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The solar wind is a supersonic flow of protons and electrons emitted in all directions from the sun. As the supersonic solar wind encounters Earth’s magnetic field, it creates the Earth’s bow shock, which increases the kinetic entropy of electrons passing through it. In this study, the aim is to analyze shock crossings of Earth’s bow shock in order to draw conclusions of which shock parameters that are important forkinetic entropy generation. Due to knowledge gained from an earlier study by M. Lindberg et al. [1], the shock crossings of interest in this study are quasi-perpendicular shocks with a low electron plasma beta. The data used is measured with the NASA MMS spacecraft and accessed through IRF Uppsala. As a result,a database with 13 shock crossings was created and the entropy change was related to, among other parameters, temperature and density change, shock angle, Alfv´en Mach number, ion ram pressure and upstream magnetic field. We found that a highAlfv´en Mach number related nearly proportionally to a large change in electron entropy for low electron plasma beta quasiperpendicularcollisionless shock crossing. / Solvinden består av protoner och elektroner som emitteras ut från solen i alla riktningar med enorma hastigheter. När dessa partiklar, med en hastighet som överstiger signalhastigheten, träffar Jordens magnetfält uppstår Jordens bågchock. Bågchocken ökar den kinetiska entropin hos elektroner som färdas genom den. För den här studien är målet att analysera chockkorsningar vid Jordens bågchock för att kunna dra slutsatser om vilka chockparametrar som är viktiga för generering av kinetisk entropi. Till följd av en tidigare studie av M. Lindberg et al. [1] är det endast kvasi-vinkelräta chockkorsningar med ett lågt plasma beta som denna studie avser. Den uppmätta datan erhålls från NASAs MMS satelliter och kan nås genom IRF Uppsala. Resultatet blev en databas med 13 chocker där entropiförändringen plottades mot bl. a. temperaturoch densitetsändring, chockvinkel, Alfve´n Machtal, jontrycket och magnetfältet uppströms. Det upptäcktes då att ett högt Alfve´n Mach-tal indikerade på en stor entropiökning hos kollisionslösa, kvasi-vinkelräta chockkorsningar med låga elektronplasmabeta. / Kandidatexjobb i elektroteknik 2022, KTH, Stockholm

Ce travail de thèse porte sur l'extension et l'analyse d'un solveur volumes finis eulérien, co-localisé avec capture d'interfaces pour la simulation des écoulements multi-matériaux non miscibles. Les extensions proposées s'inscrivent dans la volonté d'élaborer un outil de simulation multi-physiques. Dans le cadre de ce mémoire, le caractère multi-physiques recouvre les champs que nous allons détailler. Nous traitons le cas des écoulements radiatifs modélisés par un système à deux températures qui couple les phénomènes purement hydrodynamiques aux phénomènes radiatifs. Nous proposons un solveur permettant la prise en compte des effets de tension superficielle à l'interface entre deux fluides. Nous développons un solveur implicite permettant la simulation précise d'écoulements faisant intervenir de faibles nombres de Mach par le biais d'une méthode de renormalisation de la diffusion numérique. Enfin, les effets tri-dimensionnels sont considérés ainsi que la possibilité d'étendre le schéma de base aux écoulements à un nombre quelconque de matériaux. A chaque étape, les solveurs développés sont validés sur des cas-tests. / This work is devoted to the extension of a eulerian cell-centered finite volume scheme with interfaces capturing for the simulation of multimaterial fluid flows. Our purpose is to develop a simulation tool which could be able to handle multi-physics problems in the following sense. We address the case of radiating flows, modeled by a two temperature system of equations where the hydrodynamics are coupled to radiation transport. We address a numerical scheme for taking surface tension forces into account. An implicit scheme is proposed to handle low Mach number fluid flows by means of a renormalization of the numerical diffusion. Eventually, the scheme is extended to three-dimensional flows and to multimaterial flows, that is with an arbitrary number of materials. At each step, numerical simulations validate our schemes.

