Étude expérimentale du mélange solide-liquide : caractérisation des suspensions concentrées en milieu visqueux

Ce mémoire présente une étude expérimentale du mélange solide-liquide en milieu visqueux et pour des concentrations élevées en solides, un système de mélange encore peu connu et responsable de fortes pertes industrielles. Le mélangeur est une cuve mécaniquement agitée par une turbine à pales inclinées, un agitateur fréquemment utilisé par les industries chimiques. Dans un objectif de compréhension hydrodynamique et phénoménologique, trois paramètres ont été caractérisés: la vitesse minimale de suspension complète (Njs), la vitesse d’homogénéisation (NH) et le temps d’homogénéisation (tH). La technique de pression de jauge (PGT) et la tomographie par résistance électrique (ERT) ont été implémentées pour la détermination respective de Njs et NH et tH. L’étude est complétée par la mesure du couple et de la hauteur de suspension, ainsi que par l’utilisation d’un modèle numérique développé dans le groupe. Tout d’abord, la méthode de pression de jauge a été adaptée avec succès aux régimes laminaire et transitoire, et montre une répétabilité et une stabilité adéquates. Un plan d’expérience optimal a permis d’évaluer l’effet de cinq facteurs majeurs sur l’hydrodynamique du mélange: le diamètre des particules (dp), la fraction massique de solides (Xw), la viscosité du fluide (μ), le diamètre de l’agitateur (D) et le dégagement au fond (C). En régime transitoire, comme en régime turbulent, Njs et NH diminuent pour de larges agitateurs. Les effets de dp et de μ montrent un comportement opposé à celui observé en turbulent puisque Njs diminue lorsque dp et μ augmentent. De plus, Xw présente un impact complexe, dépendant en partie de la taille des particules. Ces observations ont été associées à un phénomène d’érosion de lit dont le mécanisme diffère largement de la suspension en régime turbulent. Ces particularités expliquent les déviations observées avec les valeurs prédites par la corrélation de Zwietering (Zwietering, 1958). Tout comme pour D/T, les effets de Xw, dp et C/T sur NH sont équivalents à ceux rapportés en régime turbulent, puisque NH augmente lorsque Xw et dp augmentent, et lorsque C/T diminue. L’étude de tH démontre que l’obtention d’une suspension homogène à partir de particules sédimentées est majoritairement contrôlée par leur mise en suspension. La coopération entre caractérisation expérimentale et étude numérique a permis d’une part d’attester de la validité phénoménologique du modèle, et d’autre part d’apporter de nouveau éléments à la compréhension hydrodynamique du système étudié. Mots-clefs: mélange solide-liquide – fluide visqueux – suspensions concentrées – cuve mécaniquement agitée – vitesse minimale de suspension ---------- To address a considerable lack of knowledge in solid-liquid mixing, the suspension of large concentrations of spherical particles in a viscous fluid is investigated through the experimental characterization of fundamental mixing parameters: the just-suspension speed (Njs), the homogenization speed (NH) and the homogenization time (tH). Known for its great efficiency for suspending particles in turbulent regime, and commonly used in the chemical industry, the pitched blade turbine is investigated. Njs is characterized by the pressure gauge technique (PGT), NH and tH are measured using a robust and simple technique of electrical resistance tomography (ERT). The description of the system is further characterized by means of power consumption and cloud height measurements, and by comparing the experimental data to numerical results. First, the PGT method was successfully adapted to laminar and transitional regimes of operation, with good reproducibility and stability. To explore the effect of particle diameter (dp), solid mass concentration (Xw), viscosity (μ), impeller diameter (D) and bottom-off clearance (C), an optimal design of experiment was carried out, from which the effects of every factor was determined. In early transitional regime with non-dilute concentration of solid particles, an increase in D causes Njs and NH to considerably decrease, as also reported in turbulent regime. Unlike the prediction of the well-known Zwietering correlation (Zwietering, 1958), it is found that increasing dp or μ leads to a decrease of Njs. In addition, the effect of solid concentration is more complex than what is predicted by the Zwietering correlation, showing a dependency on dp. The large discrepancies observed between our experimental values and Zwietering correlation values of Njs are related to the differences in hydrodynamics and suspension mechanisms regarding the operating regime. The effects of dp and μ for solid suspensions in a viscous liquid appear to correspond to the erosion of a bed of particles. The impact of Xw, dp and C/T on NH are similar to those reported on turbulent regime. The study on the homogenization time tH shows that the erosion of the particle bed is the dominating phenomenon to consider in order to achieve a fully suspended state and an uniform distribution of the particles. Finally, the numerical model developed in our group is validated by comparison with experimental data, and is used to fully understand the mixing system investigated. Keywords: solid-liquid mixing - viscous fluid - high solid loading – stirred tank – just suspended spee

