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.

Les buts principaux recherchés de la présente thèse visent au développement et à l’expertise d’une méthodologie de simulation numérique des problèmes d’interactions fluides-structures. Afin de cerner progressivement le problème étudié, nous nous sommes intéressés en premier lieu à la simulation numérique des écoulements autour d’obstacles solides, plus particulièrement au phénomène d’éclatements tourbillonnaires dans la zone de sillage d’obstacles de différentes formes. Nous avons utilisé la méthode des éléments finis en adoptant la technique de stabilisation GLS (Galerkin Least-Square). Pour le traitement de la turbulence, nous avons opté pour la méthode LES (Large-Eddy Simulation) en utilisant le filtre de Smagorinsky. En deuxième phase, nous nous sommes intéressés aux écoulements en milieux déformables. Nous avons entrepris la formulation ALE (Arbitrairement Lagrangienne Eulérienne) en considérant un maillage déformable. Pour la mise à jour de la grille du maillage dynamique, nous avons utilisé une approche pseudo-élastique. Afin d’expertiser la méthodologie mise en oeuvre, nous avons choisi d’aborder le problème des ballottements à la surface libre de réservoirs partiellement remplis de liquide. En dernière partie, nous nous sommes intéressés au comportement vibratoire d’un corps solide sous l’effet d’un écoulement de fluide. Par l’utilisation d’un algorithme de couplage totalement implicite basé sur la méthode de Gauss-Seidel par Bloc, nous avons abordé le phénomène des instabilités aéroélastiques des ponts à haubans. Pour la validation du modèle numérique traitant les interactions fluides-structures par les données expérimentales, nous nous sommes intéressés au comportement vibratoire d’une maquette sectionnelle d’un tablier de pont réel sous l’effet d’un vent soufflant uniforme. / The main goals sought by this thesis target the development and expertise of a methodology for numerical simulation of fluid-structure interactions problems. In order to identify the studied problem progressively, we are interested primarily in numerical simulation of flows around bluff bodies, especially the phenomenon of vortex shedding in the wake zone of a bluff body of different shapes. We used the finite element method by adopting the stabilized GLS (Galerkin Least-Square) technique. For the treatment of turbulence, we opted the LES (Large-Eddy Simulation) method using the Smagorinsky filter. In the second phase, we were interested in flows in deformable media. We undertook the ALE (Arbitrary Lagrangian Eulerian) formulation by considering a deformable mesh. To update the grid of the dynamic mesh, we used a pseudo-elastic approach. To appraise the implemented methodology, we decided to approach the problem of sloshing at the free surface of a tank partially filled with liquid. In the final part, we were interested in vibration behavior of a solid body under the effect of fluid flow. By using a fully implicit coupling algorithm based on a relaxed Bloc Gauss-Seidel method, we studied the phenomenon of aeroelastic instability of cable-stayed bridges. To validate the numerical model treating fluid-structure interactions by experimental data, we investigated the vibration behavior of a real deck sectional model under the effect of a uniform wind.

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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.

La compréhension des phénoménes turbulents représente un des problèmes majeurs actuels. Bien que les équations qui décrivent ces phénomènes soient bien connues (les équations de Navier-Stokes), leur résolution analytique ou numérique reste limitée à des écoulements en géométries simples et à des nombres de Reynolds faibles. La méthode de Simulation des Grandes Echelles (LES) est bien adaptée pour la prédiction des écoulements turbulents, sans faire appel à des moyens informatiques prohibitifs. Cette méthode consiste à ne calculer que les grandes structures d'un écoulement turbulent, l'influence des petites structures étant prise en compte via un modèle de turbulence. Trois principaux objectifs ont déterminé l'orientation de ce travail: l'étude théorique du modèle de Smagorinsky, le développement de modèles de turbulence et l'étude numérique du comportement de quelques modèles sous-maille dans deux configurations: la reconnection des deux tubes de vorticité et la turbulence homogène et isotrope. Sur la base de résultats théoriques dus à P. Constantin et Ch. Fefferman, on s'intéresse à une variante sélective du modèle de Smagorinsky et à un modèle anisotrope sélectif. Nous évaluons les forces et les faiblesses de ces modèles par des comparaisons avec des résultats obtenus par des simulations numériques directes ou utilisant d'autres modèles (le modèle de Smagorinsky classique et un modèle de type différentiel).