Cette thèse est consacrée à l’analyse mathématique de trois problèmes d’écoulements de fluides viscoélastiques de type Oldroyd. Tout d’abord, nous étudions des écoulements stationnaires faiblement compressibles dans un domaine borné avec des conditions au bord de type "rentrante-sortante". Nous étudions aussi le problème d’écoulements stationnaires faiblement compressibles dans un coin convexe. En utilisant une méthode de point fixe (premier et deuxième problèmes) et une décomposition de Helmoltz (deuxième problème), nous montrons des résultats d’existence et d’unicité des solutions. Nous étudions également le cas d’un écoulement non stationnaire. Nous montrons un résultat d’existence locale et un résultat d’existence globale, avec des conditions initiales suffisamment petites, pour des fluides compressibles. Nous démontrons aussi la convergence du modèle d’écoulement viscoélastique compressible à faible nombre de Mach vers le modèle incompressible lorsque les données initiales sont "bien préparées" / In this PHD thesis, we study three problems for viscoelastic flows of Oldroyd type. First, we study steady flows of slightly compressible in a bounded domain with non-zero velocities on the boundary ; the pressure and the extra-stress tensor are prescribed on the part of the boundary corresponding to entering velocity. This causes a weak singularity in the solution at the junction of incoming and outgoing flows. We also study the problem of steady flows of slightly compressible fluids with zero boundary conditions in a domain with an isolated corner point. Using a method of fixed point (first and second problems) and a Helmoltz decomposition (second problem), we show some results of existence and uniqueness of solutions. In the last part, we study the case of a non-steady flow : we show some results of local and of global existence, with sufficiently small initial data, for compressible flows. The zero-Mach number limit is also established

Le modèle numérique que nous avons développé au cours de cette thèse présente deux caractéristiques principales : un modèle dilatable pour l'eau et la prise en compte de domaines ouverts. Les difficultés associées au premier aspect concernent l'adaptation de la loi d'état de l’eau au modèle dilatable sous l’approximation à faibles nombres de Mach, tandis que celles associées au second sont relatives à la mise en œuvre de conditions aux limites numériques de sortie compatibles avec l'algorithme de projection utilisé. Les résultats de simulations d'écoulement de convection mixte en canal horizontal chauffé par le bas ont été confrontés à celles utilisant l'approximation de Boussinesq et aux expériences. / The 3D numerical model which we developed in this thesis presents two main features: a Low-Mach-Number approximation for water along with an open boundary condition formulation. Indeed, the difficulties related to the former point stand in a computationally efficient adaptation of the water equation of state in the framework of Low Mach number approximation, whereas the difficulties related to the latter concern the introduction of Open Boundary Conditions in the projection algorithm used. We have computed a mixed convection flow in a horizontal channel uniformly heated from below and compared the results obtained with both the Boussinesq approximation and experimental results.

