Wall-bounded turbulent flows are prevalent in engineering and industrial applications. Walls greatly affect turbulent characteristics in many ways including production and propagation of turbulent stresses. While computational fluid dynamics can be used as an important design tool, its use is hindered due to the fine-mesh requirements in the near-wall region to capture all of the pertinent turbulent data. To resolve all relevant scales of motion, the number of grid points scales with Reynolds number as N ≈ Re9/4, making it nearly impossible to solve real engineering problems, most of which feature high Reynolds numbers. A method to help alleviate the resolution requirements is the use of wall models. This method allows for a coarser mesh to be used in which the near-wall region is modeled and the first grid point is placed in the log-law region. The shear stress at the wall is correlated with the velocity at a point outside the near-wall region, drastically reducing the number of elements required and reducing the computational time and cost of the simulation. The goal of this study was to test the speed increase and element reduction capabilities of combining a wall function solution with the massively-parallel, spectral element solver, Nek5000, and verify the method using a turbulent channel simulation. The first grid point is placed at y+ = 100, in the log-law region, for Reτ = 950 and the sub-grid scales are modeled using a dynamic Smagorinski model. The results are then compared to a DNS performed by Jimenez and Hoyas for model verification.

In this dissertation, Immersed Boundary Method (IBM) is evaluated in ribbed duct geometries to show the potential of simulating complex geometry with a simple structured grid. IBM is first investigated in well-accepted benchmark cases: channel flow and pipe flow with circular cross-section. IBM captures all the flow features with very good accuracy in these two cases. Then a two side ribbed duct geometry is test using IBM at Reynolds number of 20,000 under fully developed assumption. The IBM results agrees well with body conforming grid predictions. A one side ribbed duct geometry is also tested at a bulk Reynolds number of 1.5⨉10⁴. Three cases have been examined for this geometry: a stationary case; a case of positive rotation at a rotation number (Ro=ΩDₕ/U) of 0.3 (destabilizing); and a case of negative rotation at Ro= -0.3 (stabilizing). Time averaged mean, turbulent quantities are presented, together with heat transfer. The overall good agreement between IBM, BCG and experimental results suggests that IBM is a promising method to apply to complex blade geometries. Due to the disadvantage of IBM that it requires large amount of cells to resolve the boundary near the immersed surface, wall modeled LES (WMLES) is evaluated in the final part of this thesis. WMLES is used for simulating turbulent flow in a developing staggered ribbed U-bend duct. Three cases have been tested at a bulk Reynolds number of 10⁵: a stationary case; a positive rotation case at a rotation number Ro=0.2; and a negative rotation case at Ro=-0.2. Coriolis force effects are included in the calculation to evaluate the wall model under the influence of these effects which are known to affect shear layer turbulence production on the leading and trailing sides of the duct. Wall model LES prediction shows good agreement with experimental data. / Master of Science

In recent years, jet noise has been an active area of research due to an increase in the use of aircraft in both commercial and military applications. To meet the noise standards laid out by government agencies, novel nozzle design concepts are being developed with an aim to attenuate the noise levels. To reduce the high costs incurred by experiments, simulation techniques such as large eddy simulation (LES) in combination with a surface integral acoustic method have received much attention for investigating various nozzle concepts. LES is utilized to predict the unsteady flow in the nearfield, whereas the surface integral acoustic method is used for the computation of noise in the farfield. However, Reynolds numbers at which nozzles operate in the real world are very high making wall-resolved LES simulations prohibitively expensive. To make LES simulations affordable, wall-models are being used to model the flow in the near wall region. Using a highly scalable, sixth-order finite-difference-based, in-house LES code, both wall-resolved and wall-modeled simulations of jets through the baseline short metal chevron (SMC000) nozzle were carried out earlier using an implicit LES (ILES) approach. However, differences exist in noise levels between the two simulations. Understanding the cause and reducing the differences between the two methodologies, while at the same time improving the fidelity of the wall-modeled LES is the main aim of the present work. Three new wall-models are implemented in the in-house LES code. A generalized equilibrium wall-model (GEWM) is implemented along with two wall-models that can account for non-equilibrium effects. First, a series of preliminary SMC000 wall-modeled LES simulations were performed and analyzed using the GEWM. The