This thesis is concerned with the numerical simulation of high Reynolds number, three-dimensional, incompressible flows in open domains. Many problems treated in Computational Fluid Dynamics (CFD) occur in free space: e.g., external aerodynamics past vehicles, bluff bodies or aircraft; shear flows such as shear layers or jets. In observing all these flows, we can remark that they are often unsteady, appear chaotic with the presence of a large range of eddies, and are mainly dominated by convection. For years, it was shown that Lagrangian Vortex Element Methods (VEM) are particularly well appropriate for simulating such flows. In VEM, two approaches are classically used for solving the Poisson equation. The first one is the Biot-Savart approach where the Poisson equation is solved using the Green's function approach. The unbounded domain is thus implicitly taken into account. In that case, Parallel Fast Multipole (PFM) solvers are usually used. The second approach is the Vortex-In-Cell (VIC) method where the Poisson equation is solved on a grid using fast grid solvers. This requires to impose boundary conditions or to assume periodicity. An important difference is that fast grid solvers are much faster than fast multipole solvers. We here combine these two approaches by taking the advantages of each one and, eventually, we obtain an efficient VIC-PFM method to solve incompressible flows in open domain. The major interest of this combination is its computational efficiency: compared to the PFM solver used alone, the VIC-PFM combination is 15 to 20 times faster. The second major advantage is the possibility to run Large Eddy Simulations (LES) at high Reynolds number. Indeed, as a part of the operations are done in an Eulerian way (i.e. on the VIC grid), all the existing subgrid scale (SGS) models used in classical Eulerian codes, including the recent "multiscale" models, can be easily implemented.

This thesis is concerned with the numerical simulation of high Reynolds number, three-dimensional, incompressible flows in open domains. Many problems treated in Computational Fluid Dynamics (CFD) occur in free space: e.g., external aerodynamics past vehicles, bluff bodies or aircraft; shear flows such as shear layers or jets. In observing all these flows, we can remark that they are often unsteady, appear chaotic with the presence of a large range of eddies, and are mainly dominated by convection. For years, it was shown that Lagrangian Vortex Element Methods (VEM) are particularly well appropriate for simulating such flows. In VEM, two approaches are classically used for solving the Poisson equation. The first one is the Biot-Savart approach where the Poisson equation is solved using the Green's function approach. The unbounded domain is thus implicitly taken into account. In that case, Parallel Fast Multipole (PFM) solvers are usually used. The second approach is the Vortex-In-Cell (VIC) method where the Poisson equation is solved on a grid using fast grid solvers. This requires to impose boundary conditions or to assume periodicity. An important difference is that fast grid solvers are much faster than fast multipole solvers. We here combine these two approaches by taking the advantages of each one and, eventually, we obtain an efficient VIC-PFM method to solve incompressible flows in open domain. The major interest of this combination is its computational efficiency: compared to the PFM solver used alone, the VIC-PFM combination is 15 to 20 times faster. The second major advantage is the possibility to run Large Eddy Simulations (LES) at high Reynolds number. Indeed, as a part of the operations are done in an Eulerian way (i.e. on the VIC grid), all the existing subgrid scale (SGS) models used in classical Eulerian codes, including the recent "multiscale" models, can be easily implemented.

Reservoir releases for generating power need to be reconciled with efforts to maintain healthy ecosystems in regulated rivers having irregular channel topography. Fluctuating, complex flow patterns near river obstructions such as boulders and large woody debris provide unique habitat for many aquatic organisms. Numerical modeling of the flow structures surrounding these obstructions is challenging, yet it represents an important tool for aquatic habitat assessment. Moreover, efforts for modeling the morphologically and biologically important transient flows, as well as quantifying their impacts on physical fish habitat during the unsteady-flow period remain rare. In this dissertation, the ability of two- (2-D) and three-dimensional (3-D) hydraulic models to reproduce the localized complex flow features at steady base and peak flows is examined first. The performance of the two hydraulic models is evaluated by comparing the numerical results with measurements of flow around a laboratory hemisphere and boulders located at a reach of the Smith River in Virginia. Close agreement between measured values and the velocity profiles predicted by the two models is obtained outside the wakes behind these obstructions. However, results suggest that in the vicinity of theses obstructions the 3-D model is better suited for reproducing the circulation flow behavior favored by many aquatic species over a broad range of flows. Further, time-dependent flow features affecting channel morphology and aquatic physical habitat are investigated using the numerical models for the same reach in the Smith River. Temporal variation measurements of water surface elevation and velocity profile obtained in the field during a reservoir release are in good agreement with the numerical results. A hypothetical "staggering" flow release scenario simulated by the 3-D model leads to reduced erosional area and longer refugia availability for juvenile brown trout during hydropeaking. Finally, an unsteadiness parameter β is proposed for determining whether an unsteady flow regime can be either modeled using a truly dynamic flow approach or a quasi-steady flow method. / Ph. D.

