L'objectif de cette thèse est d'analyser l'influence des non linéarités, du comportement rhéologique des fluides rhéofluidifiants, sur les conditions de stabilité et de transition vers la turbulence. Dans un premier temps, une analyse linéaire de stabilité avec une approche modale a été réalisée. Les résultats obtenus mettent clairement en évidence l'effet stabilisant de la rhéofluidification. Ensuite, une analyse faiblement non linéaire de stabilité a été menée en vue d'examiner l'influence de la perturbation de la viscosité sur la stabilité vis à vis de perturbations d'amplitude finie. L'analyse de la contribution des termes non linéaires d'inertie et visqueux montre que, contrairement aux termes d'inertie, les termes non linéaires visqueux ont tendance à accélérer l'écoulement et favoriser une bifurcation sur-critique. Les effets rhéofluidifiants tendent à réduire la dissipation visqueuse. Finalement, une analyse fortement non linéaire de stabilité a été conduite en utilisant les techniques de suivi de branches de solutions par des méthodes de continuation. Pour pouvoir traiter les termes visqueux fortement non linéaires, un code de calcul pseudo-spectral a été développé. Des solutions non linéaires d'équilibre ont été obtenues et caractérisées pour différentes valeurs des paramètres rhéologiques / The aim of this study is to understand the influence of the nonlinear rheological behaviour of the shear-thinning fluids on the flow stability and transition to turbulence. First, a linear stability analysis using modal approach was carried out. Results clearly highlight the stabilizing effect of shear-thinning. Then, as a first approach to take into account nonlinear effects of viscosity perturbation on the flow stability, a weakly nonlinear stability analysis is performed in the neighbourhood of the critical conditions. Results indicate that shear-thinning reduces the viscous dissipation and, in contrast to inertial terms, the nonlinear viscous terms tend to accelerate the flow and act in favour of supercritical bifurcation. Finally, a nonlinear stability analysis is done by following solution branches in the parameter space using continuation techniques. To deal with highly nonlinear viscous terms, a pseudo-spectral code is developed. Nonlinear equilibrium solutions was found and characterized for various values of the rheological parameters

Philosophiae Doctor - PhD / Fitted Numerical Methods for Delay Di erential Equations Arising in Biology E.B.M. Bashier PhD thesis, Department of Mathematics and Applied Mathematics,Faculty of Natural Sciences, University of the Western Cape. This thesis deals with the design and analysis of tted numerical methods for some delay di erential models that arise in biology. Very often such di erential equations are very complex in nature and hence the well-known standard numerical methods seldom produce reliable numerical solutions to these problems. Ine ciencies of these methods are mostly accumulated due to their dependence on crude step sizes and unrealistic stability conditions.This usually happens because standard numerical methods are initially designed to solve a class of general problems without considering the structure of any individual problems. In this thesis, issues like these are resolved for a set of delay di erential equations. Though the developed approaches are very simplistic in nature, they could solve very complex problems as is shown in di erent chapters.The underlying idea behind the construction of most of the numerical methods in this thesis is to incorporate some of the qualitative features of the solution of the problems into the discrete models. Resulting methods are termed as tted numerical methods. These methods have high stability properties, acceptable (better in many cases) orders of convergence, less computational complexities and they provide reliable solutions with less CPU times as compared to most of the other conventional solvers. The results obtained by these methods are comparable to those found in the literature. The other salient feature of the proposed tted methods is that they are unconditionally stable for most of the problems under consideration.We have compared the performances of our tted numerical methods with well-known software packages, for example, the classical fourth-order Runge-Kutta method, standard nite di erence methods, dde23 (a MATLAB routine) and found that our methods perform much better. Finally, wherever appropriate, we have indicated possible extensions of our approaches to cater for other classes of problems. May 2009.

This diploma thesis describes the design and assessment of steel structural design of the steel aggregate bins including roofing. The construction has a ground plan of about 33 x 9 m and it is divided into 8 cells bins. Main material is steel, grade S355 and S235. There is developed a static analysis of the main load-bearing parts of the structure, including joints and selected details.

In this study, the initial hydrostatic stability, the hydrostatic stability and the structure realibility of three different barge-shaped vessels is simulated and evaluated in order to see which of the vessels would be the most optimal to use for deployment of wave energy converters, WECs. The vessels differ in their hull type: Bulbous-bow hull vessel, Barge hull vessel and Modified-barge hull vessel. In order to do the evaluation, the hull of each vessel is designed in DELFTship and further design is proceeded in SolidWorks 2014. Structural strength analysis is performed in SolidWorks 2014 and hydrostatic properties are simualted in Ansys Aqwa 16.0. The collected results are pointing at that the Modified-barge hull vessel is slightly superior to the others in terms of hydrostatic stability, while the structure stability is equal. The results of this study will provide a foundation for further evaluation of vessels capable of deploying wave energy converters.

