During machining, the cutting tool wears out and affects the machined surface quality and overall production cost. The prediction of tool wear and analysis of cutting mechanics has significant importance for process optimization and cutting-edge design. In this present study, an efficient FE simulation approach (Arbitrary Eulerian-Lagrangian) on the Abaqus/Explicit platform has been developed to improve the predictability of flank wear and to select the appropriate tool edge geometry in the orthogonal turning operation. The FE model was calibrated by comparing the simulation and experimental force values. A new approach was applied to capture the worn tool geometry based on the frictional stress value acting on the cutting tool. The effect of wear geometry on the cutting zone was investigated with respect to temperature, normal stress, sliding velocity, and plastic deformation. The experimental tool wear pattern and characteristics for the differently prepared edges were studied and compared to the thermo-mechanical value retrieved from the FE model. Tool wear for differently prepared edges was calculated using Usui’s wear rate equation, which was calibrated using a hybrid calibration method. The efficiency of the calibration method was investigated at different cutting speeds and feed rates. The performance of pre-coating edge preparation was evaluated in both experimental and numerical studies. / Thesis / Master of Applied Science (MASc)

Cette thèse se situe au carrefour de la combinatoire énumérative, algébrique et bijective. Elle se consacre d’une part à traduire des problèmes algébriques en des problèmes combinatoires, et inversement, utilise le formalisme algébrique pour traiter des questions combinatoires.Après un rappel des notions classiques de combinatoire et de structures algébriques, nous abordons l’étude des tableaux de dominos décalés, qui sont des objets combinatoires définis dans le but de mieux comprendre la combinatoire des fonctions symétriques P et Q de Schur. Nous donnons la définition de ces tableaux et nous démontrons qu'ils sont en bijection avec les paires de tableaux de Young décalés. Cette bijection nous permet de voir ces objets comme des éléments du super monoïde plaxique décalé, qui est l'analogue décalé du super monoïde plaxique de Carré et Leclerc. Nous montrons aussi que ces tableaux décrivent un produit de deux fonctions P de Schur et en prenant un autre type de tableaux de dominos décalés, nous décrivons un produit de deux fonctions Q de Schur. Nous proposons aussi deux algorithmes d'insertion pour les tableaux de dominos décalés, analogues aux algorithmes d'insertion mixte et d'insertion gauche-droit de Haiman. Toujours dans le domaine de la combinatoire bijective, nous nous intéressons dans la deuxième partie de notre travail à des bijections en lien avec des statistiques sur les permutations et les nombres eulériens.Dans cette deuxième partie de thèse, nous introduisons l'unimodalité des suites finies associées aux différentes directions dans le triangle eulérien. Nous donnons dans un premier temps une interprétation combinatoire ainsi que la relation de récurrence des suites associées à la direction (1,t) dans le triangle eulérien, où t≥1. Ces suites sont les coefficients de polynômes appelés les polynômes eulériens avec succession d'ordre t, qui généralisent les polynômes eulériens. Nous démontrons par une bijection entre les permutations et des chemins nord-est étiquetés que ces suites sont log-concaves et donc unimodales. Puis nous prouvons que les suites associées aux directions (r,q), où r est un entier positif et q est un entier, tel que r+q≥0, sont aussi log-concaves et donc unimodales / This thesis is at the crossroads of enumerative, algebraic and bijective combinatorics. It studies some algebraic problems from a combinatorial point of view, and conversely, uses algebraic formalism to deal with combinatorial questions.After a reminder about classical notions of combinatoics and algebraic structures, We introduce new combinatorial objects called the shifted domino tableaux, these objects can be seen as a shifted analog of domino tableaux or as an extension of shifted Young tableaux. We prove that these objects are in bijection with pairs of shifted Young tableaux. This bijection shows that shifted domino tableaux can be seen as elements of the super shifted plactic monoid, which is the shifted analog of the super plactic monoid. We also show that the sum over all shifted domino tableaux of a fixed shape describe a product of two P-Schur functions, and by taking a different kind of shifted domino tableaux we describe a product of two Q-Schur functions. We also propose two insertion