La cavitation est la transformation d'un liquide en vapeur qui est causée par une chute de pression en dessous de la pression de saturation vapeur. Ce phénomène se manifeste le plus souvent dans les turbomachines qui sont en interaction avec des liquides. On peut citer les pompes hydrauliques, les injecteurs, les inducteurs ou encore les hélices de bateaux. Vue les effets néfastes qu'elle engendre : bruit, vibrations, détérioration du métal et baisse des performances (chute des rendements et pertes de charges), sa prise en compte est indispensable dans le design des turbomachines. Cette thèse a pour objectif de modéliser ce phénomène de manière à reproduire la nucléation, la convection et l'implosion des bulles de cavitation. Nous nous basons sur un modèle à interface diffuse (le modèle d'équilibre homogène) sur lequel nous greffons un modèle de tension de surface basé sur les équations de Navier Stokes & Korteweg compressibles. Nous réalisons en somme une étude sur l'influence de la tension de surface sur le phénomène de collapse. Nous utilisons un code de volumes finis dont la discrétisation spatiale est assurée par méthode des moindres carrés mobiles. Combinée à un solveur de Riemann de type SLAU, le modèle numérique permet d'outre passer les difficultés liés à la nature du phénomène de cavitation qui sont principalement les forts gradients qui subsistent à travers l'interface liquide-vapeur. L'autre point traité dans la thèse est la détermination d'un coefficient capillaire numérique qui correspond à une tension de surface réelle en fonction de l'épaisseur de l'interface artificiellement élargie pour un maillage donné. / Cavitation is the transformation of a liquid into vapor which is caused by a pressure drop below the vapor saturation pressure. This phenomenon usually occurs in turbine engines that interact with liquids like: hydraulic pumps, injectors, inductors or boat propellers. View its negative effects: noise, vibrations, damage to the metal and decreased performance, it should be included in the design of turbomachinery The main objective of this thesis is to model this phenomenon so as to reproduce the nucleation, convection and the implosion of cavitation bubbles. We rely on a diffuse interface model (the homogeneous equilibrium model) on which we graft a surface tension model based on compressible Navier Stokes & Korteweg equations. We study the influence of surface tension on the bubble collapse. We used a finite volume approach whose spatial discretization is made by moving least squared method. Coupled with a Riemann solver called SLAU, the numerical model can go further difficulties related to the nature of the cavitation phenomenon which is mainly the strong gradients that remain through the liquid-vapor interface. Another issue addressed in this thesis is the determination of a numerical capillary coefficient which corresponds to a real surface tension in function of the thickness of the artificially extended interface for a given mesh.

[pt] O Brasil possui uma já extensa malha offshore de gasodutos e, no desenvolvimento da produção do Pré-Sal, esta deve continuar se expandindo em razão das necessidades de aumento da capacidade de escoamento de gás e também da sua reinjeção nos próprios reservatórios (seja apenas como descarte ou como um método de recuperação avançado). Uma vez instalada, esta malha deve ser periodicamente passar por manutenção, o que implica em eventos esporádicos de esvaziamento destes dutos, normalmente operando a altas pressões. Devido ao custo elevado de tais operações, deve-se estimar com boa precisão o tempo total necessário para despressurização, que pode levar várias horas ou até dias. Além disso, também é importante a previsão do inventário de líquido remanescente nos dutos após a despressurização. No presente trabalho, foi desenvolvido um modelo numérico para prever a despressurização de gasodutos considerando escoamento bifásico homogêneo e unidimensional. A formação e o consumo de condensado é obtida a partir de um inventário inicial de fluido supercrítico, com premissa de equilíbrio entre as fases. As propriedades termodinâmicas dos fluidos são determinadas utilizando-se pacotes comerciais e pré-tabuladas em função de pressão e temperatura. As equações de conservação foram discretizadas pelo método das diferenças finitas, utilizando o método de Euler implícito para o termo temporal e aproximação upwind nas derivadas espaciais. O sistema algébrico resultante foi resolvido diretamente de forma acoplada. Os resultados obtidos mostram boa concordância ao compará-los a dados reais de campo e resultados de simuladores comerciais de referência. / [en] Although Brazilian gas pipeline grid is already quite extensive, it continues to expand due to the Pre Salt development, since there is a growing need to increase the flowing capacity towards onshore facilities and injection wells (gas to be discarded or used for advanced oil recovery). Once pipelines are installed, maintenance operation must be performed quite often to guarantee process efficiency. Usually these operations demand depressurization from very high pressures. Considering the costs involved in such operations it is mandatory to accurately predict the total time for a complete blowdown, which may take several hours or even a couple of days. Furthermore, it is also important to evaluate the condensate content in the pipeline after the depressurization event. In the present work, a numerical model was developed to simulate gas pipeline depressurization considering unidimensional two-phase homogeneous flow. The formation and consumption of condensate from an initial supercritical state is obtained assuming phase equilibrium. Fluid properties are taken from tables generated by PVT packages. Conservation equations are discretized through the finite difference method employing Euler implicit approximation for the time derivatives and upwind scheme for spatial terms. A coupled direct algorithm was adopted to solve the resulting algebraic system. The results are compared to real field data and commercial software showing good agreement.