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This work describes an experimental investigation on the mixing induced by a swarm of high Reynolds number air bubbles rising through a nearly homogeneous and isotropic turbulent flow. The gas volume fraction $\alpha$ and the velocity fluctuations $u'_0$ of the carrier flow before bubble injection are varied, respectively, in the ranges $0\leq \alpha \leq 0.93\%$ and 2.3 cm/s $\leq u'_0 \leq 5.5$ cm/s, resulting in a variation of the bubblance parameter $b$ in the range [0, 1.3] ($b = \frac{V_r^2 \alpha}{{u'}_0^2}$, where $V_r$ is the relative rising velocity). Mixing in the horizontal direction can be modelled as a diffusive process, with an effective diffusivity $D_{xx}$. Two different diffusion regimes are observed experimentally, depending on the turbulence intensity. At low turbulence levels, $D_{xx}$ increases with gas volume fraction $\alpha$, while at high turbulence levels the enhancement in $D_{xx}$ is negligible. When normalizing by the time scale of successive bubble passage, the effective diffusivity can be modelled as a sole function of the gas volume fraction $\alpha^* \equiv \alpha/\alpha_c$, where $\alpha_c$ is a theoretically estimated critical gas volume fraction. The present explorative study provides insights into modeling the mixing induced by high Reynolds number bubbles in turbulent flows., Comment: 8 pages, 6 figures (submitted manuscript)

In this work we study the heat transport in inhomogeneous bubbly flow. The experiments were performed in a rectangular bubble column heated from one side wall and cooled from the other, with millimetric bubbles introduced through one half of the injection section (close to the hot wall or close to the cold wall). We characterise the global heat transport while varying two parameters: the gas volume fraction $\alpha = 0.4\% - 5.1 \%$, and the Rayleigh number $Ra_H=4\times10^9-2.2\times10^{10}$. As captured by imaging and characterised using Laser Doppler Anemometry (LDA), different flow regimes occur with increasing gas flow rates. In the generated inhomogeneous bubbly flow there are three main contributions to the mixing: (\textit{i}) transport by the buoyancy driven recirculation, (\textit{ii}) bubble induced turbulence (BIT) and (\textit{iii}) shear-induced turbulence (SIT). The strength of these contributions and their interplay depends on the gas volume fraction which is reflected in the measured heat transport enhancement. We compare our results with the findings for heat transport in homogeneous bubbly flow from Gvozdi{\'c} \emph{et al.} (2018). We find that for the lower gas volume fractions ($\alpha4\%$, when the contribution of SIT becomes stronger, but so does the competition between all three contributions, the homogeneous injection is more efficient.

International audience; 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.

This work reports an experimental characterisation of the flow properties in a homogeneous bubble swarm rising at high-Reynolds-numbers within a homogeneous and isotropic turbulent flow. Both the gas volume fraction �� and the velocity fluctuations of the carrier flow before bubble injection are varied, respectively, in the ranges 0% < alpha < 0.93% and 2.3 cm/s < urms < 5.5 cm/s. The so-called bubblance parameter is used to compare the ratio of the kinetic energy generated by the bubbles to the one produced by the incident turbulence, and is varied from 0 to 1.3. Conditional measurements of the velocity field downstream of the bubbles in the vertical direction allow us to disentangle three regions that have specific statistical properties, namely the primary wake, the secondary wake and the far field. While the fluctuations in the primary wake are similar to the one of a single bubble rising in a liquid at rest, the statistics of the velocity fluctuations in the far field follow Gaussian distribution, similar to the one produced by the homogenous and isotropic turbulence at the largest scales. In the secondary wake region, the conditional probability density function (pdf) of the velocity fluctuations is asymmetric and shows an exponential tail for the positive fluctuations and a Gaussian one for the negative fluctuations. The overall agitation thus results from the combination of these three contributions and depends mainly on the bubblance parameter., 21 papges, JFM (accepted)

A new vertical water tunnel with global temperature control and the possibility for bubble and local heat & 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 $1.5 \times 10^4$ to $3 \times 10^5$ 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 liters. The tunnel has three interchangeable measurement sections of $1$ m height but with different cross sections ($0.3 \times 0.04 m^2$, $0.3 \times 0.06 m^2$, $0.3 \times 0.08 m^2$). 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 e.g. 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 quantitatvely and precisely.

International audience; 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%

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 Almeras 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.

International audience; 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.

We present results on the global and local characterisation of heat transport in homogeneous bubbly flow. Experimental measurements were performed with and without the injection of $\sim 2.5$ mm diameter bubbles (corresponding to $Re_b \approx 600$) in a rectangular water column heated from one side and cooled from the other. The gas volume fraction $\alpha$ was varied in the range $0\% - 5\%$, and the Rayleigh number $Ra_H$ in the range $4.0 \times 10^9 - 1.2 \times 10^{11}$. We find that the global heat transfer is enhanced up to 20 times due to bubble injection. Interestingly, for bubbly flow, for our lowest concentration $\alpha = 0.5\% $ onwards, the Nusselt number $\overline{Nu}$ is nearly independent of $Ra_H$, and depends solely on the gas volume fraction~$\alpha$. We observe the scaling $\overline{Nu} \propto \alpha^{0.45}$, which is suggestive of a diffusive transport mechanism. Through local temperature measurements, we show that the bubbles induce a huge increase in the strength of liquid temperature fluctuations, e.g. by a factor of 200 for $\alpha = 0.9\%$. Further, we compare the power spectra of the temperature fluctuations for the single- and two-phase cases. In the single-phase cases, most of the spectral power of the temperature fluctuations is concentrated in the large-scale rolls. However, with the injection of bubbles, we observe intense fluctuations over a wide range of scales, extending up to very high frequencies. Thus, while in the single-phase flow the thermal boundary layers control the heat transport, once the bubbles are injected, the bubble-induced liquid agitation governs the process from a very small bubble concentration onwards., Comment: Journal of Fluid Mechanics (accepted)