algorithms for shifted domino tablaux, analogous to Haiman's left-right and mixed insertion algorithms. Still in the field of bijective combinatorics, we are interested in the second part of our work with bijections related to statistics on permutations and Eulerian numbers.In this second part of this thesis, we introduce the unimodality of finite sequences associated to different directions in the Eulerian triangle. We first give a combinatorial interpretations as well as recurrence relations of sequences associated with the direction (1, t) in the Eulerian triangle, where t≥1. These sequences are the coefficients of polynomials called the t-successive eulerian polynomials, which generalize the eulerian polynomials. We prove using a bijection between premutations and north-east lattice paths that those sequences are unomodal. Then we prove that the sequences associated with the directions (r, q), where r is a positive integer and q is an integer such that r + q ≥ 0, are also log-concave and therefore unimodal

En 2010 Chung, Graham et Knuth ont démontré une remarquable identité symétrique sur les nombres eulériens et posé le problème de trouver un q-analogue de leur identité. En utilisant les q-polynômes eulériens introduits par Shareshian-Wachs, nous avons pu obtenir une telle q-identité. La preuve bijective que nous avons imaginée, nous a permis ensuite de démontrer d'autres q-identités symétriques, en utilisant un modèle combinatoire dû à Foata-Han. Entre temps, Hyatt a introduit les fonctions quasisymétriques eulériennes colorées afin d'étudier la distribution conjointe du nombre d'excédances et de l'indice majeur sur les permutations colorées. En appliquant le Decrease Value Theorem de Foata-Han, nous donnons d'abord une nouvelle preuve de sa formule principale sur la fonction génératrice des fonctions quasisymétriques eulériennes colorées, puis généralisons certaines identités eulériennes symétriques, en les exprimant comme des identités sur les fonctions quasisymétriques eulériennes colorées. D'autre part, en prolongeant les travaux récents de Savage-Visontai et Bec-raun, nous considérons plusieurs q-polynômes de descente des mots signés. Leurs fonctions génératrices factorielles et multivariées sont explicitement calculées. Par ailleurs, nous montrons que certains de ces polynômes n'ont que des zéros réels. Enfin, nous étudions la fonction génératrice diagonale des nombres de Jacobi Stirling de deuxième espèce, en généralisant des résultats analogues pour les nombres de Stirling et Legendre-Stirling de deuxième espèce. Il s'avère que cette fonction génératrice est une série rationnelle dont le numérateur est un polynôme à coefficients entiers positifs. En appliquant la théorie des P-partitions de Stanley nous trouvons des interprétations combinatoires de ces coefficients / In 2010 Chung-Graham-Knuth proved an interesting symmetric identity for the Eulerian numbers and asked for a q-analog version. Using the q-Eulerian polynomials introduced by Shareshian-Wachs we find such a q-identity. Moreover, we provide a bijective proof that we further generalize to prove other symmetric qidentities using a combinatorial model due to Foata-Han. Meanwhile, Hyatt has introduced the colored Eulerian quasisymmetric functions to study the joint distribution of the excedance number and major index on colored permutations. Using the Decrease Value Theorem of Foata-Han we give a new proof of his main generating function formula for the colored Eulerian quasisymmetric functions. Furthermore, certain symmetric q-Eulerian identities are generalized and expressed as identities involving the colored Eulerian quasisymmetric functions. Next, generalizing the recent works of Savage-Visontai and Beck-Braun we investigate some q-descent polynomials of general signed multipermutations. The factorial and multivariate generating functions for these q-descent polynomials are obtained and the real rootedness results of some of these polynomials are given. Finally, we study the diagonal generating function of the Jacobi-Stirling numbers of the second kind by generalizing the analogous results for the Stirling and Legendre-Stirling numbers of the second kind. It turns out that the generating function is a rational function, whose numerator is a polynomial with nonnegative integral coefficients. By applying Stanley’s theory of P-partitions we find combinatorial interpretations of those coefficients

