Mixing mechanism in a two-dimensional bubble column

The present contribution investigates the mixing of a passive scalar by a homogeneous bidimensional bubble swarm rising at high Reynolds number in a liquid initially at rest. Mixing experiments are performed in a Hele-Shaw cell for gas volume fractions α ranging from 3.0% to 14.0%. A weakly diffusive passive dye is injected within the swarm, and the temporal evolution of the spatial distribution of concentration is measured. The vertical distribution of concentration shows an upward propagation and a spreading due to the mixing induced by the unsteady open wakes of the bubbles. A one-dimensional large-scale model involving an intermittent and convective mechanism has been developed to describe the global evolution of the concentration distribution in the vertical direction. Based on experimental observations, it assumes that each bubble catches a given volume of fluid V t in its wake and transports it over a certain length L before releasing it. A good agreement is found between the experimental concentration profiles measured in the vertical direction and the model prediction. The comparison between the model and the experiments allows the determination of the transported volume V t and the transport length L as a function of the gas volume fraction. It appears that the transported volume is related to the characteristic length of the velocity deficit at the rear of the bubble. The transport length, which is related to the correlation length of the dye patches, shows two regimes. At low gas volume fraction, it is controlled by the viscous length related to the flow damping at the walls, whereas, at higher gas volume fraction, it is limited by the distance between two successive bubbles. The mixing properties are finally characterized from the first three-order moments of the dye distribution, which are determined by means of the model. The upward propagation of the dye is shown to scale as αV , where V is the bubble rise velocity. The spreading of the concentration distribution is characterized by an effective diffusivity, which presents strong similarities with the diffusion coefficient measured in a three-dimensional bubble column [Alméras et al. J. Fluid Mech. 776, 458 (2015)]. At low gas volume fraction, it √ increases as α, whereas it saturates at high gas volume fraction. The dye distribution also is asymmetric with a significant skewness coefficient which slowly decreases in time. Therefore, the dye transport cannot be described as a purely diffusive process over the time required for the dye to spread over the cell

Mixing mechanisms in a low-sheared inhomogeneous bubble column

This paper reports an experimental study of the mixing of a passive scalar in a bubble column at high Reynolds number and average gas volume fractions ranging from 2.0% to 7.5%. Starting from a homogeneous bubble column, the bubbly flow is progressively destabilized by imposing a gradient of gas volume fraction at the bottom of the tank. In that way, a single recirculation is produced, which allows to investigate the impact of a large-scale buoyancy-driven flow on the mixing of a passive scalar. It is shown that, as long as the shear-induced turbulence generated by the recirculation is negligible, mixing results from two main mixing mechanisms: the transport by the mean liquid velocity and the mixing induced by the bubbles. While the transport by the liquid recirculation can be accounted for by an advection term, the mixing induced by the bubbles is a diffusive process, the effective diffusivity of which has been measured in a homogeneous bubble column by Alméras et al. (2015). However, once the shear-induced turbulence produced by the shear develops, its role upon the mixing has to be taken into account too

Statistics of velocity fluctuations in a homogeneous liquid fluidized bed

This work reports an experimental investigation of a liquid-solid fluidized bed involving inertial particles at a large Reynolds number. Owing to optical techniques and index matching, the statistics of the velocity fluctuations of both the particles and the liquid are measured for a wide range of the particle volume fraction αp. The dynamics of the fluctuations suggests that the flow possesses the following three properties: (1) The liquid volume involves a wake region in which vertical fluctuations are negative and an interstitial region where they are positive. (2) The statistics of the horizontal fluctuations are similar to vertical ones, except that they are symmetric. (3) Local instant particle fluctuations are proportional to liquid ones. Assuming these properties are true allows us to derive a model for the probability density functions (PDFs) of the two components of the velocity fluctuations of the two phases. This model involves a single reference PDF that is independent of αp and one weighting parameter for each phase. The weighting parameter of the liquid phase is an affine function of αp, which characterizes the volume of the wakes relative to that of the interstices. That of the particle phase depends on the preferential concentration of the particles, which tend to avoid the wakes at low αp. This model accurately describes the experimental PDFs up to the third-order moment and reproduces all their peculiar features: the skewness of the vertical fluctuations which reverses at a given volume fraction, the presence of exponential tails corresponding to rare intense events, and the symmetry between low and large volume fractions

