In this paper we present detailed Euler-Euler Large Eddy Simulations (LES) of dispersed bubbly flow in a rectangular bubble column. The motivation of this study is to investigate potential of this approach for the prediction of bubbly flows, in terms of mean quantities. The set of physical models describing the momentum exchange between the phases was chosen according to previous experiences of the authors. Experimental data, Euler-Lagrange LES and unsteady Euler-Euler Reynolds-Averaged Navier-Stokes model are used for comparison. It was found that the presented modelling combination provides good agreement with experimental data for the mean flow and liquid velocity fluctuations. The energy spectrum made from the resolved velocity from Euler-Euler LES is presented and discussed.

In CANDU reactors, under normal operating conditions, the inlet headers collect and distribute single-phase liquid flow (heavy water) to the fuel cooling channels via the feeders. However, under some postulated loss of coolant accidents, the inlet headers may receive two-phase fluid (steam/water) and the fluid forms a stratified region inside the header. To predict the thermalhydraulic behaviour of headers for the reactor safety analysis, the two-phase flow distribution within the headers and through the feeders must be modelled. In order to analyse the two-phase flow behaviour of a scaled CANDU inlet header / a transparent and instrumented version of a header with 5 feeders was previously built in the Mechanical Engineering Department of Middle East Technical University (METU-Two Phase Flow Test Facility / METU-TPFTF). The aim of this study is to investigate two-phase flow distribution through multiple outlets from such a horizontal drum both numerically and experimentally. For this purpose, three-dimensional incompressible finite difference equations in cylindrical coordinates were derived by using two-fluid model to simulate adiabatic two-phase flow (air/water) in the header numerically. The discretized equations were then programmed into a computer code which was developed specifically for modelling the header type geometry. A method based on the principles of Implicit Multi Field (IMF) technique has been utilised to solve those equations. The solution algorithm was tested by using some numerical benchmark problems. A number of experimental tests covering single and two-phase flow distribution through outlet pairs from the header were performed. Void fractions and flow rates obtained from these tests are in good agreement with the code results. The code also predicts the void fraction and pressure distribution in the header satisfactorily.

[pt] Escoamentos bifásicos no regime anular são caracterizados pela formação de um filme de líquido ao redor das paredes do duto com a fase gasosa escoando na área central do duto. O presente trabalho consiste na simulação numérica de um escoamento anular em tubulação horizontal, com e sem transferência de calor através de um código unidimensional baseado no Modelo de Dois Fluidos. São considerados dois pares de fluidos, sendo o primeiro ar-água, o qual é vastamente estudado na literatura e um fluido típico encontrado na produção de petróleo formado de gás natural e óleo. Parâmetros característicos do padrão de escoamento anular como gradiente de pressão, fator de atrito da interface e espessura do filme de líquido são determinados e comparados com dados experimentais e numéricos, apresentando boa concordância. O gás natural é modelado como gás real, através da aplicação da Equação de Estado de Peng-Robinson e comparado com a modelagem utilizando Equação de Gases Ideais. Para o fluido típico selecionado, este efeito é muito pequeno tanto com relação aos parâmetros hidrodinâmicos como velocidades das fases e queda de pressão como nos parâmetros térmicos como campo de temperatura, perda de calor para o ambiente e coeficiente bifásico de troca de calor. / [en] Annular two-phase flow is characterized by the formation of a liquid layer spread around the pipe circumference with gas flowing in the core area of the pipe. The present work consists in the numerical simulation of an annular flow in horizontal pipe, with and without heat transfer through a one-dimensional code based on the Two Fluid Model. Two pairs of fluids are considered, being the first air-water, which is widely studied in the literature and a typical natural gas and oil fluid from production oil fields. Characteristics parameters of annular flow such as pressure drop, interface friction factor e liquid film height are obtained and compared with experimental and numerical data, showing in both cases good agreement. The natural gas is modeled as real gas, using the Peng-Robinson Equation of State, and compared with the ideal gas modeling. For the typical fluid selected, this effect is quite small on the hydrodynamics parameters such as phases velocities and pressure drop and on the thermal parameters such as temperature, heat loss for the environment and heat exchange coefficient.