Thesis (PhD (Electrical and Electronic Engineering))--University of Stellenbosch, 2011. / AFRIKAANSE OPSOMMING: Hierdie proefskrif handel oor die natuurlike balanserings meganismes van veelvlakkige en modulêre omsetters wat fase-skuif dragolf puls wydte modulasie gebruik. Die meganismes kan in twee hoof groepe verdeel word: ‘n swak balanserings meganisme wat afhanklik is van die oorvleuling van die skakelfunksies en ‘n sterk meganisme wat voorkom ongeag of die skakelfunksies oorvleul al dan nie. Die sterk meganisme verdeel verder in twee subgroepe, ‘n direkte oordrag van onbalans energie en ‘n meganisme wat afhang van die verliese in die stelsel. Elkeen van die meganismes word aan die hand van ‘n omsetter topologie waarin die spesifieke meganisme oorheers beskryf en ontleed. In die ondersoek word klem geplaas op die daarstelling van uitdrukkings om die tydskonstantes van herbalansering na ’n afwyking vir elk van die omsetter toplologieë te beskryf. / ENGLISH ABSTRACT: This thesis investigates the natural balancing mechanisms in multilevel and modular converters using phase shifted carrier pulse width modulation. Two groups of mechanisms are identified; a weak balancing mechanism that is only present when the switching functions are interleaved and a strong mechanism that occurs irrespective of the interleaving of the switching functions. It is further shown that the strong balancing mechanism can be divided into a balancing mechanism that depends on the direct exchange of unbalance energy and a loss based balancing mechanism. Each of the mechanisms is discussed and analysed using a converter where the specific mechanism dominates as example. Emphasis is placed on the calculation of the rebalancing time constant following a perturbation. Closed form expressions for the rebalancing time constants for each of the analysed converters are presented.

This work is concerned with stability and receptivity analysis as well as studies on control of the laminar-turbulent transition in boundary-layer flows through direct numerical simulations. Various flow configurations are considered to address flow around straight and swept wings. The aim of this study is to contribute to a better understanding of stability characteristics and different means of transition control of such flows which are of great interest in aeronautical applications. Acoustic receptivity of flow over a finite-thickness flat plate with elliptic leading edge is considered. The objective is to compute receptivity coefficient defined as the relative amplitude of acoustic disturbances and TS wave. The existing results in the literature for this flow case plot a scattered image and are inconclusive. We have approached this problem in both compressible and incompressible frameworks and used high-order numerical methods. Our results have shown that the generally-accepted level of acoustic receptivity coefficient for this flow case is one order of magnitude too high. The continuous increase of computational power has enabled us to perform global stability analysis of three-dimensional boundary layers. A swept flat plate of FSC type boundary layer with surface roughness is considered. The aim is to determine the critical roughness height for which the flow becomes turbulent. Global stability characteristics of this flow have been addressed and sensitivity of such analysis to domain size and numerical parameters have been discussed. The last flow configuration studied here is infinite swept-wing flow. Two numerical set ups are considered which conform to wind-tunnel experiments where passive control of crossflow instabilities is investigated. Robustness of distributed roughness elements in the presence of acoustic waves have been studied. Moreover, ring-type plasma actuators are employed as virtual roughness elements to delay laminar-turbulent transition. / <p>QC 20161124</p>

It is specifically important to focus on voltage stability analysis of the power system to avoid worst case scenarios such as voltage collapse. The purpose of this thesis is to identify methods for enhancing the steady-state voltage stability using FACTS devices and determining their impact on real and reactive power losses, improvement of bus voltage magnitude, and transmission line loadability. To achieve this, FACTS devices such as Static VAR Compensator (SVC), Static Synchronous Compensator (STATCOM), and Thyristor Controlled Series Capacitor (TCSC) are used in the test system as three separate test cases. The results obtained assist in drawing conclusions on the effectiveness of each FACTS devices at generator, load and swing buses, on lines between two load buses, and between a load bus and a generator bus, in terms of metrics such as voltage magnitude profile, PV curves, and active and reactive power losses.

