Increased knowledge into the physics and chemistrycontrolling emissions from flame-surface interactions shouldhelp in the design of combustion engines featuring improvedfuel economy and reduced emissions. The overall aim of this work has been to obtain afundamental understanding of wall-related, premixed combustionusing numerical modeling with detailed chemical kinetics. Thiswork has utilized CHEMKIN®, one of the leading softwarepackages for modeling combustion kinetics. The simple fuels hydrogen and methane as well as the morecomplex fuels propane and gasified biomass have been used inthe model. The main emphasis has been on lean combustion, andthe principal flow field studied is a laminar boundary layerflow in two-dimensional channels. The assumption has been madethat the wall effects may at least in principle be the same forlaminar and turbulent flames. Different flame geometries have been investigated, includingfor example autoignition flames (Papers I and II) and premixedflame fronts propagating toward a wall (Papers III and IV).Analysis of the results has shown that the wall effects arisingdue to the surface chemistry are strongly affected by changesin flame geometry. When a wall material promoting catalyticcombustion (Pt) is used, the homogeneous reactions in theboundary layer are inhibited (Papers I, II and IV). This isexplained by a process whereby water produced by catalyticcombustion increases the rate of the third-body recombinationreaction: H+O2+M ⇔ HO2+M. In addition, the water produced at higherpressures increases the rate of the 2CH3(+M) ⇔ C2H6(+M) reaction, giving rise to increased unburnedhydrocarbon emissions (Paper IV). The thermal coupling between the flame and the wall (theheat transfer and development of the boundary layers) issignificant in lean combustion. This leads to a sloweroxidation rate of the fuel than of the intermediatehydrocarbons (Paper III). Finally in Paper V, a well-known problem in the combustionof gasified biomass has been addressed, being the formation offuel-NOx due to the presence of NH3 in the biogas. A hybridcatalytic gas-turbine combustor has been designed, which cansignificantly reduce fuel-NOx formation. Keywords:wall effects, premixed flames, flamequenching, numerical modeling, CHEMKIN, boundarylayerapproximation, gasified biomass, fuel-NOx, hybrid catalytic combustor. / QC 20100504

Cette thèse est consacrée à la modélisation mathématique et simulations numériques des écoulements sanguins dans des artères en présence d’une endoprothèse vasculaire de type stent. La présence de stent peut être considérée comme une perturbation locale d’un bord lisse d’écoulement, plus précisément les parois de l’artère sont assimilées à une surface fortement rugueuse. Nous nous sommes principalement intéressés au contrôle de la régularité H² sur un modèle simplifié permettant de prendre en compte l’effet de ces stents lorsque le flux sanguin est gouverné par une équation de Laplace (en lien avec la composante axiale de la vitesse d’écoulement) avec une condition aux limites de type Dirichlet, dans un domaine à bord rugueux (en fonction d’un petit paramètre ε). Dans une première partie, nous soulevons la question d’existence et d’unicité de la solution de ce modèle d’écoulement sanguin et nous traitons la régularité H² par des techniques d’analyse variationnelle. Une étude minutieuse permet de contrôler la régularité H² en O(ε−1). Le deuxième axe est dédié à l’étude de la régularité H² par des analyse asymptotiques multiéchelles. Nous montrons que la norme H² de la solution de ce modèle d’écoulement sanguin est singulière en O(ε−½ ). D’autre part, nous améliorons les ordres de convergence des résultats existants concernant la construction des approximations multiéchelles. Dans un troisième temps, nous présentons des estimations d’erreur et des résultats numériques. Ces résultats illustrent le bien fondé des estimations d’erreur sur le plan pratique. Nous montrons bien l’importance des méthodes asymptotiques qui se révèlent plus efficaces qu’un calcul direct. / This thesis is devoted to mathematical modeling and numerical simulations of the blood-flows in arteries in the presence of a vascular prosthesis of type stent. The presence of stent can be considered as a local perturbation of a smooth edge of flow, more precisely the walls artery can be seen as a strongly rough surface.Weare mainly interested in controlling the H² regularity of a simplified model which takes into account the impact of these stents when the blood flow is controlled by a Laplace equation (in link with the axial component rateof flow) with a Dirichlet boundary condition, in a domain with a rough board (according to a small parameter ε). First, we raise the question of existence and unicity of the solution of this model of blood-flow and we study the H² regularity using variational analysis methods. By a detailed study, we control the H² regularity of order O(ε−1). The second part is devoted to the study of the regularity H² regularity using multi-scale analysis.We prove that the H² norm of the solution of this model is singular of order O(ε−½). Moreover, we improve the convergence rate of the existing results on the construction of the multi-scale approximation. Finally, we present an error estimation and numerical results. These numerical results illustrate the well-founded of the error estimates on a practical level. We show the importance of the asymptotic methods that seem to be more effective than a direct computation.