La prédiction des vibrations induites par un écoulement est essentielle dans la conception des conduits de nombreuses installations industrielles, en particulier dans l’industrie du gaz. Notre étude concerne la prévision du bruit et la vibration des conduits soumis à un écoulement turbulent à faible nombre de Mach. Notre objectif est de présenter une étude numérique et expérimentale permettant aux ingénieurs de mieux comprendre le couplage entre l’excitation aléatoire et le conduit pour deux géométries (circulaire ou rectangulaire). Une approche expérimentale est développée et utilisée pour valider les prévisions numériques. Deux cas sont étudiés : (i) un conduit droit sans singularité, où les modes acoustiques du conduit sont excités par une couche limite turbulente (TBL) et (ii) un conduit droit avec un diaphragme inséré en amont qui génère une source acoustique localisée. La contribution acoustique est déterminée soit par des méthodes de mesure d’interspectres, soit à l’aide des outils de mécanique des fluides numérique (CFD) et d’analogies aéroacoustiques. La réponse de la structure est estimée par une approche dite de « couplage faible » qui utilise des fonctions de transfert modale d’un conduit fini simplement appuyé. Les mesures conduiront à évaluer et suggérer des améliorations de modèles empiriques existants de densité interspectrale de puissance (CPSD) dans un contexte d’écoulements internes turbulents. Une analyse modale expérimentale d’un conduit rectangulaire finie est confrontée à des méthodes de calcul pour évaluer l’effet des conditions aux limites, du rayonnement acoustique et de l’amortissement aérodynamique. Le couplage fluide structure est analysé par la fonction de « joint acceptance » à la fois dans le domaine spatial et dans le domaine des nombres d’onde. L’excitation comprend à la fois les contributions acoustiques et hydrodynamiques à l’aide des CPSD exprimées sur la base des fonctions de cohérence de type Corcos, champ diffus et modes acoustiques d’ordre élevé. Enfin, les études numériques et expérimentales de cette thèse ont été utilisées pour développer un cadre d’étude et de modélisation du bruit et des vibrations dans les conduites, qui relie la dynamique des fluides, les modèles analytiques et empiriques à des techniques efficaces d’analyse aléatoire. / Pipeline and duct vibrations can cause a range of issues from unplanned shutdownsto decreased equipment life time. Thus, the prediction of flow-induced vibrations is essential in piping design in many industrial plants, especially, for Gas industry. This study deals with the prediction of pipe flow noise and vibration at low Mach number. We aim to present a numerical and experimental study which can offer engineers a better understanding of the coupling between random excitation and duct section for two geometries (circular or rectangular). An experimental facility and measurement approach is developed and used to validate numerical predictions. Two cases are investigated: (i) a straight duct with no singularity, duct acoustic modes are excited by the Turbulent Boundary Layer (TBL) and (ii) a straight duct with a diaphragm inserted upstream generating a localized acoustic source. The acoustic contribution is either measured via cross-spectra based methods or calculated using Computational Fluid Dynamics (CFD) and aeroacoustic analogies. The response of the structure is estimated via a ‘blocked’ approach using analytical modal Frequency Response Functions (FRFs) of a simply supported finite duct. Measurements will lead to evaluate and suggest improvements to existing Cross Power Spectral Density (CPSD) empirical models in a context of internal turbulent flows. Experimental modalanalysis of a finite rectangular duct are confronted to computational methods to assess the effect of the Boundary Conditions (BCs), the resistive damping from coupling with the internal acoustic medium and aerodynamic damping. The fluid-structure coupling is analyzed through the joint acceptance function both in the spatial and wave number domain. The excitation includes both the acoustic and hydrodynamic contributions using CPSD written on the basis of Corcos, Diffuse Acoustic Field (DAF) and acoustic duct mode coherence functions. Finally, the numerical and experimental studies in this thesis were used to develop a framework for studying and modelling pipe flow noise and vibration which links CFD, analytical and empirical models to efficient random analysis techniques.