The evolution of numerical methods and computational facilities allow re- searchers to explore complex physical phenomenons such as multiphase flows. The specific regime of incompressible, turbulent, bubbly two-phase flow (where a car- rier fluid is infused with bubbles or particles) is also receiving increased attention due to it’s appearance in major industrial processes. The main challenges arise from coupling individual aspects of the physics into a unified model and to provide a robust numerical framework. The presented work aimed at to achieve the second part by employing the most frequently used dispersed two-phase flow model and another incompressible, turbulent single phase solver as a base flow provider for coupled Lagrangian or surface tracking tools. Among the numerical techniques, the finite element method is a powerful can- didate when the need arises for multiphysics simulations (for example coupling with an electrochemical module) where the counterpart has a node based ap- proach. Stabilization schemes such as PSPG/SUPG/BULK provide remedies for the pressure decoupling and the inherent instability of the central discretization when applied for convective flow problems. As an alternative to unsteady solvers based upon an explicit or a fully im- plicit nonlinear treatment of the convective terms, a semi-implicit scheme results in a method of second order accurate in both space and time, has absolute linear stability and requires only a single or two linear system solution per time step. The application of the skew symmetric approach to the convective term further stabilizes the solution procedure and in some cases it even prevents divergence. The Eulerian-Eulerian two-phase flow model poses various issues to be over- come. The major difficulty is the density ratio between the phases; for an ordinary engineering problem it is in the order of thousands or more. The seemingly minus- cule differences in the formulation of the stabilizations can cause very different end results and require careful analysis. Volume fraction boundedness is of concern as well, but it is treatable by solving for its logarithm. Since the equations allow jumps (even separation of the phases) in the volume fraction field, discontinuity capturing techniques are also needed. Besides the standard ’spatial’ stabilization temporal smoothing is also necessary, otherwise the limitation in time step size becomes too stringent. Designing a flow solver is one side of the adventure, but verification is equally important. Comparison against analytical solution (such as the single and two- phase Taylor-Green testcase) provides insight and confirmation about the mathe- matical and physical properties. Meanwhile comparing with real life experiments prove the industrialization and usability of a code, dealing with low quality meshes and effective utilization of computer clusters. / Doctorat en Sciences de l'ingénieur et technologie / info:eu-repo/semantics/nonPublished

Die Dynamik von elastischen Membranen, Kapseln und Schalen hat sich zu einem aktiven Forschungsgebiet in der simulationsgestützten Physik und Biologie entwickelt. Die dünne Oberfläche dieser elastischen Materialien ermöglicht es, sie effizient als Hyperfläche zu approximieren. Solche Oberflächen reagieren auf Dehnungen in Oberflächenrichtung und Verformungen in Normalenrichtung mit einer elastischen Kraft. Zusätzlich können Oberflächenspannungskräfte auftreten. In dieser Arbeit präsentieren wir eine neuartige Arbitrary Lagrangian-Eulerian (ALE) Methode um solche in (Navier-Stokes) Fluiden eingebetteten elastischen Schalen zu simulieren. Dadurch, dass das Gitter an die elastische Oberfläche angepasst ist, kombiniert die vorgeschlagene Methode hohe Genauigkeit mit Effizienz in der Berechnung der Lösungen. Folglich kann man die Simulationen mit einer verhältnismäßig geringen Gitterauflösung durchführen. Der Fokus dieser Arbeit liegt bei achsensymmetrischen Formen und Strömungen, wie sie bei vielen biophysikalischen Anwendungen zu finden sind. Neben einer allgemeinen dreidimensionalen Beschreibung formulieren wir achsensymmetrische Kräfte auf der Oberfläche, für welche wir eine Diskretisierung mit der Finite Differenzen Methode vorschlagen, welche an eine Finite-Elemente Methode für die umgebenden Fluide gekoppelt ist. Weiterhin entwickeln wir eine Strategie zur impliziten Kopplung der Kräfte, um Zeitschrittrestriktionen zu reduzieren. In verschiedenen numerischen Tests werden wir zeigen, dass akkurate Ergebnisse schon in einer Größenordnung von Minuten auf einer Single-Core CPU erreicht werden können. Die Methode wurde in drei aktuellen Anwendungen verwendet, wobei mindestens zwei davon nach unserer Kenntnis im Moment mit keiner anderen numerischen Methode simuliert werden können: Zunächst präsentieren wir Simulationen von biologischen Zellen, die im Zuge eines RT-DC (Real-Time Deformability Cytometry) Experiments durch einen schmalen mikrofluidischen Kanal