The interaction of a shock wave and boundary layer often occurs in high speed flows. For sufficiently strong shock strengths the boundary layer separates, generating shock patterns in the contiguous inviscid flow (termed strong interactions); which may also affect the performances of the systems where they occur, demanding control of the interaction to enhance the performances. The case of impinging shock wave boundary layer interaction is of fundamental importance and can throw light on the physics of the interaction in general. Although various aspects of the interaction are studied at supersonic speeds, the complexities involved in the interaction at hypersonic speeds are not well understood. Of importance is the high total enthalpy associated with hypersonic flows the simulation of which requires shock tunnels. The present experimental study focuses on the interaction between strong impinging shock and boundary layer in hypersonic flows of moderate to high total enthalpies. Experiments are performed in hypersonic shock tunnels HST-2 and FPST (free piston driven shock tunnel), at nominal Mach numbers 6 and 8, with total enthalpy ranging from 1.3 MJ/kg to 6 MJ/kg, and freestream Reynolds number ranging from 0.3 million/m to 4 million/m. The strong impinging shock is generated by a wedge of angle 30.960 to the freestream. The shock is made to impinge on a flat plate (made of Hylem which is adiabatic, except for one case with plate made of aluminium which allows heat transfer). The position of (inviscid) shock impingement may be varied (from 55 mm from the leading edge to 100 mm from the leading edge) by moving the plate back and forth on the fixture which holds the wedge and the plate. Expectedly the strong shock generates a large separation bubble of length comparable to the distance of the location of shock impingement from the leading edge of the plate. Such large separation bubbles are typical of supersonic/hypersonic intakes at off-design operation. The evolution of the flow field- including the evolution of impinging shock and subsequent evolution of the large separation bubble- within the short test duration of the shock tunnels is one of the main concerns addressed in the study. Time resolved schlieren flow visualizations using high speed camera, surface pressure measurements using PCB, kulite and MEMS sensors, surface convective heat transfer measurements using platinum thin film sensors are the flow diagnostics used. From the time resolved visualizations and surface pressure measurements with the fast response sensors, the flow field, even with a separation bubble as large as 75 mm (at Mach 5.96, with shock impingement at 95 mm from the leading edge) was found to be established within the short shock tunnel test time. The effects of various parameters- freestream Mach number, distance of the location of shock impingement, freestream total enthalpy and wall heat transfer- on the interaction are investigated. With increase in Mach number from 5.96 to 8.67, for nearly the same shock impingement locations (95 mm and 100 mm from the leading edge respectively), the separation length decreased from 75 mm to 60 mm despite the fact that the shocks are doubly stronger at the higher Mach number. Inflectional trend in separation length was observed with enthalpy at nominal Mach number 8- separation length increased from 60 mm at 1.6 MJ/kg to 70 mm at 2.4 MJ/kg, and decreased drastically to ~40 mm at 6 MJ/kg (when dissociations are expected). The separation length Lsep for all the experiments, except the experiments at 6 MJ/kg, were found to be large, i.e. comparable with the distance xi of location of shock impingement from the leading edge of the flat plate. The scaled separation length (with Hylem wall) was found to obey the inviscid similarity law proposed from the present study for large separation bubbles with strong impinging shocks, where M∞ is the freestream Mach number, p∞ is the freestream pressure and pr is the measured reattachment pressure; this holds for freestream total enthalpy ranging from 1.3 MJ/kg to 2.4 MJ/kg and Reynolds number (based on location of shock impingement) ranging from 1x105 to 4x105. While the increase in separation length from 1.6 MJ/kg to 2.4 MJ/kg could thus be attributed to the small difference in Mach number between the cases (due to inverse variation with cube of Mach number), the decrease in separation length and the non-confirmation to the proposed similarity law for the 6 MJ/kg case is attributed to the real gas effects. At Mach 6 the flow was observed to separate close to the leading edge, even when the (inviscid) shock impingement was at 95 mm from the leading edge. This prompted the proposal of an approximate inviscid model of the interaction for the Mach 6 case with separation at leading edge, and reattachment at the location of (inviscid) shock impingement; Accordingly, the closer the location of impingement, the more the angle that the separated shear layer makes with the plate and hence more the pressure inside the separation bubble. A small reduction in separation length was also observed with aluminium wall when compared with Hylem wall, emphasizing the importance of wall heat conductivity (especially when concerning separated flows) even within the short test durations of shock tunnels. The free interaction theory over adiabatic wall was found to predict the pressure at the location of separation, but under-predict the plateau pressure (at nominal Mach number 8). Numerical simulations (steady, planar) were also carried out using commercial CFD solver FLUENT to complement the experiments. Simulations using one equation turbulence model (Spalart-Allmaras model) were closer to the experimental results than the laminar simulations, suggesting that the flow field may be transitional or turbulent after separation. Significant reduction of the separation bubble length was demonstrated with the control of the interaction using boundary layer bleed within the short test time of the shock tunnel; with tangential blowing at the separation location20% reduction in separation length was observed, while with suction at separation location the reduction was 13.33 %.

