Mixing is a common feature of stratified fluids. In stratified fluids the density varies with the height. This is true for the most fluids in geophysical environments, like lakes, the atmosphere or the ocean. Turbulent mixing plays a crucial role for the overall energy budget of the earth and has therefore an huge impact on the global climate. By introducing the mixing efficiency, it is possible to quantify mixing. It is defined as the ratio of gain of potential energy to the injection of mechanical energy. In the ocean energy provided by tidal forces leads to turbulence and thus highly dense water is lifted up from the deep sea to the surface. For this process, a mixing efficiency of 0.2 is estimated. Until now it is not completely understood how this high value can be achieved. Thus we measured the mixing efficiency by using a Couette-Taylor system, which can produce steady-state homogeneous turbulence. This is similar to what we find in the ocean. The Couette-Taylor system consists of two concentric cylinders that can be rotated independently. In between a stratified fluid is filled using salt as a stratifying agent. In the laboratory experiment, we obtained mixing efficiencies in the order of 0.001 as a result. Moreover we found that the mixing efficiency decreases with decreasing stratification like previous laboratory experiments have shown. As this value is two orders of magnitude smaller than what we find in the ocean, further studies will be necessary. / text

Rayleigh-Taylor instability has been an area of active research in fluid dynamics for the last twenty years, but relatively little attention has been paid to the dynamics of problems where Rayleigh-Taylor instability plays a role, but is only one component of a more complex system. Here, Rayleigh-Taylor instability between miscible fluids is examined in situations where it is confined by various means: by geometric restriction, by penetration into a stable linear stratification, and by impingement on a stable density interface. Water-based experiments are modelled using a variety of techniques, ranging from simple hand calculation of energy exchange to full three-dimensional numerical simulation. Since there are well known difficulties in modelling unconfined Rayleigh-Taylor instability, the confined test cases have been sequenced to begin with dynamically simple benchmark systems on which existing modelling approaches perform well, then they progress to more complex systems and explore the limitations of the various models. Some work on the phenomenology of turbulent mixing is also presented, including a new experimental technique that allows mixed fluid to be visualised directly, and an analysis of energy transport and mixing efficiency in variable density flows dominated by mixing.

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<p>Intermeshing counter-rotating twin screw extruders (ICRTSE) are used extensively in the polymer processing industry for pelletizing, devolatilization and extrusion of various plastic products. ICRTSE have better positive displacement ability and are more suitable for shear sensitive materials compared to other types of twin screw extruders.</p> <p>The objectives of this thesis are to understand the flow mechanism and the effects of screw geometries and processing conditions in the ICRTSE. First, a simple flow model based on a volume of the conveying element of ICRTSE was used to calculate flow rate. Since ICRTSE do not give complete positive displacement, the various leakage flows were identified and taken into account in the simple flow model. Although the simple flow model provided reasonable results in terms of flow rate, computer simulations were found necessary due to the limitations of simple flow model. Second, a 3D computer simulation of ICRTSE was developed for various screw geometries and processing conditions. Both Newtonian and non-Newtonian fluids were examined.</p> <p>It was shown the simple model based on geometrical parameters for pumping behaviour give reasonable prediction of flow rate. It was found that determination of negative pressure should be taken into account in numerical simulations. The pumping efficiency is influenced positively by the ratio of flight width-to-channel width but it is affected negatively by the screw pitch length. It is negligibly changed with screw speed. Finally, the dominant flow is shear flow in ICRTSE and therefore, dispersive mixing capacity is very limited due to a lack of elongational effects.</p> / Master of Applied Science (MASc)

The present study investigates experimentally the laminar mixing and heat transfer of a range of helical ribbon and anchor impellers for both Newtonian and inelastic non-Newtonian fluids. The work also correlates the experimental data empirically in the form of dimensionless groups. In order to estimate the relative importance and the effect of all the geometrical parameters on the mixing power and heat transfer, data from the published literature sources will be utilized and combined with the results from this study. Thus, reliable empirical correlations will be obtained which are applicable over the widest range of operating conditions. The study also investigates the ablity of the various impellers to level out temerature distributions. The measurement of these temperature gradients and the impeller power requirements gives a measure of the mixing efficiency of the impeller used.

