This work deals with the study of heat transfer between a porous medium and a free medium, using multi scale approaches. First, we derive the boundary conditions that must be applied at a free-porous interface for laminar heat transfer at local thermal equilibrium and, then, at local thermal non-equilibrium. For turbulent heat transfer, a direct numerical simulation is performed supplying a better understanding of the physic at the free-porous interface. Then, we determine a turbulent model with associated jump conditions. These studies answer fundamental questions regarding the physical meaning of the jump conditions, the values of the jump parameters and the location of the interface for heat transfer.

We study boundary value problems for linear elliptic differential operators of order one. The underlying manifold may be noncompact, but the boundary is assumed to be compact. We require a symmetry property of the principal symbol of the operator along the boundary. This is satisfied by Dirac type operators, for instance. We provide a selfcontained introduction to (nonlocal) elliptic boundary conditions, boundary regularity of solutions, and index theory. In particular, we simplify and generalize the traditional theory of elliptic boundary value problems for Dirac type operators. We also prove a related decomposition theorem, a general version of Gromov and Lawson's relative index theorem and a generalization of the cobordism theorem.

New measuring methods continue to be developed in the field of wind anemometry for various environments subject to low-speed and high-speed flows, turbulent-present flows, and ideal and non-ideal flows. As a result, anemometry has taken different avenues for these environments from the traditional cup model to sonar, hot-wire, and recent developments with sphere anemometers. Several measurement methods have modeled the air drag force as a quadratic function of the corresponding wind speed. Furthermore, by incorporating non-drag fluid forces in addition to the main drag force, a dynamic set of equations of motion for the deflection and strain of a spherical anemometer's beam can be derived. By utilizing the equations of motion to develop a direct relationship to a measurable parameter, such as strain, an approximation for wind speed based on a measurement is available. These ODE's for the strain model can then be used to relate directly the fluid speed (wind) to the strain along the beam’s length. The spherical anemometer introduced by the German researcher Holling presents the opportunity to incorporate the theoretical cantilevered Euler-Bernoulli beam with a spherical mass tip to develop a deflection and wind relationship driven by cross-area of the spherical mass and constriction of the shaft or the beam's bending properties. The application of Hamilton's principle and separation of variables to the Lagrangian Mechanics of an Euler-Bernoulli beam results in the equations of motion for the deflection of the beam as a second order partial differential equation (PDE). The boundary conditions of our beam's motion are influenced by the applied fluid forces of a relative drag force and the added mass and buoyancy of the sphere. Strain gauges will provide measurements in a practical but non-intrusive method and thus the concept of a measuring strain gauge is simulated. Young's Modulus creates a relationship between deflection and strain of an Euler-Bernoulli system and thus a strain and wind relation can be modeled as an ODE. This theoretical sphere anemometer's second order ODE allows for analysis of the linear and non-linear accuracies of the motion of this dynamic system at conventional high speed conditions.

When CO₂ is injected in deep saline aquifers on the scale of gigatonnes, pressure buildup in the aquifer during injection will be a critical issue. Because fracturing, fault activation and leakage of brine along pathways such as abandoned wells all require a threshold pressure (Nicot et al., 2009); operators and regulators will be concerned with the spatial extent of the pressure buildup. Thus a critical contour of overpressure is a convenient proxy for risk. The location of this contour varies depending on the target aquifer properties (porosity, permeability etc.), the geology (presence of faults, abandoned wells etc.), and boundary conditions. Importantly, the extent also depends on relative permeability (Burton et al., 2008). First we describe ways of quantifying the risk due to pressure buildup in an aquifer with a constant pressure boundary, using the three-region injection model to derive analytical expressions for a specific contour of overpressure at any given time. All else being the same, the two-phase-region mobilities (and hence relative permeability characteristics) provide a basis for the ranking of storage formations based on risk associated with pressure elevation during injection. The pressure buildup during CO₂ injection will depend strongly upon the boundary conditions at the boundary of the storage formation. An analytical model for pressure profile in the infinite-acting aquifer is developed by combining existing water influx models in traditional reservoir engineering (Van-Everdingen and Hurst model, Carter-Tracy model) to the current problem for describing brine efflux from the storage aquifer when CO₂ injection creates a "three-region" saturation distribution. We determine evolution of overpressure with time for constant pressure, no-flow and infinite-acting boundary conditions, and conclude that constant pressure and no-flow boundary conditions give the most optimistic and pessimistic estimates of risk respectively. Compositional reservoir simulation results, using CMG-GEM simulator are presented, to show the effect of an isolated no-flow boundary on pressure buildup and injectivity in saline aquifers. We investigate the effect of multiple injection wells on single-phase fluid flow on aquifer pressure buildup, and demonstrate the use of an equivalent injection well concept to approximate the aquifer pressure profile. We show a relatively inexpensive method of predicting the presence of unanticipated heterogeneities in the formation, by employing routine measurements such as injection rate and injection pressure to track deviation in the plume path. This idea is implemented by combining Pro-HMS (probabilistic history matching software, that carries out geologically consistent parameter estimation), and a CMG-GEM model which has been tuned to the physics of the CO₂-brine system. / text