effect of turbulent length scales and velocity fluctuations specified at the inflow, wall-model formulation, and wall-normal grid refinement are analyzed. The adjustment of the fluctuations levels at the inflow proves to be useful in producing flowfields similar to that of the wall-resolved simulation. The newly implemented wall-models are validated for non-canonical problems such as an accelerating boundary layer developing over a flat plate and flow through a converging-diverging channel. It is noticed that the Reynolds number should be high enough for the non-equilibrium wall-models to be effective. At low Reynolds numbers, both equilibrium and non-equilibrium models produce similar wall shear-stresses. However, the wall shear stress boundary conditions supplied by the wall-models do not affect the mean velocity, turbulent kinetic energy, and Reynolds shear stress. Since all the wall-models produce similar results, and the GEWM is the most economical among the implemented wall-models, it is used in performing two wall-modeled LES SMC000 nozzle simulations for noise predictions. The inflow velocity and density fluctuations are varied between the simulations. The first SMC000 simulation uses similar inflow conditions as the previous wall-resolved SMC000 simulation. The second wall-modeled simulation was carried out by reducing the density and velocity fluctuations added to the mean flow at the inlet by 65%. The flowfield and acoustics agree reasonably well in comparison with the wall-resolved LES and similar experiments. Lowering of the velocity and density fluctuations in the wall-model LES improves the agreement of the far-field noise predictions with the wall-resolved LES at most observer locations. However, the preliminary SMC000 simulations performed using a higher Reynolds number and Mach number than that of the previous case show that the approach of adjusting the velocity and density fluctuations added to the mean flow have minimal impact on the developing flowfield which in turn affects the farfield noise. Thus, unless a more effective wall-modeling method is developed, possibly employing an explicit SGS model, the postdictive process of using a wall-model while adjusting the velocity and density fluctuations, seems to be an affordable tool for testing various nozzle designs, subject to the Reynolds number and Mach number being used.

If radiation plays an important role in many engineering applications, especially in those including combustion systems, influence of radiation on turbulent flows, particularly on the turbulent boundary layers, is still not well known. The objective is here to perform a detailed study of radiation effect on turbulent flows. An optimized emission-based reciprocal (OERM) approach of the Monte-Carlo method is proposed for radiation simulation using the CK model for radiative gas properties. OERM allows the uncertainty of results to be locally controlled while it overcomes the drawback of the original emission-based reciprocity approach by introducing a new frequency distribution function that is based on the maximum temperature of the domain. Direct Numerical Simulation (DNS) has been performed for turbulent channel flows under different pressure, wall temperatures and wall emissivity conditions. Flow field DNS simulations are fully coupled with radiation simulation using the OERM approach. The role of radiation on the mean temperature field and fluctuation field are analyzed in details. Modification of the mean temperature profile leads to changes in wall conductive heat fluxes and new wall laws for temperature when radiation is accounted for. The influence on temperature fluctuations and the turbulent heat flux is investigated through their respective transport equations whose balance is modified by radiation. A new wall-scaling based on the energy balance is proposed to improve collapsing of wall-normal turbulent flux profiles among different channel flows with/without considering radiation transfer. This scaling enables a new turbulent Prandtl number model to be introduced to take into account the effects of radiation. In order to consider the influence of radiation in the near-wall region and predict the modified wall law, a one-dimensional wall model for Large Eddy Simulation (LES) is proposed. The 1D turbulent equilibrium boundary layer equations are solved on an embedded grid in the inner layer. The obtained wall friction stress and wall conductive flux are then fed back to the LES solver. The radiative power term in the energy equation of the 1D wall model is computed from an analytical model. The proposed wall model is validated by a comparison with the former DNS/Monte-Carlo results. Finally, two criteria are proposed and validated. The first one is aimed to predict the importance of wall radiative heat flux while the other one predicts whether a wall model accounting for radiation in the near wall region is necessary. A parametric study is then performed where a k-ǫ model and a turbulent Prandtl number model are applied to simulate the velocity and temperature field of different channel flows under various flow conditions. The obtained criteria values are analyzed and compared.

