Among the different types of flows encountered in practical applications, the physics of turbulent separated flows and turbulence induced secondary motion are not fully understood despite the large amount of previous experimental and numerical work. The objectives of this work are to study theoretically and computationally the conditions at the separation and reattachment point, the numerical simulation of turbulence induced secondary motion in non-circular ducts, and to provide a comprehensive test of different RANS models of these types of flow. In a theoretical study of flow separation, a Lagrangian approach was first used to derive an Eulerian criterion, which associates separation and reattachment points to a critical point in the eigenvalues of the Cauchy-Green tensor. A turbulent separated boundary layer under the influence of an adverse pressure gradient was simulated using DNS and LES techniques. A bootstrapping method was used to obtain high fidelity results at a relatively high Reynolds number with which the performance of some of the most commonly used eddy-viscosity turbulence models was evaluated. The DNS and LES results were used to assess the consistency of the different terms in the k−e , ζ −f , k −ω and Spalart-Allmaras models. Different wall-modelling techniques were employed for the calculation of separated boundary layers. The exact values of the modelled terms were calculated using the reference DNS and LES dataset. These results were used for both a priori and a posteriori tests. It was determined that the eddy-viscosity assumption works well, and that anisotropic effects are not significant in separated boundary layer. For the secondary flow calculation in non-circular ducts, direct numerical simulations of turbulent flow in square and skewed ducts were carried out to determine the effect of the duct (rhombus) included angle on both the mean and turbulence energy budgets. Two skewed ducts, with included angles of 30 and 60 degrees, were simulated. The capability of different turbulence models to predict the secondary velocity field was investigated. Results obtained from a non-linear stress-strain constitutive relation was found to be fairly accurate for the flows at the range of Reynolds number considered in this study. / Thesis (Ph.D, Mechanical and Materials Engineering) -- Queen's University, 2010-11-26 13:52:18.361

The work developed in this thesis focusses on the electrical activity of the heart, from the modeling of the action potential originating from cardiac cells and propagating through the heart, as well as its electrical manifestation at the body surface. The study is divided in two main parts: modeling the action potential, and numerical simulations. For modeling the action potential a dimensional and asymptotic analysis is done. The key advance in this part of the work is that this analysis gives the steps to reliably control the action potential. It allows predicting the time/space scales and speed of any action potential that is to say the shape of the action potential and its propagation. This can be done as the explicit relations on all the physiological constants are defined precisely. This method facilitates the integrative modeling of a complete human heart with tissue-specific ionic models. It even proves that using a single model for the cardiac action potential is enough in many situations. For efficient numerical simulations, a numerical method for solving the heart-torso coupling problem is explored according to a level set description of the domains. This is done in the perspective of using directly medical images for building computational domains. A finite element method is then developed to manage meshes not adapted to internal interfaces. Finally, an anisotropic adaptive remeshing methods for unstructured finite element meshes is used to efficiently capture propagating action potentials within complex, realistic two dimensional geometries.

