We investigate (i) pull-in instabilities in a microelectromechanical (MEM) beam due to the Coulomb force and in MEM membranes due to the Coulomb and the Casimir forces, and (ii) thermomechanical instability in a heat-conducting thermoelastoviscoplastic solid due to thermal softening overcoming hardening caused by strain- and strain-rate effects. Each of these nonlinear multiphysics problems is analyzed by the meshless local Petrov-Galerkin (MLPG) method. The moving least squares (MLS) approximation is used to generate basis functions for the trial solution, and the basis for test functions is taken to be either the weight functions used in the MLS approximation, or the same as for the trial solution. In this case the method becomes Bubnov-Galerkin. Essential (displacement, temperature, electric potential) boundary conditions are enforced by the method of Lagrange multipliers. For the electromechanical problem, the pull-in voltage and the corresponding deflection are extracted by combining the MLPG method with either the displacement iteration pull-in extraction algorithm or the pseudoarclength continuation method. For the thermomechanical problem, the localization of deformation into narrow regions of intense plastic deformation is delineated. For every problem studied, computed results are found to compare well with those obtained either analytically or by the finite element (FE) method. For the same accuracy, the MLPG method generally requires fewer nodes but more CPU time than the FE method; thus additional computational cost is compensated somewhat by the increased efficiency of the MLPG method. / Ph. D.

This work addresses the issue of transverse combustion instabilities in annular gas turbine combustor geometries. While modern low-emissions combustion strategies have made great strides in reducing the production of toxic emissions in aircraft engines and power generation gas turbines, combustion instability remains one of the foremost technical challenges in the development of next generation combustor technology. To that end, this work investigates the response of a swirling flow and swirl-stabilized flame to a transverse acoustic field is using a variety of high-speed laser techniques, especially high-speed particle image velocimetry (PIV) for detailed velocity measurements of this highly unsteady flow phenomenon. A description of the velocity-coupled transverse instability mechanism is explained with companion measurements describing each of the velocity disturbance pathways. Dependence on acoustic frequency, amplitude, and field symmetry is discussed. Significant emphasis is placed on the response of a swirling flow field to a transverse acoustic field. Details of the dynamics of the vortex breakdown bubble and the shear layers are explained using a wide variety of measurements for both non-reacting and reacting flow cases. This thesis concludes with an overview of the impact of this work and suggestions for future research in this area.

In recent years, many alternative models of the substorm process have been proposed to explain different aspects of this magnetospheric phenomenon. Some features in these competing models are compatible while others, such as the nature and location of substorm onset, remain controversial. The objective of this thesis is to assess the viability of the ballooning instability as a mechanism for initiating substorms. A review of the history and development of magnetospheric substorm research as well as a review of substorm models is presented. In these models, the crosstail current disruption responsible for the onset of the expansion phase is usually ascribed to the onset of some microinstability. An alternative triggering mechanism is a macroscopic magnetohydrodynamic instability such as the ballooning instability. To derive a threshold condition for the ballooning instability, a simplified magnetotail geometry with cylindrical symmetry near the equatorial plane is assumed. In such circumstances, the torsion of the magnetic field lines is zero and they can be characterised by their curvature. The hydromagnetic equations with isotropic pressure are linearised to find the dispersion relation. This leads to a threshold condition which depends on the pressure and magnetic field intensity gradients. In order to obtain realistic numerical results for the threshold condition, a quasistatic, self-consistent, two-dimensional numerical model of the magnetotail during conditions typical of substorm growth phase is used. The model involves solving the Grad-Shafranov equation with appropriate boundary conditions. It provides time-dependent magnetospheric magnetic field configurations that are characterised by the development of a minimum in Bz in the equatorial plane. Calculations of the detailed configuration of the magnetotail during onset allow an estimate of the instability criterion. In a model which does not allow an increase of pressure with radius, it is found that the magnetotail is not unstable to ballooning. Part of this work has been presented at a conference, viz.: Dormer, L.A. and A.D.M. Walker, Investigation of local MHD instabilities in the magnetotail using a two-dimensional magnetospheric convection model. Poster presented at the 39th annual South African Institute of Physics conference, University of Bophuthatswana, 1994. / Thesis (M.Sc.)-University of Natal, 1995.