Fluctuations in inertial dense homogeneous suspensions

A theoretical model of liquid and particle random fluctuations is proposed for gravity-driven flows of inertial homogeneous suspensions. It is based on a paradigm assuming that fluctuations of both liquid velocity and particle slip velocity are driven by fluctuations of the phase indicator function. It is shown that this model accurately predicts the energy of the fluctuations of both the fluid and particle phases measured in a homogeneous solid-liquid fluidized bed over a wide range of particle volume fractions, from 10% to 45

Twente mass and heat transfer water tunnel: Temperature controlled turbulent multiphase channel flow with heat and mass transfer

A new vertical water tunnel with global temperature control and the possibility for bubble and local heat and mass injection has been designed and constructed. The new facility offers the possibility to accurately study heat and mass transfer in turbulent multiphase flow (gas volume fraction up to 8%) with a Reynolds-number range from 1.5 × 104 to 3 × 105 in the case of water at room temperature. The tunnel is made of high-grade stainless steel permitting the use of salt solutions in excess of 15% mass fraction. The tunnel has a volume of 300 l. The tunnel has three interchangeable measurement sections of 1 m height but with different cross sections (0.3 × 0.04 m2, 0.3 × 0.06 m2, and 0.3 × 0.08 m2). The glass vertical measurement sections allow for optical access to the flow, enabling techniques such as laser Doppler anemometry, particle image velocimetry, particle tracking velocimetry, and laser-induced fluorescent imaging. Local sensors can be introduced from the top and can be traversed using a built-in traverse system, allowing, for example, local temperature, hot-wire, or local phase measurements. Combined with simultaneous velocity measurements, the local heat flux in single phase and two phase turbulent flows can thus be studied quantitatively and precisel

Mixing and tranport properties in bubbly flows

Les réacteurs chimiques impliquant une phase liquide et une phase gazeuse sont couramment utilisés dans l'industrie pétrochimique et biologique car les écoulements à bulles ont de très bonnes propriétés de transfert et de mélange. Cela permet de mêler intimement différents composés et d'optimiser les réactions chimiques. Néanmoins, les mécanismes et les phénomènes mis en jeu dans le mélange au sein d'un écoulement à bulles restent encore mal connus. Ce travail a donc consisté à identifier les différents mécanismes de mélange en écoulement à bulles pour réviser le modèle physique de transport des espèces chimiques. Afin de distinguer et séparer les différents mécanismes, le mélange d'un traceur passif a été étudié dans différentes configurations expérimentales. Premièrement, l'étude du mélange dans un écoulement à bulles fortement confiné dans une cellule de Hele-Shaw a permis de mettre en évidence le mélange par capture du traceur dans les sillages. Ce mécanisme de mélange, fortement intermittent et convectif, s'est révélé être incompatible avec un processus purement diffusif. Deuxièmement, l'étude du mélange dans un essaim de bulles homogène tridimensionnel a été entreprise. Au contraire du cas confiné, le mélange, qui est causé par l'agitation induite par les bulles dans le liquide, est bien de nature diffusive. Nous avons donc pu mesurer les coefficients de diffusion effectifs en fonction de la fraction volumique de gaz. Ces coefficients sont différents dans les directions verticale et horizontale, ce qui traduit le caractère anisotrope du mélange. De plus, ils deviennent constants au-delà d'une certaine valeur de fraction volumique. Pour finir, nous avons considéré le mélange dans un essaim inhomogène de bulles, où se développe une boucle de recirculation du liquide. Dans le cas d'une recirculation modérée, la dispersion du traceur peut être estimée en combinant le mélange résultant de l'agitation des bulles avec l'advection par le mouvement moyen du fluide.Bubble columns are commonly used for chemical processes because of their good mixing and transfer capabilities. This work aims at understanding and modelling the mixing induced by bubbles. In order to distinguish the differents mixing mechanisms, the dispersion of a low-diffusive scalar has been investigated in various experimental configurations. The first one is a bubbly flow in a Hele-Shaw cell where the confinement prevents from the developpement of turbulence. In this case, the mixing is controlled by the capture and the transport by the bubble wakes. This mechanism, which cannot be described by an effective diffusivity, has been modelled by considering the intermittent transport of finite volumes of dye. The second configuration is a homogeneous swarm of rising bubbles where the mixing results from the dispersion by the bubble-induced turbulence. It can therefore be modelled by an anistropic effective diffusivity, which becomes independent of the gas volume fraction beyond a certain value. Finally, an inhomogenous bubbly flow, where a liquid recirculation loop is present, has been considered. In the case of a moderate inhomogeneity, shear induced-turbulence is not generated by the gradients of the mean flow and the mixing can be modelled by the sum of the bubble-induced dispersion and the advection by the mean flow