As many of the world’s nuclear power plants are near the end of their supposed life span a need arise to assess the components crucial to the safety of these plants. One of these crucial components is the concrete reactor confinement; to assess its condition, non-destructive testing (NDT) is an attractive method. Traditional testing of concrete structures has comprised of drilling out a sample and performing stress tests on it, but because of the radioactive environment inside the containment this method is far from ideal. NDT is of course possible to use at any structure but at reactor containments the benefits from not creating holes in the structure are prominent; NDT is also an attractive option from an esthetical point of view because it leaves the structure intact. The NDT method pertaining to this study is the impact echo method which comprise of applying a force on the structure, usually a hammer blow, and measuring the response with a receiver. The impact will excite waves propagating in the structure which gives rise to Lamb modes. Lamb modes are structural oscillations of the wall and it is the frequency of these modes that are used to determine the thickness of the wall. The elastic properties of the structure can in turn be obtained by measuring the velocities of the waves propagation. It is also possible to use the impact echo method to detect irregularities in the structure such as cracks or delamination. To simulate the dynamics of a system using NDT numerical methods such as finite element modeling (FEM) is often used. The purpose of this study is to assess the possibility to utilize absorbing layers using increasing damping (ALID) in models to reduce the computational time of FEM analyses. ALIDs are used at the edges to simulate an infinite system and are thus supposed to cancel out incoming waves to prevent unwanted reflection from the edges. The models in this study have all pertained to two dimensional plates utilizing infinitesimal strain theory; the decrease in computational time is significant when using ALIDs and for three dimensional models it would be even more so. The ALIDs are specified by length and maximum mass proportional Rayleigh damping (CMmax), in this study three different lengths are tested, 0.5, 1.5 and 4.5 m for CMmax ranging from 103 to 2*105 Ns/m. The damping is increased with increasing distance into the ALID with specified maximum value at the back edge. However, it should be noted that the increase in damping causes difference in impedance between elements and if this difference is too large it will cause reflections of waves at the boundary between the elements. The ALID must thus be defined so that it sufficiently cancels out the wave without causing unwanted reflections due to impedance differences. The conclusion is that the 0.5 m long ALID does not provide good results for any choice of maximum mass proportional Rayleigh damping. Both the 1.5 and 4.5 m long ALIDs are, however, concluded to be applicable; the 1.5 m ALID having 2*104 < CMmax <5*104 Ns/m and the 4.5 m ALID having 5*103 < CMmax < 104 Ns/m are choices that have shown promise in the performed simulations. The hope is that the results obtained in this study will aid in the development of numerical analysis techniques for NDT methods that can be used in the construction of new reactor confinements and/or maintenance of existing reactor confinements and other thick concrete structures. / Många av världens kärnkraftverk närmar sig slutet på sin beräknade livslängd och ett behov uppstår då att kunna utvärdera de komponenter som är väsentliga för säkerheten på dessa verk. Reaktoromslutningen i betong är en av dessa komponenter och oförstörande provning (NDT) är en attraktiv metod för att bedöma dess tillstånd. Traditionellt har utvärdering av betongkonstruktioner bestått av stresstester på borrprover men p.g.a. den radioaktiva miljön på insidan av omslutningen är denna metod ej att föredra. NDT är självklart möjligt att använda på allsköns betongkonstruktioner då det ger både konstruktionsmässiga och estetiska fördelar. NDT metoden som rör denna studie kallas impact echo och går ut på att man med en hammare slår till en punkt på väggen och mäter responsen en bit därifrån. Lasten ger upphov till vågor i form av deformation som propagerar i väggen och dessa ger i sin tur upphov till Lamb moder. Lamb moderna är strukturella oscillationer av väggen och genom att studera dess frekvenser kan väggens tjocklek bestämmas. Elastiska egenskaper i väggen erhålls utifrån de olika vågornas propageringshastigheter. Impact echo metoden kan även användas för att finna strukturella oegentligheter inuti väggen så som sprickor och delaminering. För att utföra numeriska simuleringar av dynamiska system med NDT-metoder är finita elementmetoden (FEM) användbar. Syftet med denna studie är att bedöma vilka möjligheter som finns för att implementera absorberande ränder med ökande dämpning (ALID) i datamodeller för att minska beräkningstiden av FEM-analyser. ALID används vid kanterna för att simulera ett oändligt system, dess uppgift är att dämpa bort inkommande vågor så att dessa ej reflekteras tillbaka och stör mätningarna. Samtliga modeller i denna studie är två-dimensionella med antagen oändligt liten spänning i normalriktningen. Vinsten i beräkningstid av att använda ALID är stor och ökar ytterligare om modellen utökas till tre dimensioner. Ett ALID definieras genom dess längd och maximala massproportionerlig Rayleigh-dämpning (CMmax). I denna rapport har längderna 0.5, 1.5 and 4.5 m använts med CMmax i intervallet från 103 till 2*105 Ns/m. Dämpningen ökar med ökat avstånd in i ALID med det specificerade maxvärdet vid den bakre kanten. Det bör noteras att skillnad i dämpning mellan element leder till skillnad i impedans; reflektioner av vågorna uppstår vid övergång från ett element med lägre impedans till ett med högre impedans. Ett ALID måste således vara definierat så att det dämpar bort tillräckligt av de inkommande vågorna utan att oönskade reflektioner i ALID uppstår. Studien pekar på att ett 0.5 m långt ALID inte åstadkommer önskvärda resultat för något av valen för CMmax som använts i denna rapport. Både det 1.5 och 4.5 m långa ALID har däremot get bra resultat; ett 1.5 m långt ALID bör ha 2*104 < CMmax <5*104 Ns/m och ett 4.5 m långt ALID 5*103 < CMmax < 104 Ns/m. Förhoppningen med studien är att resultaten skall underlätta utvecklingen av NDT-metoder som kan användas vid konstruktion och underhåll av reaktoromslutningar och andra tjocka betongkonstruktioner.