Émissions polluantes, les motoristes souhaitent contrôler au mieux l’atomisation du carburant, injecté généralement sous forme de jets ou de nappes liquides. Les essais étant long et coûteux, leur remplacement par un outil numérique capable de simuler le processus d’atomisation permettrait non seulement une réduction des coûts importante mais faciliterait également la phase de conception. Toutefois, en raison du caractère multi-échelle du phénomène, il est difficile de le décrire dans son ensemble avec les approches habituellement utilisées en mécanique des fluides numérique.L’objectif de cette thèse est de concevoir une nouvelle approche qui permettra à terme de simuler l’atomisation pour une configuration industrielle complète. Celle-ci consiste à coupler deux types de modèles. Le premier, dit modèle bifluide, est un modèle à deux fluides compressibles basé sur les équations de Navier-Stokes diphasiques. Celui-ci permet de décrire les grandes échelles du phénomène d’atomisation correspondant à la formation de ligaments et d’amas liquides dans la zone proche de l’injecteur. Le second, dit modèle de spray, est basé sur une équation cinétique. Dans la zone située en aval de l’injecteur, ce dernier permet de décrire de manière statistique l’évolution du brouillard de gouttelettes issues de la fragmentation primaire du jet de carburant. Le point délicat, à la fois sur le plan de la modélisation et sur celui de l’algorithmique, réside dans le couplage des deux modèles. Celui ci a été réalisé grâce à l’introduction de deux modèles auxiliaires permettant de traiter le transfert de liquide entre le modèle bifluide et le modèle de spray par atomisation ou ré-impact.L’approche proposée a été appliquée à la simulation numérique de nappes liquides cisaillées. Les comparaisons entre les résultats numériques et des résultats expérimentaux montrent que le modèle bifluide permet de prévoir l’influence de la géométrie et des conditions d’injection sur l’atomisation primaire de la nappe liquide. Le modèle d’atomisation permet quant à lui, de reproduire le caractère instationnaire des mécanismes de production de gouttes lors du transfert de la phase liquide depuis le modèle bifluide vers celui de spray. Des cas de ré-impact valident également la robustesse et la généralité de la méthodologie de couplage. / In order to improve efficiency of aircraft combustion chambers and reduce polluting emissions,engine manufacturers try to achieve a better control on fuel atomization, which is usually injectedas a jet or liquid sheet. As experiments are expensive and time consuming, a numerical tool able to simulate atomization would be a powerful asset in engine conception design. However, simulation ofthe whole atomization process with commonly used approach in computational fluid dynamics is still prohibitive due to the multi-scale nature of the phenomenon.The objective of this thesis is to develop a new approach allowing the simulation of the spray formation for a industrial configuration in the near future. This involves coupling of two types of models.The first one, called two-fluid model, is based on the Navier-Stokes equations for two immiscible compressible fluids. This one is used to describe the large scales of the atomization mechanism corresponding to the formation of ligaments and liquids blobs in the near-injector area. The second one,called spray model, is based on a kinetic equation. Further downstream from the injector, this model describes statistically the evolution of the droplet cloud produced by the primary fragmentation of liquid jet. The main difficulty, in terms of both modeling and algorithmic, is the coupling of these twomodels.This has been achieved by introducing an atomization and an impact models which ensure liquid transfer between the two-fluid model and the spray model.This new approach was applied to the numerical simulation of sheared liquid sheets. Comparisons between numerical and experimental results show how the two-fluid model predicts the influence of injector geometry and injection conditions on the primary atomization of the liquid sheet. Concerning droplets production, the atomization model is able to reproduce the unsteady nature of this mechanism when transferring liquid phase from the two-fluid model to the spray model. Test cases for the impact model also validate the robustness and generality of the coupling approach.