advektiert und dabei verformt werden. Danach zeigen wir die Ergebnisse erster Simulationen der uniaxialen Kompression biologischer Zellen zwischen zwei parallelen Platten im Zuge eines AFM Experiments. Schließlich präsentieren wir Resultate erster Simulationen von neuartigen mikroschwimmenden Schalen, welche lediglich durch äußere Einflüsse (wie z.B. Ultraschall), zum Schwimmen angeregt werden können. / The dynamics of membranes, shells, and capsules in fluid flow has become an active research area in computational physics and computational biology. The small thickness of these elastic materials enables their efficient approximation as a hypersurface, which exhibits an elastic response to in-plane stretching and out-of-plane bending, possibly accompanied by a surface tension force. In this work, we present a novel arbitrary Lagrangian-Eulerian (ALE) method to simulate such elastic surfaces immersed in Navier-Stokes fluids. The method combines high accuracy with computational efficiency, since the grid is matched to the elastic surface and can therefore be resolved with relatively few grid points. The focus of this work is on axisymmetric shapes and flow conditions, which are present in a wide range of biophysical problems. Next to a general three-dimensional description, we formulate axisymmetric elastic surface forces and propose a discretization with surface finite-differences coupled to evolving finite elements. We further develop an implicit coupling strategy to reduce time step restrictions. Several numerical test cases show that accurate results can be achieved at computational times on the order of minutes on a single core CPU. Three state-of-the-art applications are demonstrated, where to our knowledge at least two of them cannot be simulated with any other numerical method so far. First, simulations of biological cells being advected through a microfluidic channel and therefore being deformed during an RT-DC (Real-Time Deformability Cytometry) experiment are presented. Then, the uniaxial compression of the cortex of a biological cell during an AFM experiment is investigated. Finally, we present the results of first simulations of the observed shape oscillations of novel microswimming shells which can be locomoted by exterior influences (e.g. ultrasound waves) only.

In the semestral thesis is given basic methods of non-contact measurement heart rate. There is explained Eulerian video magnification method deals with the visualization of the pulse in the videosequence of face. The semestral thesis describes algorithm Viola-Jones face detection in images and algorithm Kanade-Lucas-Tomasi for tracking faces in the videosequence. Part of the work includes design and realization of measurement. There is explained realization of the program and documented execution results, which are discussed. From the results it is designed to guide for optimal recording.

Interactions between three immiscible phases, including incompressible viscoelastic structures and fluids, form standard constellations for countless scenarios in natural science. The complexity of many such scenarios has motivated various research efforts in scientific computing. This work presents novel numerical approaches for two specific of these ternary fluid-structure interaction constellations. The potential of these approaches is demonstrated by diverse applications. First, a phase field model is developed describing the interaction between a fluid and a viscoelastic solid. For this purpose, a Navier-Stokes-Cahn-Hilliard system is considered together with a hyperelastic neo-Hookean model. Based on this, an arbitrary Lagrangian-Eulerian (ALE) method is implemented to simulate the indentation of the solid material in the context of atomic force microscopy, capable of predicting physical parameters. Next, the second approach is developed to describe the interaction between a two-phase fluid and a viscoelastic solid, where fluid and solid are defined on separate domains but aligned at the interface between them. The previously introduced phase field model is used to represent the fluid and an ALE method is used for the motion of the grid, where the fluid-solid interface moves with flow velocity. A unified system is solved in all subdomains, which includes both the balance of mass and momentum and the balance of forces at the fluid-solid interface. Simulations of static and dynamic soft wetting are subsequently presented, in particular a contact line moving over a substrate with oscillating stick-slip behavior. This work combines the advantages of phase field and ALE methods for meaningful simulations and emphasizes validity and numerical stability in all approaches.

