The dynamic motion of floating wind turbines is studied using numerical simulations. Floating wind turbines in the deep ocean avoid many of the concerns with land-based wind turbines while allowing access to strong stable winds. The full three-dimensional Navier-Stokes equations are solved on a regular structured grid, using a level set method for the free surface and an immersed boundary method for the turbine platform. The tethers, the tower, the nacelle and the rotor weight are included using reduced order dynamic models, resulting in an efficient numerical approach which can handle nearly all the nonlinear wave forces on the platform, while imposing no limitation on the platform motion. Wind is modeled as a constant thrust force and rotor gyroscopic effects are accounted for. Other aerodynamic loadings and aero-elastic effects are not considered. Several tests, including comparison with other numerical, experimental and grid study tests, have been done to validate and verify the numerical approach. Also for further validation, a 100:1 scale model Tension Leg Platform (TLP) floating wind turbine has been simulated and the results are compared with water flume experiments conducted by our research group. The model has been extended to full scale systems and the response of the tension leg and spar buoy floating wind turbines has been studied. The tension leg platform response to different amplitude waves is examined and for large waves a nonlinear trend is seen. The nonlinearity limits the motion and shows that the linear assumption will lead to over prediction of the TLP response. Studying the flow field behind the TLP for moderate amplitude waves shows vortices during the transient response of the platform but not at the steady state, probably due to the small Keulegan-Carpenter number. The effects of changing the platform shape are considered and finally the nonlinear response of the platform to a large amplitude wave leading to slacking of the tethers is simulated. For the spar buoy floating wind turbine, the response to regular periodic waves is studied first. Then, the model is extended to irregular waves to study the interaction of the buoy with more realistic sea state. The results are presented for a harsh condition, in which waves over 17 m are generated, and linear models might not be accurate enough. The results are studied in both time and frequency domain without relying on any experimental data or linear assumption. Finally a design study has been conducted on the spar buoy platform to study the effects of tethers position, tethers stiffness, and platform aspect ratio, on the response of the floating wind turbine. It is shown that higher aspect ratio platforms generally lead to lower mean pitch and surge responses, but it may also lead to nonlinear trend in standard deviation in pitch and heave, and that the tether attachment points design near the platform center of gravity generally leads to a more stable platform in comparison with attachment points near the tank top or bottom of the platform.

A sharp interface cavitation model has been developed for computational fluid dynamics. A phase change model based on a simplification of the Rayleigh-Plesset equation is combined with a second-order volume-of-fluid method with a constructed level set function in an incompressible fluid dynamics model. The semi-implicit phase change model predicts the mass flux between liquid and vapor phases based on the difference between the local pressure at the interface and the vapor pressure at the ambient conditions. The mass flux between phases determines the volume source strength and jump velocities at the interface. To prevent difficulties computing derivatives near the interface, two separate velocity fields from the momentum equation are solved considering the interface velocity jump. The interface velocity jump is extended into the liquid and vapor domains using a fast marching method. A description of the mathematical and numerical models is included, as well as an explanation and derivation of the phase change model. Hypothetical vapor bubble problems are demonstrated to test the components of the model. Finally, cavity evolution on a hydrofoil is computed for a range of parameters.

A numerical study of flow of power law fluid in an elbow bend has been carried out. The motivation behind this study is to analyze the velocity profiles, especially the pattern of the secondary flow of power law fluid in a bend as there are several important technological applications to which such a problem has relevance. This problem especially finds applications in the polymer processing industries and food industries where the fluid needs to be pumped through bent pipes. Hence, it is very important to study the secondary flow to determine the amount of power required to pump the fluid. This problem also finds application in heat exchangers.