The production from an oil reservoir is a mixture of liquids (oil and water) and gas, and is often maintained by using a pump placed in the well to ensure a continuous flow to the surface. Electrical Submersible Pumps consist of stacked centrifugal pump stages, each comprising a bladed impeller (rotating part) and diffuser (stationary part). In multiphase conditions, the gas tends to accumulate in the impeller, severely reducing the pressure produced by the pump. Radial-flow pumps operate in a plane perpendicular to their rotation axis, while mixed-flow pumps are characterised by a lower meridional angle (generally 40 to 80 degrees), and are generally better at handling gas-liquid mixtures. We first describe the impact of gas on the whole pumping system, from the reservoir to the storage facility, and give context to the subject. The available literature shows that the size of the gas bubbles present in the fluid is critical to the pump performance. A transparent, full-scale pump was built in order to explore the flow features in single and multiphase flows. Laser Doppler Velocimetry and high speed imaging in single phase flow showed a high turbulence level in the wake of the impeller blades, and recirculation cells at low flow rates. In gas-liquid conditions, we demonstrated that the bubble size varies within a pump stage, as break-up occurs at the impeller tip, and coalescence is dominant in the diffuser, especially because of recirculation. The first impeller acted as a mixer, and at moderate to high gas fractions (10 to 30%), the flow patterns at the stage level alternated between bubbly and radially separated flows. Finally, a dispersed-gas model was developed to predict the pressure rise in a mixed-flow pump impeller under gas-liquid conditions. This model based on the forces acting on a single spherical gas bubble, was implemented with a simplified, parametric representation of the flow field in a mixed-flow impeller. In the meridional direction, the Coriolis force opposes the centrifugal force and the adverse pressure gradient. Both forces tend to retain the gas bubble within the impeller. The relative magnitude of the drag force strongly depends on the maximal bubble diameter, which was determined as a function of the flow conditions and used to calculate the gas velocity through the impeller. This method resulted in a better agreement with the experimental data than a one-dimensional two-fluid model where the gas phase follows the same path as the liquid. We used the dispersed-gas model to give quantitative evidence that low blade and meridional angles reduce the gas accumulation and the associated performance degradation.

[pt] Diversos processos práticos apresentam uma seqüência de diferentes configurações de escoamentos bifásicos, com diferentes padrões de escoamento. Dependendo das razões entre as velocidades superficiais do gás e do líquido, diferentes padrões de escoamento bifásico podem ser encontrados. O padrão de escoamento slug pode ser formado a partir do padrão estratificado, devido ao crescimento das instabilidades hidrodinâmicas ou devido às ondulações no terreno onde se instala a tubulação. O presente trabalho consiste na análise do escoamento bifásico no padrão slug, ao longo de tubulações horizontais, mediante a aplicação do modelo de dois fluidos em sua forma transiente e unidimensional. Através de uma análise de estabilidade de Kelvin-Helmholtz para escoamento estratificado, estima-se a possível faixa de operação para a obtenção de um modelo matemático bem posto. Diferentes técnicas de discretização foram implementadas e testadas. Comparações com dados disponíveis na literatura foram realizadas. / [en] Several practical processes show a sequence of different configurations of two-phase flows, with different flows pattern. Depending upon the relation between the superficial velocities of gas and liquid, different two- phase flows patterns can be found. Slug flow can be formed from the stratified flow, due to growth of hydrodynamic instabilities or due to undulations of the surface where the pipes are installed. The present work consists in the analysis of two-phase flow in slug flow through horizontal pipes using the two-fluid model in its transient and one-dimensional form. By means of a Kelvin-Helmholtz stability analysis for stratified flows, the operation range for obtaining of a well-posed mathematical model is estimated. Different techniques of discretization were implemented and tested. Comparisons with result obtained in the literature were done.

Submitted by Maike Costa (maiksebas@gmail.com) on 2017-05-24T14:26:07Z No. of bitstreams: 1 arquivototal.pdf: 2237346 bytes, checksum: 088238fab84060042b385a40d43c4c3b (MD5) / Made available in DSpace on 2017-05-24T14:26:07Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 2237346 bytes, checksum: 088238fab84060042b385a40d43c4c3b (MD5) Previous issue date: 2016-02-04 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / The present paper makes an analysis of multiphase flow up (oil-gas) in laminar regime, with hidrodynamically developed profiles and interacting heat. The fluids analyzed are considered immiscible, developing into separated speed and temperature fields. The energy equations are applied to obtain of heat fields in the thermal entry region of the fluids flowing in the same direction. Although the results of parameters of practical interest has been obtained by purely numerical procedures, the