A three-dimensional flow field produced by supersonic twin-jet impingement is studied using a large eddy simulation (LES). The numerical model consists of two parallel axisymmetric jets of diameter 𝐷*, 3𝐷* apart, issuing from a plane which is at a distance H*=4𝐷* above the ground. The jet diameter 𝐷*, mean velocity 𝑊ₒ*, mean density 𝜌ₒ* and mean temperature 𝑇ₒ* at the jet center in the exit plane are used as reference values. The Mach number and Reynolds number of the jets are M=1.5 and Re=550,000, respectively. This model is closely related to the experimental setup of Elavarasan <i>et al.</i>(Elavarasan <i>et al.</i>, 2000). The three-dimensional time-dependent compressible Navier-Stokes equations are solved using the method of lines. The convective terms are discretized using a fifth-order WENO scheme, whereas the viscous terms are discretized using a fourth-order central-differencing scheme. A low-storage five-stage fourth-order Runge-Kutta scheme is used to advance the solution in time. Code verification is achieved by comparison with flat-plate boundary-layer linear stability analysis, and computational data by Bendiks <i>et al.</i> (Bendiks <i>et al.</i>, 1999). for a compressible turbulent round jet. Instantaneous flow, mean flow and Reynolds stresses for the twin-jet impingement are presented and discussed. The results reveal the existence of flapping behavior in the fountain. The flapping fountain is the vortical structure formed by the alternating merging of a primary vortex tube with a secondary vortex tube induced by the neighboring primary vortex tube. The nondimensional period of flapping is found to be 7𝐷*/𝑊ₒ*. High unsteadiness and strong interaction between the fountain and the jets are also observed. Due to the high diffusion and spreading rate of the fountain, the interaction between the fountain and the jets is only significant up to a height which is less than 3𝐷*. It is found that the mean peak velocity in the fountain is 0.40406 𝑊ₒ* and it occurs at 0.536607𝐷* from the ground. The suitability of the fifth-order WENO scheme to simulate turbulent flow field with embedded shocks is also demonstrated by its capability to capture unsteady shock waves in the impingement regions. / Ph. D.

When a semi-infinite body of homogeneous fluid initially at rest behind a vertical retaining wall is suddenly released by the removal of the barrier the resulting flow over a horizontal or sloping bed is referred to as a dam-break flow. When resistance to the flow is neglected the exact solution, in the case of a stable horizontal bed with or without `tail water', may be obtained on the basis of shallow-water theory via the method of characteristics and the results are well known. Discrepancies between these shallow-water based solutions and experiments have been partially accounted for by the introduction of flow resistance in the form of basal friction. This added friction significantly modifies the wave speed and flow profile near the head of the wave so that the simple exact solutions no longer apply and various asymptotic or numerical approaches must be implemented to solve these frictionally modified depth-averaged shallow-water equations. When the bed is no longer stable so that solid particles may be exchanged between the bed and the water column the dynamics of the flow becomes highly complex as the buoyancy forces vary in space and time according to the competing rates of erosion and deposition. Furthermore, when the Froude number of the flow is close to unity perturbations in the height and velocity profiles grow into N-waves and the bed below develops ripples which act to sustain the N-waves in the fluid above. It is our intention here to study dam-break flows over erodible sloping beds as agents of sediment transport taking into account basal friction as well as the effects of particle concentrations on flow dynamics including both erosion and deposition. We shall consider shallow flows over initially dry beds and investigate the effects of changes in the depositional and erosional models employed as well as in the nature of the drag acting on the flow and the slope of the bed. These models include effects hitherto neglected in such studies and offer insights into the transport of sediment in the worst case scenario of the complete and instantaneous collapse of a dam. / Mathematics