Dans cette thèse on s'intéresse aux jets en écoulement transverse dans une configuration générique de celle du refroidissement par effusion de chambres de combustion aéronautiques. L'amélioration des modèles de paroi avec transfert de masse passe par une meilleure connaissance de l'interaction entre les jets et l’écoulement principal. Nous avons donc réalisé la simulation numérique directe d'un jet issu d'un perçage incliné avec ou sans giration, pour des écoulements isothermes, turbulents et à bas nombre de Mach, dans un contexte compressible. Pour cela nous avons travaillé avec la bibliothèque AeroSol d'éléments finis continus et discontinus sur maillage hybride. En particulier nous nous sommes intéressés à la stabilité des flux numériques pour le compressible instationnaire associés à la méthode de Galerkin discontinue lorsque le nombre de Mach tend vers zéro. Nous avons pu mettre en évidence des comportements instables lors de l'utilisation de discrétisation temporelle explicite que nous avons corrigés en proposant un nouveau flux. Dans un deuxième temps, nous avons effectué les développements nécessaires à la réalisation des calculs. Nous nous sommes en particulier intéressés à la génération d'un champ de vitesse turbulent synthétique par la méthode SEM (Synthetic Eddy Method) que nous avons implantée dans AeroSol et validée. Grâce aux outils de post-traitement développés, nous avons conduit l'analyse de nos résultats. Dans le cas sans giration, les comparaisons avec les résultats expérimentaux et les résultats de simulations RANS que nous avons obtenus en parallèle sur la configuration du banc d'essai MAVERIC sont encourageants. La structure moyenne d'ensemble du jet est notamment correctement reproduite. En ce qui concerne la cas avec giration, le comportement attendu de déflexion successive du jet dans les deux plans caractéristiques (plan d'injection et plan de l'écoulement transverse) est bien reproduit et illustre tout le potentiel prévisionnel de la librairie de calcul que nous avons contribué à développer. / In this work we are interested in jet in crossflow in a generic configuration to the one used in effusion cooling for combustion chambers. Improved wall models with mass transfer requires a better knowledge of the interaction between the jets and the main flow. We therefore carried out the direct numerical simulation of a jet issuing from an inclined hole with or without gyration, for isothermal turbulent flow at low Mach number, in a compressible context. To achieved this, we worked with the continuous and discontinuous finite element library : AeroSol on hybrid grid. In particular we studied the stability of numerical flux for the unsteady compressible flow associated with discontinuous Galerkin method when the Mach number tends to zero. We were able to demonstrate unstable behavior when using explicit time discretization and we corrected them by providing a new flux. In a second time, we have performed the necessary development to achieve the calculations. We have been especially interested in the generation of a synthetic turbulent velocity field using the SEM method (Synthetic Eddy Method) that we have implemented in aerosol and validate. Thanks to the developed post-processing tools, we have conducted an analysis of our results. In the case without gyration, comparisons with experimental results and the results of RANS simulations we obtained on the Maveric test-bench configuration are encouraging. The mean flow of the jet is correctly reproduced. In the case with gyration, the expected behavior of successive deflection of the jet in both planes (injection plane and transverse plane of the flow) is reproduced and shows all the potential of the AeroSol library we helped to develop.

Hypersonic vehicles are exposed to severe heating loads during their flight in the atmosphere. In order to minimize the heating problem, a variety of cooling techniques are presently available for hypersonic blunt bodies. Introduction of a forward-facing cavity in the nose tip of a blunt body configuration of hypersonic vehicle is one of the most simple and attractive methods of reducing the convective heating rates on such a vehicle. In addition to aerodynamic heating, the overall drag force experienced by vehicles flying at hypersonic speeds is predominate due to formation of strong shock waves in the flow. Hence, the effective management of heat transfer rate and aerodynamic drag is a primary element to the success of any hypersonic vehicle design. So, precise information on both aerodynamic forces and heat transfer rates are essential in deciding the performance of the vehicle. In order to address the issue of both forces and heat transfer rates, right kind of measurement techniques must be incorporated in the ground-based testing facilities for such type of body configurations. Impulse facilities are the only devices that can simulate high altitude flight conditions. Uncertainties in test flow conditions of impulse facilities are some of the critical issues that essentially affect the final experimental results. Hence, more reliable and carefully designed experimental