Compressibility profoundly affects many aspects of turbulence in high-speed flows - most notably stability characteristics, anisotropy, kinetic-potential energy interchange and spectral cascade rate. Many of the features observed in compressible flows are due to the changing nature of pressure. Whereas for incompressible flows pressure merely serves to enforce incompressibility, in compressible flows pressure becomes a thermodynamic variable that introduces a strong coupling between energy, state, and momentum equations. Closure models that attempt to address compressibility effects must begin their development from sound first-principles related to the changing nature of pressure as a flow goes from incompressible to compressible regime. In this thesis, a unified framework is developed for modeling pressure-related compressibility effects by characterizing the role and action of pressure at different speed regimes. Rapid distortion theory is used to examine the physical connection between the various compressibility effects leading to model form suggestions for the pressure-strain correlation, pressure-dilatation and dissipation evolution equation. The pressure-strain correlation closure coefficients are established using fixed point analysis by requiring consistency between model and direct numerical simulation asymptotic behavior in compressible homogeneous shear flow. The closure models are employed to compute high-speed mixing-layers and boundary layers in a differential Reynolds stress modeling solver. The self-similar mixing-layer profile, increased Reynolds stress anisotropy and diminished mixing-layer growth rates with increasing relative Mach number are all well captured. High-speed boundary layer results are also adequately replicated even without the use of advanced thermal-flux models or low Reynolds number corrections. To reduce the computational burden required for differential Reynolds stress calculations, the present compressible pressure-strain correlation model is incorporated into the algebraic modeling framework. The resulting closure is fully explicit, physically realizable, and is a function of mean flow strain rate, rotation rate, turbulent kinetic energy, dissipation rate, and gradient Mach number. The new algebraic model is validated with direct numerical simulations of homogeneous shear flow and experimental data of high-speed mixing-layers. Homogeneous shear flow calculations show that the model captures the asymptotic behavior of direct numerical simulations quite well. Calculations of plane supersonic mixing-layers are performed and comparison with experimental data shows good agreement. Therefore the algebraic model may serve as a surrogate for the more computationally expensive differential Reynolds stress model for flows that permit the weak-equilibrium simplification.

L'étude porte sur une couche de mélange plane horizontale générée par la rencontre de deux écoulements parallèles à vitesse et température différentes. Le mélange turbulent est analysé pour différentes conditions initiales en termes de gradients de vitesse et de température. On distingue en particulier des configurations en régime de stratification stable et instable sous l'effet des forces de flottabilité. L'analyse des corrélations entre les fluctuations de vitesse et de température s'appuie sur la technique expérimentale d'anémométrie à température de fil variable (PCTA), qui permet la mesure instantanée de la vitesse et de la température en un même point grâce à la variation périodique et par palier du coefficient de surchauffe du fil chaud utilisé. Un premier travail a consisté à étendre la technique PCTA à l'utilisation de fils croisés pour la mesure simultanée de la température et de deux composantes de la vitesse. Dans un premier temps, les statistiques en un point permettent d'identifier les caractéristiques de l'écoulement dans la région de similitude et d'y établir les équations de bilan pour l'énergie cinétique turbulente, l'intensité des fluctuations de température et les flux de quantité de mouvement et de chaleur. Il apparaît, vu les faibles nombres de Richardson en jeu (Rif<0,03), que les forces de flottabilité sont quasi-négligeables devant les moteurs principaux du mouvement. Pourtant, ce forçage thermique peu énergétique est suffisant, en configuration instable, pour augmenter significativement le taux d'expansion et la contrainte de cisaillement, ce qui correspond de fait à une augmentation de la production de turbulence. L'analyse des densités de probabilité jointes permet ensuite de mettre en évidence les mécanismes et évènements qui contribuent significativement aux flux transversaux de quantité de mouvement et de chaleur. Ces différentes contributions sont différenciées et quantifiées par une analyse en quadrants qui fait ressortir la prépondérance des mouvements d'entraînement et d'éjection. On examine enfin les statistiques en deux points associées aux incréments de vitesse et de température. Le comportement de ces incréments est étudié à travers leurs densités de probabilité et leurs coefficients de dissymétrie et d'aplatissement. Les exposants des fonctions de structure confirment l'intermittence plus grande de la température par rapport à celle de la vitesse. Les différents termes des équations de Kolmogorov et de Yaglom sont mesurés. L'équilibre de ces bilans par échelle permet de quantifier le terme qui intègre les différents forçages proposés dans la littérature. / The turbulent mixing is studied in a plane mixing layer for a range of initial conditions applied in terms of velocity and temperature gradients between the two parallel inlet flows. A particular attention is paid to the effect of buoyancy forces, especially in the difference between the so-called stable and unstable configurations, in relation to the sign of the vertical temperature gradient applied. In this study, the novel experimental technique called PCTA, for Parameterizable Constant Temperature Anemometry, is used to enable the analysis of correlations between the velocity and temperature fluctuations. In a preliminary work, the PCTA technique, based on the implementation of repetitive multiple-overheat patterns to a hot wire, is extended and adapted for the instantaneous measurement of temperature and two components of velocity with X-wire probes. In a first stage, one point statistics are analysed. They provide a description of the flow features in the similarity region, where the balance equations for turbulent kinetic energy, temperature variance and the momentum and heat fluxes are established. Considering the low Richardson numbers at stake (Rif <0.03), the buoyancy forces appear logically to be quantitatively negligible compared to the main driving forces, but such a low energy forcing mechanism is in fact sufficient, in unstable configuration, to significantly increase the shear stress and the expansion rate of the mixing layer, both phenomena being associated to an enhanced production of turbulence. In a second stage, a joint probability density function analysis highlights the mechanisms and events that significantly contribute to the transverse momentum and heat fluxes. These contributions are differentiated and quantified through a quadrant analysis which emphasizes the dominance of the local movements of entrainment and ejection associated to the Kelvin-Helmholtz structures. Finally, the study focuses on the two points statistics associated with velocity and temperature increments. The behaviour of these increments is studied through their probability densities, examined along with the skewness and kurtosis coefficients. The structure function exponents confirm the stronger intermittency of temperature compared to that of the velocity. The different terms of the Kolmogorov and Yaglom equations are estimated. The balance of these scale budgets allows the quantification of the forcing term that has been introduced in the literature.