When a semi-infinite body of homogeneous fluid initially at rest behind a vertical retaining wall is suddenly released by the removal of the barrier the resulting flow over a horizontal or sloping bed is referred to as a dam-break flow. When resistance to the flow is neglected the exact solution, in the case of a stable horizontal bed with or without `tail water', may be obtained on the basis of shallow-water theory via the method of characteristics and the results are well known. Discrepancies between these shallow-water based solutions and experiments have been partially accounted for by the introduction of flow resistance in the form of basal friction. This added friction significantly modifies the wave speed and flow profile near the head of the wave so that the simple exact solutions no longer apply and various asymptotic or numerical approaches must be implemented to solve these frictionally modified depth-averaged shallow-water equations. When the bed is no longer stable so that solid particles may be exchanged between the bed and the water column the dynamics of the flow becomes highly complex as the buoyancy forces vary in space and time according to the competing rates of erosion and deposition. Furthermore, when the Froude number of the flow is close to unity perturbations in the height and velocity profiles grow into N-waves and the bed below develops ripples which act to sustain the N-waves in the fluid above. It is our intention here to study dam-break flows over erodible sloping beds as agents of sediment transport taking into account basal friction as well as the effects of particle concentrations on flow dynamics including both erosion and deposition. We shall consider shallow flows over initially dry beds and investigate the effects of changes in the depositional and erosional models employed as well as in the nature of the drag acting on the flow and the slope of the bed. These models include effects hitherto neglected in such studies and offer insights into the transport of sediment in the worst case scenario of the complete and instantaneous collapse of a dam. / Mathematics

An interface-preserving level set method is incorporated into the Reynolds-Averaged Navier-Stokes (RANS) numerical method to simulate the application of the green water phenomena around a platform and the breaking wave above the deck. In the present study, this method is used to evaluate the laminar in two dimension plane with fixed orthogonal grids. In this method, it is assumed that the free surface is modeled as immiscible two-phase flow (air and water). A level set function can present the individual fluids, and the interface between two-phase is represented by the zero level set. In addition, the level set evolution equation is coupled with the conservation equations for mass and momentum, which will be solved in the transformed plane. For different purposes, there are several block domains in the application grid. Chimera domain decomposition technique is employed to handle such embedding, overlapping, or matching grids. Several simple test cases were performed to demonstrate the feasibility of this method. The comparisons between the ENO scheme and the WENO scheme will be illustrated in the Zalesak's disk case and will further prove that the WENO scheme is superior to the ENO scheme. The propagation of continuous wave case will validate some properties of wave and determine the importance of some parameters in code. Moreover, the method will be applied in simulation of green water around a two dimensional platform. By configuring different deck heights, some distinct phenomena can be represented. Lastly, it is crucial to observe the green water phenomena around the platform deck by applying the velocity-extrapolation routine.

No description available.

Esta tesis está dedicada al desarrollo, aplicación y test de métodos para la simulación numérica de problemas procedentes de la física y de la ingeniería electrónica. La principal herramienta aplicada a lo largo de todo el trabajo es la ecuación de Vlasov (transporte) en la forma de la Boltzmann Transport Equation (BTE) para la descripción del transporte de partículas cargadas en plasmas y dispositivos electrónicos: las cargas se mueven bajo el efecto de un campo de fuerza y sufren scattering debido a otras cargas o fonones (pseudo-partículas que describen de manera efectiva las vibraciones de los iones del retículo cristalino).La BTE ha de ser acoplada con una ecuación o sistema de ecuaciones para calcular el campo de fuerza: para estructuras simples se usa la ecuación de Poisson; para plasmas, donde los efectos magnéticos no se pueden despreciar debido a las altas velocidades de las partículas, se usa la fuerza de Lorentz, por lo cual se han de resolver las ecuaciones de Maxwell; en nanoestructuras, por ejemplo transistores con dimensiones confinadas, la ecuación de Poisson necesita ser acoplada con la ecuación de Schrödinger para la descripción de las dimensiones cuánticas y para la descomposición en sub-bandas, o niveles de energía.Las colisiones son el scattering que las cargas padecen debido a las interacciones con otras cargas o con el retículo cristalino fijo, representado en forma de fonones. En la tesis se emplean diversos operadores de scattering: los más simples son operadores lineales de relajación; se estudia un modelo para la simulación de semiconductores donde se tienen en cuenta colisiones con fonones acústicos, en aproximación elástica, y fonones ópticos.Tras la introducción, en el primer capítulo se desarrollan los métodos numéricos más importantes: primero un método de interpolación no oscilante (PWENO), necesario para evitar las oscilaciones