Combustion devices are prone to combustion instabilities. They arise from a constructive coupling between the unsteady heat release rate of the flame and the resonant acoustic modes of the entire system. The occurence of such instabilities can pose a threat to both performance and integrity of combustion systems. Although these phenomena have been known for more than a century, avoiding their appearance in industrial engines is still challenging. The objective of this thesis is threefold: (1) study the dynamics of the resonant acoustic modes, (2) investigate the flame response of a liquid rocket engine under unstable conditions using Large Eddy Simulation(LES) and (3) derive, use and study Time Domain Impedance Boundary Conditions (TDIBCs), i.e. boundary conditions modeling complex acoustic impedances.

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Cross-laminated timber (CLT) is an emerging engineered wood product in North America. Past research effort to establish the behaviour of CLT under extreme loading conditions has focussed CLT slabs with idealized simply-supported boundary conditions. Connections between the wall and the floor systems above and below are critical to fully describing the overall behaviour of CLT structures when subjected to blast loads. The current study investigates the effects of “realistic” boundary conditions on the behaviour of cross-laminated timber walls when subjected to simulated out-of-plane blast loads. The methodology followed in the current research consists of experimental and analytical components. The experimental component was conducted in the Blast Research Laboratory at the University of Ottawa, where shock waves were applied to the specimens. Configurations with seismic detailing were considered, in order to evaluate whether existing structures that have adequate capacities to resist high seismic loads would also be capable of resisting a blast load with reasonable damage. In addition, typical connections used in construction to resist gravity and lateral loads, as well as connections designed specifically to resist a given blast load were investigated. The results indicate that the detailing of the connections appears to significantly affect the behaviour of the CLT slab. Typical detailing for platform construction where long screws connect the floor slab to the wall in end grain performed poorly and experienced brittle failure through splitting in the perpendicular to grain direction in the CLT. Bearing type connections generally behaved well and yielding in the fasteners and/or angles brackets meant that a significant portion of the energy was dissipated there reducing the energy imparted on the CLT slab significantly. Hence less displacement and thereby damage was observed in the slab. The study also concluded that using simplified tools such as single-degree-of-freedom (SDOF) models together with current available material models for CLT is not sufficient to adequately describe the behaviour and estimate the damage. More testing and development of models with higher fidelity are required in order to develop robust tools for the design of CLT element subjected to blast loading.

The postbuckling load carrying capacity of composite plates offers immense potential to their applications for loads exceeding their primary buckling load. However, such an efficient and economical usage of these plates can be reliable only if the nonlinear postbuckling behavior of these plates, which includes a good understanding of secondary buckling, is understood thoroughly. The present investigation is an attempt to understand secondary buckling of almost square composite clamped-simply supported plates, both unstiffened as well as stiffened, in some detail. With the help of the finite element method, a large number of numerical studies have been conducted to understand the secondary buckling characteristics. The sensitivity of these characteristics to variations in boundary conditions, lamination sequence, imperfections, and stiffener geometry has been considered. It has been found that the occurrence of secondary buckling in clamped-simply supported plates under uniform end shortening critically depends on the intensity of restrictions imposed on the inplane normal displacements along the unloaded simply supported edges of the plate. These restrictions could be due to the actual boundary conditions at these edges, or due to the presence of stiffeners along these edges. It has also been found that the presence of imperfections significantly delays the event of secondary buckling. Finally, it has been found that changes in lamination sequence of the plate alter its secondary buckling characteristics in ways that are, in general, quantitative in nature. The numerical investigations were followed by a limited number of experiments involving the testing of unstiffened as well as stiffened composite plates with the intent of augmenting the confidence in the numerical predictions made. Three different lamination sequences were considered during the testing phase of this investigation. It was found that the agreement between experimental data and numerical predictions was quite good. The occurrence of secondary buckling followed the predictions closely. / Ph. D.

We study positive solutions to classes of steady state reaction diffusion equations that arise naturally in applications. In particular, we study models arising from population dynamics and combustion theory. The main focus of this dissertation is the mathematical analysis of a challenging new class of problems when a certain nonlinear boundary condition is satisfied. In particular, we establish existence and multiplicity results by making use of the Quadrature method, the method of sub-super solutions, and degree theory. The results in this dissertation provide a significant contribution towards the analysis of elliptic boundary value problems with nonlinear boundary conditions.