Philosophiae Doctor - PhD / Prevailing astronomical and astrophysical observations suggest that we live in a spatially flat cold dark matter (CDM) universe - currently going through a period of accelerated expansion possibly driven by “dark energy” in form of a cosmological constant. Within the standard cosmological paradigm, dark energy and dark matter are the dual dominant sources in the evolution of the late-time universe contributing about 70% and 25% respectively to the total energy density in the Universe, but these are only currently detected via their gravitational interaction. There could be a non-gravitational interaction within the “dark sector” without violating current observational data, thus giving rise to changes in the dark equations of state and affecting the process of galaxy formation. In this thesis, we investigate two new interesting large-scale structure formation scenarios using interacting fluids. Firstly, in departure from the standard approach in which dark matter is treated as a single independent fluid, we split the dark matter fluid into two interacting components: a strongly clustered “halo” component and a weakly clustered “free” component- accreted by the halos. By defining the fraction of the matter inside CDM “halos” to the total matter as a time evolving function of the total matter density F (ρm), we derive the governing background and perturbation equations and the energy-momentum transfer four-vectors. We then perform numerical calculations for three models for F (ρm) that are in agreement with recently published results from halo theory of N-body simulations, and compare our results to the standard ΛCDM model. Our results show that, whereas there’s a good agreement between our model and the ΛCDM model, the perturbations are much more sensitive to the interaction and can deviate strongly from the standard case for large interaction strengths. Secondly, motivated by our current poor knowledge on the underlying “dark- sector” physics and the need to understand the nature of the two most dominant components of our universe: dark energy and dark matter; we investigate a new scenario in which the two dark components interact via an energy-momentum exchange. By re-writing the evolution equations in a more suitable form, we eliminate previously reported singularities in interacting dark energy models in which dark energy is tested to be vacuum energy with w → −1. This makes it possible to numerically integrate the resulting background and perturbation equations, comparing our results to the standard model. We show that this treatment, yields a simple model that provides a good natural extension to the standard ΛCDM model. We go further to explore in detail the cosmological implications of the interaction strength and the direction of the energy-momentum transfer in vacuum interacting dark energy. This thesis provides useful insights on the possible significance of a dark sector interaction in structure formation and shows that such an interaction provides a good natural explanation for the high value of the Hubble parameters measured by BOSS and SDSS surveys. Indeed a small and positive coupling is shown to alleviate the well-known cosmological coincidence problem.

The microscopic traffic simulation program VISSIM is a powerful tool that has been used by transportation engineers and urban planners around the world. A VISSIM simulation is meant to depict the performance of the physical road network through the use of modeling tools and behavioral parameters. The process which gets the model to the point of matching real world conditions is called calibration and requires a means of relating the real world to the simulated world. The topic of this thesis discusses a new means of calibration using the two-fluid model. The two-fluid model is a macroscopic modeling technique which provides quantitative characteristics of the performance of traffic flow on an urban road network. The model does this by generating a relationship between the travel time, stopped time, and running time per mile. The two-fluid model has been used to evaluate the performance of road networks for decades but now it is possible to use it to calibrate a VISSIM model. For this thesis, the two-fluid model to be used for calibration was generated from data collected on the Orlando, Florida, downtown network in February, 2008, during three traffic peaks for three typical weekdays. The network was then modeled in VISSIM which required a large amount of data regarding network geometry, signal timings, signal coordination schemes, and turning movement volumes. A similar data collection exercise was conducted during November, 2008, to capture the effects of changes that took place in the network during the ten month period. Another VISSIM network was also made to match the conditions of the November network. The February field data was used to successfully calibrate the VISSIM model and the November data was used to validate the calibrated network. The validation proved that the two-fluid models from the November field data and VISSIM data are statistically similar. With the network calibrated and validated, it could be used to perform scenario tests to see how the network performance would be affected by changes to the network. The two-fluid model has often been used to compare two different physical networks or explore how the performance of a single physical network has changed over time. A similar comparison can be done with the two-fluid models from a calibrated, simulated network. By using the original calibrated models as base cases, scenarios ranging from lane closures due to traffic incidents to the addition of a whole new signalized corridor on the network can be modeled in VISSIM and compared with the corresponding base case. This would allow a governing agency to preview the effects of proposed changes.

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.

<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>

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.

