The Richtmyer-Meshkov instability (RMI) in the convergent geometry is numerically studied in the framework of ideal magnetohydrodynamics (MHD) and two-fluid plasma in this thesis. The converging RMI usually occurs along with the Rayleigh-Taylor instability (RTI) due to the non-uniform motion or continuous acceleration of the interface. First, we investigate the interaction between a converging cylindrical shock and double density interfaces in the presence of a saddle magnetic field with ideal MHD model. We show that the RMI is suppressed by the magnetic field . However, the extent of the suppression varies on the interface which leads to non-axisymmetric growth of the perturbations. The degree of asymmetry increases when the seed field strength increases. The perturbation amplitude is affected by the competition mechanism between RMI and RTI. It increases when RMI dominates RTI while decreases when RTI dominates. Then, we research the two-fluid plasma RMI of a cylindrical density interface without an initial magnetic field. Varying the Debye length scale, we examine the effects of the coupling between the electron and ion fluids. The charge separation is responsible for the self-generated electromagnetic fields. We show that the Biermann battery effect dominates the generation of magnetic field when the coupling effect is weak. In addition to the RT stabilization effect during flow deceleration, the interfaces are accelerated by the induced Lorentz force. As a consequence, the perturbations develop into the RTI, leading to an enhancement of the perturbation amplitude compared with the hydrodynamic case. Finally, we investigate the linear evolution of two-fluid plasma RMI. We show that the increase of perturbation amplitude is almost contributed by the ion shock-interface interaction. We also examine the effect of magnetic field in the streamwise direction. For a short duration after the ion shock-interface interaction, the growth rate is similar for different initial magnetic field strengths. As time progresses the suppression of the instability due to the magnetic field is observed. The growth rate shows oscillations with a frequency that is related to the ion or electron cyclotron frequency. The instability is suppressed due to the vorticity being transported away from the interface.

The ideal two-fluid plasma model is a more generalized plasma model compared to the ideal MHD and it couples the ion and electron Euler equations via Maxwell's equations. Two-fluid plasma model is essential when the ion and electron fluids are at different temperatures. In this work, a fundamental investigation on the effect of non-dimensional light speed, ion-to-electron mass ratio and plasma beta on the plasma dynamics in the Brio-Wu shock tube Riemann problem is presented. A one dimensional finite volume code is developed based on the macroscopic governing equations, with second order accuracy in space and time. The source terms are treated implicitly and the homogeneous flux terms are treated explicitly. The credibility of the numerical results is assessed by performing several linear and nonlinear tests. Realistic light speed results in increasing the stiffness of the equations and severe time step restriction, which poses a challenge to the numerical simulations. In the context of the Brio-Wu shock tube problem, it is observed that the light speed is not important with respect to the hydrodynamics. However, light speed does affect the magnitude of the self generated electric field. Mass ratio affects the electron plasma dynamics. The speed of the fast moving electron plasma waves changes with the mass ratio. The results obtained using a mass ratio of 500 are in close agreement with that of realistic mass ratio of 1836. Increasing plasma beta suppresses the amplitude of the fast moving electron plasma waves.

In this thesis, we study a two fluid system which describes the motion of two charged particles in a strict neutral incompressible plasma. We study the well-posdness of the system in both space dimensions two and three. Regardless of the size of the initial data, we prove the global well-posedness of the Cauchy problem when the space dimension is two. In space dimension three, we construct global weak-solutions, and we prove the local well-posedness of Kato-type solutions. These solutions turn out to be global when the initial data are sufficiently small. We also study the stability of the solution around zero given that the initial data is small and has sufficient regularity. It turns out that our system is a system of regularity-loss and the L2 norm of lower derivatives of the solution decays. At last, this two fluid system can be used to derive the classic MHD at least formally. Arsenio, Ibrahim and Masmoudi (2015) proved that the two fluid system converges to MHD under some constraints. We showed numerically that the two fluid system converges to MHD with no such constraint and found the approximate converge rate. / Graduate

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 CFD model to simulate two-phase flow in refrigerant ejectors is described. This work is part of an effort to develop the ejector expansion refrigeration cycle, a device which increases performance of a standard vapor compression cycle by replacing the throttling valve with a work-producing ejector. Experimental results have confirmed the performance benefit of the ejector cycle, but significant improvement can be obtained by optimally designing the ejector. The poorly understood two-phase, non-equilibrium flow occuring in the ejector complicates this task. The CFD code is based on a parabolic two-fluid model. The applicable two-phase flow conservation equations are presented. Also described are the interfacial interaction terms, important in modelling non-equilibrium effects. Other features of the code, such as a mixing length turbulence model and wall function approximation, are discussed. Discretization of the equations by the control volume method and organization of the computer program is described. Code results are shown and compared to experimental data. It is shown that experimental pressure rise through the mixing section matches well against code results. Variable parameters in the code, such as droplet diameter and turbulence constants, are shown to have a large influence on the results. Results are shown in which an unexpected problem, separation in the mixing section, occurs. Also described is the distribution of liquid across the mixing section, which matches qualitative experimental observations. From these results, conclusions regarding ejector design and two-phase CFD modelling are drawn. / Ph. D.

