Large Eddy Simulation is a method of obtaining high accuracy computational results for modelling fluid flow. Unfortunately it is computationally expensive limiting it to users of large parallel machines. However, it may be that the use of LES leads to an over-resolution of the problem because the bulk of the computational domain could be adequately modelled using the Reynolds averaged approach. A study has been undertaken to assess the feasibility, both in accuracy and computational efficiency of using a parallel computer to solve both LES and RANS type turbulence models on the same domain for the problem flow over a circular cylinder at Reynolds number 3 900 To do this the domain has been created and then divided into two sub-domains, one for the LES model and one for the kappa - epsilon turbulence model. The hybrid model has been developed specifically for a parallel computing environment and the user is able to allocate modelling techniques to processors in a way which enables expansion of the model to any number of processors. Computational experimentation has shown that the combination of the Smagorinsky model can be used to capture the vortex shedding from the cylinder and the information successfully passed to the kappa - epsilon model for the dissipation of the vortices further downstream. The results have been compared to high accuracy LES results and with both kappa - epsilon and Smagorinsky LES computations on the same domain. The hybrid models developed compare well with the Smagorinsky model capturing the vortex shedding with the correct periodicity. Suggestions for future work have been made to develop this idea further, and to investigate the possibility of using the technology for the modelling of mixing and fast chemical reactions based on the more accurate prediction of the turbulence levels in the LES sub-domain.

Large Eddy Simulation is a method of obtaining high accuracy computational results for modelling fluid flow. Unfortunately it is computationally expensive limiting it to users of large parallel machines. However, it may be that the use of LES leads to an over-resolution of the problem because the bulk of the computational domain could be adequately modelled using the Reynolds averaged approach. A study has been undertaken to assess the feasibility, both in accuracy and computational efficiency of using a parallel computer to solve both LES and RANS type turbulence models on the same domain for the problem flow over a circular cylinder at Reynolds number 3 900 To do this the domain has been created and then divided into two sub-domains, one for the LES model and one for the kappa-epsilon turbulence model. The hybrid model has been developed specifically for a parallel computing environment and the user is able to allocate modelling techniques to processors in a way which enables expansion of the model to any number of processors. Computational experimentation has shown that the combination of the Smagorinsky model can be used to capture the vortex shedding from the cylinder and the information successfully passed to the kappa - epsilon model for the dissipation of the vortices further downstream. The results have been compared to high accuracy LES results and with both kappa - epsilon and Smagorinsky LES computations on the same domain. The hybrid models developed compare well with the Smagorinsky model capturing the vortex shedding with the correct periodicity. Suggestions for future work have been made to develop this idea further, and to investigate the possibility of using the technology for the modelling of mixing and fast chemical reactions based on the more accurate prediction of the turbulence levels in the LES sub-domain.

In this work, we investigate the performance limitations characterizing certain common closure models for nonlinear models of fluid flow. The need for closures arises when for computational reasons first-principles models, such as the Navier-Stokes equations, are replaced with their simplified (filtered) versions such as the Large-Eddy Simulation (LES). In the present work, we focus on a simple model problem based on the 1D Kuramoto-Sivashinsky equation with a Smagorinsky-type eddy-viscosity closure model. The eddy viscosity is assumed to be a function of the state (flow) variable whose optimal functional form is determined in a very general form in the continuous setting. It is found by solving a PDE-constrained optimization problem in which the least-squares error between the output of the LES and the true flow evolution is minimized with respect to the functional form of the eddy viscosity. This problem is solved using a gradient-based technique utilizing a suitable adjoint-based variational data-assimilation approach implemented in the optimize-then-discretize setting using state-of-the-art techniques. The numerical computations are thoroughly validated. The obtained results indicate how the standard Smagorinsky closure model can be refined such that the corresponding LES evolution approximates more accurately the evolution of the original (unfiltered) flow. / Thesis / Master of Science (MSc)

The separation and reattachment of the suction surface boundary layer in a low pressure turbine is characterized using large-eddy simulation at Re=68,000 based on freestream velocity and suction surface length. A high pass filtered Smagorinsky model is used for modeling the sub-grid scales. The onset of time mean separation is at s=so = 0:61 and reattachment at s=so = 0:81, extending over 20% of the suction surface. The boundary layer is convectively unstable with a maximum reverse flow velocity of about 13% of freestream. The breakdown to turbulence occurs over a very short distance of suction surface which is followed by reattachment. Detailed investigations into the structure and kinematics of the bubble and turbulence statistics are presented. The vortex shed from the bubble, convects downstream and interacts with the trailing edge vortices increasing the turbulence intensity. On the suction side, dominant hairpin structures near the transitional and turbulent flow regime are observed. These hairpin vortices are carried by the freestream even downstream of the trailing edge of the blade with a possibility of reaching the next stage. Longitudinal streaks that evolve from the breakdown of hairpin vortices formed near the leading edge are observed on the pressure surface.