Le rayonnement joue un rôle important dans de nombreuses applications industrielles, en particulier celles mettant en jeu un processus de combustion. Cependant, son influence sur les écoulements turbulents, notamment les couches limites, n’est pas encore bien connu. L’objectif est ici d’analyser en détail l’effet du rayonnement sur les écoulements turbulents. Utilisant le modèle CK pour décrire les propriétés radiatives des gaz, une approche optimisée de la méthode de Monte-Carlo (OERM) basée sur l’émission et le principe de réciprocité est développée. La méthode OERM permet de contrôler localement l’imprécision des résultats tout en corrigeant l’inconvénient de la méthode originale en introduisant une nouvelle fonction de répartition des fréquences basée sur la température maximale du domaine. Plusieurs écoulements de canal plan turbulent sous différentes conditions de pression, de températures et d’émissivités de parois sont résolus par simulation numérique directe (DNS). Les simulations DNS de l’écoulement et du champ de rayonnement par la méthode OERM sont entièrement couplées. L’impact du rayonnement sur le champ moyen de température et ses fluctuations est analysé en détail. La modification du profil de température moyenne induit un changement des flux de chaleur conductifs aux parois et de nouvelles lois de paroi pour la température lorsque le rayonnement est pris en compte. L’impact sur les fluctuations de température et le flux de chaleur par transport turbulent est étudié au travers de leurs équations de transport respectives dont l’équilibre est modifié par le rayonnement. Une nouvelle normalisation (wall-scaling) basée sur le bilan d’énergie est proposée pour améliorer le recouvrement des profils obtenus sous les différentes configurations étudiées avec et sans transfert radiatif. Cette normalisation permet d’introduire un modèle pour le nombre de Prandtl turbulent lorsque le rayonnement est pris en compte. Afin de prédire l’effet du rayonnement sur la zone proche paroi et sa modification des lois de paroi, un modèle de paroi pour la simulation aux grandes échelles (LES) est développé. Les équations 1D de couche limite turbulente à l’équilibre sont résolues sur une grille intégrée au maillage LES pour traiter la zone interne. La contrainte pariétale et le flux de chaleur conductif obtenus sont renvoyés au code LES. La puissance radiative dans l’équation d’énergie du modèle de paroi 1D est évaluée à partir d’un modèle analytique. Le modèle de paroi est validé par comparaison avec les résultats des calculs couplés DNS/Monte-Carlo. Deux critères sont finalement proposés et validés. Le premier a pour but de prédire l’importance du flux radiatif pariétal tandis que le second détermine si un modèle de paroi prenant en compte l’effet du rayonnement dans la zone interne de la couche limite est nécessaire. Une étude paramétrique est ensuite réalisée où un modèle κ-ϵ et un modèle de nombre de Prandtl turbulent sont utilisés pour estimer les champs moyens de vitesse et température d’écoulements de canal plan sous différentes conditions. Les valeurs des critères obtenues sont analysées puis comparées. / If radiation plays an important role in many engineering applications, especially in those including combustion systems, influence of radiation on turbulent flows, particularly on the turbulent boundary layers, is still not well known. The objective is here to perform a detailed study of radiation effect on turbulent flows. An optimized emission-based reciprocal (OERM) approach of the Monte-Carlo method is proposed for radiation simulation using the CK model for radiative gas properties. OERM allows the uncertainty of results to be locally controlled while it overcomes the drawback of the original emission-based reciprocity approach by introducing a new frequency distribution function that is based on the maximum temperature of the domain. Direct Numerical Simulation (DNS) has been performed for turbulent channel flows under different pressure, wall temperatures and wall emissivity conditions. Flow field DNS simulations are fully coupled with radiation simulation using the OERM approach. The role of radiation on the mean temperature field and fluctuation field are analyzed in details. Modification of the mean temperature profile leads to changes in wall conductive heat fluxes and new wall laws for temperature when radiation is accounted for. The influence on temperature fluctuations and the turbulent heat flux is investigated through their respective transport equations whose balance is modified by radiation. A new wall-scaling based on the energy balance is proposed to improve collapsing of wall-normal turbulent flux profiles among different channel flows with/without considering radiation transfer. This scaling enables a new turbulent Prandtl number model to be introduced to take into account the effects of radiation. In order to consider the influence of radiation in the near-wall region and predict the modified wall law, a one-dimensional wall model for Large Eddy Simulation (LES) is proposed. The 1D turbulent equilibrium boundary layer equations are solved on an embedded grid in the inner layer. The obtained wall friction stress and wall conductive flux are then fed back to the LES solver. The radiative power term in the energy equation of the 1D wall model is computed from an analytical model. The proposed wall model is validated by a comparison with the former DNS/Monte-Carlo results. Finally, two criteria are proposed and validated. The first one is aimed to predict the importance of wall radiative heat flux while the other one predicts whether a wall model accounting for radiation in the near wall region is necessary. A parametric study is then performed where a k-ǫ model and a turbulent Prandtl number model are applied to simulate the velocity and temperature field of different channel flows under various flow conditions. The obtained criteria values are analyzed and compared.