producidas por la reconstrucción por polinomios de Lagrange, que incrementa la variación total cuando aparecen choques: las oscilaciones en el espacio de fases son características del problema, pero si el método añade oscilaciones espúreas (es decir, debidas al método en sí), entonces el resultado numérico no tiene sentido, o simplemente explota. El segundo método numérico fundamental es la técnica de splitting: cuando se resuelve un problema complicado, si se puede dividir en sub-problemas y resolverlos por separado, entonces se puede reconstruir una aproximación para el problema completo; esta técnica se usa para el time splitting (separación de la parte de transporte y de colisión) y el splitting dimensional (dividir el espacio de fases en posición y velocidad). La tercera herramienta fundamental es un sólver para advección lineal: se usan dos métodos, uno basado en trazar hacia atrás las características a nivel puntual y otro basado en reconstruir valores integrales en segmentos en lugar de puntos; el primero controla mejor las oscilaciones, el segundo fuerza la conservación de masa.En el capítulo 2 estos métodos se aplican a algunos tests conocidos para averiguar su solidez.En el capítulo 3 estos métodos se aplican a la simulación de un diodo, y los resultados se comparan con resultados anteriores obtenidos por esquemas Runge-Kutta basados en diferencias finitas para aproximar las derivadas parciales.El capítulo 4 está dedicado a la construcción y simulación de modelos intermedios entre una ecuación cinética, con operador de colisión de tipo relajación, y su aproximación más grosera, ésta última siendo la ecuación del calor. Para obtener modelos intermedios, se busca un cierre de las ecuaciones de los momentos de orden cero y uno. Se proponen esquemas "asymptotic-preserving" para la ecuación cinética, que evitan la stiffness de la parte de advección a través de una descomposición de la función de distribución en su media más fluctuaciones. En cuanto a las clausuras de las ecuaciones de los momentos, se proponen esquemas de relajación para aislar las no-linealidades. Estos métodos son aplicados a un test conocido, el Su-Olson test.El último capítulo está dedicado a la simulación de un MOSFET (Metal Oxide Semiconductor Field Effect Transistor) 2D de dimensión nanométrica en el que los electrones se comportan como partículas en una dimensión y como ondas en las dimensiones confinadas. La descomposición en sub-bandas se realiza a través de una ecuación de Schrödinger 1D en estado estacionario. Las dimensiones, así como las sub-bandas, están acopladas por la ecuación de Poisson en la expresión de la densidad, y por el operador de colisión. Se propone un sólver microscópico para estados transitorios, basado en técnicas de splitting para las BTEs (una para cada nivel de energía), métodos de características para el transporte y una iteración de tipo Newton para resolver el problema acoplado Schrödinger-Poisson para el cálculo del campo de fuerza. / This thesis is dedicated to the development, application and test of numerical methods for the numerical simulation of problems arising from physics and electronic engineering. The main tool which is used all along the work is the Vlasov (transport) equation in the form of the Boltzmann Transport Equation (BTE) for the description of the transport and collisions of charged particles in plasmas and electronic devices: charge carriers are driven by a force field and scattered by other carriers or phonons (pseudo-particles giving an effective representation of the oscillating field produced by the vibrating ions).The BTE must be coupled to an equation or a system of equations for the computation of the force field: for simple structures the Poisson equation is used; for plasmas, where the magnetic phenomena cannot be neglected due to the high velocities of the particles, the Lorentz force is used, so the Maxwell equations have to be solved; for nanostructures, e.g. transistors with confined dimensions, the Poisson equation needs coupling with Schrödinger equation for the description of the quantum dimensions and the decomposition into subbands, or energy levels.Collisions mean the scattering the carriers suffer due to the interactions with other carriers or the fixed lattice, in form of phonons. All along the thesis several scattering operator are used: the simplest ones are linear relaxation-time operators; a model for the simulation of a semiconductor is studied in which collisions are taken into account with acoustic phonons, in the elastic approximation, and optical phonons.After the introduction, in the first chapter the most important numerical methods are developed: first of all a pointwise non-oscillatory interpolation method (PWENO) needed to avoid the simple Lagrange polynomial reconstruction, which increases the total variation when shocks appear: oscillations are part of the physics of the problem, but if the method adds spurious, non-physical oscillations, then the numerical result is meaningless, or