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Using the Taylor–Couette geometry we experimentally investigate the effect of salt on drag reduction caused by bubbles present in the flow. We combine torque measurements with optical high-speed imaging to relate the bubble size to the drag experienced by the flow. Previous studies have shown that a small percentage of air (4%) can lead to dramatic drag reduction (40%). In contrast to previous laboratory experiments, which mainly used fresh water, we will vary the salinity from that of fresh water to the average salinity of ocean water. We find that the drag reduction is increasingly more inhibited for increasing salt concentrations, going from 40% for fresh water to just 15% for sea water. Salts present in the working fluid inhibit coalescence events, resulting in smaller bubbles in the flow and, with that, a decrease in the drag reduction. Above a critical salinity, increasing the salinity has no further effect on the size of bubbles in the flow and thus the drag experienced by the flow. Our new findings demonstrate the importance of sodium chloride on the bubbly drag reduction mechanism, and will further challenge naval architects to implement promising air lubrication systems on marine vessels. This article is part of the theme issue ‘Taylor–Couette and related flows on the centennial of Taylor’s seminal Philosophical Transactions paper (part 1)’.

In this study are presented the numerical results obtained when simulating the abruptly stoppage of the outer cylinder in a Taylor-Couette system where the inner cylinder is static. The results are compared with the experimental observations published in the Journal of Fluid Mechanics. En este estudio se presentan los resultados numéricos obtenidos al simular un sistema Taylor-Couette en el cual el cilindro exterior se para mientras que el cilindro interior está estático. Los resultados se comparan con las observaciones experimentales ya publicas en el Journal of Fluid Mechanics En aquest estudi es presenta els resultats numèrics quan es simula un sistema Taylor-Couette en el qual es para el cilindre exterior de cop, tenint el cilindre interior sempre estàtic. Els resultats es comparan amb les observacions experimentals ja obtingudes anteriorment, publicades al Journal of Fluid Mechanics.

Turbulent reactive flows are ubiquitous in industrial processes. Decoupling transport effects from intrinsic chemical reactions requires an in-depth understanding of fluid flow physics; computational fluid dynamics (CFD) methods have been widely used for this purpose. Most CFD simulations of reactive liquid-phase flows, where the Schmidt numbers (Sc) are large, rely on isotropic eddy viscosity models. However, the assumption of turbulent isotropy in most stirred reactors and wall-bounded flows is fundamentally incorrect and leads to erroneous results. Here, we apply a systematic CFD approach to simulate liquid-phase diffusive and convective transport phenomena that occur in a Taylor-Couette (TC) reactor. We resolve the turbulent flow by extracting statistics from large eddy simulation (LES) which is used to tune the anisotropic Reynolds stress model (RSM). In addition, we conducted a series of turbulent precipitation and mixing studies in a TC reactor that was designed and fabricated in-house. The numerical model is successfully validated against a published torque correlation and it is found to accurately describe the advection and diffusion of chemical species. The validated model is then used to demonstrate key flow properties in the reactor. We define new local turbulent Peclét numbers to characterize the relative increase in diffusivity from turbulent advection and observe a 29% increase in the turbulent contribution as Reynolds number is doubled. Both reactive simulations and experiments show an increase in overall reaction rates with increased turbulence. The results from reactive simulations provide a deeper understanding of flow-kinetics interactions at turbulent conditions.

