The prediction of two-phase fluid-solid (gas-solid and liquid-solid) flow remains a major challenge in many engineering and industrial applications. Numerical modeling of these flows is complicated and various studies have been conducted to improve the model performance. In the present work, the two-fluid model of Bolio et al. (1995), developed for dilute turbulent gas-solid flows, is employed to investigate turbulent two-phase liquid-solid flows in both a vertical pipe and a horizontal channel. <p>Fully developed turbulent gas-solid and liquid-solid flows in a vertical pipe and liquid-solid (slurry) flow in a horizontal channel are numerically simulated. The momentum equations for the fluid and solid phases were solved using the finite volume technique developed by Patankar (1980). Mean and fluctuating velocities for both phases, solids concentration, and pressure drop were predicted and compared with the available experimental data. In general, the mean velocity predictions for both phases were in good agreement with the experimental data for vertical flow cases, considered in this work. <p>For dilute gas-solid vertical flows, the predictions were compared with the experimental data of Tsuji et al. (1984). The gas-phase fluctuating velocity in the axial direction was significantly under-predicted while the results for the solids fluctuating velocity were mixed. There was no data to compare the solids concentration but the profiles looked realistic. The pressure drop was observed to increase with increasing Reynolds number and mass loading when compared with the data of Henthorn et al. (2005). The pressure drop first decreased as particle size increased and then started increasing. This behaviour was shown by both experimental data and model predictions. <p>For the liquid-solid flow simulations the mean velocity profiles for both phases, and the liquid-phase turbulence kinetic energy predictions (for dilute flow case), were in excellent agreement with the experimental data of Alejbegovic et al. (1995) and Sumner et al. (1990). The solids concentration profiles were poorly predicted, especially for the lighter particles. The granular temperature profiles, accounting for the solids velocity fluctuations, for the dilute flow case failed to agree with the data, although they captured the overall trend. The liquid-solid pressure drop predictions, using the present model, were only successful for some particles. <p>The solids concentration predictions for the horizontal flow case were similar to the experimental measurements of Salomon (1965), except for a sharp peak at the bottom wall and the opposite curvature. The mixture velocity profiles were asymmetric, due to the addition of particles, and were similar to the experimental data, though only a partial agreement was observed between the predictions and the data.<p>A conclusion from this work is that the present model, which was developed for dilute gas-solid flows, is inadequate when liquid-solid flows are considered. Further improvements, such as including the interstitial fluid effects while computing the liquid-phase stress, are needed to improve the predictive capability of this two-fluid model.

The prediction of two-phase fluid-solid (gas-solid and liquid-solid) flow remains a major challenge in many engineering and industrial applications. Numerical modeling of these flows is complicated and various studies have been conducted to improve the model performance. In the present work, the two-fluid model of Bolio et al. (1995), developed for dilute turbulent gas-solid flows, is employed to investigate turbulent two-phase liquid-solid flows in both a vertical pipe and a horizontal channel. <p>Fully developed turbulent gas-solid and liquid-solid flows in a vertical pipe and liquid-solid (slurry) flow in a horizontal channel are numerically simulated. The momentum equations for the fluid and solid phases were solved using the finite volume technique developed by Patankar (1980). Mean and fluctuating velocities for both phases, solids concentration, and pressure drop were predicted and compared with the available experimental data. In general, the mean velocity predictions for both phases were in good agreement with the experimental data for vertical flow cases, considered in this work. <p>For dilute gas-solid vertical flows, the predictions were compared with the experimental data of Tsuji et al. (1984). The gas-phase fluctuating velocity in the axial direction was significantly under-predicted while the results for the solids fluctuating velocity were mixed. There was no data to compare the solids concentration but the profiles looked realistic. The pressure drop was observed to increase with increasing Reynolds number and mass loading when compared with the data of Henthorn et al. (2005). The pressure drop first decreased as particle size increased and then started increasing. This behaviour was shown by both experimental data and model predictions. <p>For the liquid-solid flow simulations the mean velocity profiles for both phases, and the liquid-phase turbulence kinetic energy predictions (for dilute flow case), were in excellent agreement with the experimental data of Alejbegovic et al. (1995) and Sumner et al. (1990). The solids concentration profiles were poorly predicted, especially for the lighter particles. The granular temperature profiles, accounting for the solids velocity fluctuations, for the dilute flow case failed to agree with the data, although they captured the overall trend. The liquid-solid pressure drop predictions, using the present model, were only successful for some particles. <p>The solids concentration predictions for the horizontal flow case were similar to the experimental measurements of Salomon (1965), except for a sharp peak at the bottom wall and the opposite curvature. The mixture velocity profiles were asymmetric, due to the addition of particles, and were similar to the experimental data, though only a partial agreement was observed between the predictions and the data.<p>A conclusion from this work is that the present model, which was developed for dilute gas-solid flows, is inadequate when liquid-solid flows are considered. Further improvements, such as including the interstitial fluid effects while computing the liquid-phase stress, are needed to improve the predictive capability of this two-fluid model.

