Prévoir la transition laminaire-turbulent de la couche limite sur l'avant-corps d'un véhicule hypersonique est importantpour optimiser l'entrée d'air du superstatoréacteur qui lui est associé, mais reste très difficile après un demi-siècle derecherches intensives sur le sujet. Dans ce travail, les approches numériques et expérimentales sont mises en oeuvre etcomparées. Expérimentalement, la transition naturelle est détectée à Mach 4 et Mach 6 dans la soufflerie continue T-313de l'ITAM à Novossibirsk à l'aide de mesures de pression Pitot. Dans une autre soufflerie de l'ITAM, la AT-303 à rafale,on a détecté la transition naturelle à Mach 6 et la transition déclenchée par rugosités à Mach 8 à l'aide d'un procédéoptique basé sur l'emploi de peintures thermosensibles. Ces essais ont été réalisés sur maquette à échelle 1/3. Toutesles rugosités testées se sont montrées efficaces. La prévision théorique de la transition naturelle a été réalisée au moyende la théorie de la stabilité linéaire locale modale couplée à la méthode du eN. En vol, sur avant-corps à échelle 1, lesfacteurs N atteignent difficilement 8 à 9, ce qui est insuffisant pour assurer la transition avec certitude. Pour appliquer laméthode aux essais au sol, on a besoin de connaître les facteurs N de transition des souffleries, ce qui est réalisé à partird'essais de calibration sur plaque plane dans T-313. Un excellent accord théorie/expérience est obtenu à Mach 4. AMach 6, on doit prendre en compte la présence d'instabilité ‘’crossflow’’ inflexionnelle au nez de l'engin, moyennant quoil'accord est aussi très bon. Les calculs de stabilité ont été réalisés sur des solutions de base obtenues par simulationnumérique (CFD) des conditions de vol ou des essais au sol. Ces simulations ont également permis de bien comprendrela structure de l'écoulement autour de l'avant-corps et de concevoir en grande partie les moyens d'essai. / The prediction of the laminar-turbulent transition in the boundary layer on a hypersonic vehicle forebody is important tooptimize the air inlet of the associated scramjet engine, but is still very difficult after half a century of intensive research onthe subject. In this work, numerical and experimental approaches are applied and compared. Experimentally, the naturaltransition is detected at Mach 4 and Mach 6 in the blow down wind tunnel T-313 in ITAM Novosibirsk using Pitot pressuremeasurements. In the impulse AT-303 wind tunnel in ITAM, the natural transition at Mach 6 and the roughness inducedtransition at Mach 8 are detected using an optical method based on thermosensitive paints. These tests have beenperformed on a 1/3 scale model. All the trips tested have shown their effectiveness. The theoretical prediction of thenatural transition has been performed using the local modal linear stability theory coupled with the eN method. In flight, onthe full scale forebody, N factors hardly reach 8 to 9, which is insufficient for the transition. To apply the method to groundtests, the wind tunnels transition N factors are needed. They are obtained from calibration tests on a flat plate in T-313. Avery good agreement with experiments is found at Mach 4. At Mach 6, the presence of inflexional crossflow instabilitynear the nose of the body must be taken into account, which gives also a good agreement. Stability calculations havebeen done for mean flow solutions obtained by numerical simulations (CFD) of flight or ground tests conditions. Thesesimulations have also helped to understand the structure of the flow around the forebody and to design efficiently theexperimental setup.

