Hydrodynamics and Metzner-Otto correlation in stirred vessels for yield stress fluids

This paper investigates the hydrodynamics and power consumption in laminar stirred vessel flowusing numerical computation. The Metzner–Otto correlation was established for mixing in power-law fluids. This paper focuses on its application to yield stress fluids. Distributions of shear rates and their link to power consumption for helical and anchor agitators are discussed. Insight is sought from the analytical formula for Taylor–Couette flows. Laws are established for Bingham, Herschel-Bulkley and Casson fluids and reveal similar results. Fully or partially sheared flow situations with plug regions are considered. Depending on the fluid model, the concept is valid or constitutes a satisfactory approximation for fully sheared flows. When the flow is partially sheared, the expression depends on the Bingham number and the concept must be adapted. The results of the numerical simulations are interpreted in the light of this analysis and results from the literature

Numerical modelling of grinding in a stirred media mill: Hydrodynamics and collision characteristics

Producing nanoparticles in dense suspensions can be achieved in a stirred media mill. However the mechanisms of fragmentation in the mill are still not fully understood and the process remains laborious because of the large amount of supplied energy. We focus on the numerical analysis of the local hydrodynamics in the mill. Based on the flow simulations we determine the parameters which control the efficiency of the collisions between grinding beads (impact velocities and orientation of the collisions). The suspension flow (grinding beads, particles, carrying fluid) is modelled with effective physical properties. We solve directly the continuity and Navier–Stokes equations for the equivalent fluid assuming that the flow is two-dimensional and steady. Depending on the Reynolds number and the non-Newtonian behaviour of the fluid, we found that the flow is composed of several toroidal vortices. The most energetic collisions are driven by the strong shear experienced by the suspension within the gap between the disc tip and the wall chamber

Irreducible coupling between physical and biological phenomena: overview of on-line and off-line physical measurements during high cell density cultures of yarrowia lipolytica

During cell cultures in bioreactor, micro-organism physiology closely interacts with physico-chemical parameters (gas and feed flow rates, mixing, temperature, pH, pressure). The specificity of microbial bioreactions in relation with irreducible couplings between heat and mass transfers and fluid mechanics, led into complex (three phases medium) and dynamic (auto-biocatalytic reaction) systems. Our scientific approach aims to investigate, understand and control dynamic interactions between physical and biological systems at different scales (macro, micro and molecular) for molecules, strains and/or bioprocess innovation in a white biotechnology context. Cells (concentration, shape, dimension, physiology) strongly affect physico-chemical properties of broth and the modification of these characteristics interacts with bioprocess performances (specific rates, yields…) with an improvement or, more generally, a decrease of yields. Among these properties, rheological behaviour is a strategy widely used to understand the impact of cells and the modification of bioprocess performances. Our approach rests on physical and physico-chemical on-line and off-line measurements in respect with accurate and stringent conditions imposed by cell culture strategy. This work leads to design and realise an original pilot based on a bioreactor (20L) with a derivation loop including a specific on-line rheometric device as well as additional physical and biological measurements. Y. lipolytica cultures were investigated with a control of growth rate by carbon feed within concentrations ranging from 0.1 up to 60gCDW/L. On-line and off-line measurements are discussed regarding similar or opposite tendencies along culture. If the off-line density could be correlated with cell concentration, on-line measurement exhibit opposite tendancy. On-line and off-line rheological measurements are consistent. Results are discussed in terms of size, morphology, surface properties, concentration, biological activity and compared to scientific literature. On-line rheology highlight about the Non-newtonian rheological behaviour of broths and the gap between on-line and off-line measurements

In-situ and ex-situ rheometry of high density Yarrowia lipolytica broth: determination of critical concentration and impact of yeastmycelial transition

The specificity of microbial bioreactions which give rise to irreducible couplings with hydrodynamics and heat and mass transfers, led into complex (three phases medium) and dynamic (auto-biocatalytic reaction) systems. Cells (concentration, shape, dimension, physiology…) strongly affect physico-chemical properties of broth and the modification of these characteristics interacts with bioprocess performances (specific rates, yields…) with an improvement or, more generally, a decrease of yields

Aggregation of silica nanoparticles in concentrated suspensions under turbulent, shear and extensional flows.