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Cette étude est consacrée à l’analyse des écoulements réactifs supersoniques cisailléset, plus particulièrement, des couches de mélange compressibles pouvant se développerdans les moteurs ramjet et scramjet. Des méthodes numériques appropriées ont été implémentéeset vérifiées pour aboutir au développement d’un code de calcul numériquemassivement parallèle, appelé CREAMS (compressible reactive multi-species solver). Cedernier a été spécialement conçu pour conduire des simulations numériques haute précision(simulations numériques directes ou DNS) de ce type d’écoulements. Une attentionparticulière a été portée à la description des termes de transport moléculaire et des termessources chimiques de façon à considérer la description physique la plus fidèle possible desmélanges des gaz réactifs à haute vitesse, au sein desquelles les temps caractéristiqueschimiques et de mélange aux petites échelles sont susceptibles d’être du même ordre degrandeur. Les simulations des couches de mélange bidimensionnelles et tridimensionnelles,inertes et réactives, confirment l’importance des effets associés à la compressibilité et autaux de dégagement de chaleur. Les résultats ainsi obtenus diffèrent en certains points deceux issus d’autres simulations qui introduisaient certaines hypothèses simplificatrices :développement temporel, emploi d’une chimie globale ou encore lois de transport simplifiées.En revanche, ils reproduisent certains tendances déjà observées dans un certainnombre d’études expérimentales conduites dans des conditions similaires. / This study is devoted to the analysis of supersonic reactive shear flows and, in particular,compressible mixing layers that can develop inside the ramjet and scramjet engines.Appropriate numerical methods have been implemented and tested to achieve the developmentof a massively parallel numerical solver, called CREAMS (compressible reactivemulti-species solver). This tool was designed to conduct high-precision numerical simulations(direct numerical simulations or DNS) of such flows. Particular attention waspaid to the description of the molecular transport terms and chemical source terms toconsider the most accurate physical description of reactive gas mixtures at high velocity,in which the chemical and mixing time scales, corresponding to the smallest scalesof the flow, are susceptible to be of the same order of magnitude. Simulations of twoandthree-dimensional, inert and reactive, mixing layers confirm the importance of theeffects associated with compressibility and rate of heat release. The results obtained differin some points from other simulations which introduced simplifying assumptions such astemporal development, use of a global chemistry or a simplified description of the moleculartransport terms. Nevertheless, they reproduce some trends already observed in severalexperimental studies conducted under similar conditions.