Two types of shear flows are investigated in this thesis; numerical simulations are performed for the analysis and control of the perturbation arising in a boundary layer over a flat plate, whereas PIV measurements are analysed for the investigation of a confined turbulent jet. Modal structures of the flows are identified: the aim is to understand the flow phenomena and to identify reduced-order models for the feedback control design. The attenuation of three-dimensional wavepackets of streaks and Tollmien-Schlichting (TS) waves in the boundary layer is obtained using feedback control based on arrays of spatially localized sensors and actuators distributed near the rigid wall. In order to tackle the difficulties arising due to the dimension of the discretized Navier-Stokes operator, a reduced-order model is identified, preserving the dynamics between the inputs and the outputs; to this end, approximate balanced truncation is used. Thus, control theory tools can be easily handled using the low-order model. We demonstrate that the energy growth of both TS wavepackets and streak-packets is substantially and efficiently mitigated, using relatively few sensors and actuators. The robustness of the controller is investigated by varying the number of actuators and ensors, the Reynolds number and the pressure gradient. The configuration can be possibly reproduced in experiments, due to the localization of sensing and actuation devices. A complete analysis of a confined turbulent jet is carried out using timeresolved PIV measurements. Proper orthogonal decomposition (POD) modes and Koopman modes are computed and analysed for understanding the main features of the flow. The frequencies related to the dominating mechanisms are identified; the most energetic structures show temporal periodicity. / QC 20110214

Laminar-turbulent transition has a strong impact on aerodynamic performance in many practical applications. Hence, there is a practical need for developing reliable and efficient transition prediction models, which form a critical element of the CFD process for aerospace vehicles across multiple flow regimes. This dissertation explores machine learning approaches to develop transition models using data from computations based on linear stability theory. Such data provide strong correlation with the underlying physics governed by linearized disturbance equations. In the proposed transition model, a convolutional neural network-based model encodes information from boundary layer profiles into integral quantities. Such automated feature extraction capability enables generalization of the proposed model to multiple instability mechanisms, even for those where physically defined shape factor parameters cannot be defined/determined in a consistent manner. Furthermore, sequence-to-sequence mapping is used to predict the transition location based on the mean boundary layer profiles. Such an end-to-end transition model provides a significantly simplified workflow. Although the proposed model has been analyzed for two-dimensional boundary layer flows, the embedded feature extraction capability enables their generalization to other flows as well. Neural network-based nonlinear functional approximation has also been presented in the context of transport equation-based closure models. Such models have been examined for their computational complexity and invariance properties based on the transport equation of a general scalar quantity. The data-driven approaches explored here demonstrate the potential for improved transition prediction models. / Doctor of Philosophy / Surface skin friction and aerodynamic heating caused by the flow over a body significantly increases due to the transition from laminar to turbulent flow. Hence, efficient and reliable prediction of transition onset location is a critical component of simulating fluid flows in engineering applications. Currently available transition prediction tools do not provide a good balance between computational efficiency and accuracy. This dissertation explores machine learning approach to develop efficient and reliable models for predicting transition in a significantly simplified manner. Convolutional neural network is used to extract features from the state of boundary layer flow at each location along the body. These extracted features are then processed sequentially using recurrent neural network to predict the amplification of instabilities in the flow, which is directly correlated to the onset of transition. Such an automated nature of feature extraction enables the generalization of this model to multiple transition mechanisms associated with different flow conditions and geometries. Furthermore, an end-to-end mapping from flow data to transition prediction requires no user expertise in stability theory and provides a significantly simplified workflow as compared to traditional stability-based computations. Another category of neural network-based models (known as neural operators) is also examined which can learn functional mapping from input variable field to output quantities. Such models can learn directly from data for complex set of problems, without the knowledge of underlying governing equations. Such attribute can be leveraged to develop a transition prediction model which can be integrated seamlessly in flow solvers. While further development is needed, such data-driven models demonstrate the potential for improved transition prediction models.