Development of an unresolved CFD–DEM model for the flow of viscous suspensions and its application to solid–liquid mixing

Although viscous solid–liquid mixing plays a key role in the industry, the vast majority of the literature on the mixing of suspensions is centered around the turbulent regime of operation. However, the laminar and transitional regimes face considerable challenges. In particular, it is important to know the minimum impeller speed () that guarantees the suspension of all particles. In addition, local information on the flow patterns is necessary to evaluate the quality of mixing and identify the presence of dead zones. Multiphase computational fluid dynamics (CFD) is a powerful tool that can be used to gain insight into local and macroscopic properties of mixing processes. Among the variety of numerical models available in the literature, which are reviewed in this work, unresolved CFD–DEM, which combines CFD for the fluid phase with the discrete element method (DEM) for the solid particles, is an interesting approach due to its accurate prediction of the granular dynamics and its capability to simulate large amounts of particles. In this work, the unresolved CFD–DEM method is extended to viscous solid–liquid flows. Different solid–liquid momentum coupling strategies, along with their stability criteria, are investigated and their accuracies are compared. Furthermore, it is shown that an additional sub-grid viscosity model is necessary to ensure the correct rheology of the suspensions. The proposed model is used to study solid–liquid mixing in a stirred tank equipped with a pitched blade turbine. It is validated qualitatively by comparing the particle distribution against experimental observations, and quantitatively by compairing the fraction of suspended solids with results obtained via the pressure gauge technique

A semi-implicit immersed boundary method and its application to viscous mixing

Computational fluid dynamics (CFD) simulations in the context of single-phase mixing remain challenging notably due the presence of a complex rotating geometry within the domain. In this work, we develop a parallel semi-implicit immersed boundary method based on Open∇FOAM, which is applicable to unstructured meshes. This method is first verified on academic test cases before it is applied to single phase mixing. It is then applied to baffled and unbaffled stirred tanks equipped with a pitched blade impeller. The results obtained are compared to experimental data and those predicted with the single rotating frame and sliding mesh techniques. The proposed method is found to be of comparable accuracy in predicting the flow patterns and the torque values while being straightforwardly applicable to complex systems with multiples impellers for which the swept volumes overlap

Mixing of viscous liquids and large concentrations of spherical particles in stirred tanks

Despite the importance of laminar solid-liquid mixing operations in industry for the production of various goods such as pastes, greases, paints, pharmaceuticals and food products, a large proportion of the reported results in this field has been obtained in the turbulent regime. The intrinsic multiscale nature of solid-liquid flows in stirred tanks and the complexity arising from both the geometry of the impeller and the rheology of such suspensions, particularly in the case of high solids contents, create complex flow patterns within the tank, which may drastically affect both the yield and the quality of the desired product. Furthermore, the estimation of key mixing parameters such as the impeller torque, the just-suspension speed (Njs) and the cloud height remains unclear in all flow regimes. In particular, the Zwietering correlation has several limitations that may lead to poor predictions of Njs. Therefore, more modeling and experimental work is needed in order to shed light on these issues. A variety of models have been developed to simulate solid-liquid flows. These include the classical Eulerian-Eulerian (or two-fluid) model and the combination of the Discrete Element Method (DEM) for the particles and CFD methods for the liquid (CFD-DEM). Despite their relative advantages and drawbacks, which will be briefly discussed during this talk, we believe that the CFD-DEM approach can be both efficient and accurate for the simulation of such flows. The objective of this work is then to introduce a multiscale CFD-DEM model, applicable to concentrated suspensions, wherein the particles are not resolved explicitly on the CFD grid but taken into account through the so-called volume-averaged Navier-Stokes equations. This entails projecting the particles onto the grid so that the solid-liquid momentum transfer term appearing in these equations, such as the drag force exerted by the particles on the liquid, can be locally evaluated. After describing the proposed model in detail, simulation results obtained with it for the laminar mixing of concentrated solid-liquid suspensions in stirred tanks will be presented