Ce travail a été consacré à la simulation numérique des équations de la mécanique des fluides par des méthodes de volumes finis implicites. Tout d’abord, nous avons étudié et mis en place une version implicite du schéma de Roe pour les écoulements monophasiques et diphasiques compressibles. Grâce à la méthode de Newton utilisée pour résoudre les systèmes nonlinéaires, nos schémas sont conservatifs. Malheureusement, la résolution de ces systèmes est très coûteuse. Il est donc impératif d’utiliser des algorithmes de résolution performants. Pour des matrices de grande taille, on utilise souvent des méthodes itératives dont la convergence dépend de leur spectre. Nous avons donc étudié le spectre du système linéaire et proposé une stratégie de Scaling pour améliorer le conditionnement de la matrice. Combinée avec le préconditionneur classique ILU, notre stratégie de Scaling a réduit de façon significative le nombre d’itérations GMRES du système local et le temps de calcul. Nous avons également montré l’intérêt du schéma centré pour la simulation de certains écoulements à faible nombre de Mach. Nous avons ensuite étudié et implémenté la méthode de décomposition de domaine pour les écoulements compressibles. Nous avons proposé une nouvelle variable interface qui rend la méthode du complément de Schur plus facile à construire et nous permet de traiter les termes de diffusion. L’utilisation du solveur itératif GMRES plutôt que Richardson pour le système interface apporte aussi une amélioration des performances par rapport aux autres méthodes. Nous pouvons également découper notre domaine de calcul en un nombre quelconque de sous-domaines. En utilisant la stratégie de Scaling pour le système interface, nous avons amélioré le conditionnement de la matrice et réduit le nombre d’itérations GMRES de ce système. En comparaison avec le calcul distribué classique, nous avons montré que notre méthode est robuste et efficace. / This thesis deals with numerical simulations of compressible fluid flows by implicit finite volume methods. Firstly, we studied and implemented an implicit version of the Roe scheme for compressible single-phase and two-phase flows. Thanks to Newton method for solving nonlinear systems, our schemes are conservative. Unfortunately, the resolution of nonlinear systems is very expensive. It is therefore essential to use an efficient algorithm to solve these systems. For large size matrices, we often use iterative methods whose convergence depends on the spectrum. We have studied the spectrum of the linear system and proposed a strategy, called Scaling, to improve the condition number of the matrix. Combined with the classical ILU preconditioner, our strategy has reduced significantly the GMRES iterations for local systems and the computation time. We also show some satisfactory results for low Mach-number flows using the implicit centered scheme. We then studied and implemented a domain decomposition method for compressible fluid flows. We have proposed a new interface variable which makes the Schur complement method easy to build and allows us to treat diffusion terms. Using GMRES iterative solver rather than Richardson for the interface system also provides a better performance compared to other methods. We can also decompose the computational domain into any number of subdomains. Moreover, the Scaling strategy for the interface system has improved the condition number of the matrix and reduced the number of GMRES iterations. In comparison with the classical distributed computing, we have shown that our method is more robust and efficient.

We develop a two-fluid model (TFM) for heat transfer in dense non-Brownian suspensions. Specifically, we propose closure relations for the inter-phase heat transfer coefficient and the thermal diffusivity of the particle phase based on calibration against experimental data. The model is then employed to simulate non-isothermal flow in an annular Couette cell. We find that, when the shear rate is controlled by the rotation of the inner cylinder, both the shear and thermal gradients are responsible for particle migration. Within the TFM framework, we identify the origin and functional form of a "thermo-rheological" migration force that rationalizes our observations. Furthermore, we apply our model to flow in eccentric Couette cells. Our simulations reveal that the system's heat transfer coefficient is affected by both the classic shear-induced migration of particles and the newly identified thermo-rheological migration effect. Finally, we employed the proposed computational TFM framework to analyze electronics cooling by forced convection for microchannel cooling. We used a suspensions of high thermal conductivity (Boron Nitride) particles in a 3M Fluorinert FC-43 cooling fluid. Three-dimensional simulations were run to quantify the temperature distributions under uniform heating (5 W) and under hot-spot heating (2 W/cm^2) conditions. A 100 K junction level temperature improvement (enhanced thermal spreading) was seen for hot-spot heating and 15 K was observed for uniform heating, demonstrating the enhanced cooling capabilities of dense particulate suspensions of high-conductivity particles, over a clear FC-43 fluid.