Significant effort has been placed on the development of surfaces which reduce the amount of drag experienced by a fluid as it passes over the surface. Alterations to the fluid itself, as well as the chemical and physical composition of the surface have been investigated with varying success. Investigations into turbulent drag reduction have been mostly limited to those involving bubbles and riblets. Superhydrophobic surfaces, which combine hydrophobic surface chemistry with a regular array of microfeatures, have been shown to provide significant drag reduction in the laminar regime, with the possibility of extending these results into turbulent flows. Direct numerical simulations are used to investigate the drag reducing performance of superhydrophobic surfaces in turbulent channel flow. Slip velocities, wall shear stresses, and Reynolds stresses are considered for a variety of superhydrophobic surface microfeature geometry configurations at friction Reynolds numbers of Re = 180, Re = 395, and Re = 590. This work provides evidence that superhydrophobic surfaces are capable of reducing drag in turbulent flow situations by manipulating the laminar sublayer and turbulent energy cascade. For the largest micro-feature spacing of 90 microns an average slip velocity over 80% of the bulk velocity is obtained, and the wall shear stress reduction is found to be greater than 50%. The simulation results suggest that the mean velocity profile near the superhydrophobic wall continues to scale with the wall shear stress, but is offset by a slip velocity that increases with increasing micro-feature spacing.

Simulation and modelling of turbulent flows under influence of streamline curvature and system rotation have been considered. Direct numerical simulations have been performed for fully developed rotating turbulent channel flow using a pseudo-spectral code. The rotation numbers considered are larger than unity. For the range of rotation numbers studied, an increase in rotation number has a damping effect on the turbulence. DNS-data obtained from previous simulations are used to perform a priori tests of different pressure-strain and dissipation rate models. Furthermore, the ideal behaviour of the coefficients of different model formulations is investigated. The main part of the modelling is focused on explicit algebraic Reynolds stress models (EARSMs). An EARSM based on a pressure strain rate model including terms that are tensorially nonlinear in the mean velocity gradients is proposed. The new model is tested for a number of flows including a high-lift aeronautics application. The linear extensions are demonstrated to have a significant effect on the predictions. Representation techniques for EARSMs based on incomplete sets of basis tensors are also considered. It is shown that a least-squares approach is favourable compared to the Galerkin method. The corresponding optimality aspects are considered and it is deduced that Galerkin based EARSMs are not optimal in a more strict sense. EARSMs derived with the least-squares method are, on the other hand, optimal in the sense that the error of the underlying implicit relation is minimized. It is further demonstrated that the predictions of the least-squares EARSMs are in significantly better agreement with the corresponding complete EARSMs when tested for fully developed rotating turbulent pipe flow. / QC 20100825

Fundamental aspects of turbulence and turbulent mixing are investigated using direct numerical simulations (DNS) of stationary isotropic turbulence, with Taylor-scale Reynolds numbers ranging from 8 to 650 and Schmidt numbers from 1/8 to 1024. The primary emphasis is on important scaling issues that arise in the study of intermittency, mixing and turbulence under solid-body rotation. Simulations up to 2048^3 in size have been performed using large resource allocations on Terascale computers at leading supercomputing centers. Substantial efforts in algorithmic development have also been undertaken and resulted in a new code based on a two-dimensional domain decomposition which allows the use of very large number of processors.Benchmark tests indicate very good parallel performance for resolutions up to 4096^3 on up to 32768 processors. Investigation of intermittency through the statistics of dissipation and enstrophy in a series of simulations at the same Reynolds number but different resolution indicate that accurate results in high-order moments require a higher degree of fine-scale resolution than commonly practiced. At the highest Reynolds number in our simulations (400 and 650) dissipation and enstrophy exhibit extreme fluctuations of O(1000) the mean which have not been studied in the literature before and suggest a universal scaling of small scales. Simulations at Reynolds number of 650 on 2048^3 grids with scalars at Sc=1/8 and 1 have allowed us to obtain the clearest evidence of attainment of inertial-convective scaling in the scalar spectrum in numerical simulations to date whereas results at high Sc support k^{-1} viscous-convective scaling. Intermittency for scalars as measured by the tail of the PDF of scalar dissipation and moments of scalar gradient fluctuations is found to saturate at high Sc. Persistent departures from isotropy are observed as the Reynolds number increases. However, results suggest a return to isotropy at high Schmidt numbers, a tendency that appears to be stronger at high Reynolds numbers. The effects of the Coriolis force on turbulence under solid-body rotation are investigated using simulations on enlarged solution domains which reduce the effects of periodic boundary conditions.