In this work we report experimental results on the transition to the turbulent vortices in the Couette-Taylor flow, the flow produced between independently rotating coaxial cylinders. Once the geometry and the nature of the fluid are fixed, the flow is gouverned by two control parameters, the outer and the inner Reynolds numbers 〖Re〗_o and 〖Re〗_i associated with the rotation of the outer and inner cylinders respectively. The variation of these parameters produces a large variety of regimes, which have been described by Coles [7], and Andereck et al. [13]. In the counter-rotating case, we have identified three main regimes on the diagram of Andereck et al. [13] When considering the variation of 〖Re〗_ifor a fixed value of〖 Re〗_o, the flow is laminar for low〖 Re〗_i. It becomes unstable for higher values of 〖Re〗_i. Before reaching turbulence, the flow passes by a regime of laminar-turbulent coexistence [7 13 14 16]. For our series of measurements, we fixed the outer Reynolds number at 〖Re〗_o=-4368, and varied 〖Re〗_ifrom the laminar to the turbulent regime. For 3000 < 〖Re〗_i< 4000, the space-time diagrams indicate the occurrence of disordered coherent structures. These structures are then well organized in time and space for 4000 < 〖Re〗_i< 10000, and become stationnary for the highest 〖Re〗_i [35]. These regimes are studied by visualizations using kalliroscope, as well as measurements of the velocity by stereoscopic PIV and LDV. This later allows us to calculate the various mean quantities (kinetic energy, Reynolds stress, time and length of correlation, etc…)., Dans ce travail, nous représentons des résultats expérimentaux sur la transition vers les rouleaux turbulents dans l’écoulement de Couette-Taylor, l’écoulement produit entre deux cylindres coaxiaux tournant indépendamment l’un par rapport à l’autre. Une fois la géométrie et la nature du fluide sont fixes, l’écoulement est gouverné par deux paramètres de contrôle, les nombres de Reynolds intérieur et extérieur 〖Re〗_o et 〖Re〗_i associés à la rotation des cylindres extérieur et intérieur respectivement. La variation de ces paramètres confère à l’écoulement une variété de régimes, décrits par Coles [7] et par Andereck et al. [13]. Dans le cas de la contra-rotation, nous avons identifié trois régimes principaux sur le diagramme d'Andereck et al. [13] En considérant la variation de 〖Re〗_i pour une valeur fixe de〖 Re〗_o, l’écoulement est laminaire pour des faibles〖 Re〗_i. Il devient instable pour des valeurs plus élevées de〖 Re〗_i. Avant d'atteindre la turbulence, l'écoulement passe par un régime de coexistence laminaire-turbulent [7 13 14 16]. Pour notre série de mesures, nous avons fixé le nombre de Reynolds extérieur à 〖Re〗_o=-4368 et nous avons varié 〖Re〗_i du régime laminaire vers le régime turbulent. Pour 3000 < 〖Re〗_i < 4000, les diagrammes spatio-temporels indiquent la présence de structures cohérentes désordonnées. Ces structures sont bien organisées dans le temps et dans l’espace pour 4000

In this work we report experimental results on the transition to the turbulent vortices in the Couette-Taylor flow, the flow produced between independently rotating coaxial cylinders. Once the geometry and the nature of the fluid are fixed, the flow is gouverned by two control parameters, the outer and the inner Reynolds numbers 〖Re〗_o and 〖Re〗_i associated with the rotation of the outer and inner cylinders respectively. The variation of these parameters produces a large variety of regimes, which have been described by Coles [7], and Andereck et al. [13]. In the counter-rotating case, we have identified three main regimes on the diagram of Andereck et al. [13] When considering the variation of 〖Re〗_ifor a fixed value of〖 Re〗_o, the flow is laminar for low〖 Re〗_i. It becomes unstable for higher values of 〖Re〗_i. Before reaching turbulence, the flow passes by a regime of laminar-turbulent coexistence [7 13 14 16]. For our series of measurements, we fixed the outer Reynolds number at 〖Re〗_o=-4368, and varied 〖Re〗_ifrom the laminar to the turbulent regime. For 3000 < 〖Re〗_i< 4000, the space-time diagrams indicate the occurrence of disordered coherent structures. These structures are then well organized in time and space for 4000 < 〖Re〗_i< 10000, and become stationnary for the highest 〖Re〗_i [35]. These regimes are studied by visualizations using kalliroscope, as well as measurements of the velocity by stereoscopic PIV and LDV. This later allows us to calculate the various mean quantities (kinetic energy, Reynolds stress, time and length of correlation, etc…).; Dans ce travail, nous représentons des résultats expérimentaux sur la transition vers les rouleaux turbulents dans l’écoulement de Couette-Taylor, l’écoulement produit entre deux cylindres coaxiaux tournant indépendamment l’un par rapport à l’autre. Une fois la géométrie et la nature du fluide sont fixes, l’écoulement est gouverné par deux paramètres de contrôle, les nombres de Reynolds intérieur et extérieur 〖Re〗_o et 〖Re〗_i associés à la rotation des cylindres extérieur et intérieur respectivement. La variation de ces paramètres confère à l’écoulement une variété de régimes, décrits par Coles [7] et par Andereck et al. [13]. Dans le cas de la contra-rotation, nous avons identifié trois régimes principaux sur le diagramme d'Andereck et al. [13] En considérant la variation de 〖Re〗_i pour une valeur fixe de〖 Re〗_o, l’écoulement est laminaire pour des faibles〖 Re〗_i. Il devient instable pour des valeurs plus élevées de〖 Re〗_i. Avant d'atteindre la turbulence, l'écoulement passe par un régime de coexistence laminaire-turbulent [7 13 14 16]. Pour notre série de mesures, nous avons fixé le nombre de Reynolds extérieur à 〖Re〗_o=-4368 et nous avons varié 〖Re〗_i du régime laminaire vers le régime turbulent. Pour 3000 < 〖Re〗_i < 4000, les diagrammes spatio-temporels indiquent la présence de structures cohérentes désordonnées. Ces structures sont bien organisées dans le temps et dans l’espace pour 4000