it simply blows up. The second fundamental numerical method is the splitting technique: when solving a complicated problem, if we are able to subdivide it into sub-problem and solve them for separate, then we can reconstruct an approximation for the complete problem; this technique is used for both time splitting (separate transport from collisions) and dimensional splitting (split the phase space into either dimensions). The third fundamental instrument is the solver for linear advections: two methods are used, one based on pointwise following backwards the characteristics and another one based on reconstructing integral values along segments instead of point values; the first one controls better oscillations, the second one forces mass conservation.These methods are applied in chapter 2 to some well-known benchmark tests to control their robustness.In chapter 3 these methods are applied to the simulation of a diode, and the results compared to previous results obtained by Runge-Kutta schemes based on finite differences schemes for the approximation of the partial derivatives.Chapter 4 is dedicated to the construction and simulation of intermediate models between a kinetic equation, with relaxation-time collision operator, and its coarsest approximation, this one being the heat equations. In order to obtain intermediate models, the moment equations are closed at zeroth and first order. Asymptotic-preserving schemes are proposed for the kinetic equation, which avoid the stiffness of the advection part by decomposing the distribution function into its average plus fluctuations. As for the moment closures, relaxation schemes are proposed in order to confine the non-linearities in the right hand side. These methods are then applied to a known benchmark, the Su-Olson test.The last chapter is dedicated to the simulation of a nanoscaled 2D MOSFET (Metal Oxide Field Effect Transistor) in which electrons behave as particles in one dimension and as waves in the confined dimensions. The subband decomposition is realized through a stationary-state 1D Schrödinger equation. The dimensions as well as the subbands are coupled by the Poisson equation in the expression of the density and by the collision operator. A transient-state microscopic solver is proposed, based on splitting techniques for the BTE's (one for each energy level), characteristics methods for the transport and a Newton iteration for the solution of the coupled Schrödinger-Poisson system for computing the force field.

No description available.

Cette étude a été l'occasion d'étudier les effets liés à la présence d'un cisaillement particulier de l'écoulement moyen sur le phénomène d'interaction choc/turbulence. Dans un premier temps, un outil de calcul performant et modulaire fondé sur une approche orientée objet a été développé afin de réaliser des simulations numériques directes de ce type d'écoulement. L'utilisation de schémas numériques à capture de choc et d'ordre élevé de type WENO ont permis une résolution fidèle des équations de Navier-Stokes compressibles. Dans un deuxième temps, une analyse poussée des effets de ce type de cisaillement sur la turbulence en l'absence de choc a été réalisée. Cette première étude a été l'occasion de dégager l'influence de plusieurs paramètres influents pour cette configuration d'écoulement. Enfin, dans un dernier temps, l'étude du phénomène d'interaction choc/turbulence cisaillée en présence de gradients moyens de température et de masse volumique a permis de souligner l'activation de phénomènes physiques caractéristiques à cette configuration. Ce travail permet également d'apporter une base de données de résultats susceptible d'être confrontée avec les modèles de turbulence et constitue un point de vue intéressant pour l'étude du phénomène d'interaction choc/couche limite. / This study sheds some light on the effects of a specific sheared flow over the shock / turbulence interaction phenomenon. An efficient and modular computational tool using an oriented object approach has first been developed in order to carry out direct numerical simulations of this configuration. The use of high order shock capturing schemes allows to solve accurately the turbulent flow, even in presence of physical discontinuities. A detailed study concerning the effects of this specific mean shear on the turbulent flow has then been conducted in a shock-free configuration. This preliminary study emphases some significant parameters of this flow configuration. In a second step, DNS of the interaction between the turbulent shear flow and a normal shock ware are performed. These simulations are compared to the isotropic turbulence / shock interaction situation, which allows to underline the activationof specific mechanisms due to the presence of the mean shear in the upstream flow. An interesting database is now available and can be used to assess and improve turbulence models. This is also an interesting point of view for studying the shock/boundary layer interaction phenomenon.