Ce travail porte sur l’évaluation de la méthode ZDES pour la simulation de jets propulsifs. L’analyse se concentre sur le positionnement des cellules de chocs et le développement des couches de mélange d’une tuyère double-flux avec plug externe, typique des moteurs d’avions modernes. Les champs statistiques sont comparés aux résultats expérimentaux et discutés en termes de grandeurs moyennes, fluctuantes et dans le domaine fréquentiel. L’intérêt d’utiliser un schéma spatial peu dissipatif ainsi qu’une échelle de longueur sous-maille basée sur la vorticité locale est mis en évidence, notamment pour le dévelopement de la couche de mélange interne, et le mode 2 ("automatique") de la ZDES a démontré un comportement similaire au mode 1 ("manuel") dans les couches de mélange. Par ailleurs, la technique Random Flow Generation (RFG) mise en oeuvre afin de reproduire la turbulence amont existant au coeur des jets primaire et secondaire a permis d’accélérer la transition RANS-LES dans les deux couches de mélanges, plus conformément à l’expérience. La transition est d’autant plus rapide que le taux de turbulence est élevé et l’échelle de la turbulence injectée est petite. Le positionnement des cellules de choc est également amélioré, soulignant l’importance de prendre en compte la turbulence amont dans les simulations de jets. / In this thesis, the ZDES method is assessed for the simulation of propulsive jets. This work focuses on the shock-cell positioning and the mixing layer development of a dual-stream nozzle configuration with an external plug, typical of modern aircraft engines. Reynolds averaged data are discussed in terms of mean and fluctuating quantities as well as in the frequency domain and compared with experimental data. First, the advantage of using a low dissipative spatial scheme as well as a subgrid length scale based on the local vorticity is demonstrated, especially for the development of the core mixing layer. Besides, the "automatic" mode of ZDES (mode 2) is found to provide similar mixing layers as the user defined mode.Then, the use of the Random Flow Generation (RFG) technique at the inlet boundaries of the core and fan channels in order to reproduce the turbulence rate at the center of the nozzle ducts is shown to accelerate the RANS-to-LES transition in both external and internal mixing layers, which is in better agreement with the experimental results. The transition length is further reduced when the injected turbulent ratio is higher, but also when the injected turbulent length scale is smaller. Of interest, the shock-cell positioning in the fan jet is also improved using RFG, which emphasizes the importance of accounting for upstream turbulence for this type of simulations.

<p>Turbulent mixing layers have been researched for many years. Currently, research is focused on studying compressible mixing layers because of their widespread applications in high-speed flight systems. While the effect of compressibility on the shear layer growth rate is well established, there is a lack of consensus over its effect on the turbulent stresses and hence warrants additional research in this area. Computational studies on compressible shear layers could provide a deep cognizance of the dynamics of fluid structures present in these flow fields which in turn would be viable for understanding the effects of compressibility on such flows. However, performing a Direct Numerical Simulation (DNS) of a highly compressible shear layer with experimental flow conditions is extremely expensive, especially when resolving the boundary layers that lead into the mixing section. The attractive alternative is to use Large Eddy Simulation (LES), as it possesses the potential to resolve the flow physics at a reasonable computational cost. Therefore the current work deals with developing a methodology to perform LES of a compressible mixing layer with experimental flow conditions, with resolving the boundary layers that lead into the mixing section through a wall model. The wall model approach, as opposed to a wall resolved simulation, greatly reduces the computational cost associated with the boundary layer regions, especially when using an explicit time-stepping scheme. An in house LES solver which has been used previously for performing simulations of jets, has been chosen for this purpose. The solver is first verified and validated for mixing layer flows by performing simulations of laminar and incompressible turbulent mixing layer flows and comparing the results with the literature. Following this, LES of a compressible mixing layer at a convective Mach number of 0.53 is performed. The inflow profiles for the LES are taken from a precursor RANS solution based on the k-ε and RSM turbulence models. The results of the LES present good agreement with the reference experiment for the upstream boundary layer properties, the mean velocity profile of the shear layer and the shear layer growth rate. The turbulent stresses, however, have been found to be underpredicted. The anisotropy of the normal Reynolds stresses have been found to be in good agreement with the literature. Based on the present results, suggestions for future work are also discussed.</p>

A new parametric model for the growth rate of turbulent mixing layers is proposed. A database of experimental and numerical mixing layer studies was extracted from the literature to support this effort. The domain of the model was limited to planar, spatial, nonreacting, free shear layers that were not affected by artificial mixing enhancement techniques. The model is split into two parts which were each tuned to optimally fit the database; equations for an incompressible growth rate were derived from the error function velocity profile, and a function for a compressibility factor was generalized from existing theory on the convective Mach number. The compressible model is supported by a detailed evaluation of the currently accepted models and practices, including error analysis of the convective Mach number derivation and a critical analysis of Slessor’s re-normalization technique which affected his 1998 compressibility parameter. Analysis of the database suggested that a distinction should be made between thickness definitions that are based on the velocity profile and those based on the density profile. Additionally, the accumulation of different normalization approaches throughout the literature was shown to have introduced non-physical variance in the trends. Resolution of this issue through a consistent normalization process has greatly improved the normality and scatter of the data and the goodness-of-fit of the models, resulting in R2 = 0.9856 for the incompressible model and R2 = 0.9004 for the compressible model.

