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A simple morphological classification of the galaxies in the local Universe shows two main families: (1) the disc galaxies, with spiral arms and in two-thirds of these galaxies a stellar bar; and (2) the elliptical and lenticular galaxies, labelled early-type galaxies (ETGs), which are dominated by a spheroidal stellar component. ETGs are among the most massive galaxies of the local Universe and present a red color, meaning that their stars are old. These galaxies also present a large diversity of stellar dynamics: they may have a regular rotation pattern aligned with the photometry or perpendicular to it; they can present no global rotation at all; or may hold a central stellar component with a rotation axis distinct from the outer stellar body called a Kinematically Distinct Core (KDC). These features observed in the dynamics of the ETGs and their large mass are clearly signs of past interactions, especially signs of galaxy mergers. The main goal of my thesis is to analyse a large sample of high-resolution numerical simulations of binary galaxy mergers. These binary mergers are called "idealized" because they do not take into account the full cosmological context of galaxy formation: two isolated spiral galaxies are launched in an orbit resulting in a merger of the galaxies, the final remnant is an ETG. The statistical analysis of this large sample of simulations enables us to link the initial conditions of the merger to the final merger remnant. I demonstrated that the mass ratio between the spiral progenitors and the orientation of their spins of angular momentum are the main drivers for the formation of fast and slow rotating ETGs and the KDCs. The morphology of the initial spiral (Bulge/Disc ratio) seems also to play a major role for the formation of the different types of ETGs but its impact is not completelly clear, and other simulations are planned to clarify this problem. During my thesis, I also studied the importance of the resolution in the numerical simulations of galaxy mergers. I showed that the number of particles and the size of the computational grid have a predominant role in the final product of the merger. A too low resolution (i.e. too few particles and a coarse grid) can not follow the rapid evolution of the gravitational potential during the merger. In this case, the angular momentum is not as efficiently transfered to the outer parts of the galaxy: the merger remnant keeps thus a strong and regular rotation. At higher resolution, the scattering of the orbit is resolved and the merger remnant may end-up with, under some special initial conditions, a slow rotation and may form a KDC.

Polymer electrolyte membrane (PEM) fuel cells have increasingly become promising green energy sources for automobile and stationary cogeneration applications but its success in commercialization depends on performance optimization and manufacturing cost. The activation losses, expensive platinum catalyst, and water flooding phenomenon are the key factors currently hindering commercialization of PEM fuel cells. These factors are associated with the cathode catalyst layer (CCL), which is about ten micrometers thick. Given the small scale of this layer, it is extremely difficult to study transport phenomena inside the catalyst layer experimentally, either intrusively or non-intrusively. Therefore, mathematical and numerical models become the only means to provide insight on the physical phenomena occurring inside the CCL and to optimize the CCL designs before building a prototype for engineering application. In this thesis research, a comprehensive two-phase mathematical model for the CCL has been derived from the fundamental conservation equations using a volume-averaging method. The model also considers several water transport and physical processes that are involved in the CCL. The processes are: (a) electro-osmotic transport from the membrane to the CCL, (b) back-diffusion of water from the CCL to the membrane, (c) condensation and evaporation of water, and (d) removal of liquid water to the gas flow channel through the gas diffusion layer (GDL). A simple analytical model for the activation overpotential in the CCL has also been developed and an optimization study has been carried out using the analytical activation overpotential formulation. Further, the mathematical model has been simplified for the CCL and an analytical approach has been provided for the liquid water transport in the catalyst layer. The volume-averaged mathematical model of the CCL is finally implemented numerically along with an investigation how the physical structure of a catalyst layer affects fuel cell performance. Since the numerical model requires various effective transport properties, a set of mathematical expressions has been developed for estimating the effective transport properties in the CCL and GDL of a PEM fuel cell. The two-dimensional (2D) numerical model has been compared with the analytical model to validate the numerical results. Subsequently, using this validated model, 2D numerical studies have been carried out to investigate the effect of various physical and wetting properties of CCL and GDL on the performance of a PEM fuel cell. It has been observed that the wetting properties of a CCL control the flooding behavior, and hydrophilic characteristics of the CCL play a significant role on the cell performance. To investigate the effect of concentration variation in the flow channel, a three-dimensional numerical simulation is also presented.