The flow between two rotating and concentric cylinders is defined as Taylor-Couette Flow. This configuration has been widely studied theoretically, numerically and experimentally because of its relative simplicity and for the implications it can bear in geophysical and industrial applications. In this work, we developed numerical tools to analyse the experimental data obtained via laser doppler anemometry technique. We performed experiments at low Reynolds number and investigated the regime transition. We analyzed the data in terms of both mean and time dependent quantities and we characterise the transition. In particular, we characterise the time-dependent flow by means of Fourier analysis. Data are processed with the codes developed in this work, which allowed an accurate comparison of the results obtained in correspondence of different Reynolds and Taylor numbers, i.e. different velocities. Data are processed with in house codes, which allowed an accurate comparison of the results obtained in correspondence of different Reynolds numbers, i.e. different velocities. Finally, we provide indications for future investigations with the aim of extending the regimes currently observed.

This paper concerns experimental investigation of the sequenced flocculation of latex particles in a Taylor-Couette reactor. The aim of this work was to investigate the evolution of both the size and the shape of aggregates under sequenced hydrodynamics. A number of studies have focused on the evolution of the aggregate size or size distribution during steps of growth-breakage-regrowth, but aggregates generally experience steps of breakage-regrowth on repeated occasions in real operating conditions (passages near the impeller or during the transfer processes, for example). The experiments conducted in this work consisted thus of an alternation of six steps with alternately low and high shear rates under turbulent conditions. The particle size distributions were monitored throughout the sequencing, and the circularity and convexity (shape parameters) distributions were measured, enabling a more precise description of the entire floc population, rather than a fractal dimension. While the aggregate size distribution was clearly controlled by hydrodynamics, the shape distributions continuously evolved during the sequencing. The main new finding of our work notes the independence between the aggregate shape and hydrodynamics. Indeed, after multiples steps of breakage-regrowth, regardless of the aggregate size distribution and hydrodynamics, the aggregate shape seemed to reach a unique steady-state morphological distribution.

Turbulent flows in an opened Taylor-Couette system with an axial throughflow is studied here by the means of large eddy simulations. The ultimate industrial application is the effective cooling of the rotor-stator gap of an electrical motor.

Taylor-Couette flow is defined as the flow confined between two coaxial cylinders which can rotate independently. Several different flow states can be observed in the gap between the cylinders by changing the rotation speeds and the rotating directions of the cylinders. The aim of this thesis is to investigate the previously reported change of torque values with the rotation speeds of the cylinders and to study its relation to coherent turbulent flow structures. The flow structures are investigated using tomographic PIV, which is a fully volumetric measurement method that resolves all three velocity components. Different flow states, and their contribution to the Reynolds stresses are revealed. Initially, the Taylor-Couette setup was used to investigate the spatial resolution of tomographic PIV, by exploiting the fact that the power input to the system, as determined from the torque measurements and the cylinder rotation speed, is balanced by the viscous dissipation rate, which can be computed using the measured velocities. Next, time-resolved tomographic PIV measurements were performed at fully turbulent flow to demonstrate the capability of the measurement system and the flow geometry to study dynamic events in turbulence. Turbulent flow with an approximately zero mean velocity was created by rotating the cylinders in opposite directions with the same wall velocities. Using this idea, the observation times of the flow structures could be increased by an order of magnitude as compared to similar studies in turbulent boundary layers. Finally, the connection between turbulent flow structures and the change of the torque was made by using tomographic PIV. In order to compute the contribution of the large and the smaller-scale structures to the torque, the instantaneous flow was decomposed into the large and the smaller-scale motions by filtering. The Reynolds stresses associated with these structures indicate that the orientational change of the structures may be the mechanism responsible for the reported change of the torque scaling.