The present study investigates experimentally the laminar mixing and heat transfer of a range of helical ribbon and anchor impellers for both Newtonian and inelastic non-Newtonian fluids. The work also correlates the experimental data empirically in the form of dimensionless groups. In order to estimate the relative importance and the effect of all the geometrical parameters on the mixing power and heat transfer, data from the published literature sources will be utilized and combined with the results from this study. Thus, reliable empirical correlations will be obtained which are applicable over the widest range of operating conditions. The study also investigates the ablity of the various impellers to level out temerature distributions. The measurement of these temperature gradients and the impeller power requirements gives a measure of the mixing efficiency of the impeller used. / Science Research Council

Le climat de la Terre dépend en grande partie des échanges énergétiques entre les masses d’eau chaudes et froides de nos océans. Afin de prédire et de comprendre les variations de notre climat, les modèles numériques globaux de l’océan doivent pouvoir déterminer quelle fraction d'énergie est convertie en mélange irréversible dans un écoulement turbulent et stablement stratifié. Il apparaît que cette fraction est sensible aux paramètres de l’écoulement, ce qui a récemment conduit les océanographes à remettre en question la paramétrisation d'Osborn pour le coefficient de diffusion turbulente kz, qui utilise une efficacité de mélange constante et fixée à ŋ=0,17. Ceci nous a poussé à réaliser au laboratoire de Mécanique des Fluides et d'Acoustique (LMFA) des mesures conjointes de ŋ et kz, afin de mieux comprendre leur inter-dépendance. Cette étude est avant tout expérimentale et se base sur plusieurs dispositifs permettant de quantifier le mélange dans différents types d'écoulement. Trois de ses expériences ont été réalisées au LMFA : une expérience de lock-exchange dans laquelle le mélange est issu du cisaillement à l'interface de deux courants de gravité se déplaçant en sens opposés, une expérience de grille tractée dans un fluide stratifié et une expérience d’injection de stratification dans la grille d’un canal hydraulique. Ce travail a été complété, d'une part par une collaboration sur la plateforme Coriolis du LEGI à Grenoble, permettant d’atteindre de plus grands nombres de Reynolds ; et d'autre part par une campagne de mesure in situ dans le fjord du Saguenay au Canada en collaboration avec l'ISMER, visant à estimer le mélange turbulent conduisant au renouvellement des eaux profondes du fjord, à partir de l'analyse de transects successifs de densité. Dans ces différentes configurations, l'évolution temporelle des profils verticaux de densité ont permis d'analyser la dépendance du coefficient de diffusion turbulente et de l'efficacité de mélange avec les nombres de Reynolds et de Froude. Nos résultats ont permis de quantifier la décroissance de l'efficacité de mélange avec l'augmentation du nombre de Froude dans un écoulement turbulent, ainsi que la sensibilité du coefficient de diffusion turbulente aux nombres de Froude et de Reynolds de flottabilité. L'utilisation de trois dispositifs expérimentaux différents permet de montrer qu'au-delà de ces lois dites universelles, la variabilité propre à chaque géométrie influence fortement les valeurs de l'efficacité de mélange. Ceci est particulièrement mis en lumière dans la configuration de lock-exchange, pour laquelle la valeur limite de ŋ=0.25 prédite par la physique statistique n'est atteinte que dans une configuration fortement tri-dimensionnelle, jusqu'alors peu utilisée dans la littérature. Enfin, toutes les méthodes d'analyse développées pour les expériences de laboratoire ont pu être utilisées pour l'analyse des données in situ, permettant de clore ce travail de thèse sur une étude environnementale. / Our climate partly depends on energy exchange between warm and cold water masses in the ocean's interior. In order to understand and forecast the climate variations, numerical models of the ocean must estimate the amount of energy converted into irreversible mixing in turbulent stably stratified flows. It seems that this quantity depends on the flow parameters. This assertion challenges the famous Osborn model for turbulent diffusivity kz which uses a fixed mixing efficiency of ŋ=0.17. This motivated us to measure separately kz and ŋ in order to obtain a better understanding of their inter-dependencies. The present work is an experimental study based on set-ups which enable to quantify the mixing in different types of flow. Three of those experiments are held in our lab (LMFA) and consist respectively in a lock-exchange experiment where mixing is generated by the shear at the interface of two opposite gravity currents, a stratified towed grid experiment, and a hydraulic channel experiment where the stratification is injected directly by the grid. This study has been complemented with two international collaborations. The first one, on the Coriolis platform (LEGI) consisted in a stratified towed grid experiment in a rotating tank allowing to broaden our parameter spectrum. The second one is a series of in situ measurements led in collaboration with ISMER in the Saguenay fjord (Canada) aiming at measuring density transects over time in order to quantify the turbulent mixing that participates in the renewal of the fjord's deep water. In all of those configurations, dependencies of mixing efficiency and turbulent diffusivity along with the Froude and the Reynolds numbers are extracted from the time evolution of density profiles. In our results, we were able to quantify the decay of the mixing efficiency with the increase of the Froude number. We also highlighted the sensitivity of turbulent diffusivity on the buoyancy Reynolds number. We used three different experimental setups to show that beyond the so called universal turbulence laws, the flow geometry has a huge impact on the mixing efficiency values. This is especially true in the lock-exchange configuration where the asymptotic value of ŋ=0.25, predicted by statistical physics, can only be reached in a set-up which allows 3D flows. Such investigations are still scarce in the literature. Finally, all the data analysis methods developed for the lab experiments were of great help for the analysis of in situ data and thereby enabled us to consider a real-life environnemental flow.