The use of B-spline interpolation functions in the finite element method (FEM) is not a new subject. B-splines have been utilized in finite elements for many reasons. One reason is the higher continuity of derivatives and smoothness of B-splines. Another reason is the possibility of reducing the required number of degrees of freedom compared to a conventional finite element analysis. Furthermore, if B-splines are utilized to represent the geometry of a finite element model, interfacing a finite element analysis program with existing computer aided design programs (which make extensive use of B-splines) is possible. While B-splines have been used in finite element analysis due to the aforementioned goals, it is difficult to find resources that describe the process of implementing B-splines into an existing finite element framework. Therefore, it is necessary to document this methodology. This implementation should conform to the structure of conventional finite elements and only require exceptions in methodology where absolutely necessary. One goal is to implement B-spline interpolation functions in a finite element framework such that it appears very similar to conventional finite elements and is easily understandable by those with a finite element background. The use of B-spline functions in finite element analysis has been studied for advantages and disadvantages. Two-dimensional B-spline and standard FEM have been compared. This comparison has addressed the accuracy as well as the computational efficiency of B-spline FEM. Results show that for a given number of degrees of freedom, B-spline FEM can produce solutions with lower error than standard FEM. Furthermore, for a given solution time and total analysis time B-spline FEM will typically produce solutions with lower error than standard FEM. However, due to a more coupled system of equations and larger elemental stiffness matrix, B-spline FEM will take longer per degree of freedom for solution and assembly times than standard FEM. Three-dimensional B-spline FEM has also been validated by the comparison of a three-dimensional model with plane-strain boundary conditions to an equivalent two-dimensional model using plane strain conditions.

This dissertation attempts to establish an analytical and comprehensive framework to deal with two critical challenges associated with voltage stability analysis: 1. To study the new competitive environment appropriately and give more incentive for reactive power supports, one has to evaluate the impacts of distributed market forces on voltage stability, which complicates the voltage stability analysis. 2. Accurately estimating voltage stability margin online is always the goal of the industry. Industry used to apply static analysis for its computation speed at the cost of losing accuracy. On the other hand, dynamic analysis can result in more accurate estimation, but generally has a huge computation cost. So a challenge is to estimate the voltage stability margin accurately and efficiently at a reasonable cost, especially for large system. Considering the first challenge, this dissertation applied eigenvalue based bifurcation analysis to allocate the contribution of voltage stability. We investigate how parameters of the system influence the bifurcations. Three bifurcations (singularity induced bifurcation, saddle-node and Hopf bifurcation) and their relationship to several commonly used controllers are analyzed. Their parameters’ impact on these bifurcations have been investigated, from which we found a way to allocate the contribution by analyzing the relative positions of the bifurcations. For the second challenge, a new fast numerical scheme is developed to estimate voltage stability margin by intelligently adjusting the load increase ratio. A criterion, named EMD (Equilibrium Manifold Deviation) criterion, is proposed to gauge the accuracy of the estimation. And based on this criterion, a new computation scheme is proposed. The validity of our new approach is proven based on the well-known Runge-Kutta-Fehlberg method, and can be extended to other explicit single-step methods easily. Numerical tests demonstrate that the new approach is very practical and has great potential for industrial applications. This dissertation extends our new numerical scheme to stiff systems. When a system is ill-conditioned, the implicit method would be applied to achieve numerical stability. We further demonstrate the validity to combine the intelligent load adjustment technique with the implicit method to save the computation cost without loss of accuracy. This dissertation also delves into the auto detection of stiffness of the power system, and extends our new numerical scheme to general sytems.

In oil and gas field operations, the dynamic interactions between reservoir and wellbore cannot be ignored, especially during transient flow in the near-wellbore region. As gas hydrocarbons are produced from underground reservoirs to the surface, liquids can come from condensate dropout, water break-through from the reservoir, or vapor condensation in the wellbore. In all three cases, the higher density liquid needs to be transported to the surface by the gas. If the gas phase does not provide sufficient energy to lift the liquid out of the well, the liquid will accumulate in the wellbore. The accumulation of liquid will impose an additional backpressure on the formation that can significantly affect the productivity of the well. The additional backpressure appears to result in a "U-shaped" pressure distribution along the radius in the near-wellbore region that explains the physics of the backflow scenario. However, current modeling approaches cannot capture this U-shaped pressure distribution, and the conventional pressure profile cannot explain the physics of the reinjection. In particular, current steady-state models to predict the arrival of liquid loading, diagnose its impact on production, and screen remedial options are inadequate, including Turner's criterion and Nodal Analysis. However, the dynamic interactions between the reservoir and the wellbore present a fully transient scenario, therefore none of the above solutions captures the complexity of flow transients associated with liquid loading in gas wells. The most satisfactory solution would be to couple a transient reservoir model to a transient well model, which will provide reliable predictive models to link the well dynamics with the intermittent response of a reservoir that is typical of liquid loading in gas wells. The modeling work presented here can be applied to investigate liquid loading mechanisms, and evaluate any other situation where the transient flow behavior of the near-wellbore region of the reservoir cannot be ignored, including system start-up and shut-down.