In this work the model ASAM is enriched with new eddy viscosity based dynamic Smagorinsky subgrid-scale models. Therefore the model is more physically based to study atmospheric flow configurations at several atmospheric scales with main focus to urban scale flow with building-resolved resolution. The implemented dynamic procedures work well and showed good agreement to literature data. In a convective atmospheric boundary layer (ABL) the dynamic Smagorinsky coefficient reaches maximum values of 0.15 and decreases towards the surface or in stable stratified flow regimes. Vertical profiles of the Smagorinsky coefficient in a diurnal cycle of ABL depict typical behaviour of the dynamic Smagorinsky coefficient in near surface flow, free-stream, or stable stratified flow. Furthermore a modified inflow generation approach is proposed to produce fully turbulent flow fields. To modify a mean flow turbulent fluctuations are generated by superposition of sinusoidal and cosinesoidal modes. Due to the implementation of this inflow method the model ASAM has the ability to reproduce a given wind field with information from its mean wind speed and their fluctuation energy spectrum. The model configuration developed in this work is able to reproduce flow structure in a complex urban geometry. The Mock Urban Setting Test (MUST) experiment represent an urban roughness geometry by placing 120 shipping containers ordinary arranged in an array. The used building-resolved resolution is able to capture dynamic flow structures like specific wake flow, recirculation regions or eddy detachment. The dynamic fluctuating behaviour of the wind velocity components is reproduced by the model with regard to peak magnitudes and their temporal occurrence. Satisfying agreement is found between tracer gas dispersion field measurements and the model results by capturing the fluctuating concentration magnitude and in some extend the mean values.

In this work the model ASAM is enriched with new eddy viscosity based dynamic Smagorinsky subgrid-scale models. Therefore the model is more physically based to study atmospheric flow configurations at several atmospheric scales with main focus to urban scale flow with building-resolved resolution. The implemented dynamic procedures work well and showed good agreement to literature data. In a convective atmospheric boundary layer (ABL) the dynamic Smagorinsky coefficient reaches maximum values of 0.15 and decreases towards the surface or in stable stratified flow regimes. Vertical profiles of the Smagorinsky coefficient in a diurnal cycle of ABL depict typical behaviour of the dynamic Smagorinsky coefficient in near surface flow, free-stream, or stable stratified flow. Furthermore a modified inflow generation approach is proposed to produce fully turbulent flow fields. To modify a mean flow turbulent fluctuations are generated by superposition of sinusoidal and cosinesoidal modes. Due to the implementation of this inflow method the model ASAM has the ability to reproduce a given wind field with information from its mean wind speed and their fluctuation energy spectrum. The model configuration developed in this work is able to reproduce flow structure in a complex urban geometry. The Mock Urban Setting Test (MUST) experiment represent an urban roughness geometry by placing 120 shipping containers ordinary arranged in an array. The used building-resolved resolution is able to capture dynamic flow structures like specific wake flow, recirculation regions or eddy detachment. The dynamic fluctuating behaviour of the wind velocity components is reproduced by the model with regard to peak magnitudes and their temporal occurrence. Satisfying agreement is found between tracer gas dispersion field measurements and the model results by capturing the fluctuating concentration magnitude and in some extend the mean values.:1 Introduction 1 2 Fundamentals of Large-Eddy Simulation in atmospheric boundary layers 7 2.1 The atmospheric boundary layer . . . . . . . . . . . . . . . . . . . . . 7 2.2 Atmospheric turbulence . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.3 Basic equations of LES . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3 Subgrid-scale modelling 15 3.1 Eddy viscosity subgrid-scale models . . . . . . . . . . . . . . . . . . . 15 3.1.1 Smagorinsky subgrid-scale model . . . . . . . . . . . . . . . . 16 3.1.2 Dynamic Smagorinsky subgrid-scale model . . . . . . . . . . . 18 3.1.3 Scale-dependent dynamic Smagorinsky subgrid-scale model . . 23 3.2 Implementation in the All Scale Atmospheric Model (ASAM) . . . . . 26 3.2.1 General description of ASAM . . . . . . . . . . . . . . . . . . 26 3.2.2 Subgrid-scale modelling in ASAM . . . . . . . . . . . . . . . . 27 3.3 Applications to meteorological situations . . . . . . . . . . . . . . . . 37 3.3.1 Stable and unstable stratified atmospheric boundary layers . . 37 3.3.2 Flow over periodic sinusoidal hill . . . . . . . . . . . . . . . . 49 4 Generation of turbulent inflow conditions 51 4.1 The necessity of turbulent inflow . . . . . . . . . . . . . . . . . . . . 51 4.2 Synthetic turbulent inflow generation method . . . . . . . . . . . . . 53 4.3 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4.4 2D simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 5 Mock Urban Setting Test Experiment (MUST) 65 5.1 Micro-scale urban simulation . . . . . . . . . . . . . . . . . . . . . . . 65 5.2 Description of the experiment . . . . . . . . . . . . . . . . . . . . . . 68 5.3 Wind tunnel measurenments of MUST . . . . . . . . . . . . . . . . . 70 5.4 Numerical MUST simulation with ASAM . . . . . . . . . . . . . . . . 72 5.4.1 Choice of initial condition . . . . . . . . . . . . . . . . . . . . 75 5.4.2 Results of simulating case 2682353 . . . . . . . . . . . . . . . 81 5.4.3 Results of simulating case 2681829 . . . . . . . . . . . . . . . 98 5.4.4 Case resume . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 6 Summary and outlook 111 6.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 6.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 7 Bibliography 117 List of Figures 127 List of Tables 135 Acronyms 137 Nomenclature 139 Acknowledgement 143 List of Publications 145