techniques/methodologies are needed in impulse facilities for generating experimental data, especially at hypersonic Mach numbers. In view of the above, an experimental program has been initiated to develop novel techniques of measuring both the aerodynamic forces and surface heat transfer rates. In the present investigation, both aerodynamic forces and surface heat transfer rates are measured over the test models at hypersonic Mach numbers in IISc hypersonic shock tunnel HST-2, having an effective test time of 800 s. The aerodynamic coefficients are measured with a miniature type accelerometer based balance system where as platinum thin film sensors are used to measure the convective heat transfer rates over the surface of the test model. An internally mountable accelerometer based balance system (three and six-component) is used for the measurement of aerodynamic forces and moment coefficients acting on the different test models (i.e., blunt cone with after body, blunt cone with after body and frustum, blunt cone with after body-frustum-triangular fins and sharp cone with after body-frustum-triangular fins), flying at free stream Mach numbers of 5.75 and 8 in hypersonic shock tunnel. The main principle of this design is that the model along with the internally mounted accelerometer balance system are supported by rubber bushes and there-by ensuring unrestrained free floating conditions of the model in the test section during the flow duration. In order to get a better performance from the accelerometer balance system, the location of accelerometers plays a vital role during the initial design of the balance. Hence, axi-symmetric finite element modeling (FEM) of the integrated model-balance system for the missile shaped model has been carried out at 0° angle of attack in a flow Mach number of 8. The drag force of a model was determined using commercial package of MSC/NASTRAN and MSC/PATRAN. For test flow duration of 800 s, the neoprene type rubber with Young’s modulus of 3 MPa and material combinations (aluminum and stainless steel material used as the model and balance) were chosen. The simulated drag acceleration (finite element) from the drag accelerometer is compared with recorded acceleration-time history from the accelerometer during the shock tunnel testing. The agreement between the acceleration-time history from finite-element simulation and measured response from the accelerometer is very good within the test flow domain. In order to verify the performance of the balance, tests were carried out on similar standard AGARD model configurations (blunt cone with cylinder and blunt cone with cylinder-frustum) and the results indicated that the measured values match very well with the AGARD model data and theoretically estimated values. Modified Newtonian theory is used to calculate the aerodynamic force coefficient analytically for various angles of attack. Convective surface heat transfer rate measurements are carried out by using vacuum sputtered platinum thin film sensors deposited on ceramic substrate (Macor) inserts which in turn are embedded on the metallic missile shaped body. Investigations are carried out on a model with and without fin configurations in HST-2 at flow Mach number of 5.75 and 8 with a stagnation enthalpy of 2 MJ/kg for zero degree angle of attack. The measured heating rates for the missile shaped body (i.e., with fin configuration) are lower than the predicted stagnation heating rates (Fay-Riddell expression) and the maximum difference is about 8%. These differences may be due to the theoretical values of velocity gradient used in the empirical relation. The experimentally measured values are expressed in terms of normalized heat transfer rates, Stanton numbers and correlated Stanton numbers, compared with the numerically estimated results. From the results, it is inferred that the location of maximum heating occurs at stagnation point which corresponds to zero velocity gradient. The heat-transfer ratio (q1/Qo)remains same in the stagnation zone of the model when the Mach number is increased from 5.75 to 8. At the corners of the blunt cone, the heat transfer rate doesn’t increase (or) fluctuate and the effects are negligible at two different Mach numbers (5.75 and 8). On the basis of equivalent total enthalpy, the heat-transfer rate with fin configuration (i.e., at junction of cylinder and fins) is slightly higher than that of the missile model without fin. Attempts have also been made to evaluate the feasibility of using forward facing cavity as probable technique to reduce the heat transfer rate and to study its effect on aerodynamic coefficients on a 41° apex angle missile shaped body, in hypersonic shock tunnel at a free stream Mach number of 8. The forward-facing circular cavities with two different diameters of 6 and 12 mm are chosen for the present investigations. Experiments are carried out at zero degree angle of attack for heat transfer measurements. About 10-25 % reduction in heat transfer rates is observed with cavity at gauge locations close to stagnation region, whereas the reduction in surface heat transfer rate is between 10-15 % for