Les écoulements en turbomachines (et notamment en turboréacteurs) sont caractérisés par de larges structures tourbillonnaires et de fortes intensités turbulentes. Ainsi, l’écoulement secondaire dans la région du jeu, en tête d’aube, est l’origine de pertes d’énergie, d’instabilités et de nuisances sonores. Une simulation fine de ces écoulements peut être obtenue par l’emploi de méthodes LES (Large-Eddy Simulation), qui permettent de capturer les fluctuations turbulentes majeures. Compte tenu des phénomènes rencontrés, le modèle de sous-maille SISM (shear-improved Smagorinsky model) est retenu ici. Ce modèle est local dans son écriture, et prend en compte l’influence du cisaillement moyen. Nous proposons ici deux méthodes de filtrage (locales en espace elles aussi) pour obtenir une évaluation du champ moyen requis par le modèle. Ces méthodes sont, dans un premier temps, testées sur une configuration de canal plan. L’écoulement en régime sous-critique autour d’un barreau cylindrique (Re = 4, 7 ×104) est proposé comme cas-test académique sélectif pour ces méthodes : cet écoulement présente de larges structures tourbillonnaires ainsi qu’une turbulence intense, tout comme l’écoulement de jeu. Les simulations permettent l’obtention de résultats très proches des données expérimentales. Une étude comparée des deux algorithmes d’extraction du champ moyen montre que l’adaptativité du filtrage de Kalman offre toutefois des résultats légèrement meilleurs. Enfin, l’analyse d’un écoulement de jeu par une méthode zonale est réalisée (approche LES en tête d’aube, RANS en pied). La simulation de référence obtient des résultats remarquables dans la zone de tête d’aube, en retrouvant notamment les spectres de vitesse expérimentaux. Une seconde simulation avec l’emploi d’un dispositif de contrôle par aspiration au niveau du carter montre deux conséquences principales à ce dispositif: une réduction des niveaux de turbulence aux environs de la tête d’aube, et une modification de la trajectoire du tourbillon de jeu. Celui-ci rencontre l’aube suivante dans la configuration de référence, ce qui n’est plus le cas dans la configuration avec contrôle. Ces deux observations ont une importance certaine dans la réduction des sources acoustiques. / Flows in turbomachines such as jet engines are subject to large vortical structures and strong turbulent intensities. In particular, secondary flows generated in the fan tip region result in energy losses, instabilities and noise radiation. An accurate simulation of such flows can be achieved with large-eddy simulation(LES), which reproduces the most energetic turbulent eddies. In regard of the flowphysics of highly unsteady wall-bounded flows, the SISM (shear-improved Smagorinsky model) is selected to model the sub-grid scales in the present study. This model is local and takes into account the influence of the mean shear. Two smoothing algorithms that are local in space are developed to evaluate the mean flow required by the model : an exponential averaging and an adaptative Kalman filter. These methods are first tested in a channel flow configuration. The numerical approaches are then evaluated on a relevant academic test case :the flow past a circular cylinder in the sub-critical regime (Re = 4, 7 × 104). This flow is dominated by large quasi-periodic vortical structures together with high intensity turbulent fluctuations; quite similarly but much simpler than those found in the tip gap flow. The aerodynamic as well as the acoustic results of the simulations are in very good agreement with the experimental data. A comparative study of the two smoothing algorithms for mean-flow extraction shows that the adaptability of the Kalman filtering leads to slightly better results. Finally, the study of a fan tip-gap flow is carried out with a zonal approach (LES in the tip region, RANS in the hub and midspan region). The reference simulation gives remarkable results in the blade-tip region, particularly for the velocity spectra. A second simulation with a control device by suction through the casing close to the blade leading edge shows two interesting features : a reduction of the turbulence level around the blade tip, and a modification of the tip-vortex trajectory (thus preventing impingement on the adjacent blade). These effects induce a notable reduction of the noise sources.