Reatores de leito fluidizado circulante são intensamente utilizados em aplicações de larga escala como craqueamento catalítico de petróleo e combustão de carvão. Projeto e desenvolvimento nestas áreas são fortemente baseados em plantas de demonstração, a custos elevadíssimos. Nesse contexto, tratamentos utilizando mecânica dos fluidos computacional assumem considerável relevância. Os complexos padrões de escoamento gás-sólido que se desenvolvem nos reatores de leito fluidizado circulante determinam taxas de reação e exigem, portanto, descrições hidrodinâmicas rigorosas. Os modelos Eulerianos do contínuo ou de dois fluidos são correntemente considerados a escolha mais prática na busca destas descrições. Estas formulações são baseadas na aplicação da hipótese de meio contínuo tanto para fases macroscopicamente contínuas quanto dispersas. Neste trabalho, desenvolve-se simulações numéricas para descrever processos hidrodinâmicos e reativos em reatores de leito fluidizado circulante aplicando modelagem de dois fluidos. Considera-se situações típicas de combustão em leito fluidizado circulante de carvão mineral. Como processo reativo considera-se a absorção de dióxido de enxofre por calcário. Realiza-se análises hidrodinâmicas, e de efeitos hidrodinâmicos sobre a reação de interesse. Realiza-se simulações de regime permanente e de regime transiente. Mostra-se que as simulações de regime permanente permitem análises qualitativas do processo, e provêem condições iniciais para simulações transientes diretamente no regime de escoamento estatisticamente permanente. Em relação à hidrodinâmica, conclui-se que os modelos de dois fluidos correntes são ainda bastante crus. São claramente necessárias melhores descrições reológicas e relações constitutivas sub-grade mais acuradas. Em relação à reação química, conclui-se que predições reativas acuradas somente poderão ser obtidas se descrições hidrodinâmicas rigorosas forem combinadas com descrições reativas igualmente rigorosas. / Circulating fluidized bed reactors are widely used in large scale applications such as catalytic cracking of petrol and coal combustion. Development and design in those areas are strongly based on demonstration plants, at extremely high costs. In this context, treatments applying computational fluid mechanics assume considerable relevance. The complex gas-solid flow patterns which develop inside the circulating fluidized bed reactors determine reaction rates, so that rigorous hydrodynamic descriptions are required. The continuum Eulerian or two-fluid models are currently considered the more practical choice for providing such descriptions. Those formulations are based on the application of the continuum hypothesis for both macroscopically continuous and dispersed phases. In this work numerical simulation is performed to describe both hydrodynamics and reactive processes in circulating fluidized beds applying two-fluid modeling. Typical situations of circulating fluidized bed coal combustion are considered. The reactive process considered is the absorption of sulfur dioxide by limestone. Analyses are performed of hydrodynamics, and regarding hydrodynamic effects over the concerning reaction. Both steady state and transient simulations are performed. It is shown that steady state simulations allow qualitative analyses, and do provide initial conditions for transient runs straightly inside the statistical steady state flow regime. Concerning hydrodynamics, it is concluded that the current two-fluid models are still very crude. Clearly, better rheological descriptions are required alongside with more accurate sub-grid constitutive relations. Regarding chemical reaction, it is concluded that accurate reactive predictions shall only be found if rigorous hydrodynamic descriptions are combined with equally rigorous reaction descriptions.