A new method to perform direct numerical simulations of wall-bounded flows has been developed and implemented. The method uses high-order compact finite differences in wall-normal (for channel flow) or radial direction (for pipe flow) on a collocated grid, which gives high-accuracy results without the effectfof filtering caused by frequent interpolation as required on a staggered grid. The use of compact finite differences means that extreme clustering near the wall leading to small time steps in high-Reynolds number simulations is avoided. The influence matrix method is used to ensure a completely divergence-freesolution and all systems of equations are solved in banded form, which ensures an effcient solution procedure with low requirements for data storage. The method is unique in the sense that exactly divergence-free solutions on collocated meshes are calculated using arbitrary dffierence matrices. The code is validated for two flow cases, i.e. turbulent channel and turbulent pipe flow at relatively low Reynolds number. All tests show excellent agreement with analytical and existing results, confirming the accuracy and robustness ofthe method. The next step is to eciently parallelise the code so that high-Reynolds number simulations at high resolution can be performed. We furthermore investigated rare events occurring in the near-wall region of turbulent wall-bounded flows. We find that negative streamwise velocities and extreme wall-normal velocity uctuations are found rarely (on the order of 0:01%), and that they occur more frequently at higher Reynolds number. These events are caused by strong vortices lying further away from the wall and it appears that these events are universal for wall-bounded flows. / <p>QC 20150303</p>

La méso-combustion est le régime de combustion où la taille caractéristique du domaine est juste supérieure à la distance de coincement de la flamme , typiquement de l'ordre du centimètre. La difficile réalisation de systèmes de combustion fonctionnant en ce régime de flamme particulier suscite l'intérêt : il devient alors possible de tirer parti de la haute densité énergétique des hydrocarbures pour concevoir des systèmes de production d'énergie plus compacts. Nous nous intéressons à la réalisation de calculs DNS compressibles d'une chambre de combustion cubique de 8 x 10 x 8 mm3. Ce travail présente autant la mise en œuvre des calcules, en particulier la problématique de la condition frontière mur, que les résultats obtenus. Ces derniers nous permettent d'analyser la phénoménologie complexe de cet écoulement réactif confiné et serviront de base à des modélisations futures. / Meso-combustion can be defined as the combustion regime where the involved lenghts scales are close but slightly larger than the quenching distance of the flame, tipically smaller than a cm. By taking advantage of the high energetic density of liquid hydrocarbons, it would become possible to build small-sized combustion-based long-lived lighter electrical power systems. However combsution phenomena at these meso-scales have their own shortcomings. Indeed, by decreasing the system size, the usual phenomenological balance betwenne chemical reactions, mixing, turbulence and heat transfer is changed. In the present work, we focus on the DNS calculation of a cubic meso-combsution chamber of 8 x 10 x 8 mm3. This works presents the implementation of the numerical strategy used, with a specific attention to the no-slip wall compressible boundary condition. We then present an analysis of this particular reactive flow. The results are useful for future modeling of such a combustor.