A numerical study is done of a plasma in contact with a cold solid surface that is emitting a neutral gas. Two numerical models have been developed to describe the dominant phenomena of surface plasma structures. The first model entails a steady-state, kinetic treatment of the transport equations in one space dimension and one velocity dimension, to determine self-consistently the distribution functions of the interacting species and the electrostatic potential near the solid surface. The dominant phenomena in this region are the ionization of the neutral gas and the acceleration of the resulting ions by the electrostatic field in a pre-sheath region. Other effects involved are a Debye sheath structure between the solid surface and pre-sheath, and collisional trapping and untrapping of electrons in an electrostatic potential well that is predicted in the pre-sheath region. Results are presented from a nondimensional model with a monatomic returning neutral species and for diatomic molecular hydrogen returning from the surface. For each set of physical parameters chosen, a one parameter family of solutions is obtained. The second numerical model involves a steady-state treatment of the transport equations in a (x,v∥,v⊥) phase space for the interacting species. Included in this model are ionization of the refluxing monatomic neutrals, a self-consistently determined electrostatic potential and a nonlinear Fokker-Planck treatment of ion-ion Coulomb collisions. Both the region near the surface dominated by kinetic effects and the region away from the surface in which Coulomb collisional effects are significant are treated. Results are presented which identify the correct physical solution for the region near the surface from the permitted family found with the kinetic model. Additionally, results are shown which span a temperature range from the high temperature kinetic regime where Coulomb collisional effects are negligible, to the low temperature, highly collisional fluid regime. At low temperatures the collisional model agrees well with standard fluid techniques.

No description available.

Boiling in microchannels is a very efficient mode of heat transfer with high heat and mass transfer coefficients achieved. Less pumping power is required for two-phase flows than for single-phase liquid flows to achieve a given heat removal. Applications include electronics cooling such as cooling microchips in laptop computers, and process intensification with compact evaporators and heat exchangers. Evaporation of the liquid meniscus is the main contributor to the high heat fluxes achieved due to phase change at thin liquid films in a microchannel. The microscale hydrodynamic motion at the meniscus and the flow boiling heat transfer mechanisms in microchannels are not fully understood and are very different from those in macroscale flows. Flow instability phenomena are noted as the bubble diameter approaches the channel diameter. These instabilities need to be well understood and predicted due to their adverse effects on the heat transfer. A fundamental approach to the study of two-phase flow boiling in microchannels has been carried out. Simultaneous visualisation and hydrodynamic measurements were carried out investigating flow boiling instabilities in microchannels using two different working fluids (n-Pentane and FC-72). Rectangular, borosilicate microchannels of hydraulic diameter range 700-800 μm were used. The novel heating method, via electrical resistance through a transparent, metallic deposit on the microchannel walls, has enabled simultaneous heating and visualisation to be achieved. Images and video sequences have been recorded with both a high-speed camera and an IR camera. Bubble dynamics, bubble confinement and elongated bubble growth have been shown and correlated to the temporal pressure fluctuations. Both periodic and nonperiodic instabilities have been observed during flow boiling in the microchannel. Analysis of the IR images in conjunction with pressure drop readings, have allowed the correlation of the microchannel pressure drop to the wall temperature profile, during flow instabilities. Bubble size is an important parameter when understanding boiling characteristics and the dynamic bubble phenomena. In this thesis it has been demonstrated that the flow passage geometry and microchannel confinement effects have a significant impact on boiling, bubble generation and bubble growth during flow boiling in microchannels.

The presence of a giant planet in a low-viscosity disc can create a gap edge in the disc's radial density profile sharp enough to excite the Rossby wave instability. This instability may evolve into dust-trapping vortices that might explain the `banana-shaped' features in recently observed asymmetric transition discs with inner cavities. Previous hydrodynamical simulations of planet-induced vortices have neglected the time-scale of hundreds to thousands of orbits to grow a massive planet to Jupiter size. In this work, we study the effect of a giant planet's runaway growth time-scale on the lifetime and characteristics of the resulting vortex. For two different planet masses (1 and 5 Jupiter masses) and two different disc viscosities (alpha= 3 x 10-4 and 3 x 10-5), we compare the vortices induced by planets with several different growth time-scales between 10 and 4000 planet orbits. In general, we find that slowly-growing planets create significantly weaker vortices with lifetimes and surface densities reduced by more than 50 per cent. For the higher disc viscosity, the longest growth time-scales in our study inhibit vortex formation altogether. Additionally, slowly-growing planets produce vortices that are up to twice as elongated, with azimuthal extents well above 180. in some cases. These unique, elongated vortices likely create a distinct signature in the dust observations that differentiates them from the more concentrated vortices that correspond to planets with faster growth time-scales. Lastly, we find that the low viscosities necessary for vortex formation likely prevent planets from growing quickly enough to trigger the instability in self-consistent models.

No description available.