Reatores de leito fluidizado circulante são intensamente utilizados em aplicações de larga escala como craqueamento catalítico de petróleo e combustão de carvão. Projeto e desenvolvimento nestas áreas são fortemente baseados em plantas de demonstração, a custos elevadíssimos. Nesse contexto, tratamentos utilizando mecânica dos fluidos computacional assumem considerável relevância. Os complexos padrões de escoamento gás-sólido que se desenvolvem nos reatores de leito fluidizado circulante determinam taxas de reação e exigem, portanto, descrições hidrodinâmicas rigorosas. Os modelos Eulerianos do contínuo ou de dois fluidos são correntemente considerados a escolha mais prática na busca destas descrições. Estas formulações são baseadas na aplicação da hipótese de meio contínuo tanto para fases macroscopicamente contínuas quanto dispersas. Neste trabalho, desenvolve-se simulações numéricas para descrever processos hidrodinâmicos e reativos em reatores de leito fluidizado circulante aplicando modelagem de dois fluidos. Considera-se situações típicas de combustão em leito fluidizado circulante de carvão mineral. Como processo reativo considera-se a absorção de dióxido de enxofre por calcário. Realiza-se análises hidrodinâmicas, e de efeitos hidrodinâmicos sobre a reação de interesse. Realiza-se simulações de regime permanente e de regime transiente. Mostra-se que as simulações de regime permanente permitem análises qualitativas do processo, e provêem condições iniciais para simulações transientes diretamente no regime de escoamento estatisticamente permanente. Em relação à hidrodinâmica, conclui-se que os modelos de dois fluidos correntes são ainda bastante crus. São claramente necessárias melhores descrições reológicas e relações constitutivas sub-grade mais acuradas. Em relação à reação química, conclui-se que predições reativas acuradas somente poderão ser obtidas se descrições hidrodinâmicas rigorosas forem combinadas com descrições reativas igualmente rigorosas. / Circulating fluidized bed reactors are widely used in large scale applications such as catalytic cracking of petrol and coal combustion. Development and design in those areas are strongly based on demonstration plants, at extremely high costs. In this context, treatments applying computational fluid mechanics assume considerable relevance. The complex gas-solid flow patterns which develop inside the circulating fluidized bed reactors determine reaction rates, so that rigorous hydrodynamic descriptions are required. The continuum Eulerian or two-fluid models are currently considered the more practical choice for providing such descriptions. Those formulations are based on the application of the continuum hypothesis for both macroscopically continuous and dispersed phases. In this work numerical simulation is performed to describe both hydrodynamics and reactive processes in circulating fluidized beds applying two-fluid modeling. Typical situations of circulating fluidized bed coal combustion are considered. The reactive process considered is the absorption of sulfur dioxide by limestone. Analyses are performed of hydrodynamics, and regarding hydrodynamic effects over the concerning reaction. Both steady state and transient simulations are performed. It is shown that steady state simulations allow qualitative analyses, and do provide initial conditions for transient runs straightly inside the statistical steady state flow regime. Concerning hydrodynamics, it is concluded that the current two-fluid models are still very crude. Clearly, better rheological descriptions are required alongside with more accurate sub-grid constitutive relations. Regarding chemical reaction, it is concluded that accurate reactive predictions shall only be found if rigorous hydrodynamic descriptions are combined with equally rigorous reaction descriptions.

Results from direct numerical simulations (DNS) of multiphase bubbly flows in vertical and horizontal channels were compared to averaged models of multiphase flows (two-fluid model etc.). The data from the direct numerical simulation were also used to calibrate and improve the averaged models. Steady state laminar flow in a vertical channel was analyzed first. Results from direct numerical simulations are compared with prediction of the steady-state two-fluid model of Antal, Lahey, and Flaherty (1991). The simulations are done assuming a two-dimensional system and the model coefficients are adjusted slightly to match the data for upflow. The model is then tested by comparisons with different values of flow rate and gravity, as well as down flow. Results agree reasonably in the middle of the channel. However, for upflow, model performs poorly near the no-slip wall. To better understand the flow with rising bubbles hugging the no-slip wall, detailed direct numerical simulations of the problem were performed in three dimensions. Deformability of the bubbles was found to play a significant role in the flow structure and averaged flow rate. Finally, the transient buoyancy driven motion of two-dimensional bubbles across a domain bounded by two horizontal walls is studied by. The bubbles are initially released next to the lower wall and as they rise, they disperse. Eventually all the bubbles collect at the top wall. The goal of the study is to examine how a simple one-dimensional model for the averaged void fraction captures the unsteady bubble motion. By using void fraction dependent velocities, where the exact dependency is obtained from simulations of homogeneous bubbly flows, the overall dispersion of the bubbles is predicted. Significant differences remain, however. Results suggest that bubble dispersion by the bubble induced liquid velocity must be included, and by using a simple model for the bubble dispersion improved agreement is found.

O método ISPH (do inglês, Incompressible Smoothed Particle Hydrodynamics) é um método de aproximação livre de malha que, através de um conjunto finito de partículas e uma formulação completamente Lagrangeana, permite a solução de diversos tipos de escoamentos. Entretanto, sua aplicação para escoamentos bifásicos ainda é um desafio, principalmente no que refere-se à manutenabilidade da interface entre fluidos. Diante disso, nesta tese é apresentado o desenvolvimento de um código numérico baseado no método ISPH, sendo propostas duas técnicas de tratamento de interface. Para tanto é realizado um estudo a cerca do método, considerando diferentes metodologias, e analisando pontos específicos, tais como a solução do campo de pressões. São apresentados resultados que mostram a eficácia do método, tanto em escoamentos monofásicos, quanto em escoamentos multifásicos, onde, neste caso, são destacadas as melhorias obtidas através das técnicas de tratamento de interface propostas. Por fim, é realizado um estudo do comportamento de misturas bifásicas, com referência ao fenômeno da inversão de fase / Incompressible Smoothed Particle Hydrodynamics (ISPH) method is a meshless approximation that has been used to simulate several types of fluid flows, through a finite particle set and fully lagrangian formulation. The application of ISPH method in two-fluid flow simulations however, has presented many challenges, specially related to the presence of the interface between different fluids. Thus, we present in this study the development of a numerical code based on ISPH, introducing novel interface treatment techniques. A thorough study about this method is provided, considering different methodologies and analysing specific points such as the position of the interface and the obtained pressure field. Results have been presented to show the methods developed in this thesis efficiently simulate two-fluid flows, illustrating the improvements achieved by the proposed interface treatment techniques. Finally, a study of biphasic mixture behavior is carried out with reference to phase inversion phenomena