Large Eddy Simulation (LES) is a relatively more accurate and reliable alternative to solution of Reynolds Averaged Navier Stokes (RANS) equations in simulating complex turbulent flows at a lesser computational cost than a direct numerical simulation (DNS). However, LES of wall-bounded flows still requires a very high grid resolution in the inner wall layer making its widespread use difficult. Different attempts have been made in the past time to overcome this problem by modeling the near wall turbulence instead of resolving it. One such approach is a two-layer wall model that solves for a reduced one-dimensional equation in the inner wall layer, while solving for the filtered Navier-Stokes equations in the outer layer. The use of such a model allows for a coarser grid resolution than a wall resolved LES. This work validates the performance of a two-layer wall model developed for an arbitrary body fitted non-orthogonal grid in the flow over a wall mounted hump at Reynolds number 9.36x105. The wall modeled large eddy simulation (WMLES) relaxes the grid requirement compared to a wall resolved LES (WRLES) by allowing the first off-wall grid point to be placed at a y+ of approximately 20-40. It is found that the WMLES results are general good agreement with WRLES and experiments. Surface pressure coefficient, skin friction, mean velocity profiles, and the reattachment location compare very well with experiment. The WMLES and WRLES exhibit some under prediction of the peak values in the turbulent quantities close to the reattachment location, with better agreement with the experiment in the separated region. In contrast, a simulation that did not employ the wall model on the grid used for WMLES failed to predict flow separation and showed large discrepancies with the experimental data. In addition to the relaxation of the grid requirement in the wall normal direction, it was also observed that the wall model allowed a reduction in the number of computational cells in the span-wise direction by half. However an LES calculation on a grid with reduced number of cells in span-wise direction turned unstable almost immediately, thereby highlighting the effectiveness of the wall model. Besides reducing the number of grid points in the spatial domain, the relaxed grid resolution for the WMLES also permitted the use of a larger time step. This resulted in an order of magnitude reduction in the total CPU time relative to WRLES. / Master of Science

The developing flow field in a parallel plate microchannel, induced by wall motion, has been modeled numerically. This type of flow simulates the physical driving mechanism that exists in electro-osmotically generated flow with large channel diameter-to-Debye length ratios (Z). The physics of the flow field were compared between the moving wall model (MWM) and electro-osmotic flow (EOF) at Reynolds numbers of 1 and 1800, and Z > 2500. Also, Z-values between 50 and 500 were studied to investigate the accuracy of the MWM. Results show that for Z-values greater than 100 the MWM shows good agreement with EOF. The dynamics of the developing flow field for the MWM were explored for channel length-to-hydraulic diameter ratios (aspect ratio) of 5, 10, 20 and 40 at ten Reynolds numbers, Re (based on the wall velocity), below Re < 2000. The results show that far from the inlet the maximum fluid velocity occurs at the walls, as is expected, and the minimum velocity occurs at the channel center. Near the channel inlet, however, the centerline velocity is not a minimum but reaches a local maximum due to a resulting pressure imbalance generated by the wall motion. As the aspect ratio increases, the centerline velocity tends to approach the wall velocity far downstream from the inlet. Increases in the Reynolds number have the opposite effect on the centerline velocity. The hydrodynamic developing region, defined by that section of the channel where the wall shear stress is changing, also depends on the channel aspect ratio and Re, and is greater than the developing region for classical pressure-driven flow of a parallel plate channel. Also, the flow field physics was analyzed for a process called electro-mobility focusing (EMF). EMF is a process that separates and detects species of like charge with the use of electro-phoresis and EOF utilizing a varying voltage gradient. The velocity distribution and the effective diffusion were solved for analytically, for both a linear and non-linear voltage gradient, using the MWM and the creeping flow approximations. The resulting equations aid in optimizing the detection system by forcing the lowest effective diffusion (uniform velocity profile) to the detection location.