<p>Experiments were performed in the Boeing/AFOSR Mach-6 Quiet Tunnel on sharp, slender straight cones at zero degrees angle of attack. These long models allow the second mode to grow to large amplitudes without the need for introduced perturbations and without the presence of the Gortler instability. PCB pressure sensors and global thermal imaging are used to study the development of the second-mode instability. Transition was measured on both the 2.5 degree and 3 degree half-angle cones in high-Reynolds number quiet flow, indicated by increased heating and by breakdown of the second-mode instability. </p> <p><br></p> <p>Evidence of a flow-induced vibration on the 2.5 degree model was also measured for freestream unit Reynolds numbers between approximately 6.5 and 9.5 million per meter. These conditions produce large second-mode waves, and it is thought that the second-mode instability incites a resonance in the model near 100 kHz. The vibration interferes with measurements of the second mode. Since no such phenomenon is seen on the 3 degree cone, it was the predominant model studied.</p> <p><br></p> <p>Second-mode amplitudes on the 3 degree cone grew to a maximum amplitude before breakdown of 25.3% of the mean surface pressure. This value agreed with previous correlations between edge Mach number and the maximum second-mode amplitude that were found from measurements in conventional wind tunnels. The maximum second-mode amplitude was measured at a length-based Reynolds number of approximately 10 million. Small residual angles of attack (less than 0.1 degrees) did not significantly affect the maximum second-mode amplitude or the Reynolds number at which it was measured. </p> <p><br></p> <p>Heat transfer was measured on the 3 degree cone using IR thermography, and the laminar-scaled Stanton number was used to estimate the beginning of transition. The heating rose above the laminar value at a length-based Reynodls number of 9.6 million, almost simultaneously with the second mode reaching the maximum amplitude. This indicates that transition begins as the second mode begins to break down. The rise in heating coincides with the appearance of streamwise heating streaks. The streaks move forward on the cone for increasing Reynolds numbers. A second set of streaks appears downstream of the primary set for higher Reynolds numbers. The maximum heating is measured near the end of transition at a length-based Reynolds number of approximately 12.4 million before the heating decreases towards the turbulent value. </p> <p><br></p> <p>Measurements of intermittency were used to estimate the onset of transition, and good agreement was reached with the transition-onset location estimated using heat transfer. The measured intermittency compared well to the classic Narasimha-Dhawan distribution. Additionally, the intermittency indicated that the flow became always turbulent at a length-based Reynolds number of approximately 12.0 million, which is just before the maximum in heating. The ratio of the onset of transition to the end of transition for the 3 degree cone was approximately 0.85. The ratio for the Reentry F flight was approximately 0.8 and the ratio for conventional wind tunnels is typically near 0.5. These results support previous findings that the transition extent in quiet tunnels is shorter than in noisy tunnels and better approximates that seen in flight.</p>

Direct Numerical Simulations (DNS) are performed to investigate laminar-turbulent transition in a boundary layer on a sharp cone at Mach 6. The main objective of this dissertation research is to explore which nonlinear breakdown mechanisms may be dominant in a broad--band "natural" disturbance environment and then use this knowledge to perform controlled transition simulations to investigate these mechanisms in great detail. Towards this end, a "natural" transition scenario was modeled and investigated by generating wave packet disturbances. The evolution of a three-dimensional wave packet in a boundary layer has typically been used as an idealized model for "natural" transition to turbulence, since it represents the impulse response of the boundary layer and, thus, includes the interactions between all frequencies and wave numbers. These wave packet simulations provided strong evidence for a possible presence of fundamental and subharmonic resonance mechanisms in the nonlinear transition regime. However, the fundamental resonance was much stronger than the subharmonic. In addition to these two resonance mechanisms, the wave packet simulations also indicated the possible presence of oblique breakdown mechanism. To gain more insight into the nonlinear mechanisms, controlled transition simulations were performed of these mechanisms. Several small and medium scale simulations were performed to scan the parameter space for fundamental and subharmonic resonance. These simulations confirmed the findings of the wave packet simulations, namely that, fundamental resonance is much stronger compared to the subharmonic resonance. Subsequently a set of highly resolved fundamental and oblique breakdown simulations were performed. In these DNS, remarkable streamwise arranged "hot'' streaks were observed for both fundamental and oblique breakdown. The streaks were a consequence of the large amplitude steady longitudinal vortex modes in the nonlinear régime. These simulations demonstrated that both second--mode fundamental breakdown and oblique breakdown may indeed be viable paths to complete breakdown to turbulence in hypersonic boundary layers at Mach 6.