Dans ce travail de thèse, réalisé à l'IMFT, nous nous sommes intéressés aux écoulements turbulents diphasiques gaz-solides et plus particulièrement au phénomène de couplage inverse qui correspond à la modulation de la turbulence par la phase dispersée. Ce mécanisme est crucial pour les écoulements à forts chargements massiques. Dans cette thèse, nous avons considéré une turbulence homogène isotrope stationnaire sans gravité dans laquelle des particules sont suivies individuellement d'une façon Lagrangienne. La turbulence du fluide porteur est obtenue par des simulations directes (DNS). Les particules sont sphériques, rigides et d'une taille inférieure aux plus petites échelles de la turbulence. Leur densité est bien plus grande que la densité du fluide. Dans ce cadre, la force la plus importante agissant sur les particules est celle de traînée. Les interactions inter-particules ainsi que la gravité ne sont pas prises en compte. Pour modéliser ce type d'écoulement, une approche stochastique est utilisée pour laquelle l'accélération du fluide est modélisée par une équation de Langevin. L'originalité de ce travail est la prise en compte de l'effet de la modulation de la turbulence par un terme additionnel. Nous avons proposé deux modèles : une force de couplage moyenne qui est définie à partir des vitesses moyennes des phases, et une force instantanée qui est définie à l'aide du formalisme mésoscopique Eulérien. La fermeture des modèles s’appuie sur la fonction d’autocorrélation Lagrangienne et l’équation de transport de l’énergie cinétique. Les modèles sont testés en terme de prédiction de la vitesse de dérive et des corrélations fluide-particule. Les résultats montrent que le modèle moyen, plus simple, prend en compte les effets principaux du couplage inverse. Cependant, le problème de fermeture pratique est reporté sur la modélisation de l’échelle intégrale Lagrangienne et l’énergie cinétique de la turbulence du fluide vue par les particules. / In this thesis, performed in IMFT, we are interested in the turbulent gas-solid flows and more specifically, in the phenomenon of turbulence modulation which is the modification of the structure of the turbulence due to the solid particles. This mechanism is crucial in flows with high particle mass-loadings. In this work, we considered a homogeneous isotropic turbulence without gravity kept stationary with stochastic type forcing. Discrete particles are tracked individually in Lagrangian manner. Turbulence of the carrier phase is obtained by using DNS. The particles are spherical, rigid and of a diameter smaller than the smallest scales of turbulence. Their density is very large in comparison to the density of the fluid. In this configuration the only force acting on the particles is the drag force. Volume fraction of particles is very small and inter-particle interactions are not considered. To model this type of flow, a stochastic approach is used where the fluid element accel- eration is modeled using stochastic Langevin equation. The originality in this work is an additional term in the stochastic equation which integrates the effect of the particles on the trajectory of fluid elements. To model this term, we proposed two types of modeling: a mean drag model which is defined using the mean velocities from the mean transport equations of the both phases and an instantaneous drag term which is written with the help of the Mesoscopic Eulerian Approach. The closure of the models is based on the Lagrangian auto- correlation function of the fluid velocity and on the transport equation of the fluid kinetic energies. The models are tested in terms of the fluid-particle correlations and fluid-particle turbulent drift velocity. The results show that the mean model, simple, takes into account the principal physical mechanism of turbulence modulation. However, practical closure problem is brought forward to the Lagrangian integral scale and the fluid kinetic energy of the fluid turbulence viewed by the particles.