A key component of research in the aerospace industry constitutes hypersonic flights (M>5) which includes the design of commercial high-speed aircrafts and development of rockets. Computational analysis becomes more important due to the difficulty in performing experiments and reliability of its results at these harsh operating conditions. There is an increasing demand from the industry for the accurate prediction of wall-shear and heat transfer with a low computational cost. Direct Numerical Simulations (DNS) create the standard for accuracy, but its practical usage is difficult and limited because of its high cost of computation. The usage of Reynold's Averaged Navier Stokes (RANS) simulations provide an affordable gateway for industry to capitalize its lower computational time for practical applications. However, the presence of existing RANS turbulence closure models and associated wall functions result in poor prediction of wall fluxes and inaccurate solutions in comparison with high fidelity DNS data. In recent years, machine learning emerged as a new approach for physical modeling. This thesis explores the potential of employing Machine Learning (ML) to improve the predictions of wall fluxes for hypersonic turbulent boundary layers. Fine-grid RANS simulations are used as training data to construct a suitable machine learning model to improve the solutions and predictions of wall quantities for coarser meshes. This strategy eliminates the usage of wall models and extends the range of applicability of grid sizes without a significant drop in accuracy of solutions. Random forest methodology coupled with a bagged aggregation algorithm helps in modeling a correction factor for the velocity gradient at the first grid points. The training data set for the ML model extracted from fine-grid RANS, includes neighbor cell information to address the memory effect of turbulence, and an optimal set of parameters to model the gradient correction factor. The successful demonstration of accurate predictions of wall-shear for coarse grids using this methodology, provides the confidence to build machine learning models to use DNS or high-fidelity modeling results as training data for reduced-order turbulence model development. This paves the way to integrate machine learning with RANS to produce accurate solutions with significantly lesser computational costs for hypersonic boundary layer problems.

An advanced laser-Doppler velocimeter is designed to acquire fully-resolved turbulence structural measurements in high Reynolds number two- and three-dimensional turbulent boundary layers. The new instrument combines, for the first time, new techniques allowing for the direct measurement of particle acceleration and sub-measurement-volume-scale position resolution so that second-order 3D particle trajectories may be measured at high repetitions. Using these measurements, several terms in the Reynolds stress transport equations may be directly estimated, giving new data for modeling and understanding the processes leading to the transport of turbulence in boundary layer flows. Due to the unique performance of the probe, many aspects of LDV instrumentation development were addressed. The LDV configuration was optimized for lowest uncertainties by considering the demanding applications of particle position and acceleration measurements. Low noise light detection and signal conditioning was specified for the three electronic channels. A high-throughput data acquisition system allows for exceptional burst rate acquisition. Signal detection and processing algorithms have been implemented which draw from previous techniques but also address distinctive problems with the current system. In short, the instrument was designed to advance the state-of-the-art in LDV systems. Measurements presented include turbulence dissipation rate and fluctuating velocity-pressure gradient correlations that have been measured in 2D and 3D turbulent boundary layers using the unique capabilities of the CompLDV--many of these measurements are the first of their kind ever acquired in high Reynolds number turbulent flows. The flat-plate turbulent boundary layer is studied at several momentum thickness Reynolds numbers up to 7500 to examine Reynolds numbers effects on terms such as the velocity-pressure gradient correlation and the dissipation rate in the Reynolds transport equations. Measurements are also presented in a pressure-driven three-dimensional turbulent boundary layer created upstream from a wing-body junction. The current results complement the extensive data from previous studies and provide even richer depth of knowledge on the most-completely-documented 3D boundary layer flow in existence. Further measurements include the wakes of three circular-cylinder protuberances submerged in a constant pressure turbulent boundary layer. / Ph. D.

