No description available.

A mathematical model for a consolidation process of a highlyconcentrated, flocculated suspension is developed.Thesuspension is treated as a mixture of a fluid and solidparticles by an Eulerian two-phase fluid model.W e characterizethe suspension by constitutive relations correlating thestresses, interaction forces, and inter-particle forces toconcentration and velocity gradients.This results in threeempirically determined material functions: a hystereticpermeability, a non-Newtonian viscosity and a non-reversibleparticle interaction pressure.P arameters in the models arefitted to experimental data. A simulation program using finite difference methods both intime and space is applied to one and two dimensional testcases.Numer ical experiments are performed to study the effectof different viscosity and permeability models. The effect ofshear on consolidation rate is studied and it is significantwhen the permeability hysteresis model is employed.

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.

Turbulent gas-solid flows are readily encountered in many industrial and environmental processes. The development of a generic modeling technique for gas-solid turbulent flows remains a significant challenge in the field of mechanical engineering. Eulerian models are typically used to model large systems of particles. In this dissertation, a numerical analysis was carried out to assess a current state-of-the-art Eulerian two-fluid model for fully-developed turbulent gas-solid upward flow in a vertical pipe. The two-fluid formulation of Bolio et al. (1995) was adopted for the current study and the drag force was considered as the dominant interfacial force between the solids and fluid phase. In the first part of the thesis, a two-equation low Reynolds number k-ε model was used to predict the fluctuating velocities of the gas-phase which uses an eddy viscosity model. The stresses developed in the solids-phase were modeled using kinetic theory and the concept of granular temperature was used for the prediction of the solids velocity fluctuation. The fluctuating drag, i.e., turbulence modulation term in the transport equation of the turbulence kinetic energy and granular temperature was used to capture the effect of the presence of the dispersed solid particles on the gas-phase turbulence. The current study documents the performance of two popular turbulence modulation models of Crowe (2000) and Rao et al. (2011). Both models were capable of predicting the mean velocities of both the phases which were generally in good agreement with the experimental data. However, the phenomena that small particles cause turbulence suppression and large particles cause turbulence enhancement was better captured by the model of Rao et al. (2011); conversely, the model of Crowe (2000) produced turbulence enhancement in all cases. Rao et al. (2011) used a modified wake model originally proposed by Lun (2000) which is activated when the particle Reynolds number reaches 150. This enables the overall model to produce turbulence suppression and augmentation that follows the experimental trend. The granular temperature predictions of both models show good agreement with the limited experimental data of Jones (2001). The model of Rao et al. (2011) was also able to capture the effect of gas-phase turbulence on the solids velocity fluctuation for three-way coupled systems. However, the prediction of the solids volume fraction which depends on the value of the granular temperature shows noticeable deviations with the experimental data of Sheen et al. (1993) in the near-wall region. Both turbulence modulation models predict a flat profile for the solids volume fraction whereas the measurements of Sheen et al. (1993) show a significant decrease near the wall and even a particle-free region for flows with large particles. The two-fluid model typically uses a low Reynolds number k-ε model to capture the near-wall behavior of a turbulent gas-solid flow. An alternative near-wall turbulence model, i.e., the two-layer model of Durbin et al. (2001) was also implemented and its performance was assessed. The two-layer model is especially attractive because of its ability to include the effect of surface roughness. The current study compares the predictions of the two-layer model for both clear gas and gas-solid flows to the results of a conventional low Reynolds number model. The effects of surface roughness on the turbulence kinetic energy and granular temperature were also documented for gas-particle flows in both smooth and rough pipes.

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.

Understanding the physics of multiphase plumes and their simulation through numerical modeling has been an important area of research in recent times in the area of environmental fluid mechanics. The two renowned numerical modeling types that are commonly used by researchers today to simulate multiphase plumes in nature are the mixed-fluid and the two-fluid integral models. In the present study, a detailed review was performed to study and analyze the two modeling approaches for the case of a double plume (upward moving inner plume with downward moving annular outer plume) with the objective of ascertaining which of these models represent the prototype physics in the integral plume model equations with a higher degree of completeness and accuracy. A graphical user interface was designed to facilitate running the models. By comparison to laboratory scale experimental data and through sensitivity analyses, a rigorous effort was made to determine the most appropriate choice of initial conditions needed at the start of the model computation and at the peeling locations and to obtain the most consistent values of the different model parameters that are necessary for calibration of the two models. Consequently, with these selected sets of initial conditions and model parameters, the models were run and their outputs compared against each other for three different case studies with ambient conditions typical of real environmental data. The dispersed phases considered were air bubbles in two cases and liquid CO2 droplets for the third case, with water as the continuous phase in all cases. The entrainment coefficient was found to be the most important parameter that affected the model results. In all the three case studies conducted, the mixed-fluid model was found to predict about 30% higher values for the peel heights and the DMPR (Depth of Maximum Plume Rise) than the two-fluid model.