Les situations dans lesquelles une onde de choc interagit avec une couche limite sont nombreuses dans les industries aéronautiques et spatiales. Sous certaines conditions (nombre de Mach élevé, grand angle de choc…), ces interactions entrainent un décollement de la couche limite. Des études antérieures ont montré que la zone de recirculation et le choc réfléchi sont tous deux soumis à un mouvement d'oscillation longitudinale à basse fréquence connu sous le nom d’instabilité de l’interaction onde de choc / couche limite (IOCCL). Ce phénomène appelé soumet les structures à des chargement oscillants à basse fréquence qui peuvent endommager les structures.L’objectif du travail de thèse est de réaliser des simulations instationnaires de l’IOCCL afin de contribuer à une meilleure compréhension de l’instabilité de l’IOCCL et des mécanismes physiques sous-jacents.Pour effectuer cette étude, une approche numérique originale est utilisée. Un schéma « One step » volume fini qui couple l’espace et le temps, repose sur une discrétisation des flux convectifs par le schéma OSMP développé jusqu’à l’ordre 7 en temps et en espace. Les flux visqueux sont discrétisés en utilisant un schéma aux différences finies centré standard. Une contrainte de préservation de la monotonie (MP) est utilisée pour la capture de choc. La validation de cette approche démontre sa capacité à calculer les écoulements turbulents et la grande efficacité de la procédure MP pour capturer les ondes de choc sans dégrader la solution pour un surcoût négligeable. Il est également montré que l’ordre le plus élevé du schéma OSMP testé représente le meilleur compromis précision / temps de calcul. De plus un ordre de discrétisation des flux visqueux supérieur à 2 semble avoir une influence négligeable sur la solution pour les nombres de Reynolds relativement élevés considérés.En simulant un cas d’IOCCL 3D avec une couche limite incidente laminaire, l’influence des structures turbulentes de la couche limite sur l’instabilité de l’IOCCL est supprimée. Dans ce cas, l’unique cause d’IOCCL suspectée est liée à la dynamique de la zone de recirculation. Les résultats montrent que seul le choc de rattachement oscille aux fréquences caractéristiques de la respiration basse fréquence du bulbe de recirculation. Le point de séparation ainsi que le choc réfléchi ont une position fixe. Cela montre que dans cette configuration, l’instabilité de l’IOCCL n’a pas été reproduite.Afin de reproduire l’instabilité de l’IOCCL, la simulation de l’interaction entre une onde de choc et une couche limite turbulente est réalisée. Une méthode de turbulence synthétique (Synthetic Eddy Method - SEM) est développée et utilisée à l’entrée du domaine de calcul pour initier une couche limite turbulente à moindre coût. L’analyse des résultats est effectuée en utilisant notamment la méthode snapshot-POD (Proper Orthogonal Decomposition). Pour cette simulation, l’instabilité de l’IOCCL a été reproduite. Les résultats suggèrent que la dynamique du bulbe de recirculation est dominée par une respiration à moyenne fréquence. Ces cycles successifs de remplissage / vidange de la zone séparée sont irréguliers dans le temps avec une taille maximale du bulbe de recirculation variant d’un cycle à l’autre. Ce comportement du bulbe de recirculation traduit une modulation basse fréquence des amplitudes des oscillations des points de séparation et de recollement et donc une respiration basse fréquence de la zone séparée. Ces résultats suggèrent que l’instabilité de l’IOCCL est liée à cette dynamique basse fréquence du bulbe de recirculation, les oscillations du pied du choc réfléchi étant en phase avec le point de séparation. / Situations where an incident shock wave impinges upon a boundary layer are common in the aeronautical and spatial industries. Under certain circumstances (High Mach number, large shock angle...), the interaction between an incident shock wave and a boundary layer may create an unsteady separation bubble. This bubble, as well as the subsequent reflected shock wave, are known to oscillate in a low-frequency streamwise motion. This phenomenon, called the unsteadiness of the shock wave boundary layer interaction (SWBLI), subjects structures to oscillating loads that can lead to damages for the solid structure integrity.The aim of the present work is the unsteady numerical simulation of (SWBLI) in order to contribute to a better understanding of the SWBLI unsteadiness and the physical mechanism causing these low frequency oscillations of the interaction zone.To perform this study, an original numerical approach is used. The one step Finite Volume approach relies on the discretization of the convective fluxes of the Navier Stokes equations using the OSMP scheme developed up to the 7-th order both in space and time, the viscous fluxes being discretized using a standard centered Finite-Difference scheme. A Monotonicity-Preserving (MP) constraint is employed as a shock capturing procedure. The validation of this approach demonstrates the correct accuracy of the OSMP scheme to predict turbulent features and the great efficiency of the MP procedure to capture discontinuities without spoiling the solution and with an almost negligible additional cost. It is also shown that the use of the highest order tested of the OSMP scheme is relevant in term of simulation time and accuracy compromise. Moreover, an order of accuracy higher than 2-nd order for approximating the diffusive fluxes seems to have a negligible influence on the solution for such relatively high Reynolds numbers.By simulating the 3D unsteady interaction between a laminar boundary layer and an incident shock wave, we suppress the suspected influence of the large turbulent structures of the boundary layer on the SWBLI unsteadiness, the only remaining suspected cause of unsteadiness being the dynamics of the separation bubble. Results show that only the reattachment point oscillates at low frequencies characteristic of the breathing of the separation bubble. The separation point of the recirculation bubble and the foot of the reflected shock wave have a fixed location along the flat plate with respect to time. It shows that, in this configuration, the SWBLI unsteadiness is not observed.In order to reproduce and analyse the SWBLI unsteadiness, the simulation of a shock wave turbulent boundary layer interaction (SWTBLI) is performed. A Synthetic Eddy Method (SEM), adapted to compressible flows, has been developed and used at the inlet of the simulation domain for initiating the turbulent boundary layer without prohibitive additional computational costs. Analyses of the results are performed using, among others, the snapshot Proper Orthogonal Decomposition (POD) technique. For this simulation, the SWBLI unsteadiness has been observed. Results suggest that the dominant flapping mode of the recirculation bubble occurs at medium frequency. These cycles of successive enlargement and shrinkage of the separated zone are shown to be irregular in time, the maximum size of the recirculation bubble being submitted to discrepancies between successive cycles. This behaviour of the separation bubble is responsible for a low frequency temporal modulation of the amplitude of the separation and reattachment point motions and thus for the low frequency breathing of the separation bubble. These results tend to suggest that the SWBLI unsteadiness is related to this low frequency dynamics of the recirculation bubble; the oscillations of the reflected shocks foot being in phase with the motion of the separation point.