Taylor-Couette flow is defined as the flow confined between two coaxial cylinders which can rotate independently. Several different flow states can be observed in the gap between the cylinders by changing the rotation speeds and the rotating directions of the cylinders. The aim of this thesis is to investigate the previously reported change of torque values with the rotation speeds of the cylinders and to study its relation to coherent turbulent flow structures. The flow structures are investigated using tomographic PIV, which is a fully volumetric measurement method that resolves all three velocity components. Different flow states, and their contribution to the Reynolds stresses are revealed. Initially, the Taylor-Couette setup was used to investigate the spatial resolution of tomographic PIV, by exploiting the fact that the power input to the system, as determined from the torque measurements and the cylinder rotation speed, is balanced by the viscous dissipation rate, which can be computed using the measured velocities. Next, time-resolved tomographic PIV measurements were performed at fully turbulent flow to demonstrate the capability of the measurement system and the flow geometry to study dynamic events in turbulence. Turbulent flow with an approximately zero mean velocity was created by rotating the cylinders in opposite directions with the same wall velocities. Using this idea, the observation times of the flow structures could be increased by an order of magnitude as compared to similar studies in turbulent boundary layers. Finally, the connection between turbulent flow structures and the change of the torque was made by using tomographic PIV. In order to compute the contribution of the large and the smaller-scale structures to the torque, the instantaneous flow was decomposed into the large and the smaller-scale motions by filtering. The Reynolds stresses associated with these structures indicate that the orientational change of the structures may be the mechanism responsible for the reported change of the torque scaling.

International audience; We investigate bubble dispersion in turbulent Taylor-Couette flow. The aim of this study is to describe the main mechanisms yielding preferential bubble accumulation in near-wall structures of the flow. We first proceed to direct numerical simulation of Taylor-Couette flows for three different geometrical configurations (three radius ratios η = R 1/R 2: η = 0.5, η = 0.72, and η = 0.91 with the outer cylinder at rest) and Reynolds numbers corresponding to turbulent regime ranging from 3000 to 8000. The statistics of the flow are discussed using two different averaging procedures that permit to characterize the mean azimuthal velocity, the Taylor vortices contribution and the small-scale turbulent fluctuations. The simulations are compared and validated with experimental and numerical data from literature. The second part of this study is devoted to bubble dispersion. Bubble accumulation is analyzed by comparing the dispersion obtained with the full turbulent flow field to bubble dispersion occurring at lower Reynolds numbers in previous works. Several patterns of preferential accumulation of bubbles have been observed depending on bubble size and the effect of gravity. For the smaller size considered, bubbles disperse homogeneously throughout the gap, while for the larger size they accumulate along the inner wall for the large gap width (η = 0.5). Varying the intensity of buoyancy yields complex evolution of the bubble spatial distribution. For low gravity effect, bubble entrapment is strong leading to accumulation along the inner wall in outflow regions (streaks of low wall shear stress). When buoyancy effect dominates on vortex trapping, bubbles rise through the vortices, while spiral patterns stretched along the inner cylinder are clearly identified. Force balance is analyzed to identify dominating forces leading to this accumulation and accumulation patterns are compared with previous experiments.

International audience; The flow and mixing in a Taylor–Couette device have been characterized by means of simultaneous particle image velocimetry and planar laser-induced fluorescence (PLIF) measurements. Concentration of a passive tracer measurements was used to investigate mixing efficiency for different flow patterns (from steady Taylor vortex flow to modulated wavy vortex flow, MWVF). Taylor–Couette flow is known to evolve toward turbulence through a sequence of flow instabilities. Macroscopic quantities, such as axial dispersion and mixing index, are extremely sensitive to internal flow structures. PLIF measurements show clear evidences of different transport mechanisms including intravortex mixing and tracer fluxes through neighboring vortices. Under WVF and MWVF regimes, intravortex mixing is controlled by chaotic advection, due to the 3D nature of the flow, while intervortex transport occurs due to the presence of waves between neighboring vortices. The combination of these two mechanisms results in enhanced axial dispersion. We show that hysteresis may occur between consecutive regimes depending on flow history, and this may have a significant effect on mixing for a given Reynolds number