Dans cette dissertation, nous considérons l’écoulement des liquides conducteurs d’électricité dans un champ magnétique externe. De tels écoulements sont décrits par les équations de la magnétohydrodynamique (MHD) quasi-statique, et sont fréquemment rencontrés dans des applications pratiques. Il suit qu’il y a un intérêt fort pour des outils numérques qui peuvent simuler ces écoulements dans des géometries complexes. La première partie de cette thèse (chapitres 2 et 3) est dédiée à la présentation de la machinerie numérique qui a été utilisée et implémentée afin de résoudre les équations de la MHD quasi-statistique (incompressible). Plus précisément, nous avons contribué au développement d’un solveur volumes finis non-structuré parallèle. La discussion sur ces méthodes est accompagnée d’une analyse numérique qui est aussi valable pour des mailles non-structurées. Dans le chapitre 3, nous vérifions notre implémentation par la simulation d’un certain nombre de cas tests avec un accent sur des écoulements dans un champ magnétique intense. Dans la deuxième partie de cette thèse (chapitres 4-6), nous avons utilsé ce solveur pour étudier des écoulements MHD de proche paroi . La première géometrie considérée (chapitre 4) est celle d’une conduite circulaire infini d’axe à haut nombre de Hartmann. Nous avons investitgué la sensitivité des résultats numériques au schéma de discrétisation et à la topologie de la maille. Nos résultats permettent de caractériser in extenso l’écoulement MHD dans une conduite avec des bords bien conducteurs par moyen des lois d’échelle. Le sujet du cinquième chapitre est l’écoulement dans une conduite toroïdale à section carée. Une étude du régime laminaire confirme une analyse asymptotique pour ce qui concerne les couches de cisaillement. Nous avons aussi effectué des simulations des écoulements turbulents afin d’évaluer l’effet d’un champ magnétique externe sur l’état des couches limites limites. Finalement, dans le chapitre 6, nous investiguons l’écoulement MHD et dans un U-bend et dans un coude arrière. Nous expliquons comment générer une maille qui permet de toutes les couches de cisaillement à un coût computationelle acceptable. Nous comparons nos résultats aux solutions asymptotiques.

Capturing the effects of detailed-chemistry on turbulent combustion processes is a central challenge faced by the numerical combustion community. However, the inherent complexity and non-linear nature of both turbulence and chemistry require that combustion models rely heavily on engineering approximations to remain computationally tractable. This thesis proposes a computationally efficient algorithm for modelling detailed-chemistry effects in turbulent diffusion flames and numerically predicting the associated flame properties. The cornerstone of this combustion modelling tool is the use of parallel Adaptive Mesh Refinement (AMR) scheme with the recently proposed Flame Prolongation of Intrinsic low-dimensional manifold (FPI) tabulated-chemistry approach for modelling complex chemistry. The effect of turbulence on the mean chemistry is incorporated using a Presumed Conditional Moment (PCM) approach based on a beta-probability density function (PDF). The two-equation k-w turbulence model is used for modelling the effects of the unresolved turbulence on the mean flow field. The finite-rate of methane-air combustion is represented here by using the GRI-Mech 3.0 scheme. This detailed mechanism is used to build the FPI tables. A state of the art numerical scheme based on a parallel block-based solution-adaptive algorithm has been developed to solve the Favre-averaged Navier-Stokes (FANS) and other governing partial-differential equations using a second-order accurate, fully-coupled finite-volume formulation on body-fitted, multi-block, quadrilateral/hexahedral mesh for two-dimensional and three-dimensional flow geometries, respectively. A standard fourth-order Runge-Kutta time-marching scheme is used for time-accurate temporal discretizations. Numerical predictions of three different diffusion flames configurations are considered in the present work: a laminar counter-flow flame; a laminar co-flow diffusion flame; and a Sydney bluff-body turbulent reacting flow. Comparisons are made between the predicted results of the present FPI scheme and Steady Laminar Flamelet Model (SLFM) approach for diffusion flames. The effects of grid resolution on the predicted overall flame solutions are also assessed. Other non-reacting flows have also been considered to further validate other aspects of the numerical scheme. The present schemes predict results which are in good agreement with published experimental results and reduces the computational cost involved in modelling turbulent diffusion flames significantly, both in terms of storage and processing time.