all other gauge locations (which is slightly downstream of the cavity) compared with the model without cavity. In order to understand the influence of forward facing cavities on force coefficients, measurement of aerodynamic forces and moment coefficients are also carried out on a missile shaped body at angles of attack. The same six component balance is also being used for subsequent investigation of force measurement on a missile shaped body with forward facing cavity. Overall drag reductions of up to 5 % is obtained for a cavity of 6 mm diameter, where as, for the 12 mm cavity an increase in aerodynamic drag is observed (up to about 10%). The addition of cavity resulted in a slight increase in the missile L/D ratio and did not significantly affect the missile lateral components. In summary, the designed balances are found to be suitable for force measurements on different test models in flows of duration less than a millisecond. In order to compliment the experimental results, axi-symmetric, Navier-Stokes CFD computations for the above-defined models are carried out for various angles of attack using a commercial package CFX-Ansys 5.7. The experimental free stream conditions obtained from the shock tunnel are used for the boundary conditions in the CFD simulation. The fundamental aerodynamic coefficients and heat transfer rates of experimental results are shown to be in good agreement with the predicted CFD. In order to have a feeling of the shock structure over test models, flow visualization experiments have been carried out by using the Schlieren technique at flow Mach numbers of 5.75 and 8. The visualized shock wave pattern around the test model consists of a strong bow shock which is spherical in shape and symmetrical over the forebody of the cone. Experimentally measured shock stand-off distance compare well with the computed value as well as the theoretically estimated value using Van Dyke’s theory. These flow visualization experiments have given a factual proof to the quality of flow in the tunnel test section.

One of the major technological innovations that are necessary for faster and cheaper access-to-space will be the commercial realization of supersonic combustion jet engines (SCRAMJET). The establishment of the flow through the inlet is one the prime requirement for the success of a SCRAMJET engine. The flow through a SCRAMJET inlet is dominated by inviscid /viscous coupling, transition, shock-shock interaction, shock boundary layer interaction, blunt leading edge effects and flow profile effects. Although the literature is exhaustive on various aspects of flow features associated with SCRAMJET engines, very little is known on the fundamental gasdynamic features dictating the flow establishment in the SCRAMJET inlet. On one hand we need the reduction of flight Mach number to manageable supersonic values inside the SCRAMJET combustor, but on the other hand we have to achieve this with minimum total pressure loss. Hence the dynamics of ramp/cowl shock interaction process ahead of the inlet has a direct bearing on the quality and type of flow inside the SCRAMJET engine. There is virtually no data base in the open literature focusing specifically on the cowl/ramp shock interactions at hypersonic Mach numbers. Hence in this backdrop, the main aim of the present investigation is to systematically understand the ramp/cowl shock interaction processes in front of a generic inlet model. Since we are primarily concerned with the shock interaction process ahead of the cowl all the investigations are carried out without any fuel injection. Variable geometry is necessary if we want to operate the inlet for a wide range of Mach numbers in actual flight. The investigation mainly comprises of three variable geometry configurations; namely, variation of contraction ratios at 00 cowl (CR 8.4, 5.0 and 4.3), variation of cowl length for a given chamber height (four lengths of cowls at 10 mm chamber height) and variation of cowl angle (three angles cowl each for two chamber heights). The change in cowl configuration results in different ramp/cowl shock interaction processes affecting the performance of the inlet. Experiments are performed in IISc hypersonic shock tunnel HST 2 (test time ~ 1 ms) at two nominal Mach numbers 8.0 and 5.74 for design and off-design testing conditions. Exhaustive numerical simulations are also performed to compliment the experiments. Further the effect of concentrated energy deposition on forebody /cowl shock interactions has also been investigated. A 2D, planar, single ramp scramjet inlet model has been designed and fabricated along with various cowl geometries and tested in a hypersonic shock tunnel to characterize the forebody/cowl shock interaction process for different inlet configurations. Further a DC plasma power unit and a plasma torch have been designed, developed and fabricated to serve as energy source for conducting flow-alteration experiments in the inlet model. The V-I characteristics of the plasma torch is studied and an estimation of plasma temperature is also performed as a part of characterizing the plasma flame. Initial standardization