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Le but de ce travail de recherche est de contribuer à une meilleure compréhension de la dynamique de propagation et de la miscibilité de jets gravitaires au-dessous d’un liquide ambiant. Des expériences ont été réalisées en laboratoire à l’aide d’une plateforme expérimentale constituée d’un bassin parallélépipédique contenant de l’eau douce et d’un canal d’injection de section rectangulaire de jets gravitaires de concentration constante initiale fixée. Les calculs mathématiques et numériques sont basés sur les modèles RANS (Reynolds-Averaged Navier Stokes equations), k-ε (K-epsilon) et DCE (Diffusion-Convective Equation) de la fraction volumique de l’eau salée pour décrire la propagation et le mélange du jet gravitaire. L’évolution du front du jet obtenue expérimentalement est utilisée pour valider le modèle numérique. Par ailleurs, la comparaison des résultats obtenus sur l’écoulement moyen (z⁄z0.5 =U/Umax) avec ceux des études 2D expérimentales et numériques antérieures ont montré des similarités. La simulation numérique des champs hydrodynamiques montre que la vitesse maximale est atteinte à la position 0.18 z0.5, où z0.5 est la hauteur d’eau pour laquelle la vitesse moyenne u est égale à la moitié de la vitesse maximale Umax. / The aim of this investigation is to contribute to a better understanding of the propagation dynamics and the mixing process of dense gravity currents. The Laboratory experiments proceeded with a fixed initial gravity current concentration in one experimental set-up. The gravity currents are injected using a rectangular injection channel into a rectangular basin containing the ambient lighter liquid. The injection studied is said in unsteady state volume, as the Reynolds number lies in the range 1111 - 3889. The experiments provided the evolution of the boundary interface of the jet, and it is used to validate the numerical model. The numerical model depends on the Reynolds-Averaged Navier Stokes equations (RANS). The k-ε (K-epsilon) and the Diffusion-Convective Equation (DCE) of the saline water volume fraction were used to model the mixing and the propagation of the gravity current jet. On the other hand, comparison of the mean flow (z⁄z0.5 =U/Umax) with previous two-dimensional numerical simulations and experimental measurements have shown similarities. The numerical simulations of the hydrodynamic fields indicate that the velocity maximum at 0.18 z0.5, where z0.5 is the height at which the mean velocity u is the half of the maximum velocity Umax.