Better understanding of the role of vegetation in the transport of fluid and pollutants requires improved knowledge of the detailed flow structure within the vegetation. Instead of spatial averaging, this study uses discrete measurements at multiple locations within the canopy to develop velocity and turbulence intensity profiles and observe the changes in the flow characteristics as water travels through a vegetation array simulated by rigid dowels. Velocity data were collected with a one dimensional laser Doppler velocimeter (LDV) under single layer emergent and submerged flow conditions, and through two layers of vegetation. The effects of dowel arrangement, density, and roughness are also examined under the single layer experiments. The results show that the velocity within the vegetation array is constant with depth and the velocity profile is logarithmic above it. The region immediately behind a dowel, where the vorticity and turbulence intensity are highest, is characterized by a velocity spike near the bed and an inflection point near the top of the dowel arrays. With two dowel layers, the velocity profile in the region behind a tall dowel exhibits multiple inflection points and the highest turbulence intensities are found there. / Master of Science

Tanto os motores turbo-jato quanto os turbo-fan, são os maiores responsáveis pela geração de ruído durante a decolagem, segmento de subida e de aceleração de uma aeronave. Devido a isto, o problema de ruído em jatos vem sendo intensamente investigado ao longo dos últimos anos. Já na fase do pouso, o slat é uma das fontes de ruído mais importantes. Para este caso, na maioria das aplicações práticas, existe o descolamento da camada limite no intradorso do slat a partir de onde se desenvolve uma camada de mistura. Ainda assim, existem inúmeros aspectos de tais escoamentos que precisam de investigação. Uma abordagem frequentemente feita para o estudo da instabilidade hidrodinâmica e ruído em jatos é o estudo de metade do jato. A estratégia consiste em estudar os fenômenos na camada de mistura, o que é uma aproximação razoável quando o jato tem diâmetro muito grande comparado à espessura da camada cisalhante que se desenvolve nas bordas do jato. Assim, alguns aspectos do ruído gerado pelos modos axi-simétricos de instabilidade são em grande parte reproduzidos. Um aspecto aparentemente jamais estudado antes é o efeito do emparelhamento de vórtices de diferentes geometrias na camada de mistura. Caso o efeito da modulação dos vórtices produzisse um padrão de ruído com características diferentes no emparelhamento, um controle ativo de escoamento por excitação periódica poderia ser usado para reduzir o ruído em jatos. O objetivo do presente trabalho é investigar tal efeito. A idéia é investigar este emparelhamento de vórtices na camada de mistura em desenvolvimento temporal bi-dimensional. Com isto foi possível visualizar um emparelhamento isolado de outros emparelhamentos e sem o efeito Doppler (presente na camada de mistura em desenvolvimento espacial). O método adotado foi a simulação numérica direta (DNS) das equações de Navier Stokes compressíveis na forma não-conservativa escritas na formulação característica. Os resultados mostram que a modulação dos vórtices não produz alteração significativa do ruído gerado no emparelhamento. / Turbo-fan and turbo-jet engines are the most important noise sources during the aircraft take off, climb and acceleration segments. Owing to this fact, the jet flow noise has been studied in the past years. For the landing stage, the slat is an important sound source. In this case, the slat leading edge frequently experiences a boundary layer deattachment causing the development of a mixing layer inside the slot. Nevertheless, there are many aspects of such phenomenon that have not been studied yet. Mixing layers constitutes an usual approach for jet flow instability in aeroacoustics studies. The stategy is to study the mixing layer in order to understand the jet-flow. This strategy becomes better as the ratio between the jet diameter and mixing layer thickness becomes larger. This approach is only reazonable for the jet flow axi-symetric unstable modes. The effect of vortex modulation on the vortex pairing sound production has not been found in the literature. If such effect could cause a significant change in the sound generation patterns, an active flow control system could be developed in order to enhance the jet noise performance. The purpose of the present work was to investigate such effect. It was also possible to observe a single vortex pairing inside a wide domain without the Doppler effect. The strategy was to study the vortex pairing in a bi-dimensional mixing layer under temporal development. The method used was the direct numerical simulation (DNS) of the compressible bidimensional (2D) Navier Stokes equations written in a nonconservative form of the characteristics formulation. The results showed that the vortex modulation did not produce a significant change on the vortex pairing sound.