This thesis considers the stability and transition of incompressible boundary layers. In particular, the Falkner–Skan–Cooke boundary layer subject to a cylindrical surface roughness, and the Blasius boundary layer with applied localized suction are investigated. These flows are of great importance within the aviation industry, feature complex transition scenarios, and are strongly three-dimensional in nature. Consequently, no assumptions regarding homogeneity in any of the spatial directions are possible, and the stability of the flow is governed by an extensive three-dimensional eigenvalue problem. The stability of these flows is addressed by high-order direct numerical simulations using the spectral element method, in combination with a Krylov subspace projection method. Such techniques target the long-term behavior of the flow and can provide lower limits beyond which transition is unavoidable. The origin of the instabilities, as well as the mechanisms leading to transition in the aforementioned cases are studied and the findings are reported. Additionally, a novel method for computing the optimal forcing of a dynamical system is developed. This type of analysis provides valuable information about the frequencies and structures that cause the largest energy amplification in the system. The method is based on the inverse power method, and is discussed in the context of the one-dimensional Ginzburg–Landau equation and a two-dimensional flow case governed by the Navier–Stokes equations. / <p>QC 20151015</p>

Dans cette thèse, nous présentons des résultats d’homogénéisation périodique d’un problème spectral et de l’équation d’ondes de Bloch. Il permet de modéliser les ondes à basse et haute fréquences. La partie modèle à basse fréquence est bien connu et n’est pas donc abordée dans ce travail. A contrario ; la partie à haute fréquence du modèle, qui représente des oscillations aux échelles microscopiques et macroscopiques, est un problème laissé ouvert. En particulier, les conditions aux limites de l’équation macroscopique à hautes fréquences établies dans [36] n’étaient pas connues avant le début de la thèse. Ce dernier travail apporte trois contributions principales. Les deux premières contributions, portent sur le comportement asymptotique du problème d’homogénéisation périodique du problème spectral et de l’équation des ondes en une dimension. La troisième contribution consiste en une extension du modèle du problème spectral posé dans une bande bi dimensionnelle et bornée. Le résultat d’homogénéisation comprend des effets de couche limite qui se produisent dans les conditions aux limites de l’équation macroscopique à haute fréquence. / In this dissertation, we present the periodic homogenization of a spectral problem and the waveequation with periodic rapidly varying coefficients in a bounded domain. The asymptotic behavioris addressed based on a method of Bloch wave homogenization. It allows modeling both the lowand high frequency waves. The low frequency part is well-known and it is not a new point here.In the opposite, the high frequency part of the model, which represents oscillations occurringat the microscopic and macroscopic scales, was not well understood. Especially, the boundaryconditions of the high-frequency macroscopic equation established in [36] were not known prior to thecommencement of thesis. The latter brings three main contributions. The first two contributions, areabout the asymptotic behavior of the periodic homogenization of the spectral problem and waveequation in one-dimension. The third contribution consists in an extension of the model for thespectral problem to a thin two-dimensional bounded strip Ω = (0; _) _ (0; ") _ R2. The homogenizationresult includes boundary layer effects occurring in the boundary conditions of the high-frequencymacroscopic equation.

Les microphones capacitifs sont des transducteurs réciproques dont les qualités (sensibilité, bande passante et tenue dans le temps) en font des instruments de mesure performants. Couramment utilisés jusqu’à présent en récepteurs dans l’air à pression atmosphérique et à température ambiante, dans la gamme de fréquences audibles, ils sont correctement caractérisés dans ce cadre depuis près de trente ans. Mais aujourd’hui, leur miniaturisation (par procédé MEMS) et leur usage nouveau en métrologie fine (en récepteurs comme en émetteurs) - qui exigent une connaissance précise de leur comportement dans des domaines de fréquences élevées (jusqu’à 100 kHz), dans des mélanges gazeux aux propriétés différentes de celles de l’air et dans des conditions de pression et de température beaucoup plus élevées ou beaucoup plus basses que les conditions standards - nécessitent une caractérisation beaucoup plus approfondie, aussi bien en terme de modélisation qu’en terme de résultats expérimentaux. C’est ainsi que ici -i/ les effets des couches limites thermiques (seules les couches limites visqueuses sont habituellement retenues) sont introduits dans le modèle, ce qui amène dans le chapitre premier à une étude analytique de la diffusion thermique en parois minces (dont la portée dépasse le cadre strict du transducteur), -ii/ l’influence des orifices de l’électrode arrière sur la déformée de la membrane est traitée au départ par une méthode analytique originale, qui permet de traduire les conditions en frontière non uniformes sur la surface de l’électrode sous forme de sources locales virtuelles, associées à des conditions de frontière rendues uniformes (chapitre second), -iii/ des solutions analytiques nouvelles, dépendant à la fois des coordonnées radiales et azimutales, sont obtenues pour le champ de déplacement de la membrane et pour les champs de pression dans les cavités du microphone par usage de théories modales compatibles avec les couplages multiples qui y prennent place (troisième chapitre), -iv/ un modèle de « circuit à constantes localisées » (reporté pour l’essentiel en annexe) est proposé, à des degrés divers de précision, qui permet en particulier d’accéder de façon simple à la sensibilité et au bruit thermique du microphone (fin du quatrième chapitre), -v/ une étude au vibromètre laser à balayage a été réalisée (début du quatrième chapitre), qui permet non seulement de mettre en évidence pour la première fois les déformées de membrane complexes qui apparaissent en hautes fréquences, mais encore de les quantifier et par-delà de valider les résultats théoriques obtenus et donc les modèles proposés (même s’ils restent perfectibles comme indiqué dans la conclusion). / Condenser microphones are reciprocal transducers whose properties (sensitivity, bandwidth and reliability) make them powerful measurement tools. So far, they have been commonly used as receivers in the audible frequency range, in air at atmospheric pressure and ambient temperature, they have been appropriately characterised in this context for nearly thirty years. But nowadays, their miniaturisation (using MEMS processes) and their new use for metrological purposes (as receivers as well as transmitters) require much deeper theoretical and experimental characterisations because they require an accurate knowledge of their behaviour in high frequency ranges (up to 100 kHz), in gas mixtures, whose properties differ from those of air, and under pressure and temperature conditions much higher or much lower than standard conditions. Thus, here, -i/ the effects of the thermal boundary layers are introduced in the model (only viscous boundary layers are usually accounted for), leading, in the first chapter, to an analysis of the thermal diffusion of thin bodies (whose scope is beyond the strict frame of capacitive transducers), ii/ the influence of the holes in the backing electrode on the dynamic behaviour of the membrane is initially handled with an original analytical method which allows expressing the non-uniform boundary conditions at the surface of the backing electrode as fictitious localised sources associated to uniform boundary conditions (second chapter), -iii/ new analytical solutions, depending both on the radial and azimuthal coordinates, for the pressure field and for the displacement field inside the cavities behind the membrane are expressed using modal theories in agreement with the strong couplings which occur between the different parts of the transducer (chapter three), -iv/ "lumped element circuits", which are more or less approximated (presented in the Appendix), more particularly result in expressing and assessing the sensitivity and the thermal noise (end of chapter three), -v/ experimental results, obtained from measurements of the displacement field of the membrane using a laser scanning vibrometer, both highlight and quantify for the first time the complex behaviour of the membrane in the highest frequency range, and finally lead to the validation of the theoretical results and therefore, the models presented here (even if the latter may still be improved as outlined in the conclusion).

The fast-paced growth in microelectromechanical systems (MEMS), microfluidic fabrication, porous media applications, biomedical assemblies, space propulsion, and vacuum technology demands accurate and practical transport equations for rarefied gas flows. It is well-known that in rarefied situations, due to strong deviations from the continuum regime, traditional fluid models such as Navier-Stokes-Fourier (NSF) fail. The shortcoming of continuum models is rooted in nonequilibrium behavior of gas particles in miniaturized and/or low-pressure devices, where the Knudsen number (Kn) is sufficiently large. Since kinetic solutions are computationally very expensive, there has been a great desire to develop macroscopic transport equations for dilute gas flows, and as a result, several sets of extended equations are proposed for gas flow in nonequilibrium states. However, applications of many of these extended equations are limited due to their instabilities and/or the absence of suitable boundary conditions. In this work, we concentrate on regularized 13-moment (R13) equations, which are a set of macroscopic transport equations for flows in the transition regime, i.e., Kn≤1. The R13 system provides a stable set of equations in Super-Burnett order, with a great potential to be a powerful CFD tool for rarefied flow simulations at moderate Knudsen numbers. The goal of this research is to implement the R13 equations for problems of practical interest in arbitrary geometries. This is done by transformation of the R13 equations and boundary conditions into general curvilinear coordinate systems. Next steps include adaptation of the transformed equations in order to solve some of the popular test cases, i.e., shear-driven, force-driven, and temperature-driven flows in both planar and curved flow passages. It is shown that inexpensive analytical solutions of the R13 equations for the considered problems are comparable to expensive numerical solutions of the Boltzmann equation. The new results present a wide range of linear and nonlinear rarefaction effects which alter the classical flow patterns both in the bulk and near boundary regions. Among these, multiple Knudsen boundary layers (mechanocaloric heat flows) and their influence on mass and energy transfer must be highlighted. Furthermore, the phenomenon of temperature dip and Knudsen paradox in Poiseuille flow; Onsager's reciprocity relation, two-way flow pattern, and thermomolecular pressure difference in simultaneous Poiseuille and transpiration flows are described theoretically. Through comparisons it is shown that for Knudsen numbers up to 0.5 the compact R13 solutions exhibit a good agreement with expensive solutions of the Boltzmann equation.