experiments of blunt body flow field alteration using the plasma torch and hence its drag reduction, are performed to check the torch’s suitability to be used as a flow-altering device in a shock tunnel. The plasma torch is integrated successfully with the inlet model in a shock tunnel to perform experiments with plasma jet as the energy source. The above experiments are first of its kind to be conducted in a shock tunnel. They are performed at various pressure ratios and supply currents. Time resolved schlieren flow visualization using Phantom 7.1 (Ms Vision Research USA) high speed camera, surface static pressure measurements inside a generic inlet using miniature kulite transducer and surface convective heat transfer rate measurements inside a generic inlet using platinum thin film sensors deposited on Macor substrate are some of the shock tunnel flow diagnostics that have been used in this study. Some of the important conclusions from the study are: • Experiments performed at different contraction ratios show different shock patterns. At CR 8.4, the SOL condition is satisfied, but the flow gets choked due to over contraction and flow through inlet is not established. For CR 5.0, formation of a small Mach stem before the chamber is observed with the reflection point on the cowl and the weak reflected shock entering inside the chamber. The Mach stem grows with time. For CR 4.3, the forebody/cowl shock interference created an Edney’s Type II shock interaction pattern. However, at off-design conditions, for CR 5 the shock reflection is regular and at CR 4.3, the Edney’s Type II pattern lasts for a short time. • For all lengths of cowl tested, 131mm and 141mm showed Edney’s Type II shock interference where as 151mm showed Edney’s Type I pattern at design condition. In all cases the flow is choked for high contraction ratio. At off-design condition these shock patterns do not last for the entire test time but rather it becomes a lambda pattern with the normal shock before the inlet. • For inlet configurations with cowl angle other than 00, the flow is found to be established for all cases at designed condition and except for 100 cowl at off-design condition. • For CR 8.4 the peak value of pressure (~1.7x104 Pa) occurs at a location of 151mm, where as for CR 5.0 and 4.3 they occur at 188mm and 206mm having values ~1.6x104 Pa and ~1.4x104 Pa respectively. These locations indicate the likely locations of shock impingements inside the chamber. • For cowl angle of 00 for a 10 mm chamber the maximum pressure value recorded is ~1.7x104 Pa whereas for 100 and 200 cowl it is ~1.1x104 Pa and 1.2 x104 Pa respectively. This is because in the first case the inlet is choked because of over contraction whereas in the other two cases the CR is less and flow is established inside the inlet. • The average heat transfer rates of last four heat transfer gauges (180 mm, 190 mm, 200 mm and 210 mm from the forebody tip) for all lengths of cowls tested are found to be almost same (~ 20 W/cm2). This is because the flow is choked in all these cases. The numerical simulation also shows uniform distribution here, consistent with the experimental findings. • The locations of heat transfer peaks for 100 cowl at design condition can be observed to be occurring at 170 mm and 200 mm from the forebody tip having values ~44 W/cm2 and ~39 W/cm2 respectively. For a 200 cowl they seem to be occurring at 170 mm and 180 mm from the forebody tip having values ~50 W/cm2 and ~30 W/cm2. These locations indicate the likely locations of shock impingements inside the chamber. With the evolution of concept of upstream fuel injection in recent times these may the most appropriate locations for fuel injection. • At higher jet pressure ratios the plasma jet/ramp shock interaction results in a lambda shock pattern with the triple point forming vertically above the cowl level. This means the normal shock stands in front of the inlet making a part of the flow entering the inlet subsonic. The reflected shock from the triple point also separates the ramp boundary layer. • At lower jet pressure ratios the triple point is formed below the cowl level and the flow entering inside the inlet is supersonic. The reflected shock interacts with the cowl shock and a weak separation shock is seen. • Experiments are performed with concentrated DC electric discharge as energy source. Even though the amount of energy dumped here is less than 0.25% of the total energy it creates a perceptible disturbance in the flow. • Experiments are also performed to see the effect of electric discharge as energy source on height of Mach stem for a given inlet configuration. Deposition of energy in the present location does not seem to alter the Mach stem height. However more experiments need to be performed by varying the energy location to see its effect. Non-intrusive energy sources like microwave and lasers can be thought of as options for depositing energy to study its effect on Mach stem height. Since they provide more flexibility on varying the location of energy the optimum location of energy can be found out for highest reduction of Mach stem height.

