The flow of fluids over solid surfaces is an integral part of many technologies, and the analysis of such flows is important to the design and operation of these technologies. Solid surfaces, however, are generally rough at some scale, and analyzing the effects of such roughness on fluid flows represents a significant challenge. There are two fluid flow situations in which roughness is particularly important, because the fluid shear layers they create can be very thin, of order the height of the roughness. These are very high Reynolds number turbulent wall-bounded flows (the viscous wall layer is very thin), and very low Reynolds number lubrication flows (the lubrication layer between moving surfaces is very thin). Analysis in both of these flow domains has long accounted for roughness through empirical adjustments to the smooth-wall analysis, with empirical parameters describing the fluid dynamic roughness effects. The ability to determine these effects from a topographic description of the roughness is limited (lubrication) or non-existent (turbulence). The commonly used parameter, the equivalent sand grain roughness, can be determined in terms of the change in the rate of viscous energy dissipation caused by the roughness and is generally obtained by measuring the effects on a fluid flow. However, determining fluid dynamic effects from roughness characteristics is critical to effective engineering analysis. Characterization of this mapping from roughness topography to fluid dynamic impact is the main topic of the dissertation. Using the mathematical tools of shape calculus, we construct this mapping by defining the roughness functional and derive its first- and second- order shape derivatives, i.e., the derivatives of the roughness functional with respect to the roughness topography. The results of the shape gradient and complete spectrum of the shape Hessian are presented for the low Reynolds number lubrication flows. Flow predictions based on this derivative information is shown to be very accurate for small roughness. However, for the study of high Reynolds number turbulent flows, the direct extension of the current approach fails due to the chaotic nature of turbulent flows. Challenges and possible approaches are discussed for the turbulence problem as well as a model problem, the sensitivity analysis of the Lorenz system. / text

Le contrôle et à la maîtrise de l’état des surfaces est un besoin majeur pour les industriels. De nombreuses études sur les interactions entre la morphologie de surface et les mécanismes physiques, chimiques ou mécaniques, ont été réalisées. Cependant une caractérisation plus précise en fonction des domaines et des besoins est nécessaire. Elle consiste à chercher les paramètres de rugosité les plus pertinents qui relient la topographie d’une surface aux phénomènes physiques qu’elle subit ou aux propriétés du matériau dont elle composé.Dans ce travail, un logiciel pour caractériser l’état de surface a été développé. Cet outil nommé « MesRug » permet de calculer des paramètres de rugosité et d’extraire les plus pertinents ainsi que de définir l’échelle la plus adéquate pour une application donnée. La recherche des paramètres les plus pertinent se fait par une approche statistique (l'analyse de la variance ‘ANOVA’ combinée avec la théorie du Bootstrap).Une caractérisation a été effectuée en utilisant des données de mesures (2D) sur des surfaces abrasives. L’influence de la forme des ondelettes discrètes et continues sur la détection de l’échelle pertinente du mécanisme d’abrasion a été testée. On déduit que la décomposition en ondelettes permet de quantifier et de localiser les échelles de l'abrasion des processus d'usinage pour tous les paramètres du processus. Cependant, la pertinence de caractériser les échelles appropriées d'abrasion ne dépend pas de la forme de l'ondelette.Dans ce travail, un nouveau paramètre de rugosité 3D est proposé pour quantifier la régularité d'une surface indépendamment de l'amplitude et des unités de longueur de balayage. L'efficacité de ce paramètre est testée sur des surfaces périodiques bruitées avec différents degrés d'anisotropie. La valeur de ce paramètre est comprise entre zéro (bruit parfait) et 100% (surface sinusoïdale parfaite). Il nous a permis de détecter les directions d'anisotropie de régularité pour une surface donnée. / Monitoring and control of the state of the surfaces is a major need for industry. Numerous studies on the interactions between the surface morphology and the physical, chemical or mechanical mechanisms have been conducted. However, a more precise characterization related to industrial domains and needs is necessary. It consists in finding the most relevant roughness parameters that connect the topography of a surface with the physical phenomena which it undergoes or in the properties of the material of which it consisted.In this work, a software designed to characterize the surface condition was developed. This tool named "MesRug" allows to calculate roughness parameters then extract the most relevant ones and to define the most appropriate scale for a given application. The search for the most relevant parameters is done by a statistical approach (analysis of variance ANOVA combined with the theory of Bootstrap).A characterization was performed using (2D) data of measurement on abrasive surfaces. The influence of the form of discrete and continuous wavelet on the detection on the relevant scale mechanism of the abrasion was tested. We conclude that the wavelet decomposition allows to quantify and localize the scales of abrasion of the machining process for all process parameters. However, the relevance of appropriate scales to characterize abrasion does not depend on the shape of the wavelet.In this work, a new 3D roughness parameter is proposed to quantify the smoothness of a surface, independently of the amplitude and the scanning length units of the surface. The efficiency of this parameter is tested on noisy periodic surfaces with varying degrees of anisotropy. The value of this parameter is between zero (perfect sound) and 100 % (sine perfect surface). It enables us to identify the anisotropy directions of regularity for a given surface.

Advanced ceramics have long held the front of the list of promising materials for high-tech applications. The most common problem is the high cost of design, production and machining of advanced ceramics parts. The main sense of advanced ceramics processing techniques development is affordable, high-volume production. The dissertation is focused on SiC silicon carbide grinding. SiC is used in the design of machine parts due to its excellent properties The deep knowledge of the diamond wheel grinding process is important because it is one of the finishing methods and therefore has a direct impact on the quality and strength of the SiC parts. The key issue here is the overall surface quality of the parts after diamond wheel grinding and the knowledge of the factors that influence the surface quality. These include, in particular, grinding vibrations. The main purpose of the thesis is to create a system of specific scientific and technical information, which will allow applying optimal technological procedures in the processing of ceramic components. The theoretical part of the thesis contains an analysis of the current state of the art in the advanced ceramics machining area, detailed analysis of the ceramics grinding with diamond grinding wheels, signal analysis theory and analysis of surface quality assessment methods. The experimental part contains analysis and discussion of the results obtained during the monitoring of the silicon carbide grinding process with a diamond grinding wheel. Various diagnostic methods have confirmed the presence of vibrations at a frequency close to the speed frequency of the grinding wheel, which had a significant, negative effect on the samples surface quality. Vibration diagnostics has identified a specific source of vibration (clamping of the workpiece) and it has been removed subsequently.