Flush-mounted cavity hot-wire probes have been around since two decades, but have typically not been applied as often compared to the traditional wall hot-wires mounted several wire diameters above the surface. While the latter suffer from heat conduction from the hot wire to the substrate in particular when used in air flows, the former is belived to significantly enhance the frequency response of the sensor. The recent work using a cavity hotwire by Gubian et al. (2019) came to the surprising conclusion that the magnitute of the fluctuating wall-shear stress τ+w,rms reaches an asymptotic value of 0.44 beyond the friction Reynolds number Re τ ∼ 600. In an effort to explain this result, which is at odds with the majority of the literature, the present work combines direct numerical simulations (DNS) of a turbulent channel flow with a cavity modelled using the immersed boundary method, as well as an experimental replication of the study of Gubian et al. in a turbulent boundary layer to explain how the contradicting results could have been obtained. It is shown that the measurements of the mentioned study can be replicated qualitatively as a result of measurement problems. We will present why cavity hot-wire probes should neither be used for quantitative nor qualitative measurements of wall-bounded flows, and that several experimental short-comings can interact to sometimes falsely yield seemingly correct results.

Nous cherchons à modéliser numériquement un jet flottant air-hélium dans une cavité avec deux ouvertures à partir de simulations aux grandes échelles (LES) et de simulations numériques directes (DNS). La configuration considérée est basée sur une étude expérimentale menée au CEA de Saclay reproduisant une fuite d'hydrogène en environnement confiné. La dimension de la cavité a été choisie pour permettre une transition laminaire-turbulent intervenant environ à la mi-hauteur de la cavité. Cette étude porte principalement sur trois points majeurs : l'influence des conditions aux limites sur le développement du jet et son interaction avec l'environnement extérieur, la validité du modèle numérique qui est analysée en comparant la distribution de vitesse obtenue numériquement aux mesures expérimentales (PIV) et, enfin, la compréhension de la distribution air-hélium et le phénomène de stratification qui s'établit à l'intérieur de la cavité. Nous observons dans un premier temps que des conditions limites de pression constante appliquées directement au ras des évents conduisent à une sous-estimation du débit volumique d'air entrant dans la cavité et donc à une surestimation de la masse de l'hélium à l'intérieur de la cavité, ce qui n'est pas acceptable dans un contexte d'évaluation du risque hydrogène. En revanche, la prise en compte, dans le domaine de calcul, d'une région extérieure à la cavité prédit correctement le flux d'air entrant. Les résultats numériques sont alors en bon accord avec les données PIV. Il a été montré que les prédictions de la DNS, par rapport à la LES, concordent mieux avec les mesures de vitesse par PIV. Le champ de concentration prédit numériquement présente une couche homogène en haut de la cavité, dont la concentration est en accord avec le modèle théorique de Linden et al. 1990. Cependant, sa position et son épaisseur ne correspondent pas au modèle. Ceci est principalement dû aux interactions directes entre le jet flottant et, d'une part, avec les limites solides de la cavité et d'autre part, avec l'environnement extérieur. L'analyse statistique concernant la production de la flottabilité de l'énergie cinétique turbulente (TKE) a permis d'identifier les limites du jet flottant. / We present numerical results from large eddy simulations (LES) and coarse direct numerical simulations (DNS) of an air-helium buoyant jet rising in a two vented cavity. The geometrical configuration mimics the helium release experimental set-up studied at CEA Saclay in the framework of security assessment of hydrogen-based systems with an indoor usage. The dimension of the enclosure was chosen to ensure a laminar-turbulent transition occurring at about the middle height of the cavity. This study focuses mainly on three key points : the influence of the boundary conditions on the jet development and its interaction with the exterior environment, the validity of the numerical model which is analyzed by comparing the numerical velocity distribution versus the measured particle image velocimetry (PIV) ones, and finally understanding the distribution of air-helium and the stratification phenomenon that takes place inside the cavity. We observe at first that applying constant pressure outlet boundary conditions directly at the vent surfaces underestimates the volumetric flow rate of air entering the enclosure and thus overestimate the helium mass inside the cavity. On the contrary, modelling an exterior region in the computational domain better predicts the air flow-rate entrance and numerical results matches better with the experimental PIV data. It has been figured out that the coarse DNS predictions match better with the velocities PIV measurements, compared to the LES. Numerical prediction of the helium field depicts a homogeneous layer formed at the top of the cavity, with a concentration in good agreement with the theoretical model of Linden et al. 1990. However, the position and the thickness of the layer do not correspond to the theory. This is mainly due to the direct interactions between the buoyant jet and both the solid boundaries of the cavity and the exterior environment. Statistical analysis regarding the buoyancy production of the turbulent kinetic energy (TKE) served to identify the limits of the buoyant jet.