L’objectif de cette thèse est de faire progresser la modélisation de la transition de couche limite sur des aubes de turbines basse-pression fortement chargées. Cette modélisation repose sur l’utilisation du modèle de transition de Menter et Langtry utilisé pour des calculs RANS dans le code elsA. Une fois les limitations du modèle de transition clairement identifiées par une étude sur la mise en données des calculs, nous avons entrepris de modifier ce dernier. Pour cela, un processus d’optimisation a été développé afin de permettre la recalibration des fonctions de corrélation internes au modèle de transition. Cette nouvelle version du modèle nous permet d’obtenir des gains sur la modélisation d’environ 20 % sur les cas T106C du VKI en capturant mieux la transition au sein du bulbe de décollement. Ces précédents calculs correspondent à des cas idéaux, où l’on peut considérer les surfaces comme étant lisses. Cependant, nous avons aussi un besoin de se rapprocher de surfaces plus réalistes pour lesquelles les rugosités peuvent avoir un impact sur l’écoule- ment. En effet, les rugosités de surface peuvent notamment avoir un effet sur la transition. En particulier, si les rugosités entraînent le déclenchement de la transition en amont du point de décollement laminaire théorique en surface lisse, ce décollement sera supprimé. Vu nos efforts pour améliorer la prévision de la transition par bulbe de décollement par le modèle γ-Rθt, il parait intéressant que celui-ci puisse prendre en compte l’état des surfaces. Pour cela, nous avons implanté une méthode de prévision de la transition sur surfaces rugueuses développée par Stripf et al. au sein du modèle γ-Rθt. Enfin, l’utilisation du modèle de transition γ-Rθt a été étendue au modèle de turbulence k-l de Smith. / The goal of this thesis is to enhance laminar-turbulent transition modeling on high-lift low- pressure turbine blades. The presented transition modeling method relies on the Menter and Langtry transition model used in a RANS framework in the elsA solver. Once the model’s limits were clearly identified through a parametric study, we moved on to modification of the model. To do so, an optimization method was developed that allows recalibration of the model’s inner correlation functions. This new version of the model allows us to obtain modeling gains of about 20% on the VKI T106C cases through better capture of the separation-induced transition process. These previous computations correspond to ideal cases, for which surfaces may be considered as being smooth. However, we also have the need to consider more realistic surfaces for which roughness may influence the flow. Indeed, among those effects, is the potential influence of surface roughness on transition. In particular, if surface roughness induces transition up-stream of the smooth separation point, the separation bubble will be suppressed. Considering our efforts on modeling separation-induced transition with the γ-Rθt model, it seemed natural to add roughness-induced transition modeling capacities to it. To do so, we implemented in the γ-Rθt model a method developed by Stripf et al. to take into account surface roughness. Finally, the use of the γ-Rθt transition model was extended to the k-l of Smith tur- bulence model. Indeed, this turbulence model is widely used in turbomachinery. In order that our works on transition modeling over turbine blades be more widely usable, we have completed this thesis by proposing an evolution of the transition model so that it may be used alongside the k-l model.