We develop a simple model to predict the radial distribution of planetesimal formation. The model is based on the observed growth of dust to millimeter-sized particles, which drift radially, pile-up, and form planetesimals where the stopping time and dust-to-gas ratio intersect the allowed region for streaming instability-induced gravitational collapse. Using an approximate analytic treatment, we first show that drifting particles define a track in metallicity-stopping time space whose only substantial dependence is on the disk's angular momentum transport efficiency. Prompt planetesimal formation is feasible for high particle accretion rates (relative to the gas, (M) over dot(p)/(M) over dot greater than or similar to 3 x 10(-2) for alpha = 10(-2)), which could only be sustained for a limited period of time. If it is possible, it would lead to the deposition of a broad and massive belt of planetesimals with a sharp outer edge. Numerically including turbulent diffusion and vapor condensation processes, we find that a modest enhancement of solids near the snow line occurs for centimeter-sized particles, but that this is largely immaterial for planetesimal formation. We note that radial drift couples planetesimal formation across radii in the disk, and suggest that considerations of planetesimal formation favor a model in which the initial deposition of material for giant planet cores occurs well beyond the snow line.

Cette thèse est dédiée à l'étude d'ondes non linéaires dans des écoulements en rotation. Dans une première partie, je me suis intéressé aux ondes de Rossby apparaissant par instabilités de thermoconvection dans une coquille sphérique en rotation représentant un modèle simplifié de noyau planétaire tellurique, et ce pour deux types de forçage: un chauffage interne correspondant à une activité radioactive du noyau et un chauffage différentiel lié à la différence de température entre les frontières interne et externe. Selon le théorème de Proudman-Taylor, l'écoulement possède une faible dépendance en la coordonnée axiale à cause de la rotation rapide. Cela permet de simplifier les modèles 3D en des modèles quasi géostrophiques 2D reposant sur une intégration axiale. Cette thèse présente la première comparaison systématique entre modèles 2D et 3D (Simitev, U-Glasgow) concernant des ondes de Rossby faiblement non linéaires. En 2D l'équation de Landau régissant l'amplitude de l'onde critique est calculée; l'amplitude de la convection et celle des écoulements zonaux ainsi prédites se comparent assez bien aux résultats 3D. L'existence d'une bifurcation sous-critique est établie à très bas nombre d'Ekman en chauffage interne et en chauffage différentiel, à condition dans ce dernier cas que le nombre de Prandtl soit petit. La seconde partie est une étude expérimentale de l'écoulement d'eau et de ses premières instabilités dans un canal annulaire creusé dans un plateau éventuellement en rotation surmonté d'un couvercle tournant. Trois cas sont étudiés: le cisaillement pur correspondant à la rotation du couvercle seul, la corotation rapide et la contrarotation pure. Le seuil d'instabilité détecté par mesures globales (visualisations par caméra vidéo) et locales par Vélocimétrie Laser Doppler se caractérise par des ondes spiralées. Dans le cas de la contrarotation pure, des structures localisées dans l'espace-temps peuvent coexister avec les ondes. Une comparaison est effectuée avec des calculs numériques (Serre, CNRS-Marseille). Un accord relativement bon est obtenu pour l'écoulement de base (vitesse azimutale) et la première instabilité (nombre de Reynolds, nombre d'onde et fréquence angulaire critiques) / A first part is devoted to the study of the Rossby waves that appear in a rotating spherical shell representing the core of a terrestrial planet by thermal instabilities for two heating types. Internal heating is driven by radioactive sources and differential heating is driven by a difference of temperature between the internal and external frontiers. According to the Proudman-Taylor theorem, the flow depends only weakly on the axial coordinate because of the high rotation rate. Thus the 3D models can be simplified into quasi-geostrophic 2D models \textit{via} an axial integration. I present the first systematic comparison between 2D and 3D models (Simitev, U-Glasgow) for weakly nonlinear Rossby waves. In 2D the Landau equation that controls the amplitude of the critical wave is calculated. Predicted convection' amplitude and zonal flows agree rather well with the 3D results. The existence of a subcritical bifurcation is established at very low Ekman numbers with internal and differential heating; in this latter case, the Prandtl number also has to be small for the bifurcation to be subcritical. The second part is an experimental study of water flows and its first instabilities in an annular channel digged in a plate which may rotate, and which is sheared by a rotating lid. Three cases are studied: a pure shear where only the lid turns, a rapid corotation and a pure contrarotation. The onset of instability is studied with global measurements (using a video camera) and local ones (Laser Doppler Anemometry) and is characterized by spiralling waves. In the case of contrarotation, patterns localized in space and time may coexist with the waves. The comparison of these results with numerical ones (Serre, CNRS-Marseille) is done and shows a rather good agreement for the basic azimutal flow and the first instability (critical Reynolds number, wavenumber and angular frequency)