Le contexte de cette étude est l’optimisation de la combustion turbulente prémélangée de syngaz pour la production propre d’énergie. Un brûleur CH4/air de type bec Bunsen avec forçage turbulent multi-échelles produit par un système de trois grilles, est simulé numériquement par différentes techniques de simulation des grandes échelles (SGE), et les résultats sont comparés à l’expérience. On a développé et appliqué une formulation bas-Mach du solveur Navier-Stokes basé sur différents schémas numériques, allant des différences finies centrées d’ordre 4 à des versions avancées des schémas WENO d’ordre 5. La méthodologie est évaluée sur une série de cas-tests classiques (flamme laminaire 1D prémélangée, turbulence homogène et isotrope en auto-amortissement), et sur des simulations 2D de la flamme turbulente prémélangée expérimentale. Les SGE implicites (ILES), i.e. sans aucune modélisation sous-maille, et explicites avec le modèle de flamme épaissie et un modèle de plissement sous-maille nouvellement élaboré (TFLES), sont appliquées à la simulation 3D du brûleur expérimental. Les résultats montrent que l’approche TFLES avec un schéma d’ordre élevé à faible dissipation numérique prédit correctement la longueur de la flamme et la densité de surface de flamme. La SGE implicite avec un schéma WENO avancé produit une flamme trop courte mais réaliste à condition que la taille de la maille soit de l’ordre de l’épaisseur de flamme laminaire. La représentation des interactions flamme/turbulence est néanmoins très différente entre TFLES et ILES. / The context of this study is the optimization of premixed turbulent combustion of syngas for clean energy production. A Bunsen-type CH4/air turbulent premixed burner with a multi-scale grid generator is simulated with different Large Eddy Simulation (LES) strategies and compared to experimental results. A low-Mach formulation of a compressible Navier-Stokes solver based on different numerical methods, ranging from 4th order central finite difference to 5th order advanced WENO schemes, is developed and applied. Classical test cases (1D laminar premixed flame, decaying HIT), and 2D simulations of the turbulent premixed flame are performed to assess the numerical methodology. Implicit LES (ILES), i.e. LES without any explicit subgrid modeling, and explicit LES with the Thickened Flame model and subgrid scale flame wrinkling modelling (TFLES) are applied to simulate numerically the 3D experimental burner. Results show that TFLES with a high-order low dissipation scheme predicts quite well the experimental flame length and flame surface density. ILES with advanced WENO schemes produces a slightly shorter although realistic flame provided the grid spacing is of order of the laminar flame thickness. The representation of flame/turbulence interactions in TFLES and ILES are however quite different.