The production of nanoparticles in concentrated suspensions requires strict control of the stability of the systems which are strongly influenced by the physico-chemical properties and the hydrodynamic conditions they are placed in. This study deals with the analysis of the aggregation processes of a colloidal silica suspension destabilized by addition of salt under different flows: a turbulent flow performed in a stirred tank, a pure shear flow created thanks to a Couette geometry and an extensional flow obtained in a four-roll mill (Taylor cell). During the aggregation process, the silica suspensions behave as shear-thinning fluids and the variation of their apparent viscosity can be related to the evolution of the size distribution of the aggregates in the suspension. Pure shear and turbulent flows at an equivalent strain rate exhibit almost the same behaviour. The viscosity and the aggregate size decrease with the shear rate. On the contrary, the apparent viscosity and the aggregate size distributions were not very sensitive to a change of an extensional constraint within the considered range. Indeed, although aggregates obtained in the Taylor cell were bigger than in the Couette cell, the apparent viscosity was higher in the latter case. Different aggregate structures, characterized by their fractal dimension, were finally predicted depending on the hydrodynamic nature of the main flow under which they were produced

Rheological characterization of mixed liquor in a submerged membrane bioreactor: Interest for process management

Rheological analyses of a submerged membrane bioreactor mixed liquor were performed in the aim of characterizing the mixed liquor present in the bioreactor and thus proposing a process management. These analyses pointed out that the mixed liquor was characterized by its viscoplastic property, which leads to a possible restructuring ability when a shear stress lower than the yield stress is applied. As the shear stress in the bioreactor is essentially generated by coarse bubbles, specific experiments were carried out in which coarse bubbles were injected in an intermittent way. The results of these experiments showed that this method could avoid damage to the mixed liquor. So working with intermittent coarse bubbles is useful to prevent fouling, keep good flocculation and minimize the energy cost

Generation and maturation of a vortex ring in non-Newtonian fluids

Vortex rings are coherent structures that dominate the dynamics of many flows. They are present in a wide range of situations : in industrial mixing systems (in the vicinity of the agitation moving blades), but also in nature during the ejection of volcanic gas or in the wakes behind insects, birds and fishes, where a periodic release of vortex rings is observed. In this work we study the formation and maturation of a vortex ring in non-Newtonian fluids, with a special focus on shear-thinning fluids and yield stress fluids. The experimental system consists of a cylindrical tube-piston device whose lower part is immersed in a tank containing the fluid. Particle Image Velocimetry (PIV) is used to analyze the flow. A preliminary study is realized with Newtonian fluids to validate the device the device. It allows exploration of low Reynolds numbers configurations, showing the existence of a vortex ring for Reynolds numbers as low as 10. This work is then extended to non-Newtonian fluids, using shear-thinning Xanthane solutions (behavior index between 0.6 and 1) and two yield stress fluids (Carbopol) with yield stress between 1 and 3 Pa. The results are analyzed in terms of vorticity fields and of characteristics of the ring (velocity and geometry). T, the time evolution of these variables as a function of the characteristics of the fluid is reported. Then we focus on the rolling up and detachment mechanisms for the larger Reynolds numbers while, at low Reynolds numbers, the investigation is focused on the more complicated dynamical mechanisms involved, taking into account the influence of the nature of the fluid on this dynamics

Impact of cell physiology and densities during oxidative axenic cultures of Yarrowia lipolytica on physico-chemical properties of broth

Impact of cell physiology and densities during oxidative axenic cultures of Yarrowia lipolytica on physico-chemical properties of brot

Piv study of mixing characteristics in a stirred vessel with a non-Newtonian fluid

PIV is used to analyze the flow induced by a Rushton turbine in a shear-thinning fluid, at constant input power, constant impeller velocity but different concentrations. The rheology of each shear-thinning fluid is first addressed. The mean velocity fields are compared. POD methodology is applied to estimate coherent structures and turbulence levels. Finally, the heterogeneity of shear rate is estimated and the spatial distribution of dissipation rate of total kinetic energy is addressed

Intercorrélation d’images PIV sur GPU–application à un écoulement en fluide turbide