<div>Aerospace and shipboard power systems, as well as merging terrestrial microgrids, typically include a large ercentage of regulated power-electronic loads. It is well nown that such systems are prone to so-called negative- mpedance instabilities that may lead to deleterious scillations and/or the complete collapse of bus voltage. umerous small-displacement criteria have been developed o ensure dynamic stability for small load perturbations, and echniques for estimating the regions of asymptotic stability bout specic equilibrium points have previously been established. However, these criteria and analysis techniques o not guarantee system stability following large nd/or rapid changes in net load power. More recent research as focused on establishing criteria that ensure arge-displacement stability for arbitrary time varying loads rovided that the net load power is bounded. These yapunov-based techniques and recent advancements in eachability analysis described in this thesis are applied to xample dc and ac microgrids to not only introduce a large- isplacement stability margin, but to demonstrate that the elected systems can be designed to be large-displacement table with practicable constraints and parameters.</div>

<div>Multiscale and multiphysics have been two major challenges in analyzing and designing new emerging engineering devices, materials, circuits, and systems. When simulating a multiscale problem, numerical methods have to overcome the challenges in both space and time to account for the scales spanning many orders of magnitude difference. In the finite-difference time-domain (FDTD) method, subgridding techniques have been developed to address the multiscale challenge. However, the accuracy and stability in existing subgridding algorithms have always been two competing factors. In terms of the analysis of a multiphysics problem, it involves the solution of multiple partial differential equations. Existing partial differential equation solvers require solving a system matrix when handling inhomogeneous materials and irregular geometries discretized into unstructured meshes. When the problem size, and hence the matrix size, is large, existing methods become highly inefficient.</div><div><br></div><div>In this work, a symmetric positive semi-definite FDTD subgridding algorithm in both space and time is developed for fast transient simulations of multiscale problems. This algorithm is stable and accurate by construction. Moreover, the method is further made unconditionally stable, by analytically finding unstable modes, and subsequently deducting them from the system matrix. To address the multiphysics simulation challenge, we develop a matrix-free time domain method for solving thermal diffusion equation, and the combined Maxwell-thermal equations, in arbitrary unstructured meshes. The counterpart of the method in frequency domain is also developed for fast frequency-domain analysis. In addition, a generic time marching scheme is proposed for simulating unsymmetrical systems to guarantee their stability in time domain. </div>

Les instabilités thermoacoustiques, également appelées instabilités de combustion, sont un problème majeur pour la production d’électricité ainsi que dans l’industrie aérospatiale. Ces instabilités sont dues à un transfert d’énergie entre une source chaude, le plus souvent une flamme stabilisée dans un brûleur, et le champ acoustique environnant. Les instabilités de combustion peuvent avoir de nombreuses conséquences délétères telles que l’extinction de la flamme, l’augmentation des flux de chaleur pariétaux, l’émission d’ondes sonores de grande amplitude à certaines fréquences, des vibrations importantes, des dégâts structurels et même l’explosion du moteur dans certains cas. Étant donné les conséquences potentielles de tels phénomènes, d’importants moyens de recherche ont été consacrés à la prédiction de l’apparition d’instabilités de combustion dans les chaudières, les moteurs de fusée et les turbines à gaz ces dernières décennies. Néanmoins, le cadre théorique associé à l’étude de ces instabilités est complexe et nécessite l’emploi de nombreuses disciplines de la physique. De plus, les brûleurs industriels sont constitués de nombreuses cavités tridimensionnelles interagissant entre elles d’un point de vue acoustique. Pour toutes ces raisons, la prédiction de la stabilité thermoacoustique d’un brûleur demeure une tâche ardue à ce jour... (Voir le texte de la thèse pour la suite du résumé) / Thermoacoustic instabilities, also known as combustion instabilities, are a major concern in the aerospace and energy production industries. They are due to an energy transfer that occurs between a heat source, usually a flame stabilized inside a combustor, and the surrounding acoustic field and may lead to undesirable phenomena such as flame extinction, increased heat fluxes, very large sound emissions at certain frequencies, vibration, structural damage and even catastrophic failure in some cases. Given the potential consequences of such phenomena, a large research effort has been devoted to predicting the onset of combustion instabilities in modern boilers, rocket engines and gas turbines during the past few decades. Unfortunately, the theoretical framework associated with the study of thermoacoustic instabilities is complex and multi-physics and the geometry of practical combustors is an intricate arrangement of 3D cavities. As a consequence, predicting the thermoacoustic stability of a combustor at an early design stage is a challenging task to date... (See inside the manuscript for the remainder of the abstract)