Cette thèse est dédiée à la modélisation et à l'analyse mathématique de modèles asymptotiques utilisés en océanographie décrivant la propagation des ondes internes à l'interface entre deux couches de fluides de densités différentes, soumis à la seule force de gravité.L'objectif de cette thèse est de construire et justifier de nouveaux modèles asymptotiques prenant en compte la variation de la topographie. Pour ce faire, on pose plusieurs hypothèses de petitesse sur la profondeur de l'eau et sur les déformations à l'interface et au fond. On s'intéresse plus particulièrement à deux régimes de variations topographiques, celui de moyenne amplitude et celui de lentes variations de grande amplitude.La première partie de cette thèse consiste à justifier rigoureusement et étudier mathématiquement (existence, unicité, stabilité et convergence de la solution) deux classes de modèles asymptotiques. Une classe de modèles couplés et une classe de modèles scalaires. Cette dernière classe est caractérisée par la description de la propagation unidirectionnelle des ondes internes.Dans la deuxième partie on propose un schéma numérique pour résoudre le modèle asymptotique couplé dérivé dans la première partie dans le cadre d'un font plat. Ce modèle existant dans la littérature a été reformulé d'une façon plus appropriée pour la résolution numérique en gardant le même ordre de précision que l'original et en améliorant ses propriétés de dispersion. Enfin nous présentons plusieurs simulations numériques pour valider notre schéma. / This thesis is dedicated to the modeling and the mathematical analysis of asymptotic models used in oceanography describing the propagation of internal waves at the interface between two layers of fluids of different densities, under the only influence of gravity.We aim here at constructing and justifying new asymptotic models taking into account variable topography. To this end, we assume several smallness assumptions on the depth of the water and on the deformations at the interface and at the bottom. We are interested in two topographic regimes, one for variations of medium amplitude and one for slow variations with large amplitude.In the first part of this thesis we rigorously justify and mathematically study (existence, uniqueness, stability and convergence of the solution) two classes of asymptotic models. A class of coupled models and a class of scalar models. The latter class is characterized by the description of the propagation of unidirectional internal waves. In the second part we propose a numerical resolution for the coupled asymptotic model derived in the first part restricted to the flat bottom case. This existing model in the literature has been rewritten under a new formulation more suitable for numericalresolution with the same order of precision as the standard one but with improved frequency dispersion. Finally, we present several numerical simulations to validate our scheme.

Este trabalho apresenta a simulação numérica do escoamento turbulento em torno de uma turbina eólica de eixo vertical de pequeno porte, Savonius tipo helicoidal com torção de 180° nas pás. Com o intuito de avaliar a metodologia computacional empregada os resultados numéricos obtidos são comparados com os resultados experimental e numérico contidos no estado da arte. Também, compara-se o coeficiente de toque da turbina Savonius helicoidal com a turbina Savonius convencional. As simulações numéricas são baseadas no Método de Volumes Finitos, e para tal emprega-se o programa Fluent /Ansys versão 13.0 que resolve as equações da continuidade e as equações de Navier-Stokes com médias de Reynolds, juntamente com o modelo de turbulência . As simulações são desenvolvidas empregando diferentes malhas computacionais em estudos transientes, tridimensionais, com a turbina estacionária. A avaliação da qualidade da malha é realizada através do método de Índice de Convergência de Malha (GCI) o qual analisa o quão longe os resultados estão da solução assintótica para a malha utilizada. Após a análise da qualidade de malha, realizam-se simulações com a turbina em rotação as quais fazem uso da malha contendo uma região móvel possibilitando a imposição de uma velocidade angular ao rotor. O coeficiente de torque é obtido nas simulações e a partir dele calcula-se o coeficiente de potência. Além da análise do desempenho do rotor realiza-se uma análise qualitativa das características do escoamento sobre a turbina. A turbina Savonius helicoidal apresenta um valor de coeficiente de potência de 0,175 para a razão de velocidade de ponta de 0,58 considerando correção do efeito de bloqueio. Os resultados obtidos apresentam boa concordância com os resultados publicados por outros autores. / This dissertation presents the numerical simulation of the turbulent flow around of a small sized vertical axis wind turbine, consisting in a helical Savonius type with a 180° degree of blade twist. In order to evaluate the used methodology the obtained results are compared with the state of the art numerical and experimental data. It will be also presented the comparison between the torque coefficient of the conventional Savonius turbine and the helical Savonius turbine. The numerical simulations are based on the Finite Volume Method (FVM), using the commercial code Fluent/ANSYS version 13.0, which solves the continuity and Navier-Stokes through the Reynolds time-averaged methodology, including the turbulence model. The simulations are developed using different computational meshes for transient and three-dimensional studies with the stationary turbine. The evaluating the quality of the mesh is performed by of Grid Convergence Index (GCI) method which analyzes how far the results are the asymptotic solution to the mesh used. After the evaluation of the mesh quality, it was simulated a case considering the rotor motion using the moving mesh configuration, allowing the imposition of an angular velocity to the turbine. In the post-processing stage, it is possible to obtain the torque coefficient on the rotor shaft, allowing the calculation of the power coefficient for the turbine. In addition to the performance analysis, it is also made a qualitative analysis of the flow characteristics over the turbine rotor and in both cases presenting a good correspondence with the results in the literature. The helical Savonius turbine presents a value of power coefficient of 0.175 to a tip speed ratio of 0.58 whereas blocking effect correction.