International audience; The present work investigates the mixing of a low-diffusivity dye in a swarm of bubbles at high Reynolds number confined in a Hele-Shaw cell for gas volume fractions ranging from 1.4 to 5.4%. A patch of a fluo- rescent dye is injected within the swarm and, during its mixing, its concentration is measured at a given location in an observation volume of 4.5 mm2 by means of Laser Induced Fluorescence at a frequency of 250 Hz. A spectrometer is used to analyse the light issued from the observation volume and to dis- tinguish the fluoresced light from other light sources. Simultaneously, the bubble distribution around the observation volume is imaged with a high speed camera synchronised with the spectrometer in order to assess the LIF technique in bubbly flow. Thanks to the good time resolution, rapid and intense concen- tration fluctuations corresponding to dye patches passing through the observation volume are recorded and are superimposed to a slow global evolution. This slow global evolution shows first an increase of the concentration and then an exponential decrease due to the mixing by bubble-induced agitation. This exponential decay, which is incompatible with a diffusion process, is consistent with the transport by dye capture in bubbles wakes that are quickly dampened by the shear-stress at the walls. The one-point statistics of the concentration fluctuations (probability density function and spectrum) also point out that mixing in a confined bubbly flow is intermittent and convective.

International audience; Transport properties of scalars, as concentrations of a solute or temperature, are important for scale-up and design of operation units. An appropriate description of convective and diffusive mechanisms is required to predict local concentrations in complex geometries. In the case of gas-liquid bubbly flows, which are present in many chemical– or bio– reactors, effective diffusivity of scalars results from three contributions: molecular diffusion, Shear-Induced Turbulence (S.I.T.), i.e. turbulence induced by gradients of velocity in the continuous phase, and Bubble-Induced Turbulence (B.I.T.), i.e. turbulence generated by interactions of bubble wakes. In a previous work (Alméras et al., 2014, 2015), the diffusion resulting from B.I.T. has been characterized. Based on experiments performed in a homogeneous bubble column, it was shown that the transport can be modelled by an effective diffusion and a physical modelling has been proposed to predict the diffusion induced by B.I.T when other contributions are negligible. In the present work, we have investigated the transport of a passive scalar in a complex bubbly flow at moderate gas volume fraction (α g ≤ 3%), involving a large-scale flow recirculation responsible for the development of shear-induced turbulence. Experimental mixing times measured by image processing in various operating conditions have been compared to numerical simulations of scalar transport. Simulations have been performed by means of an Eulerian RANS CFD model wherein the diffusion generated by B.I.T modelled by Alméras et al. 2015 is implemented in addition to the diffusion resulting from the S.I.T. Results show that the diffusion caused by B.I.T. plays a major role in the mixing of scalars in the investigated flows. Neglecting this contribution leads to an important overestimation of the mixing time unless assigning arbitrary low values to the turbulent Schmidt number Sc t (< 0.3) adapted a posteriori to the simulated cases. On the other hand, considering the scalar diffusivity by B.I.T leads to a good agreement between experiments and CFD simulations, with keeping the Schmidt number in the usual range adopted for mixing in S.I.T. [0.7-1]. The model is generic enough to reproduce the scalar transport for various gas injections, without any further user adaptation. Research Highlights • Diffusion coefficient of a scalar in bubbly flows • Mixing by bubble-induced turbulence • Effective diffusivity implemented in a two-fluid model. • Validation by comparison between Experiments and CFD results

This work reports an experimental investigation of the dispersion of a low-diffusive dye within a homogeneous swarm of high-Reynolds-number rising bubbles at gas volume fractions ${\it\alpha}$ ranging from 1 % to 13 %. The capture and transport of dye within bubble wakes is found to be negligible and the mixing turns out to result from the bubble-induced turbulence. It is described well by a regular diffusion process. The diffusion coefficient corresponding to the vertical direction is larger than that corresponding to the horizontal direction, owing to the larger intensity of the liquid fluctuations in the vertical direction. Two regimes of diffusion have been identified. At low gas volume fraction, the diffusion time scale is given by the correlation time of the bubble-induced turbulence and the diffusion coefficients increase roughly as ${\it\alpha}^{0.4}$. At large gas volume fraction, the diffusion time scale is imposed by the time interval between two bubbles and the diffusion coefficients become almost independent of ${\it\alpha}$. The transition between the two regimes occurs sooner in the horizontal direction ($1\,\%\leqslant {\it\alpha}\leqslant 3\,\%$) than in the vertical direction ($3\,\%\leqslant {\it\alpha}\leqslant 6\,\%$). Physical models based on the hydrodynamic properties of the bubble swarm are introduced and guidelines for practical applications are suggested.

International audience; Ground patterns of liquid aerial drops for combating wildfires are considered. Based on a significant number of drop tests performed using different airplanes and helicopters, a simple model for the length, the width and the coverage distribution is presented. At first order both the length and the width of the drop pattern can be described using simple relations despite the significant difference between the conditions of the drop tests considered. These relations include factors that can be manipulated during aircraft and release system design, as well as during aerial firefighting operations. The liquid on the ground follows a Gaussian distribution that makes possible an original prediction of the maximum coverage level on the pattern centreline confirmed by the experiments. The difference between gravity systems and recent pressurised systems is also discussed. We show a clear difference between gravity systems and pressurised systems. The width is larger for pressurised systems, resulting in a smaller coverage for the same condition of drop.