Pour améliorer la conception des turbomachines, les industriels doivent appréhender des phénomènes aéroélastiques complexes présents dans les compresseurs comme les cycles limites d’interaction fluide-structure des fans. La compréhension et la modélisation de ces phénomènes impliquent de développer des modèles numériques complexes intégrant des phénomènes multi-physique et de valider ces modèles à l’aide de bancs d’essais. Le banc d’essai du compresseur CREATE est instrumenté pour étudier des instabilités aérodynamiques couplées à des vibrations, notamment sur le rotor du premier étage, et permet de valider des modèles numériques. La modélisation de l’écoulement en amont du premier étage du compresseur à l’aide du logiciel Turb’Flow, développé pour l’étude des écoulements dans les compresseurs aéronautiques, a permis de mettre en évidence l’importance des conditions limites d’entrée pour l’obtention de résultats précis. En particulier, il a été possible de modéliser correctement l’ingestion d’une alimentation non-homogène en entrée de la roue directrice d’entrée. Ce phénomène peut se produire en amont des fans et interagir avec un mode de la structure. Une stratégie de couplage partitionné fort explicite dans le domaine temporel a été introduite dans le logiciel Turb’Flow. Comme cette méthode présente un risque de décalage temporel à l’interface fluide-structure, une attention particulière a été portée à la modélisation de la conservation de l’énergie à cette interface. La conservation de l’énergie à l’interface est cruciale quand les déplacements sont importants et quand un comportement non-linéaire fort apparaît entre le fluide et la structure (onde de choc et amortissement structurel nonlinéaire). Parallèlement au développement du module aéroélastique, le schéma implicite de Runge- Kutta d’ordre 3 en temps (RKI-3) a été développé et évalué sur un cas de dynamique (vibration d’une aube de turbine transsonique) et sur un cas de propagation d’onde de choc. L’utilisation du schéma RKI-3 permet d’augmenter, à iso-précision, d’un ordre le pas de temps par rapport aux schémas de Gear et de Newmark. S’il apporte un gain en temps CPU pour l’étude de la dynamique des structures, il est pénalisant dans le cadre de simulation URANS. Cependant, le schéma RKI-3 est utilisable dans le cadre de simulations couplées fluide-structure. / To increase turbomachinery design, manufacturers have to comprehend complex aeroelastic phenomena involving compressors like fluid-structure interaction limit cycles of fans. The understanding and the modeling of these phenomena involve developing complex solvers coupling techniques and validating these techniques with bench tests. The bench test of the CREATE compressor is instrumented to study the coupling between aerodynamic instabilities and structure vibration, in particular on the first stage rotor, and allows to validate numerical techniques. The flow modeling upstream to the first stage with the Turb’Flow flow solver (targeting turbomachinery applications) shows that, to have accurate results, inlet limit conditions must take into account. The ingestion of non-homogeneous flow upstream to the inlet guide vane is accurately modeled. This phenomenon can appear upstream to fans and interact with structure Eigen-modes. Explicit partitioned strong coupling considered in time domain was implemented in a Turb’Flow flow solver. As there is a risk of time shift at the fluid-structure interface, careful attention should be paid to energy conservation at the interface. This conservation is crucial when displacements are large and when strong non-linear behaviors occur in both fluid and structure domains, namely shock waves, flow separations and non-linear structural damping. In parallel with coupling technique development, the three-order implicit Runge-Kutta scheme (RKI-3) was implemented and validated on a structure dynamic case (transonic turbine blade vibration) and on a case of shock waves propagation. The RKI-3 scheme allows increasing the time step of one order of magnitude with the same accuracy. There is a CPU time gain for structure dynamics simulations, but no for URANS simulations. However, the RKI-3 scheme can be to use for fluid-structure coupling simulations. The coupling technique was validated on a test case involving tube in which the shock wave impinges on a cross flow flexible panel, initially at rest. This case allows modeling an interaction between sonic flow and a panel movement with a tip clearance. Some numerical simulations were carried out with different temporal schemes. The RKI-3 scheme has no influence on results (compared with Gear and/or Newmark scheme) on the energy conservation at the fluid-structure interface. Compared to experimental results, pressure is in fairly good ix Liste des publications agreement. The analysis of numerical results highlighted that a vertical shock tube with up and down waves creates pressure fluctuation. Frequency is under predicted and amplitude is not in fairly good agreement. The panel root modeling might be questionable.

Multiphase flow is a familiar phenomenon from daily life and occupies an important role in physics, engineering, and medicine. The understanding of multiphase flows relies largely on the theory of interfaces, which is not well understood in many cases. To date, the Navier-Stokes-Korteweg equations and the Cahn-Hilliard equation have represented two major branches of phase-field modeling. The Navier-Stokes-Korteweg equations describe a single component fluid material with multiple states of matter, e.g., water and water vapor; the Cahn-Hilliard type models describe multi-component materials with immiscible interfaces, e.g., air and water. In this dissertation, a unified multiphase fluid modeling framework is developed based on rigorous mathematical and thermodynamic principles. This framework does not assume any ad hoc modeling procedures and is capable of formulating meaningful new models with an arbitrary number of different types of interfaces. In addition to the modeling, novel numerical technologies are developed in this dissertation focusing on the Navier-Stokes-Korteweg equations. First, the notion of entropy variables is properly generalized to the functional setting, which results in an entropy-dissipative semi-discrete formulation. Second, a family of quadrature rules is developed and applied to generate fully discrete schemes. The resulting schemes are featured with two main properties: they are provably dissipative in entropy and second-order accurate in time. In the presence of complex geometries and high-order differential terms, isogeometric analysis is invoked to provide accurate representations of computational geometries and robust numerical tools. A novel periodic transformation operator technology is also developed within the isogeometric context. It significantly simplifies the procedure of the strong imposition of periodic boundary conditions. These attributes make the proposed technologies an ideal candidate for credible numerical simulation of multiphase flows. A general-purpose parallel computing software, named PERIGEE, is developed in this work to provide an implementation framework for the above numerical methods. A comprehensive set of numerical examples has been studied to corroborate the aforementioned theories. Additionally, a variety of application examples have been investigated, culminating with the boiling simulation. Importantly, the boiling model overcomes several challenges for traditional boiling models, owing to its thermodynamically consistent nature. The numerical results indicate the promising potential of the proposed methodology for a wide range of multiphase flow problems. / text