Ultra Low Frequency (ULF) waves are a ubiquitous feature of Earth's outer atmosphere, known as the magnetosphere, having been observed on the ground for almost two centuries, and in space over the last 50 years. These waves represent small oscillations in Earth's magnetic field, most often as a response to the external influence of the solar wind. They are important for the transfer of energy throughout the magnetosphere and for coupling different regions together. In this thesis, various features of these oscillations are considered. A detailed background on the history and previous study of ULF waves relevant to our work is given in the introductory chapter. In the following chapters, we predominantly use numerical methods to model ULF waves, which are carefully developed and thoroughly tested. We consider the application of these methods to reports on ground and spaced based observations, which allows a more in depth study of the data. In one case, the simulation results provide evidence for an alternative explanation of the data to the original report, which displays the power of theoretical modelling. An analytical model is also constructed, which is tested on simulation data, to identify the incidence and reflection of a class of ULF wave in the flank magnetosphere. This technique is developed with the aim of future applications to satellite data. Further to this, we develop models both in Cartesian and dipole geometries to investigate some of the theoretical aspects of the coupling between various waves modes. New light is shed on the coupling of compressional (fast) and transverse (Alfvén) magnetohydrodynamic (MHD) wave modes in a 3D dipole geometry. Overall, this thesis aims to develop useful numerical models, which can be used to aid in the interpretation of ULF wave observations, as well as probing new aspects of the existing wave theory.

Dans les disques protoplanétaires, les grains micrométriques croissent jusqu'à atteindre des tailles de planétésimaux avant de finalement former des planètes. Cependant,des études dynamiques ont montré qu'une fois que les grains atteignent une taille critique, ils dérivent rapidement vers l'étoile et y sont accrétés. Ce problème est connu comme la barrière de dérive radiale. De plus, des expériences en laboratoire ont montré que les grains peuvent fragmenter ou rebondir et ainsi arrêter la croissance avant les tailles kilométriques.Afin de passer outre ces barrières, plusieurs méthodes ont été proposés comme les pièges à particules (dans les vortex ou les sillons planétaires) qui demandent des évolutions dynamiques à grande échelle. Dans ce travail, nous choisissons d'étudier les propriétés intrinsèques de la poussière pendant leur croissance et plus particulièrement leur porosité.Nous développons un modèle d'évolution de la porosité pendant la croissance en fonction de la masse des grains pour plusieurs régimes d'expansion/compression (Kataoka et al. 2013, Okuzumi et al. 2012) et l'implémentons dans notre code SPH bifluide (Barrière-Fouchet et al. 2005). Nous trouvons que la croissance des grains poreux est accélérée en comparaison aux grains compacts et leur taille peut atteindre plusieurs kilomètres. De surcroît,la dérive est légèrement ralentie pour les grains poreux qui peuvent croître jusqu'à de plus grandes tailles avant de commencer à dériver vers l'étoile. Nous constatons aussi que les grains des régions externes du disque grossissent plus que quand l'effet de la porosité est négligé. Ces deux mécanismes peuvent aider les grains à outrepasser la barrière de dérive radiale, notamment en passant dans le régime de traînée de Stokes, et ainsi former des planétésimaux.Nous étudions aussi l'effet de la fragmentation et du rebond sur le comportement des grains. En considérant un seuil de fragmentation constant, nous observons que la croissance de grains poreux est retardée un temps par la fragmentation mais qu'elle se poursuit vers de grandes tailles et par conséquent, permet de passer outre les problèmes dus à la fragmentation et à la dérive radiale. Cependant, les grains très poreux sont plus fragiles et peuvent se fragmenter plus facilement entraînant une accrétion massive des poussières