system governing equations involving partial differential and have not been resolved successfully analytically yet. Thus, the use of Generalizes Integral Transform Technique, as powerful mathematical tool, is proposed to solve the energy equations associated with the flow and to producing hybrid results, analytical-numerical, more extension e analysis flexibility to a large number of parameter used in oil and gas engineering. Auxiliary problems with the greatest possible number of original problem information are presented in an attempt of improving the numerical convergence. Lastly, a computational routine is developed in FORTRAN to obtain the numerical solution. The numerical results obtained for the fields are presented in tables and graphs for then be compared with the maximum care to the parameters of special cases available in the literature. / O presente trabalho realiza uma análise do escoamento multifásico (óleo-gás) ascendente em regime laminar, com perfis hidrodinamicamente desenvolvidos e interagindo termicamente. Os fluidos em análise são considerados imiscíveis, desenvolvendo-se em campos separados de velocidade e temperatura. A equação da energia é aplicada para a obtenção dos campos térmicos em desenvolvimento na região de entrada térmica dos fluidos escoando na mesma direção. Embora resultados de parâmetros de interesse prático já tenham sido obtidos através de procedimentos puramente numéricos, o sistema de equações que regem esse tipo de escoamento envolve diferenciais parciais e ainda não foram solucionadas analiticamente com sucesso. Dessa forma, o uso da Técnica de Transformada Integral Generalizada, como ferramenta matemática, é proposto para resolver as equações de energia associada ao escoamento produzindo resultados híbridos, analítico-numérico, com maior flexibilidade de análise e extensão para um grande número de parâmetros utilizados na engenharia de petróleo e gás. Problemas auxiliares com o maior número possível de informações do problema original são apresentados na busca da melhoria da convergência numérica. Por fim, uma rotina computacional é elaborada em FORTRAN para a obtenção da solução numérica. Os resultados numéricos obtidos para os campos são apresentados na forma de tabelas e gráficos para em seguida serem comparados com o máximo de esmero aos parâmetros de casos especiais disponíveis na literatura especializada.

Filtered two-fluid models used to perform large scale simulations of gas-solid fluidized flows of industrial risers require closures for filtered parameters such as filtered and residual stresses, and interphase interaction forces mainly effective drag. Closure models for those filtered parameters may be derived by averaging over results of highly resolved simulations with microscopic two-fluid modeling. This work is a contribution in that context. Recent models for filtered parameters have been written as functions of filter size, filtered solid volume fraction, and filtered slip velocity. A recent study showed that macro-scale variables like domain average solid volume fraction and gas Reynolds number also significantly affect the filtered parameters. In the current work, in addition to these filtered and macro-scale variables, the effects of two new variables over the filtered parameters are investigated: filtered solid kinetic energy and sub-grid gas turbulence. It is shown that the filtered solid kinetic energy should be accounted for in the concerning correlations, thereby improving accuracy. Regarding gas turbulence, literature shows it has no significant effects on the motion of high Stokes particles. Extending on literature, this work investigates the sub-grid gas turbulence effects on meso-scale structures formed of high Stokes particles. Results showed that sub-grid gas turbulence has no significant effects on the meso-scale structures and corresponding filtered parameters. The open source code MFIX was used for all simulations. Ranges of dilute concentration of solid and gas Reynolds number typical of riser flow regimes were considered. A modified two-fluid model with microscopic formulation was used. The sub-grid gas turbulence was generated by means of a forcing function procedure which was implemented in the physical space, over the gravitational term of the momentum conservation equation of the gas phase. First, numerical simulations of the gas phase alone were performed, accounting for literature available data, in order to set a turbulent gas field and calibrate the turbulence intensity. Then, the forcing function was introduced in to the two-fluid model and various gas-solid flows were simulated. While the current results show the necessity of accounting for additional variables in the filtered parameter correlation, they also make it clear the necessity of further developments that are required in the search for better accuracy. / Modelos filtrados de dois-fluidos usados em simulações de grandes escalas de escoamentos fluidizados de gás-sólido de risers industriais exigem fechamentos para parâmetros filtrados tais como as tensões filtradas e residuais, e forças interativas interfases, principalmente arrasto efetivo. Modelos de fechamento para estes parâmetros filtrados podem ser gerados a partir de procedimentos de media aplicados sobre resultados de simulações altamente resolvidas com modelagem microscópica de dois-fluidos. Este trabalho é uma contribuição neste contexto. Modelos de fechamento recentes para parâmetros