In multibody systems, mechanical components (bodies) can be assumed rigid (non-deformable), if their deformation is negligible. For components with non-negligible deformations several methods were developed to represent their deformation. The most widely used method is the floating frame of reference. In this formulation the deformable body is represented by a finite element model whose deformation is described with respect to a local body-fixed frame. Unfortunately, finite element models can include many degrees-of-freedom, which stand in contradiction to the requirements of multibody dynamics. System truncation is therefore inevitable to support computational efficiency. The use of modal data in representing a deformable body is well understood in the multibody community. By truncating modes associated with higher frequencies, the total degrees-of-freedom of the deformable body can be reduced while preserving its dynamic eigen-properties. However, since the finite element model may be in contact with other moving bodies, the reduction technique needs to address the issue of moving boundary conditions. The component mode synthesis reduction methods are such techniques that describe the deflection of all the nodes as a superposition of different types of modes. However, it is limited in the fact that the nodes in contact need to remain in contact throughout a simulation. In some applications these nodes may change, i.e. a node that is in contact with another body or the ground at one instant may become free at the next instant. The present methodologies in multibody modeling of a deformable body with modal data have not yet addressed the issue of changing contact nodes. This research highlights the usefulness of orientation invariant characteristics of some deformable bodies. It proposes to define orientation invariant degrees-of-freedom of the reduced model in Eulerian space, while the remaining degrees-of-freedom are defined in Lagrangian space. In some circumstances, this approach can resolve the issue of changing contact nodes. The combination of Eulerian and Lagrangian formulation for component mode synthesis reduced finite element models is a new concept in deformable multibody dynamics.

L'application de la Directive Cadre sur l'Eau et l'obligation de surveillance de la qualité d'eau pour la consommation humaine et les activités récréatives ou industrielles, telles que la production d'eau potable, entraînent une forte demande pour des systèmes d'évaluation et de suivi de la qualité de l'eau. Le projet de recherche MIGR'HYCAR (http://www.migrhycar.com) a donc été mis en place pour répondre à un besoin opérationnel et à un défaut d'outils d'aide à la décision adaptés face aux déversements d'hydrocarbures en eaux continentales (rivières, lacs et estuaires) qui représente plus de 50% des déversements accidentels en France. Au cours du projet de recherche MIGR'HYCAR, un modèle mathématique de dérive de nappe d'hydrocarbures, composé d'un modèle lagrangien couplé à un modèle eulérien, a été développé dans la plate-forme hydro-informatique TELEMAC (http://www.opentelemac.org). Le modèle lagrangien décrit le mouvement de la nappe en surface en considérant celle-ci comme un ensemble de particules. Ainsi le modèle développé est capable de modéliser les principaux phénomènes agissant sur une nappe d'hydrocarbures une fois celle-ci déversée : convection, diffusion, échouage, re-largage, étalement, évaporation, dissolution et volatilisation. Bien que le phénomène de dissolution ne concerne qu'un très faible volume d'hydrocarbures, ce processus peut avoir des conséquences importantes du point de vue de la toxicité. Afin de suivre l'évolution du pétrole dissous, un modèle eulérien de suivi de traceurs a été adopté. La quantité de traceur dépend directement de la masse dissoute des particules lagrangiennes. Cette approche permet le suivi des hydrocarbures dissous dans la colonne d'eau. Des cinétiques effectuées en laboratoire ont pour but la calibration du modèle numérique. En complément de cas tests issus de la littérature et de cas réels, des résultats expérimentaux issus d'expérimentations effectuées en canal d'essai doivent permettre de vérifier et valider la qualité des simulations numériques sur des situations où les conditions ne sont que partiellement contrôlées / The application of the European Water Framework Directive on water quality for human consumption and industrial activities creates a need for water quality assessment and monitoring systems. The MIGR'HYCAR