dans l'étoile. De plus, nous montrons que les effets du rebond peuvent être négligés devant ceux de la fragmentation.Enfin, nous observons également que la taille des monomères et du paramètre de viscosité turbulente peut avoir une influence sur l'évolution de la porosité et donc de la poussière dans le disque.La porosité permet donc de favoriser la croissance des grains et accélérer le découplage des grains. Les grains très poreux peuvent être plus sensibles à la fragmentation.Cependant, les effets collectifs de la poussière couplés à la porosité peuvent aider les grains à outrepasser les barrières de formation planétaire. La barrière de rebond peut être négligée dans le cas de grains poreux devant les autres barrières. Enfin,l'intensité de la turbulence altère la croissance et ainsi le devenir de la poussière.La taille des monomères modifie le facteur de remplissage sans toutefois impacter le découplage des grains dans les parties internes / In protoplanetary discs, micron-sized grains should grow up to planetesimal sizes in order to ultimately form planets. However, dynamical studies show that once they reach a critical size, they drift rapidly into the accreting star. This is known as the radial-drift barrier. Moreover, laboratory experiments have shown that grains can fragment or bounce, stopping the growth towards planetesimal sizes.In order to overcome those barriers, several methods have been proposed such as particles traps (e.g. vortices or planet gaps) which all involve large-scale dynamics.In this work, we choose to investigate the intrinsic properties of the grains during their growth, in particular their porosity.We thus consider the growth of grains with variable porosity as a function of their mass in several regimes of compression/expansion (Kataoka et al. 2013, Okuzumiet al. 2012) and implement it in our 3D SPH two-fluid code (Barrière-Fouchetet al. 2005).We find that growth is accelerated for porous grains that can reach kilometersizes. On the other hand, drift is slightly slowed down for porous grains that can grow up to larger sizes before drifting towards the star. As a result, grains in the outer regions of the disc reach larger sizes than when porosity is neglected. Those two mechanisms can help grains overcome the radial-drift barrier and form planetesimals.The Stokes drag regime appears to play a substantial part in maintaining grains in the disc.Considering a constant fragmentation threshold, we also find out that growth is delayed because of fragmentation but reaching large sizes and thus overcoming problems due to fragmentation and radial drift is still possible. However, very fluffy grains are fragile and can be easily disrupted leading to a massive accretion of dust into the star. Moreover, we show that the effects due to dust bouncing can be neglected compared to fragmentation.Finally, we investigate the influence of the size of monomers and -parameter on the evolution of porosity and then dust in the disc.Dust growth is accelerated by porosity and thus promotes grains decoupling. Very fluffy grains are more affected by fragmentation. However, dust collective effects and porosity can help grains to overcome planet formation barriers. Besides,the bouncing barrier can be neglected in the case of porous dust compared to other barriers. Finally, the intensity of turbulence can alter the growth and so the outcome of dust. The size of monomers modifies the grain filling factor without impacting dust decoupling in the inner parts of the disc

L'objectif de cette thèse est d'améliorer la compréhension des phénomènes jouant un rôle dans la mesure effectuée dans un analyseur sanguin, en particulier le comptage et la mesure de volumétrie d'une population de globules rouges reposant sur l'effet Coulter. Des simulations numériques sont effectuées dans le but de prédire la dynamique des globules rouges dans les zones de mesure et pour reproduire la mesure électrique associée, servant au comptage et à la volumétrie des cellules. Ces simulations sont effectuées à l'intérieur de configurations industrielles d'analyseur sanguin, en utilisant un outil numérique développé à l'IMAG, le solveur YALES2BIO. En utilisant la méthode