filtrados tem sido formulados em função de tamanho de filtro, fração volumétrica de sólido filtrada, e velocidade de deslizamento filtrada. Estudo recente mostrou que variáveis de macro-escalas como fração volumétrica de sólido e número de Reynolds de gás médios no domínio também afetam significativamente os parâmetros filtrados. No presente trabalho, além dessas variáveis filtradas e de macro-escala, os efeitos de duas novas variáveis sobre os parâmetros filtrados são investigados: energia cinética filtrada do sólido e turbulência submalha do gás. Em relação à energia cinética filtrada do sólido, mostra-se que a sua consideração refina as correlações em questão, contribuindo assim para melhor acuracidade. Com relação à turbulência do gás, a literatura mostra que não tem efeitos significativos no movimento de particulados de elevados números de Stokes. Acrescentando à literatura, este trabalho investiga os efeitos da turbulência sub-malha do gás sobre estruturas de meso-escala formados de particulados de elevados números de Stokes. Os resultados mostraram que a turbulência sub-malha do gás não tem efeitos significativos sobre estruturas de meso-escalas e parâmetros filtrados correspondentes. O código aberto MFIX foi usado para todas as simulações. Faixas de concentração diluída de sólido e número de Reynolds típicos de escoamentos em risers foram considerados. Um modelo modificado de dois fluidos com formulação microscópica foi utilizado. A turbulência sub-malha do gás foi gerada por meio de um procedimento de \'forcing function\' que foi implementado no espaço físico, sobre o termo fonte gravitacional da equação de momentum da fase gás. Primeiramente, simulações numéricas da fase gás foram realizadas separadamente, levando-se em conta dados disponíveis na literatura, a fim de gerar um campo de gás turbulento e calibrar a intensidade de turbulência. Posteriormente, a \'forcing function\' foi introduzida no modelo de dois-fluidos e vários escoamentos de gás-sólido foram simulados. Enquanto os resultados obtidos mostram a necessidade de consideração de variáveis adicionais para correlação de parâmetros filtrados, também deixam claro a necessidade de desenvolvimentos mais aprofundados na busca de melhor acuracidade.

Cette thèse traite de la modélisation et de la simulation des écoulements diphasiques transitoires eau-vapeur. Dans de nombreuses installations industrielles, des écoulements monophasiques d'eau liquide sont susceptibles de devenir diphasiques lors de certaines situations transitoires. La modélisation de ces écoulements peut s'avérer délicate car deux phénomènes physiques interagissant fortement entre eux, le changement de phase et la propagation d'ondes de pression, sont alors à prendre en compte. Une approche bifluide statistique, ne supposant aucun équilibre entre les phases, est utilisée afin de modéliser de tels écoulements. Les modèles obtenus sont de type convection-source et s'apparentent au modèle de Baer-Nunziato. Différentes lois de fermeture pour ces modèles sont comparées sur des cas expérimentaux de transitoires eau-vapeur tels que les coups de bélier et la dépressurisation d'une tuyauterie d'eau liquide suite à une rupture.La simulation numérique des différents modèles est effectuée grâce à une méthode à pas fractionnaires. Un nouveau schéma de convection, robuste et efficace, capable de gérer toute equation d'état est utilisé dans la première étape de cette méthode. La seconde étape est dédiée au traitement des termes sources et requiert différents schémas implicites. Une grande attention est accordée à la vérification de tous les schémas numériques utilisés grâce à des études de convergence. Une nouvelle modélisation du transfert de masse est également proposée, sur la base de travaux dédiés à la brusque dépressurisation d'eau liquide en approche homogène. La validation du modèle est effectuée grâce de nombreuses comparaisons calcul-expérience. / This thesis deals with the modelling and the computation of steam-water two-phase flows. Liquid water flows are involved in many industrial facilities and a second phase may appear in some transients situations. Thus, pressure wave propagation and mass transfer are physical phenomena that need to be properly included in the modelling of such two-phase flows. A statistical two-fluid approach is used, leading to models similar to the Baer-Nunziato one. They include both convective and source terms without any assumption on the equilibrium between phases. Different closure laws for such models are compared on steam-water transient experiments including water-hammers and fast depressurization of liquid water. The computation of the different models is based on a fractional step method. A new convective scheme, able to deal with any Equation Of State, is used in the first step of the method. When compared with other schemes, it appears to be accurate, efficient and very robust. The second step of the method is dedicated to the treatment of source terms and requires several implicit schemes. Particular attention is paid to the verification of every scheme involved in the method. Convergence studies are carried out on test-cases with analytical solutions to that purpose. Based on existing work on fast depressurization of liquid water in an homogeneous approach, a new formulation of the mass transfer is proposed. Many comparisons between computational and experimental results are detailled in order to validate the models.