The focus of this thesis is on the numerical study of subcritical transition to turbulence in the asymptotic suction boundary layer (ASBL). Applying constant homogeneous suction prevents the spatial growth of the boundary layer, granting access to the asymptotic dynamics. This enables research approaches which are not feasible in the spatially growing case. In a first part, the laminar–turbulent separatrix of the ASBL is investigated numerically by means of an edge-tracking algorithm. The consideration of spanwise-extended domains allows for the robust localisation of the attracting flow structures on this separatrix. The active part of the identified edge states consists of a pair of low- and high-speed streaks, which experience calm phases followed by high energy bursts. During these bursts the structure is destroyed and re-created with a shift in the spanwise direction. Depending on the streamwise extent of the domain, these shifts are either regular in direction and distance, and periodic in time, or irregular in space and erratic in time. In all cases, the same clear regeneration mechanism of streaks and vor- tices is identified, bearing strong similarities with the classical self-sustaining cycle in near-wall turbulence. Bifurcations from periodic to chaotic regimes are studied by varying the streamwise length of the (periodic) domain. The resulting bifurcation diagram contains a number of phenomena, e.g. multistability, intermittency and period doubling, usually investigated in the context of low-dimensional systems. The second part is concerned with spatio–temporal aspects of turbulent ASBL in large domains near the onset of sustained turbulence. Adiabatically decreasing the Reynolds number, starting from a fully turbulent state, we study low-Re turbulence and events leading to laminarisation. Furthermore, a robust quantitative estimate for the lowest Reynolds number at which turbulence is sustained is obtained at Re <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Capprox" /> 270. / <p>QC 20140213</p>

<p>Transition from laminar to turbulent flow has beentraditionally studied in terms of exponentially growingeigensolutions to the linearized disturbance equations.However, experimental findings show that transition may occuralso for parameters combinations such that these eigensolutionsare damped. An alternative non-modal growth mechanism has beenrecently identified, also based on the linear approximation.This consists of the transient growth of streamwise elongateddisturbances, mainly in the streamwise velocity component,called streaks. If the streak amplitude reaches a thresholdvalue, secondary instabilities can take place and provoketransition. This scenario is most likely to occur in boundarylayer flows subject to high levels of free-stream turbulenceand is the object of this thesis. Different stages of theprocess are isolated and studied with different approaches,considering the boundary layer flow over a flat plate. Thereceptivity to free-stream disturbances has been studiedthrough a weakly non-linear model which allows to disentanglethe features involved in the generation of streaks. It is shownthat the non-linear interaction of oblique waves in thefree-stream is able to induce strong streamwise vortices insidethe boundary layer, which, in turn, generate streaks by thelift-up effect. The growth of steady streaks is followed bymeans of Direct Numerical Simulation. After the streaks havereached a finite amplitude, they saturate and a new laminarflow, characterized by a strong spanwise modulation isestablished. Using Floquet theory, the instability of thesestreaks is studied to determine the features of theirbreakdown. The streak critical amplitude, beyond which unstablewaves are excited, is 26% of the free-stream velocity. Theinstability appears as spanwise (sinuous-type) oscillations ofthe streak. The late stages of the transition, originating fromthis type of secondary instability, are also studied. We foundthat the main structures observed during the transition processconsist of elongated quasi-streamwise vortices located on theflanks of the low speed streak. Vortices of alternating signare overlapping in the streamwise direction in a staggeredpattern.</p><p><strong>Descriptors:</strong>Fluid mechanics, laminar-turbulenttransition, boundary layer flow, transient growth, streamwisestreaks, lift-up effect, receptivity, free-stream turbulence,nonlinear mechanism, streak instability, secondary instability,Direct Numerical Simulation.</p> / QC 20100518

Diversas aplicações industriais utilizam escoamentos de fluidos viscoelásticos, e em muitos casos é necessário saber se os escoamentos propagam-se no estado laminar ou no turbulento. Embora a hidrodinâmica de fluidos viscoelásticos seja fortemente afetada pelo balanço entre forças inerciais e elásticas no escoamento, o efeito da elasticidade sobre a estabilidade de escoamentos inerciais não foi completamente estabelecido. Neste trabalho, estuda-se o que ocorre durante a transição laminar-turbulenta, investigando a convecção de ondas de Tollmien-Schlichting para o escoamento incompressível, para um fluido viscoelástico, entre placas paralelas, utilizando a equação constitutiva Giesekus. Para isto, adotou-se a simulação numérica direta para verificar a estabilidade dos escoamentos à perturbações não estacionárias deste fluido. Experimentos computacionais para verificação do código foram realizados. Com os resultados numéricos obtidos, foi possível verificar e analizar a estabilidade de escoamentos utilizando-se o modelo não newtoniano Giesekus. / Several industrial applications use viscoelastic fluid flows, and it is necessary to know if the flows propagate in the laminar or turbulent state. Although the hydrodynamics of viscoelastic fluids is strongly affected by the balance between inertial and elastic forces in the flow, the effect of elasticity on the stability of inertial flows has not been completely established. In this work we study what happens during the laminar-turbulent transition, investigating the convection of Tollmien-Schlichting waves for the incompressible flow, for a viscoelastic fluid, between parallel plates, using the constitutive equation Giesekus. For this, the direct numerical simulation was used to verify the stability of the flows to the non-stationary perturbations of this fluid. Computational experiments to verify the code were performed. With the numerical results obtained, it was possible to verify and analyze the stability of flows modelled by Giesekus non-newtonian model.