La thèse porte sur l'étude de la réduction de traînée par injection de bulles. La réduction de traînée présente un intérêt pour les applications navales puisqu'elle est issue d'une modification des structures cohérentes qui contribuent le plus à la résistance à l'avancement. Le but de cette étude est d'analyser les mécanismes à l'origine de cette diminution du frottement pariétal. L'approche utilisée dans le cadre de cette étude est numérique, elle emploie le code JADIM par une approche Euler-Lagrange : la phase continue est simulée par Simulation Numérique Directe et la phase dispersée est simulée en suivant individuellement chaque bulle. La configuration retenue dans le cadre de cette étude est celle de l'écoulement de Taylor-Couette (écoulement compris entre deux cylindres en rotation). La première partie de la thèse vise à adapter l'outil numérique employé, afin de pouvoir prendre en compte le retour de la phase dispersée via des termes de forçage dans les équations bilan de matière et de quantité de mouvement. La deuxième partie de la thèse vise à étudier l'écoulement porteur en configuration monophasique, afin de disposer d'une référence sur l'écoulement non perturbé. La troisième partie de la thèse a pour objectif d'étudier la dispersion passive des bulles dans le système, afin d'analyser les mécanismes de migrations mis en jeu. Enfin la dernière partie de la thèse vise à étudier l'influence des bulles sur l'écoulement porteur en analysant l'effet de certains paramètres, notamment le taux de vide et la flottabilité.

The Taylor-Couette system, consisting of shear flow between differentially rotating concentric cylinders, has been investigated experimentally and numerically in great detail since Taylor's pioneering work in 1923. Most of the studies dedicated to this topic considered cavities of small aspect ratio (defined as the ratio between the height of the cylinders and the radial distance between the cylindrical walls). They particularly focused on the rotor-stator configuration with a fixed outer cylinder. The rotation of the outer cylinder in addition to that of the inner cylinder results in more complex vortical structures; furthermore decreasing the aspect ratio changes the transition to turbulence. These cases, that have not been much studied, are the topic of this work. We use 3D direct numerical simulation based on a Chebyshev-Fourier spectral approximation that has been shown to be efficient for the complex development of rotating flows with walls. Those methods are coupled to efficient algorithms. Computations have been carried out on NEC SX-5 supercomputer. In the couter-rotating case, we found complex spiral and wavy vortex flows. DNS allowed a precise analysis of space-and-time behaviour of the vortical structures and the effect of the endwalls., Depuis les travaux pionniers de Taylor (1923), la configuration de Taylor-Couette, constituée de deux cylindres coaxiaux pouvant tourner indépendamment l'un de l'autre, a été intensivement étudiée expérimentalement et numériquement. La plupart de ces études ont considéré le cas où le rapport d'aspect - défini comme le rapport entre la hauteur des cylindres et l'épaisseur de fluide dans l'entrefer du dispositif - est grand (supposé infini) ; elles ont également portée plus particulièrement sur la configuration où seul le cylindre interne est en rotation (configuration rotor-stator). La mise en rotation de la paroi externe complexifie la phénoménologie des structures tourbillonnaires, et la diminution du rapport d'aspect modifie le scénario de transition vers la turbulence. Ces cas, moins bien documentés, constituent l'objet de notre étude. L'outil d'investigation est une simulation numérique directe (DNS) tridimensionnelle de haute précision, basée sur une approximation spectrale de la solution. Ces méthodes, couplées à des algorithmes très efficaces, ont permis de réaliser des simulations lourdes sur supercalculateur NEC SX5. Des simulations avec parois en contrarotation ont permis la mise en évidence d'écoulements complexes de type " Wavy Vortex " ou " InterPenetrating Spirals ". La DNS a permis une analyse fine du comportement spatio-temporel des structures et des effets des parois terminales.

