcation while the bubble shape is still circular. The amplitude of path oscillations first grows as Ar increases above Ar1 but then surprisingly decreases beyond a second Archimedes number Ar2. This phenomenon, observed for steady ellipsoidal shape with moderate eccentricity, can be explained by the rapid attenuation of bubble wakes caused by the confinement. Shape oscillations around a significantly elongated mean shape starts for Ar > Ar3. The wake structure progressively evolves due to changes in the bubble shape. After the break-up of the fore-aft symmetry, a fourth regime involving complicated shape oscillations is then observed for Ar > Ar4. Vortex shedding disappears and unsteady attached vortices coupled to shape oscillations trigger path oscillations of moderate amplitude. Path and shape oscillations finally decrease when Ar is further increased. For Ar > Ar5, capped bubbles followed by a steady wake rise on a straight path