Nos escoamentos em turbomáquinas temos como principais características a tridimensionalidade, possível ocorrência de separação da camada limite, relaminarização, transição laminar-turbulenta, dentre outros efeitos físicos. De acordo com alguns estudos experimentais em turbinas observouse que a transição laminar-turbulenta pode se estender por até 60% da corda de uma pá de turbina. Uma boa estimativa para se prever corretamente o local da transição é indispensável para que seja obtida uma melhoria na eficiência das turbinas. Escoamentos sobre superfícies côncavas estão sujeitos à instabilidade centrífuga, podendo dar origem a vórtices longitudinais, conhecidos como vórtices de Görtler. Esses vórtices são responsáveis por gerar distorções fortes nos perfis de velocidade e consequentemente nos perfis de temperatura. O presente estudo tem por objetivo estudar a influência da variação da curvatura de uma superfície côncava, e os efeitos do comprimento de onda transversal no processo de transição, e sua influência nas taxas de transferência de calor. Para tal, um código de simulação numérica paralelizado, com alta ordem de precisão, foi utilizado para resolver numericamente as equações de Navier-Stokes. Este código é validado através de comparações entre resultados obtidos com uso da teoria de estabilidade linear, e com resultados de simulações numéricas não lineares. Resultados obtidos evidenciam a influência da variação da curvatura, e os efeitos causados pelo comprimento de onda transversal nas instabilidades de Görtler, e secundária. Tais evidências comprovam que a variação da curvatura pode ser útil no controle do processo de transição laminar-turbulenta, e que as taxas de transferência de calor de um escoamento de Görtler desenvolvido em superfícies de curvatura variável podem ser intensificadas, atingindo valores superiores aos obtidos em escoamentos turbulentos. / Some characteristics of flows in turbomachinery are the three-dimensionality, possible occurrence of separation of the boundary layer, relaminarization, laminar-turbulent transition, among other physical effects. According to some experimental observations in turbines, it has been observed that the laminar-turbulent transition can extend over 60% chord of a turbine blade. A good estimate to correctly predict the location of the transition is essential for an improvement in the efficiency of turbines. Flow over concave surfaces is subjected to centrifugal instability, which may lead to formation of longitudinal vortices, known as the Görtler vortices. These vortices are responsible for generating strong distortions in the velocity profiles and hence the temperature profiles. The current goal aims to study the influence of the curvature variation of a concave surface and the effects of spanwise wavelength on the transition process and its influence on the heat transfer rates. For this, a parallel numerical simulation code, with a high order of precision, was used to numerically solve the Navier-Stokes equations. This code is validated through comparisons between results obtained using linear stability theory, and nonlinear numerical simulations results. Results obtained show the influence of the curvature variation, and the effects caused by the spanwise wavelength on the Görtler and secondary instabilities. This evidence proves that the curvature variation can be useful in the control of the laminar-turbulent transition process, and that heat transfer rates of a Görtler flow developed on variable curvature surfaces can be intensified, and reach values higher than these achieved in turbulent flows.