La première préoccupation de cette thèse est le problème de deux fluides ou un fluide à deux phases, c’est-à-dire que nous nous sommes intéressés à la simulation d’écoulements impliquant deux ou plusieurs fluides visqueux incompressibles immiscibles de propriétés mécaniques et rhéologiques différentes. Dans ce contexte, nous avons considéré que l’interface mobile entre les deux fluides est représentée par la ligne de niveau zéro d’une fonction ligne de niveau et régie par l’équation d’advection, où le champ advectant est la solution des équations de Navier-Stokes. La plupart des méthodes de capture d’interface utilisent une grille cartésienne fixe au cours de la simulation. Contrairement à ces approches, la nôtre est fortement basée sur l’adaptation de maillage, notamment au voisinage de l’interface. Cette adaptation de maillage permet une représentation précise de l’interface, à l’aide de ses propriétés géométriques, avec un nombre de degrés de liberté minimal.La résolution d'un problème à deux fluides est résumée par les étapes suivantes:- Résoudre les équations de Navier-Stokes par la méthode de Lagrange-Galerkin d’ordre 1;- Traitement géométrique la tension de surface se basant sur la discrétisation explicite de l'interface dans le domaine de calcul;- Résoudre l'équation d’advection par la méthode des caractéristiques;- Les techniques de l'adaptation de maillage.On propose ici un schéma entre l’advection de l’interface, la résolution des équations de Navier-Stokes et l’adaptation de maillage. Certains résultats des exemples classiques pour les deux problèmes de monofluide et bifluide comme la cavité entrainée, la rémontée d’une bulle, la coalescence de deux bulles et les instabilités Rayleigh-Taylor sont étudiés en deux et trois dimensions.La deuxième partie de cette thèse est liée à l'optimisation des formes en mécanique des fluides. Nous construisons un schéma numérique en utilisant la méthode des lignes de niveau et l’adaptation de maillage dans le contexte des systèmes de Stokes. Le calcul de la sensibilité de la fonction objective est liée à la méthode de variation des limites d’Hadamard et les dérivées des formes sont calculées par la méthode de Céa. Un exemple numérique avec la fonction objective de la dissipation d'énergie est présenté pour évaluer l'efficacité et la fiabilité du schéma proposé. / The first concern of this thesis is the problem of two fluids flow or two-phase flow, i.e weare interested in the simulation of the evolution of an interface (or a free surface) between twoimmiscible viscous fluids or two phases of a fluid. We propose a general scheme for solving two fluids flow or two-phase flow which takes advantage of the flexibility of the level set method for capturing evolution of the interfaces, including topological changes. Unlike similar approaches that solve the flow problem and the transport equation related to the evolution of the interface on Cartesian grids, our approach relies on an adaptive unstructured mesh to carry out these computations and enjoys an exact and accurate description of the interface. The explicit representation of the manifold separating the two fluids will be extracted to compute approximately the surface tension as well as some algebraic quantities like the normal vector and the curvature at the interface.In a nutshell, the resolution of a two-fluid problem is summarized by the steps involves thefollowing ingredients:– solving incompressible Navier-Stokes equations by the first order Lagrange-Galerkin method;– geometrical treatment to evaluate the surface tension basing on the explicit discretisation of the interface;– solving the level set advection by method of characteristics; – the techniques of mesh adaptation.It is obvious that no numerical method is completely exact in solving the PDE problemat hand, hence, we need a discretized computational domain. However, the accuracy of numericalsolutions or the mass loss/gain can generally be improved with mesh refinement. The question thatarises is related to where and how to refine the mesh. At each time, our mesh adaptation producesthe adapted mesh based on the geometric properties of the interface and the physical properties ofthe fluid, simply speaking, only one adapted mesh at each time step to assume both the resolutionof Navier-Stokes and the advection equations. It answers to the need for an accurate representationof the interface and an accurate approximation of the velocity of fluids with a minimal number ofelements, then decreasing the amount of computational time. Some results of the classical examples for both problems of monofluid and bifluid flows as : lid-driven cavity, rising bubble, coalescence of two bubbles, and Rayleigh-Taylor instability are investigated in two and three dimensions.The second part of this thesis is related to shape optimization in fluid mechanics. We construct a numerical scheme using level set method and mesh adaptation in the context of Stokes systems. The computation of the sensitivity of objective function is related to the Hadamard’s boundary variation method and the shape derivatives is computed by Céa’s formal method. A numerical example with theobjective function of energy dissipation is presented to assess the efficiency and the reliability of theproposed scheme.