La Vélocimétrie par Images de Particules (PIV) est une technique de mesure largement utilisée en Mécanique des Fluides, faisant intervenir une source Laser associée à une ou plusieurs caméras. L’utilisation de capteurs matriciels de haute résolution (>= à 4 Mpixels) se généralise aussi bien pour des systèmes d’acquisition basse cadence (de l’ordre de quelques Hertz), que pour des systèmes rapides autorisant des fréquences d’acquisition de plusieurs KiloHertz. Il devient désormais usuel de générer des centaines de GigaOctets de données lors d’une étude expérimentale. Ces données sont ensuite traitées numériquement avec des algorithmes itératifs de traitement d’images pour lesquels on recherche une précision et une robustesse suffisantes. Avec des algorithmes exécutés de manière séquentielle, ce temps de traitement est largement supérieur au temps nécessaire pour l’acquisition des données. Nous proposons, dans cette communication, de détailler l’algorithme d’intercorrélation d’images que nous avons porté sur une architecture GPU (Graphics Processing Units), particulièrement adaptée aux tâches de traitement d’images parallélisées. Cette application GPU, développée sous CUDA, a été utilisée pour étudier la propagation d’anneaux tourbillonnaires en fluide non newtonien par PIV2D2C. L’objectif du portage sous GPU étant de réduire les temps d’exécution, le calcul de la fonction d’intercorrélation d’images normalisée (ZNCC) est effectué spatialement. Pour des dimensions conventionnelles de maille d’analyse (16² pixels par exemple), le calcul de corrélation directe sur GPU s’avère plus rapide que le calcul dans l’espace spectral (par FFT) sur la même architecture matérielle. Par rapport aux précédentes études ([1], [2]), les temps spécifiques d’exécution des sous-routines seront détaillés. L’algorithme mis en œuvre est multi-passe avec une dimension d’analyse décroissante. Entre chaque itération, les mailles de calcul sont décalées symétriquement en valeur décimale afin de centrer le pic de corrélation sur la maille d’analyse [3]. Les temps de calcul, pour un couple d’images 2048x2048 pixels, sont quantifiés avec différentes cartes graphiques, incluant les temps de transfert mémoire CPU GPU. Les temps d’exécution en fonction du nombre de cœurs équipant les cartes sont donnés ci-dessous (tableau1). Le processus complet fait intervenir quatre itérations sur l’ensemble de l’image : 1 itération avec un maillage original en 32² pixels suivie de 3 itérations avec un maillage final de 16² pixels. On observe des temps d’exécution décroissant en fonction du nombre de cœurs et de l’amélioration globale des performances des architectures graphiques. Cela traduit une accélération du traitement par intercorrélation d’images PIV. Par ailleurs, ce type de traitement peut être effectué en local, sans transfert de grandes quantités de données ; ce qui autorise un retour rapide sur la qualité des résultats mais également sur la validation du nombre de champs de vitesse nécessaire à la convergence des données statistiques à extraire. Les résultats expérimentaux sur lesquels nous proposons des tests comparatifs sont issus de l’étude du développement d’un anneau tourbillonnaire en fluide non newtonien. Le dispositif expérimental est présenté sur la figure 1. L’anneau est généré par un système cylindre-piston ( 21mm) dans une cuve de section carrée 240x240 mm2. Le cylindre est centré dans la cuve et on réalise des mesures du champ de vitesse dans un plan diamétral sur une fenêtre 80x80mm2. Une visualisation par fluorescéine est proposée sur la figure 2 (gauche). La chaîne PIV est constituée d’un laser Quantel Nd-YAG CFR200 et d’une caméra PCO 2000 2048x2048 pixels. L’ensemencement est assuré avec des particules d’Orgasol, de diamètre Dp=60 µm. L’une des difficultés de ce travail expérimental provient de la turbidité des fluides utilisés (solutions de Xanthane pour obtenir un comportement non newtonien rhéofluidifiant). Celle-ci entraîne un rapport « signal sur bruit » des images de particules qui est très pénalisant lors du traitement PIV. La seconde des difficultés est liée à l’information recherchée dans cette étude, la vorticité, qui est calculée à partir des gradients de vitesse et qui nécessite donc des champs de vitesse de très bonne qualité. Les résultats obtenus (figure 2) montrent que l’obtention des dérivées spatiales de la vitesse, particulièrement sensible au bruit de mesure, reste accessible au moyen de la fonction de corrélation normalisée (ZNCC) calculée dans notre implémentation sur GPU