Materially non-linear analysis of reinforced concrete frame structures with infill walls requires appropriate mathematical models to be adopted for the beams and the columns as well as the infill walls. This study presents a mathematical model for frame elements based on a 3D Hermitian beam/column finite element and an equivalent strut model for the infill walls. The spread-of-plasticity approach is employed to model the material nonlinearity of the frame elements. The cross-section of the frame element is divided into triangular sub regions to evaluate the stiffness properties and the response of the element cross-section. By the help of the triangles spread over the actual area of the section, the bi-axial bending and the axial deformations are coupled in the inelastic range. A frame super-element is also formed by combining a number of frame finite elements. Two identical compression-only diagonal struts are used for modeling the infill. The equivalent geometric and material properties of the struts are determined from the geometry of the infill and the strength of the masonry units A computer code is developed using the object-oriented design paradigm and the models are implemented into this code. Efficiency and the effectiveness of the models are investigated for various cases by comparing the numerical response predictions produced by the program with those obtained from experimental studies.

A model study on laterally braced sheet pile walls retaining cohesionless soil was conducted using 1-g shaking table. Lateral dynamic earth pressures, backfill accelerations and dynamic displacement of walls were measured. Input accelerations were kept between 0.03g to 0.27g. A data acquisition system consisting of dynamic pressure transducers, accelerometers, displacement transducer, signal conditioning board and a data acquisition card compatible with a personal computer was used during the study. Three different walls with thicknesses of 6.6, 3.2 and 2.0 mm were used in order to investigate the effects of changing wall stiffness value on lateral seismic pressures developed on the wall. In addition to that, steel blocks were placed on top of the backfill in order to simulate a surcharge effect of 1.57 kPa to 3.14 kPa during shaking. Amplification of input acceleration, incremental seismic lateral thrusts and corresponding maximum dynamic pressures, application point of the resultant, effect of stiffness and surcharge on maximum seismic lateral thrust and dynamic wall deflections were calculated by processing raw data stored. The results were compared to previous model studies and some analytical methods available.

Cette thèse, initiée par un programme de coopération franco-britannique entre la DGA et la DSTL, est consacrée à l’étude des phénomènes de décollement de jet au sein des tuyères propulsives sur-détendu. L’aérothermodynamique des systèmes propulsifs (missile, avion supersonique ou lanceur) est un des domaines de la mécanique des fluides où des progrès décisifs restent à réaliser pour améliorer les performances des ensembles moteurs, en terme de bilan de poussée, de stabilité, de fiabilité et de réduction de nuisances (bruit, émission de polluants, etc.). Les conditions de vols et la complexité des phénomènes caractéristiques n’étant pas reproductibles sur bancs d’essais à l’aide des outils expérimentaux actuelles, l’utilisation de simulation numérique permettrait une étude approfondie et précise des phénomènes mis en jeu. Le besoin d’informations concernant l’instationnarité de l’écoulement s’affirmant de plus en plus, notamment sur les phénomènes basse fréquence dû aux décollements de jets, l’utilisation des simulations numériques aux grandes échelles (LES) permettrait de faire face au coût prohibitif des simulations directes (DNS). Les tuyères sur-détendu souffrent de charges latérales, caractérisées par des forces instationnaires orthogonales à la direction de l’écoulement. Ils sont causés par le décollement de la couche limite se développant le long de la paroi, provoquant des excursions de chocs importants, parfois asymétrique. Ces phénomènes instationnaires ont déjà été observés expérimentalement et numériquement. Ces instationnarités émergent d’une combinaison de phénomène complexe, tels que les interactions choc/couche limite sur la paroi de la tuyère, les couches de mélange décollées ou les zones de recirculation en aval du décollement, toutes produisant des modes énergétiques à différente fréquence caractéristique et tout particulièrement dans la plage de basse fréquence. Capturer le phénomène de décollement est un véritable défi dû à la nécessité de résoudre plusieurs