No description available.

<p>A mathematical model for a consolidation process of a highlyconcentrated, flocculated suspension is developed.Thesuspension is treated as a mixture of a fluid and solidparticles by an Eulerian two-phase fluid model.W e characterizethe suspension by constitutive relations correlating thestresses, interaction forces, and inter-particle forces toconcentration and velocity gradients.This results in threeempirically determined material functions: a hystereticpermeability, a non-Newtonian viscosity and a non-reversibleparticle interaction pressure.P arameters in the models arefitted to experimental data.</p><p>A simulation program using finite difference methods both intime and space is applied to one and two dimensional testcases.Numer ical experiments are performed to study the effectof different viscosity and permeability models. The effect ofshear on consolidation rate is studied and it is significantwhen the permeability hysteresis model is employed.</p>

In this thesis the effect of the Hall term in the generalised Ohm's law on Alfvén (shear) and fast wave propagation and dissipation in the ion cyclotron frequency range is investigated. The damping of an initially Gaussian field perturbation in a uniform Hall MHD plasma is treated analytically. Subsequently a 2D Lagrangian remap code (Lare2d) is used to study the damping and phase mixing of initially Gaussian field perturbations and a harmonic series of boundary-driven perturbations in a uniform field (in the presence of a transverse equilibrium density gradient). The same code is then used to study a range of initially shear and fast-wave perturbations in the vicinity of a magnetic X-type null point. The magnetic energy associated with an initially Gaussian field perturbation in a uniform resistive plasma is shown to decay algebraically at a rate that is unaffected by the Hall term to leading order in kδ where k is wavenumber and δ is ion skin depth. A similar decay law applies to whistler perturbations in the limit kδ>>>1. We demonstrate that in both geometries considered, the inclusion of the Hall term reduces the effectiveness of phase-mixing in plasma heating. The reduction in the damping rate in the uniform field (non-uniform density) cases, arising from dispersive effects, tends to zero in both the weak and strong phase mixing limits. In the Hall MHD X-point case, minimal reductions are seen for initially shear wave pulses, suggesting that little or no phase-mixing takes place. Nonlinear fast wave pulses which interact with the initial X-point destabilise the local field sufficiently to generate multiple null pairs; subsequent oscillatory current sheet behaviour appears unaffected by earlier differences between the MHD and Hall MHD cases.

Cette travail de thèse est lié au besoin de modélisation des écoulements diphasiques en générateurs de vapeur (entrée liquide et sortie vapeur). La démarche proposée consiste à faire le choix d'une modélisation hybride de l'écoulement, en scindant la phase gaz en deux champs, modélisés de manières différentes. Ainsi, les petites bulles sphériques sont modélisées avec une approche dispersée classique avec le modèle eulérien à deux fluides, et les bulles déformées sont simulées à l'aide d'une méthode de localisation d'interface.Le travail effectué porte sur la mise en place, la vérification et la validation du modèle dédié aux larges bulles déformées, ainsi que le couplage entre les deux approches pour le gaz gaz, permettant des premiers calculs de démonstration utilisant l'approche hybride complète. / The present study is related to the need of modeling the two-phase flows occuring in a steam generator (liquid at inlet and vapour at outlet). The choice is made to investigate a hybrid modeling of the flow, considering the gas phase as two separated fields, each one being modeled with different closure laws. In so doing, the small and spherical bubbles are modeled through a dispersed approach within the two-fluid model, and the distorted bubbles are simulated with an interface locating method.The main outcome is about the implementation, the verification and the validation of the model dedicated to the large and distorted bubbles, as well as the coupling of the two approaches for the gas, allowing the presentation of demonstration calculations using the so-called hybrid approach.