Numerical simulation of industrial reactor promises to be a precious tool that could help in prospecting new mixing technologies, in scaling-up and optimising reactors. Fast reactions, such as polymerisation and precipitations, are difficult to handle when mixing processes and reactions strongly interacts. This work aims at evaluating and validating reactive flow simulation for chemical engineering reactors using a special method which is able to take into account mixing reaction interaction for fast reactions. This method is based on solving Navier-Stokes equations in turbulent flow and then on solving the transport equation of the jointtcomposition Probability Density Function (PDF) with a Monte-Carlo solver. The validation is carried-out on a semi-batch Taylor-Couette precipitator. Each calculation step is validated. Finally, comparison between experiment and simulation proved that the method we chose has to be handle with special cares. Calculation has to be validated and 2 model constants have to be fitted and chemical kinetics known quite precisely. Besides, Monte-Carlo algorithm produces numerical noise which can highly affect reliability of the results. The calculation of the specific studied reactor didn'nt give completely good agreement with experiments. Nevertheless, the discrepancy is assigned not to the numerical approach but to the fact that the studied reactive flow is rather tricky to be calculated.; La simulation numérique de réacteurs industriels promet de devenir un outil précieux aidant à prospecter de nouvelles technologies de mélange, à dimensionner et à optimiser les conditions de fonctionnement du réacteur. Ces calculs deviennent difficiles dans le cas de réactions rapides (polymérisations anioniques, précipitations) où existe un fort couplage entre la réaction chimique et le mélange. Ce travail de thèse a pour but d'évaluer et de valider la simulation d'écoulements réactifs pour des applications de génie chimique avec une méthode que nous avons choisie pour sa capacité à tenir compte des interactions entre processus de mélange turbulent et réactions chimiques rapides. La méthode sélectionnée est une méthode basée sur la résolution numérique des équations de Navier-Stokes en milieu turbulent et l'équation de transport de la fonction de densité de probabilité jointe de la composition (PDF) à l'aide d'un algorithme de Monte-Carlo. L'évaluation s'est faite sur un réacteur de précipitation semi-batch de type Taylor-Couette. Chaque étape du calcul a été validée expérimentalement. Au terme de ce travail, il a été montré que l'emploi de ce type d'approche pour le calcul d'un réacteur industriel est hasardeux et délicat. Il demande une validation de l'écoulement, le calage de 2 constantes de modélisation et la connaissance précise des cinétiques de réaction. Enfin, l'utilisation d'un algorithme de type Monte-Carlo engendre un bruit numérique qui selon le type d'écoulement peut nuire à la fiabilité des résultats. Le cas traité n'a pas donné des résultats totalement conformes à l'expérience. La méthode numérique utilisée n'est pas pour autant remise en question car le cas traité était par nature délicat

Numerical simulation of industrial reactor promises to be a precious tool that could help in prospecting new mixing technologies, in scaling-up and optimising reactors. Fast reactions, such as polymerisation and precipitations, are difficult to handle when mixing processes and reactions strongly interacts. This work aims at evaluating and validating reactive flow simulation for chemical engineering reactors using a special method which is able to take into account mixing reaction interaction for fast reactions. This method is based on solving Navier-Stokes equations in turbulent flow and then on solving the transport equation of the jointtcomposition Probability Density Function (PDF) with a Monte-Carlo solver. The validation is carried-out on a semi-batch Taylor-Couette precipitator. Each calculation step is validated. Finally, comparison between experiment and simulation proved that the method we chose has to be handle with special cares. Calculation has to be validated and 2 model constants have to be fitted and chemical kinetics known quite precisely. Besides, Monte-Carlo algorithm produces numerical noise which can highly affect reliability of the results. The calculation of the specific studied reactor didn'nt give completely good agreement with experiments. Nevertheless, the discrepancy is assigned not to the numerical approach but to the fact that the studied reactive flow is rather tricky to be calculated., La simulation numérique de réacteurs industriels promet de devenir un outil précieux aidant à prospecter de nouvelles technologies de mélange, à dimensionner et à optimiser les conditions de fonctionnement du réacteur. Ces calculs deviennent difficiles dans le cas de réactions rapides (polymérisations anioniques, précipitations) où existe un fort couplage entre la réaction chimique et le mélange. Ce travail de thèse a pour but d'évaluer et de valider la simulation d'écoulements réactifs pour des applications de génie chimique avec une méthode que nous avons choisie pour sa capacité à tenir compte des interactions entre processus de mélange turbulent et réactions chimiques rapides. La méthode sélectionnée est une méthode basée sur la résolution numérique des équations de Navier-Stokes en milieu turbulent et l'équation de transport de la fonction de densité de probabilité jointe de la composition (PDF) à l'aide d'un algorithme de Monte-Carlo. L'évaluation s'est faite sur un réacteur de précipitation semi-batch de type Taylor-Couette. Chaque étape du calcul a été validée expérimentalement. Au terme de ce travail, il a été montré que l'emploi de ce type d'approche pour le calcul d'un réacteur industriel est hasardeux et délicat. Il demande une validation de l'écoulement, le calage de 2 constantes de modélisation et la connaissance précise des cinétiques de réaction. Enfin, l'utilisation d'un algorithme de type Monte-Carlo engendre un bruit numérique qui selon le type d'écoulement peut nuire à la fiabilité des résultats. Le cas traité n'a pas donné des résultats totalement conformes à l'expérience. La méthode numérique utilisée n'est pas pour autant remise en question car le cas traité était par nature délicat