L’amélioration des turbomachines passe par l’augmentation de leurs vitesses de rotation et peut conduire leurs composants à se trouver en présence d’un régime d’écoulement supersonique, en particulier leurs systèmes de pivoterie à air. L’étude d’une butée aérodynamique en régime supersonique est traitée dans ce manuscrit et s’inscrit dans la continuité de la recherche sur les butées hautes vitesses mais qui n’a que très peu été abordée dans la littérature. Ce problème se trouve à la frontière entre deux domaines scientifiques : la lubrification et l’aérodynamique. L’enjeu ici est développer un modèle réaliste traduit par un code de calcul écrit en FORTRAN, capable de capturer les phénomènes liés au régime supersonique (choc, détente) et d’être adapté à la géométrie des films minces. Pour cela, deux modèles ont été développés et codés à l’aide de la méthode numérique des différences finies : les équations de Reynolds Modifiées et les équations de Navier-Stokes adaptées aux films minces. Ce premier modèle est une extension de l’équation de Reynolds généralisée, prenant en compte l’inertie et déjà utilisé dans des études de la lubrification. Le second modèle a été établi à partir des équations de Navier-Stokes et conserve leur forme. Ce système possède l’avantage de pouvoir utiliser les outils numériques adaptés à la capture de choc (WENO). La comparaison des deux modèles montre que les équations de Reynolds Modifiées ne sont pas suffisantes pour l’étude d’un écoulement film mince en régime supersonique. Les résultats des simulations menées montrent la présence d’une détente sur le changement d’inclinaison du double profil qui dépend de la vitesse, de la température et de l’angle de la géométrie. Cette détente, même dans des conditions sévères de fonctionnement (grandes vitesses ou fort convergent), n’a pas beaucoup d’influence sur le comportement global statique de la butée. Les résultats montrent également que contrairement à la théorie des écoulements supersoniques, aucun choc n’est observé en film mince supersonique. Une transition géométrique obtenue par homothétie, entre un écoulement contenant un choc et un autre n’en contenant pas, a été observée à une certaine valeur du rapport des longueurs d’adimensionnement pour une vitesse et une géométrie donnée. L’extrapolation de ces résultats pour un cas réaliste montre qu’un choc ne peut se produire qu’à partir de 5500 m/s pour une épaisseur de film de 40 μm avec epsilon = 0.001. Il est donc peu probable qu’un choc ne se produise dans une butée en conditions supersoniques dans le cadre industriel. / The improvement of turbomachines requires to increase their rotational speeds and can leads components to be in presence of a supersonic regime, particularly their air bearing systems. This manuscript deals with a study of an aerodynamic thrust bearing in a supersonic regime. This work belongs to the research field on the high-speed thrust bearings, but very few studies are focused on this subject. This problem is at the boundary between two scientific fields: lubrication and aerodynamic. The aim of this study is to develop models transcribed as a FORTRAN code, able to capture phenomenon related to the supersonic regime (shock, expansion wave) and adapted to the thin film geometry. For this, two models have been developed as well as computer codes related to these models using the finite difference method: the Modified Reynolds equations and the Navier-Stokes equations adapted to thin films. The first model is an extension of the generalized Reynolds equation, taking into account inertia effects. It is a model already used in lubrication studies. The second model was developed from the Navier-Stokes and has their shape. This system has the advantage of using numerical schemes for shock capturing (WENO). The comparison of the two models shows that the Modified Reynolds equations are not appropriate to the study of a supersonic air thin film. Numerical results show the presence of an expansion wave at the end of the sloping region of the tapper flat geometry which depends on speed, on temperature and on the angle of the geometry. This expansion wave, under severe conditions, does not have much influence on the overall static behavior of the thrust bearing. The results also show that, contrary to the supersonic flow theory, a shock is not observed in a supersonic thin film. A geometrical transition obtained by homothetic, between a flow containing a shock and another with no shock, is observed at a given value of the characteristic length ratio for a given speed and geometry. Extrapolation of these results for a realistic case shows that a shock occurs from 5500 m/s for a film thickness of 40 μm with epsilon = 0.001. It is therefore unlikely that a shock occurs in a supersonic thrust bearing in industrial settings.