Squeeze Film Dampers (SFDs) are employed in high-speed Turbomachinery, particularly aircraft jet engines, to provide external damping. Despite numerous successful applications, it is widely acknowledged that the theoretical models used for SFD design are either overly simplified or incapable of taking into account all the features such as cavitation, air entrainment etc., affecting the performance of a SFD. On the other hand, experimental investigation of flow field and dynamic performance of SFDs can be expensive and time consuming. The current work simulates the flow field inside the dynamically deforming annular gap of a SFD using the commercial computational fluid dynamics (CFD) code Fluent and compares the results to the experimental data of San Andrés and Delgado. The dynamic mesh capability of Fluent and a User Defined Function (UDF) was used to replicate the deforming gap and motion of the rotor respectively. Two dimensional simulations were first performed with different combinations of rotor whirl speed, operating pressures and with and without incorporating the cavitation model. The fluid used in the simulations was ISO VG 2 Mobil Velocite no. 3. After the successful use of the cavitation model in the 2D case, a 3D model with the same dimensions as the experimental setup was built and meshed. The simulations were run for a whirl speed of 50 Hz and an orbit amplitude of 74 μm with no through flow and an inlet pressure of 31kPa (gauge). The resulting pressures at the mid-span of the SFD land were obtained. They closely agreed with those obtained experimentally by San Andrés and Delgado.

The "slot-drill" completion method, which utilizes a mechanically cut high-conductivity "slot" in the target formation created using a tensioned abrasive cable, has been proposed as an alternative stimulation technique for shale-gas and other low/ultra-low permeability formations. This thesis provides a comprehensive numerical simulation study on the "slot drill" completion technique. Using a Voronoi gridding scheme, I created representative grid systems for the slot-drill completion, as well as for the case of a vertical well with a single fracture, the case of a horizontal well with multiple hydraulic fractures, and various combinations of these completions. I also created a rectangular slot configuration, which is a simplified approximation of the actual "slot-drill" geometry, and investigated the ability of this rectangular approximation to model flow from the more complicated (actual) slot-drill configuration(s). To obtain the maximum possible diagnostic and analytical value, I simulated up to 3,000 years of production, allowing the assessment of production up to the point of depletion (or boundary-dominated flow). These scenarios provided insights into all the various flow regimes, as well as provided a quantitative evaluation of all completion schemes considered in the study. The results of my study illustrated that the "slot-drill" completion technique was not, in general, competitive in terms of reservoir performance and recovery compared to the more traditional completion techniques presently in use. Based on my modeling, it appears that the larger surface area to flow that multistage hydraulic fracturing provides is much more significant than the higher conductivity achieved using the slot-drill technique. This work provides quantitative results and diagnostic interpretations of productivity and flow behavior for low and ultra-low permeability formations completed using the slot-drill method. The results of this study can be used to (a) help evaluate the possible application of the "slot-drill" technique from the perspective of performance and recovery, and (b) to establish aggregated economic factors for comparing the slot-drill technique to more conventional completion and stimulation techniques applied to low and ultra-low permeability reservoirs.

In recent years, the electronic chip is continuously developing in turning high performance. This trend urges the heat sink of electronic chip to become gradually important, and then that will develop many type of heat sink, which is water-cooling system. Therefore, the purpose of this paper is designing a high efficiency water-cooling element (WCE). The present study mainly aims at three points to bring up: (1) The different type chamber make use of the CFD package software FLUENT to study the pressure drop, velocity field and turbulent intensity deposition. (2) The different plank thickness, thermal conductivity and convection heat transfer coefficient use finite difference method to solve heat diffusion equation, and to confer thermal resistance value. (3) Then, machined this designed WCE and then measured its thermal resistance value. The results show: (1) The pressure drop main effect parameter is inlet velocity. (2) The thermal resistance value main effect parameter is convection heat transfer coefficient. (3) The plank thickness is inverse proportion relation with thermal resistance value. (4) The surface temperature range and mean surface temperature should become reference index in heat sink developmental process. (5) The cooling performance of Type D WCE is optimum in this paper. (6) The design is cross groove on convection surface, which should reduce thermal resistance value.