Cette thèse est consacrée à l'analyse mathématique de quelques modèles hétérogènes intervenants en mécanique des fluides. En particulier, elle est consacré a l'étude théorique des systèmes d'équations aux derivées partielles décrivants les trois modèles principaux que nous voulons présenter dans la suite. Le premier modèle étudié dans cette thèse est consacré à l'étude de l'écoulement d'un fluide visqueux newtonien et incompressible dans un bassin avec bathymétrie qui dégenère proche du bord. Le modèle mathématique étudié provient alors des équations de Navier-Stokes incompressible. On cherche à montrer que le problème de Cauchy correspondant est bien posé, au sens qu'on peut garantir l'existence globale et l'unicité de solutions faibles. Nous discuterons aussi la régularité de la solution faible. Finalement,nous établissons la convergence de la solution du modèle visqueux vers celle du modèle non visqueux quand le coefficient de viscosité tend vers zéro.La deuxième partie est dédiée à l'étude d'un modèle issu du système de Navier-Stokes dispersif ( il contient une correction dispersive) qui est lui meme obtenu à partir de la théorie cinétique des gaz. Notre modèle mathématique est dérivé a partir de ce dernier en supposant que le nombre de Mach est très faible. Le modèle obtenu est nommé effet fantôme (ou ghost effect an anglais), puisqu'il ne peut pas être obtenu à partir du modèle de Navier-Stokes compressible classique. L'objectif dans ce cadre sera d'étendre un résultat concernant l'existence locale d'une solution forte vers l'existence globale d'une solution faible. L'ingrédient principal dans notre analyse est une nouvelle inégalité fonctionnelle de type Log-Sobolev.La troisième partie de ce document est une contribution à une thématique de recherche se proposant d'analyser la compréhension des phénomènes rencontrés en géophysique qui font intervenir des milieux granulaires. Le modèle mathématique choisi est de type Bingham incompressible dont on fait dépendre le seuil de plasticité et le coe fficient de viscosité de la pression. On montre un résultat d'existence globale d'une solution faible du problème de Cauchy associé. / This thesis is devoted to the mathematical analysis of heterogeneous models raised by fluid mechanics. In particular, it is devoted to the theoretical study of partial differential equations used to describe the three main models that we present below.Initially, we are interested to study the motion of a compressible newtonienfluids in a basin with degenerate topography. The mathematical model studied derives from incompressible Navier-Stokes equations. We are interested to prove that the Cauchy problem associated is well posed. Well-posedness means that there exists a solution, that it is unique. In the meantime, we prove that the solution of the viscous model converges to the one of the inviscid limit model when the viscosity coe cient tends to zero.The second part in my thesis is devoted to study a model that arises from dispersive Navier-Stokes equations (that includes dispersive corrections to the classical compressible Navier-Stokes equations). Our model is derived from the last model assuming that the Mach number is very low. The obtained system is a Ghost eect system, which is so named because it can be derived from Kinetic theory. The main goal of this part is to extend a result concerning the local existence of strong solution to a global-in time existence of weak solutions. The main ingredient in this work is a new functional inequality of Log-Sobolev type.The last part of my thesis is a part of a research theme intends to analyze the understanding of phenomena encountered in geophysics which involves granular media. The mathematical model is of Bingham incompressible type with viscosity and placticity depending on the pressure. We provide a global existence of weak solutions of the Cauchy problem associated.