échelles spatiales et temporelles. L’utilisation des simulations directes (DNS) ou résolu proche paroi (WR-LES) devient difficile compte tenu des ressources en calcul numérique actuelles. Pour parer ce problème, l’utilisation d’une stratégie de modélisation proche paroi est nécessaire. Le modèle de paroi développé par Kawai & Larsson (2013) est intégré à la simulation LES, combiné au modèle de viscosité de Duprat et al. (2011) afin de tenir compte des gradients de pression rencontré tout au long de la tuyère. Le développement d’un code curviligne a également permis de réduire le coût de calcul des simulations cylindriques en utilisant un maillage raffiné proche paroi. Les résultats obtenus à partir des simulations modélisés (WM-LES) permettent de bien mettre en évidence les phénomènes d’instationnarité menant au problème de charge latérale. Le coût de calcul étant réduit de 40 fois comparé à une simulation résolu proche paroi WR-LES, la production d’une base de donnée basse fréquence devient possible. La comparaison des calculs modélisés aux calculs résolus et aux données expérimentales confirme la bonne implémentation du modèle pour des simulations LES de tuyère propulsive. La caractérisation des différents phénomènes est faite à l’aide d’analyses spectrales effectuées sur la base de donnée permettant de mettre en avant le phénomène basse fréquence rencontré dans les tuyères sur-détendu. / The present thesis, sponsored by a Franco-British cooperation program between the DGA and the DSTL, is devoted to the study of separation phenomenon in over-expanded nozzle. The aerothermodynamic of propulsion systems (missile, supersonic aircraft or launcher) is one the fields of fluid mechanics where important progress remains to be made in order to improve the performance of the engine, in terms of thrust, stability, reliability and pollutant (noise reduction, pollutant emissions, etc.). Since the flight conditions and the complexity of the characteristic phenomena are not reproducible on experimental benches, the use of numerical simulation would allow a thorough and precise study of the phenomena involved. The instationnarity observed in the separation of the boundary layer is becoming a main concern nowadays, especially the low-frequency phenomenon observed in some experiments, the use of large scale simulations (LES) would fit perfectly the computational power allocated on supercomputer compared to the prohibitive cost of direct simulations (DNS). Over-expanded nozzles are known to suffer from side loads, characterized by undesired unsteady forces orthogonal to the flow direction. They are caused by boundary-layer separation that causes significant and asymmetrical shock excursions within the nozzle. These phenomena have been studied experimentally and numerically. They emerge from a combination of complex unsteady flow phenomena, not yet fully understood, such as shock/boundary-layer interactions at the nozzle walls, detached mixing layers, and large regions of recirculating flow, all producing energetic motions at frequencies one or two orders of magnitudes lower than the characteristic frequency of the incoming turbulence. Capturing the phenomenon is a real challenge due to the need to resolve at least four decades of time scales, from the energetic scales of the incoming turbulence. This makes both direct (DNS) and wall-resolved large-eddy simulations (WR-LES) rather impractical. Instead, a wall-modelled LES (WM-LES) strategy is employed here, following the approach of Kawai & Larsson (2013) together with the eddy-viscosity modification of Duprat et al. (2011) so as to account for pressure gradients. The WM-LES is found to accurately reproduce the flow topology, as well as the spectral content obtained by a reference WR-LES. The development of a curvilinear code has allowed us to decrease the cost of computation of the simulations by using a stretched mesh close to the wall. The results obtained from the wall-modeled simulations (WM-LES) allowed us to capture and study the phenomena of instationnarity leading to the problem of side-loads. The WM-LES being about 40 times cheaper, the low-frequency motions may be statistically converged, enabling the study of the very low frequencies. The comparison of the modeled simulations with the resolved simulations and the experimental data confirms the good implementation of the model for LES computations of over-expanded nozzle flow. The characterization of the different phenomena is done through spectral analyses, carried out on the LES database allowing the highlight of the low-frequency phenomenon encountered in the over-expanded nozzle flow.