des frontières immergées avec suivi de front, un modèle de particule déformable est introduit, celui-ci prend en compte le contraste de viscosité ainsi que les effets mécaniques de la courbure et de l'élasticité sur la membrane. Le solveur est validé grâce à de nombreux cas tests parcourant différents régimes et effets physiques. L'écoulement fluide dans cette géométrie d'analyseur sanguin est caractérisée par un fort gradient de vitesse axial dans la direction de l'écoulement, impliquant la présence d'un écoulement extensionnel au niveau du micro-orifice, là où a lieu la mesure. La dynamique des globules rouges est étudiée par des simulations numériques pour différentes conditions initiales, telles que sa position ou son orientation. Il est observé que les globules rouges vont se réorienter selon l'axe principal de l'analyseur sanguin dans tous les cas. Pour comprendre le phénomène, des modèles analytiques sont adaptés au cas des écoulements extensionnels et reproduisent correctement les tendances de réorientation.Cette thèse présente également la reproduction de la mesure électrique utilisée pour le comptage et la mesure de la distribution des volumes de globules rouges. De nombreuses simulations de la dynamique des globules rouges sont effectuées et utilisées pour générer l'impulsion électrique correspondant au passage du globule rouge dans le micro-orifice. Les amplitudes d'impulsions électriques résultantes permettent la caractérisation de la réponse électrique en fonction des paramètres initiaux de la simulation par une approche statistique. Un algorithme de Monte-Carlo est utilisé pour la quantification des erreurs de mesure liées à l'orientation et la position des globules rouges dans le micro-orifice. Ceci permet la génération d'une distribution de volume mesurée pour une population de globules rouges bien définie et la caractérisation des erreurs de mesure associées. / The aim of this thesis is to improve the understanding of the phenomena involved in the measurement performed in a blood analyzer, namely the counting and sizing of red blood cells based on the Coulter effect. Numerical simulations are performed to predict the dynamics of red blood cells in the measurement regions, and to reproduce the associated electrical measurement used to count and size the cells. These numerical simulations are performed in industrial configurations using a numerical tool developed at IMAG, the YALES2BIO solver. Using the Front-Tracking Immersed Boundary Method, a deformable particle model for the red blood cell is introduced which takes the viscosity contrast as well as the mechanical effects of the curvature and elasticity on the membrane into account. The solver is validated against several test cases spreading over a large range of regimes and physical effects.The velocity field in the blood analyzer geometry is found to consist of an intense axial velocity gradient in the direction of the flow, resulting in a extensional flow at the micro-orifice, where the measurement is performed. The dynamics of the red blood cells is studied with numerical simulations with different initial conditions, such as its position or orientation. They are found to reorient along the main axis of the blood analyzer in all cases. In order to understand the phenomenon, analytical models are adapted to the case of extensional flows and are found to reproduce the observed trends.This thesis also presents the reproduction of the electrical measurement used to count red blood cells and measure their volume distribution. Numerous dynamics simulations are performed and used to generate the electrical pulse corresponding to the passage of a red blood cell inside the micro-orifice. The resulting electrical pulse amplitudes are used to characterize the electrical response depending on the initial parameters of the simulation by means of a statistical approach. A Monte-Carlo algorithm helps quantifying the errors on the measurement of cell depending on its orientation and position inside the micro-orifice. This allows the generation of a measured volume distribution of a well defined red blood cell population and the characterization of the associated measurement errors.