research project (http://www.migrhycar.com) was initiated to provide decisional tools for risks connected to oil spills in continental waters (rivers, lakes and estuaries), which represent more than 50% of accidental spills in France. Within the framework of this project, a new numerical oil spill model has been developed, as part of the Telemac hydro-informatics system (see: (http://www.opentelemac.org), by combining Lagrangian and Eulerian methods. The Lagrangian model describes the transport of an oil spill near the free surface. The oil spill model enables to simulate the main processes driving oil plumes: advection, diffusion, oil beaching, oil re-floating, evaporation, dissolution, spreading and volatilization. Though generally considered as a minor process, dissolution is important from the point of view of toxicity. To model dissolved oil in water, an Eulerian advection-diffusion model is used. The fraction of dissolved oil is represented by a passive tracer. This approach is able to follow dissolved hydrocarbons in the water column. Laboratory experiments were conducted to characterise the numerous kinetics of the processes listed above. In addition, meso-scale dynamic experiments in artificial channels and test cases derived from the literature are used to validate the numerical model

Dans les moteurs à combustion interne, l'injection de carburant est une phase essentielle pour la préparation du mélange et la combustion. En effet, la structure du jet liquide joue un rôle essentiel pour la qualité du mélange du combustible avec le gaz. Le présent travail porte sur les phénomènes d'atomisation de jet liquides dans les conditions opératoires des moteurs diesel. Dans ces conditions, la morphologie du jet liquide comprend une phase liquide séparée (c'est à dire un noyau liquide) et une phase liquide dispersée (c'est à dire un spray). Ce manuscrit décrit les étapes de développement d'un nouveau modèle d'atomisation, pour un jet liquide à grande vitesse, basée sur une approche eulérienne diphasique. Le phénomène d'atomisation est modélisée par des équations définissant une densité de surface pour le noyau liquide en plus de celle des gouttelettes du spray. Ce nouveau modèle a été couplé avec un système d'équations diphasique et turbulent de type Baer-Nunziato. Le processus de rupture des ligaments et son éclatement subséquent en gouttelettes sont modélisés en utilisant des connaissances rassemblées à partir des expériences disponibles et des simulations numériques précises. Dans la région dense du jet de liquide, l'atomisation primaire est modélisée comme un processus de dispersion en raison de l'étirement turbulent de l'interface, à partir du côté du liquide en plus du côté du gaz. Différents cas tests académiques ont été effectués afin de vérifier la mise en œuvre numérique du modèle dans le code IFP-C3D. Enfin, le modèle est validé avec les résultats DNS récemment publiés dans des conditions typiques de moteurs Diesel à injection directe. / In internal combustion engines, the liquid fuel injection is an essential step for the air/fuel mixture preparation and the combustion process. Indeed, the structure of the liquid jet coming out from the injector plays a key role in the proper mixing of the fuel with the gas in the combustion chamber. The present work focuses on the liquid jet atomization phenomena under Diesel engine conditions. Under these conditions, liquid jet morphology includes a separate liquid phase (i.e. a liquid core) and a dispersed liquid phase (i.e. a spray). This manuscript describes the development stages of a new atomization model, for a high speed liquid jet, based on an eulerian two-phase approach. The atomization phenomenon is modeled by defining different surface density equations, for the liquid core and the spray droplets. This new model has been coupled with a turbulent two-phase system of equations of Baer-Nunziato type. The process of ligament breakup and its subsequent breakup into droplets are handled with respect to available experiments and high fidelity numerical simulations. In the dense region of the liquid jet, the atomization is modeled as a dispersion process due to the turbulent stretching of the interface, from the side of liquid in addition to the gas side. Different academic test cases have been performed in order to verify the numerical implementation of the model in the IFP-C3D software. Finally, the model is validated with the recently published DNS results under typical conditions of direct injection Diesel engines.