Capturing the effects of detailed-chemistry on turbulent combustion processes is a central challenge faced by the numerical combustion community. However, the inherent complexity and non-linear nature of both turbulence and chemistry require that combustion models rely heavily on engineering approximations to remain computationally tractable. This thesis proposes a computationally efficient algorithm for modelling detailed-chemistry effects in turbulent diffusion flames and numerically predicting the associated flame properties. The cornerstone of this combustion modelling tool is the use of parallel Adaptive Mesh Refinement (AMR) scheme with the recently proposed Flame Prolongation of Intrinsic low-dimensional manifold (FPI) tabulated-chemistry approach for modelling complex chemistry. The effect of turbulence on the mean chemistry is incorporated using a Presumed Conditional Moment (PCM) approach based on a beta-probability density function (PDF). The two-equation k-w turbulence model is used for modelling the effects of the unresolved turbulence on the mean flow field. The finite-rate of methane-air combustion is represented here by using the GRI-Mech 3.0 scheme. This detailed mechanism is used to build the FPI tables. A state of the art numerical scheme based on a parallel block-based solution-adaptive algorithm has been developed to solve the Favre-averaged Navier-Stokes (FANS) and other governing partial-differential equations using a second-order accurate, fully-coupled finite-volume formulation on body-fitted, multi-block, quadrilateral/hexahedral mesh for two-dimensional and three-dimensional flow geometries, respectively. A standard fourth-order Runge-Kutta time-marching scheme is used for time-accurate temporal discretizations. Numerical predictions of three different diffusion flames configurations are considered in the present work: a laminar counter-flow flame; a laminar co-flow diffusion flame; and a Sydney bluff-body turbulent reacting flow. Comparisons are made between the predicted results of the present FPI scheme and Steady Laminar Flamelet Model (SLFM) approach for diffusion flames. The effects of grid resolution on the predicted overall flame solutions are also assessed. Other non-reacting flows have also been considered to further validate other aspects of the numerical scheme. The present schemes predict results which are in good agreement with published experimental results and reduces the computational cost involved in modelling turbulent diffusion flames significantly, both in terms of storage and processing time.

This thesis evaluates performance of a non-mechanical conduit valve that was designed for the purpose of this research. The motivation came from the need for a cooling system of portable computers (e.g. laptops and netbooks). As the technology of micro-processors in portable computers advances, they will generate more heat, requiring a more effective and efficient way to cool the system. Based on this fact, a new method of heat dissipation using a single-phase liquid (i.e. water) instead of air was examined. This potentially allowed 80 times more heat dissipation, which translates to better and faster computers for the near future. In designing a single-phase-liquid micro-scale cooling system, various pump mechanisms and their functionalities were considered. It was concluded that a diaphragm pump design is the most effective candidate for this cooling system. The essential component when designing a diaphragm pump is a valve; however, the main issues in selecting a valve are its mechanics and required maintenance. Thus, the non-mechanical valvular conduit, which uses no moving mechanism, was studied through a combination of numerical/computational and experimental methods. The non-mechanical valvular conduit is a micro-channel with a complex geometry; hence, this conduit uses the principle of pressure resistance in the channel flow such that the flow is uni-directional. Through the numerical study, the valvular conduit design’s geometric dimensions were optimized. Then numerical simulations of the pumping/oscillating sequence of the valvular conduit were conducted to examine the effectiveness of the valve when placed in use for a diaphragm pump. It was found that the non-mechanical valve was 38 % more effective in the favorable direction than the opposite direction. As for the necessary heat dissipation, this conduit design demonstrates a great potential to dissipate the thermal design power (TDP) of Intel Pentium D processor (i.e. 130 [W]). During the experiments, the non-mechanical valve confirmed the numerical results. The experimental results also demonstrated that the favorable direction flow produced 244 % less pressure resistance than the opposite direction flow. It was concluded that the non-mechanical valvular conduit can be an effective application for diaphragm pumps in macro and micro-scale without any possibility of obstructing a mechanism.

