Cavitation is characterized by the formation of vapor bubbles when the pressure in a working fluid drops sharply below the vapor pressure. These bubbles, upon exiting the low-pressure region burst emanating tremendous amounts of energy. Unsteady cavitating flows have been influential in several aspects from being responsible for erosion damage and vibrations in hydraulic engineering devices to being used for non-invasive medical surgeries and drilling for geothermal energy. While the phenomenon has been investigated using both experimental and numerical methods, it continues to pose a challenge for numerical modelling techniques due to its flow unsteadiness and the cavitation-turbulence interaction. One of the principal aspects to modelling cavitation requires the coupling of a cavitation and a turbulence model. While, scale-resolving turbulence modelling techniques like Direct Numerical Simulations (DNS) and Large Eddy Simulations (LES) upto a certain extent may seem an intuitive solution, the physical complexities involved with cavitation result in extremely high computational costs. Thus, Unsteady Reynolds-Averaged Navier-Stokes (URANS) models have been widely utilized as a workhorse for cavitating simulations. However, URANS models are unable to reproduce the periodic vapor shedding observed in experiments and thus, are often corrected by empirical correction. Recently, some models termed as hybrid RANS-LES models that behave as RANS or LES depending on location of flow have been introduced and employed to model cavitating flows. In addition, there has also been a rise in defining some frameworks that use data from high-fidelity simulations or experiments to drive numerical algorithms and aid standard turbulence modelling procedures for accurately simulating turbulent flows. This dissertation is aimed at (1) evaluating the abilities of these corrections, traditional URANS and hybrid RANS-LES models to model cavitation and (2) optimizing the URANS modelling strategy by designing a methodology driven by experimental data to augment the turbulence modelling to simulate cavitating flow in a converging-diverging nozzle. / Doctor of Philosophy / The famous painting Arion on the Dolphin by the French artist François Boucher shows a dolphin rescuing the poet Arion from the choppy seas after being thrown overboard. Today, seeing silhouettes of dolphins swimming near the shore as the Sun sets is a calming sight. However, as these creatures splash their fins in the water, these fins create a drastic pressure difference resulting in the formation of ribbons of vapor bubbles. As the bubbles exit the low-pressure zones, they collapse and release tremendous amounts of energy. This energy manifests in the form of shockwaves rendering this pleasant sight to the human eye, extremely painful for dolphins. These shocks also impact the metal blades in hydraulic machinery like pumps and ship propellers. This dissertation aims to investigate the physics driving this phenomenon using accurate numerical simulations. We first conduct two-dimensional simulations and observe that standard numerical techniques to model the turbulence are unable to simulate cavitation accurately. The investigation is then extended to three-dimensional simulations using hybrid RANS-LES models that aim to strike a delicate balance between accuracy and efficiency. It is observed that these models are able to reproduce the flow dynamics as observed in experiments but are extremely expensive in terms of computational costs due to the three-dimensional nature of the calculations. The investigation then switches to a data-driven approach where a machine learning algorithm driven by experimental data informs the standard turbulence models and is able to simulate cavitating flows accurately and efficiently.

Cette thèse est principalement dédiée à la simulation des écoulements massivement décollés dans le domaine spatial. Nous avons restreint notre étude aux écoulements d'arrière-corps, pour lesquels ces décollements sont imposés par des changements brutaux de la géométrie. Dans le domaine spatial, le caractère fortement compressible des écoulements rencontrés impose l'utilisation de schémas numériques robustes. D'un autre coté, la simulation fine de la turbulence impose des schémas d'ordre élevé et peu dissipatifs. Ces deux spécifications, apparemment contradictoires, doivent pourtant coexister au sein d'une même simulation. Les modèles de turbulence ainsi que les schémas de discrétisation sont indissociables et leur couplage doit impérativement être considéré. Les schémas numériques doivent garder leur précision formelle dans des géométries complexes et des maillages très irréguliers imposés par le contexte industriel. Cette étude analyse le schéma de discrétisation utilisé dans le code de calcul FLUSEPA développé par Airbus Defence & Space. Ce schéma est robuste et précis pour des écoulements avec chocs et il présente une faible sensibilité au maillage (l'ordre 3 étant conservé même sur des maillages fortement perturbés). Malheureusement, le schéma possède une trop faible résolvabilité liée à un niveau de dissipation trop élevé pour envisager des simulations hybrides RANS/LES. Pour pallier à cet inconvénient, nous nous sommes penchés vers une solution basée sur un recentrage conditionnel et local : dans les zones dominées par des structures tourbillonnaires, une fonction analytique assure un recentrage local lorsque la stabilité numérique le permet. Cette condition de stabilité assure le couplage entre le schéma et le modèle. De cette manière, les viscosités laminaire et tourbillonnaire sont les seules à jouer un rôle dans les régions dominées par la vorticité et servent aussi à stabiliser le schéma numérique. Cette étude présente de plus une comparaison qualitative et quantitative de plusieurs modèles hybrides RANS/LES, à égalité de maillage et de schéma utilisés Pour cela, un certain nombre d'améliorations (notamment de leur capacité à résoudre les instabilités de Kelvin-Helmohlotz sans retard), proposées dans la littérature ou bien introduites dans cette thèse, sont prises en compte. Les applications numériques étudiées concernent des géométries allant de la marche descendante au lanceur spatial complet à échelle réduite. / This thesis is mainly dedicated to the simulation of massively separated flows in the space domain. We restricted our study to afterbody flows, where the separation is imposed by abrupt geometry changes. In the space domain, highly compressible flows require the use of robust numerical schemes. On the other hand, the simulation of turbulence imposes high-order low dissipative numerical schemes. These two specifications, apparently contradictory, must coexist within the same simulation. The coupling between turbulence models and discretization schemes is of the utmost importance and must be considered. Numerical schemes should keep their formal accuracy on complex geometries and on very irregular meshes imposed by the industrial context. In this research, we analyze the discretization scheme implemented in the FLUSEPA solver, developed by Airbus Defence & Space. Such a scheme is robust and accurate for flows with shocks and exhibits a low sensitivity to the grid (the third order of accuracy being ensured, even on highly irregular grids). Unfortunately, the scheme possesses a too low resolvability related to a too high numerical dissipation for RANS/LES simulations. To circumvent this problem, we considered a conditional and local re-centering strategy: in regions dominated by vortical structures, an analytic function provides local re-centering when a numerical stability condition is satisfied. This stability condition ensures the coupling between the numerical scheme and the model. In this way, only the turbulent and the laminar viscosities play a role in regions dominated by vorticity, and also allow to stabilize the numerical scheme. This study provides also a qualitative and quantitative assessment of several hybrid RANS/LES models, using the same grids and discretization scheme. For this purpose some recent improvements (improving their ability to trigger the Kelvin-Helmohlotz instabilities without delay), proposed in the litterature or suggested in this work, are taken into account. Numerical applications include geometrical configurations ranging from a backward facing step to realistic launcher configurations.