It is well known that most fluid flows observed in nature or encountered in engineering applications are turbulent and involve separation. Fluid flows in turbines, diffusers and channels with sudden expansions are among the widely observed areas where separation substantially alters the flow field and gives rise to complex flow dynamics. Such types of flows are referred to as internal flows since they are confined within solid surfaces and predominantly involve the generation or utilization of mechanical power. However, there is also a vast variety of engineering applications where the fluid flows past solid structures, such as the flow of air around an airplane or that of water around a submarine. These are called external flows and as in the former case the downstream evolution of the flow field is crucially influenced by separation. The present doctoral thesis addresses both internal and external separated flows by means of direct numerical simulations of the incompressible Navier-Stokes equations. For internal flows, the wall-driven flow in a onesided expansion channel and the pressure-driven flow in a plane channel with a single thin-plate obstruction have been studied in the fully developed turbulent state. Since such geometrical configurations involve spatially developing turbulent flows, proper inflow conditions are to be employed in order to provide a realistic fully turbulent flow at the input. For this purpose, a newly developed technique has been used in order to mimic an infinitely long channel section upstream of the expansion and the obstruction, respectively. With this approach, we are able to gather accurate mean flow and turbulence statistics throughout each flow domain and to explore in detail the instantaneous flow topology in the separated shear layers, recirculation regions as well as the recovery zones. For external flows, on the other hand, the flow past a prolate spheroid has been studied. Here, a wide range of Reynolds numbers is taken into consideration. Based on the characteristics of the vortical structures in the wake, the flow past a prolate spheroid is classified as laminar (steady or unsteady), transitional or turbulent. In each flow regime, the characteristic features of the flow are investigated by means of detailed frequency analysis, instantaneous vortex topology and three-dimensional flow visualizations.

Among the different types of flows encountered in practical applications, the physics of turbulent separated flows and turbulence induced secondary motion are not fully understood despite the large amount of previous experimental and numerical work. The objectives of this work are to study theoretically and computationally the conditions at the separation and reattachment point, the numerical simulation of turbulence induced secondary motion in non-circular ducts, and to provide a comprehensive test of different RANS models of these types of flow. In a theoretical study of flow separation, a Lagrangian approach was first used to derive an Eulerian criterion, which associates separation and reattachment points to a critical point in the eigenvalues of the Cauchy-Green tensor. A turbulent separated boundary layer under the influence of an adverse pressure gradient was simulated using DNS and LES techniques. A bootstrapping method was used to obtain high fidelity results at a relatively high Reynolds number with which the performance of some of the most commonly used eddy-viscosity turbulence models was evaluated. The DNS and LES results were used to assess the consistency of the different terms in the k−e , ζ −f , k −ω and Spalart-Allmaras models. Different wall-modelling techniques were employed for the calculation of separated boundary layers. The exact values of the modelled terms were calculated using the reference DNS and LES dataset. These results were used for both a priori and a posteriori tests. It was determined that the eddy-viscosity assumption works well, and that anisotropic effects are not significant in separated boundary layer. For the secondary flow calculation in non-circular ducts, direct numerical simulations of turbulent flow in square and skewed ducts were carried out to determine the effect of the duct (rhombus) included angle on both the mean and turbulence energy budgets. Two skewed ducts, with included angles of 30 and 60 degrees, were simulated. The capability of different turbulence models to predict the secondary velocity field was investigated. Results obtained from a non-linear stress-strain constitutive relation was found to be fairly accurate for the flows at the range of Reynolds number considered in this study. / Thesis (Ph.D, Mechanical and Materials Engineering) -- Queen's University, 2010-11-26 13:52:18.361