Turbulent buoyant jets are a major feature in fire hazards. The solution of the Reynolds Averaged Navier-Stokes (RANS) equations through computational fluid dynamic (CFD) techniques allow such flows to be simulated. The use of Reynolds averaging requires an empirical model to close the set of equations, this is known as the turbulence model. This thesis undertakes to investigate linear and nonlinear approaches to turbulence modelling and to apply the knowledge gained to the simulation of compartment fires. The principle contribution of this work is the reanalysis of the standard k- ε turbulence model and the implementation and application of more sophisticated models as applied to thermal plumes. Validation in this work, of the standard k- ε model against the most recent experimental data, counters the established view that the model is inadequate for the simulation of buoyant flows. Examination of previous experimental data suggests that the measurements were not taken in the self-similar region resulting in misleading comparisons with published numerical solutions. This is a significant conclusion that impacts of the general approach taken to modelling turbulence in this field. A number of methods for modelling the Reynolds stresses and the turbulent scalar fluxes have been considered and, in some cases for the first time, are applied to nonisothermal flows. The relative influence of each model has been assessed enabling its performance to be gauged. The results from this have made a valuable contribution to the knowledge in the field and have enabled the acquired experience to be applied to the simulation of compartment fires. The overall conclusion drawn from this thesis is that for the simulation of compartment fires, the most appropriate approach with current computational resources, is still the buoyancy corrected standard k- ε model. However, the turbulence scalar flux should be modelled by the generalised gradient diffusion hypothesis (GGDH) rather than the eddy-diffusivity assumption.

Internal waves in the deep ocean play a deciding role in processes such as climate change and nutrient cycles. Winds and tidal currents over topography feed energy into internal waves at large scales; through nonlinear interaction the energy then cascades to turbulence scales and contributes to deep-ocean mixing. The connection of internal waves to deep-ocean mixing is what makes them important. In this thesis we address the problem of energy transfer in internal waves by modelling a two-dimensional flow over idealized topography and analysing the spectra of the generated wave fields. The main tool used is the nonparametric spectral analysis, some aspects of which are reviewed in one of the chapters. The numerical experiments were performed for a number of latitudes, topographies and background flows. The wave field generated by tide-topography interaction includes both progressive and trapped internal waves. The wave spectrum was found to exhibit a self-similar structure with prominent peaks at tidal harmonics and interharmonics, whose magnitudes decay exponentially as a function of the frequency. Subharmonics are generated by an instability of tidal beams, which is particularly strong for near-critical latitudes, where the Coriolis frequency is half the tidal frequency; other interharmonics are produced through resonant and non-resonant triad wave-wave interaction. As the triad interaction can be either resonant or non-resonant, some harmonics and interharmonics correspond to progressive waves, if the frequency is within the free internal wave range, while the others are trapped waves if the frequency is outside the range. Spatial scales of harmonics and interharmonics were investigated. In particular, it was shown that interharmonics typically have smaller vertical scales. Through the use of spatial analysis it was shown that there is a discrete number of wave-wave interactions responsible for the total energy transfer. The results of the thesis provide insight into the complex nature of internal wave interactions and may be helpful for interpreting recent observational results.

Internal waves in the deep ocean play a deciding role in processes such as climate change and nutrient cycles. Winds and tidal currents over topography feed energy into internal waves at large scales; through nonlinear interaction the energy then cascades to turbulence scales and contributes to deep-ocean mixing. The connection of internal waves to deep-ocean mixing is what makes them important. In this thesis we address the problem of energy transfer in internal waves by modelling a two-dimensional flow over idealized topography and analysing the spectra of the generated wave fields. The main tool used is the nonparametric spectral analysis, some aspects of which are reviewed in one of the chapters. The numerical experiments were performed for a number of latitudes, topographies and background flows. The wave field generated by tide-topography interaction includes both progressive and trapped internal waves. The wave spectrum was found to exhibit a self-similar structure with prominent peaks at tidal harmonics and interharmonics, whose magnitudes decay exponentially as a function of the frequency. Subharmonics are generated by an instability of tidal beams, which is particularly strong for near-critical latitudes, where the Coriolis frequency is half the tidal frequency; other interharmonics are produced through resonant and non-resonant triad wave-wave interaction. As the triad interaction can be either resonant or non-resonant, some harmonics and interharmonics correspond to progressive waves, if the frequency is within the free internal wave range, while the others are trapped waves if the frequency is outside the range. Spatial scales of harmonics and interharmonics were investigated. In particular, it was shown that interharmonics typically have smaller vertical scales. Through the use of spatial analysis it was shown that there is a discrete number of wave-wave interactions responsible for the total energy transfer. The results of the thesis provide insight into the complex nature of internal wave interactions and may be helpful for interpreting recent observational results.