The present work is a result of collaboration between the LMFA (Laboratoire de Mécanique des Fluides et d'Acoustique, Ecole Centrale de Lyon - France), Snecma and the Cerfacs. It aims at studying the flow in the 3.5-stages high-speed axial compressor CREATE (Compresseur de Recherche pour l'Etude des effets Aérodynamique et TEchnologique - rotation speed: 11543 RPM, Rotor 1 tip speed: 313 m/s), designed and built by Snecma and investigated at LMFA on a 2-MW test rig. Steady measurements, as well as laser velocimetry, fast-response wall static and total pressure measurements have been used to experimentally investigate the flow. The analysis focuses on two main aspects: the study of the flow at stable operating points, with a special interest on the rotor-stator interactions, and the study of the instabilities arising in the machine at low mass flow rates.The description of the unsteady flow field at stable operating points is done through measurements of wall-static pressure, total pressure and velocity, but also total temperature, entropy and angle of the fluid. It is shown that the complexity and unsteadiness of the flow in a multistage compressor strongly increases in the rear part of the machine, because of the interactions between steady and rotating rows. Therefore, a modal analysis method developed at LMFA and based on the decomposition of Tyler and Sofrin is presented to analyze these interactions. It is first applied to the pressure measurements, in order to extract the contributions of each row. It shows that all the complex pressure interactions in CREATE can be reduced to three main types of interactions. The decomposition method is then applied to the entropy field extracted from URANS CFD calculations performed by the Cerfacs, in order to evaluate the impact of the interactions on the performance of the machine in term of production of losses.The last part of this work is devoted to the analysis of the instabilities arising in CREATE at low mass flows. It shows that rotating pressure waves appear at stable operating points, and increase in amplitude when going towards the surge line, until reaching a critical size provoking the onset a full span stall cell bringing the machine to surge within a few rotor revolutions. The study of these pressure waves, and the understanding of their true nature is achieved through the experimental results and the use of some analytical models. A precise description of the surge transient through wall-static pressure measurements above the rotors is also provided, as well as a description of a complete surge cycle. An anti-surge control system based on the detection of the amplitude of the pressure waves is finally proposed.

L’amélioration des performances des turboréacteurs actuels est un enjeu crucial dans un contexte de contraintes économiques et environnementales fortes. Au sein du turboréacteur, le canal inter-turbines, localisé à l’interface entre la turbine Haute Pression (HP) et le premier distributeur Basse Pression (BP), est le siège d’écoulements très complexes. Ainsi, les structures aérodynamiques issues de la turbine HP (sillages, tourbillons et ondes de choc) interagissent fortement entre elles et impactent l’écoulement du distributeur BP, engendrant ainsi des pertes de rendement de l’ensemble de la configuration. Ce travail de thèse s’attache à étudier les phénomènes d’interactions aérodynamiques entre une turbine HP et le premier distributeur BP et à analyser les mécanismes à l’origine des pertes aérodynamiques dans le distributeur BP. Une campagne expérimentale antérieure, réalisée sur un banc d’essai comprenant une turbine HP couplée à un distributeur BP, avait permis de recueillir des mesures de l’écoulement dans des plans situés dans le canal inter-turbines et à l’aval du distributeur BP. En lien avec ces résultats expérimentaux, les simulations numériques menées dans cette étude avec le logiciel elsA s’attachent à restituer précisément la nature tridimensionnelle, instationnaire et turbulente de l’écoulement au sein de cette même configuration. Ces travaux se développent alors en trois étapes principales. Dans un premier temps, une étude stationnaire avec traitement plan de mélange permet de comprendre et quantifier les aspects généraux de l’écoulement. Une évaluation de l’effet de la modélisation turbulente RANS (Reynolds-Averaged Navier-Stokes) et du schéma numérique spatial sur les structures aérodynamiques présentes dans la configuration est réalisée. Dans un deuxième temps, une modélisation turbulente avancée de type ZDES (Zonal Detached-Eddy Simulation) est employée pour la résolution de l’écoulement dans le distributeur BP. Les structures aérodynamiques instationnaires issues de la roue HP amont sont modélisées par une condition limite à l’entrée du domaine de calcul. L’approche ZDES est comparée à une approche Unsteady RANS (URANS) sur la même configuration. La formation et la dissipation des sillages et des tourbillons est significativement différente entre les deux modélisations, ce qui impacte de manière importante la génération des pertes aérodynamiques. Enfin, des simulations URANS de plusieurs configurations permettent de mieux comprendre les effets d’interaction entre les différentes rangées d’aubes. Ainsi, les approches instationnaires chorochroniques prenant en compte un seul rotor et un seul stator évaluent des effets instationnaires importants dans le canal inter-turbines. Ces approches conduisent à la mise en oeuvre d’un calcul sur une configuration multipassages-chorochronique prenant en compte les deux stators et le rotor afin de modéliser complètement les interactions déterministes existantes. Afin de quantifier celles-ci avec précision, une décomposition modale du champ instationnaire est mise en place. Les niveaux d’interactions liées aux différentes roues sont alors quantifiés et l’impact sur les pertes aérodynamiques est évalué. / Improving the performance of current aeronautical turbines is an important issue in a context of severe economical and environmental constraints. In a turbofan, the inter-turbine channel which is located between the High-Pressure (HP) turbine and the first Low Pressure (LP) vane is characterized by a complex flow. Therefore aerodynamic structures coming from the HP turbine (wakes, vortices and showkwaves) strongly interact between each other and affect the LP vane flow field. This generates efficiency losses of the overall configuration. This PhD thesis aims at studying the aerodynamic phenomena between a HP turbine and the first LP vane and at analyzing the mechanisms creating aerodynamic losses. A previous experimental campaign, which was carried out on a facility including a HP turbine coupled to a LP vane, enabled to gather flow field measurements in planes located in the inter-turbine channel and downstream of the LP vane. In comparison with these experimental data, the numerical simulations done with elsA software intend to reproduce accurately the 3D, unsteady and turbulent nature of the flow within this configuration. The work can be divided into three mains steps. As a first step, steady simulations with a sliding mesh treatment enable to understand the general aspects of the flow. An assessment of the effects of RANS (Reynolds-Averaged Navier-Stokes) turbulent predictions and of spatial numerical schemes on the aerodynamic structures present in the configuration is carried out. As a second step, the advanced turbulence approach ZDES (Zonal Detached-Eddy Simulation) is considered for the LP vane flow prediction. The unsteady aerodynamic structures coming from the upstream HP rotor are set as an inlet boundary condition of the computational domain. The ZDES approach is compared to a URANS (Unsteady RANS) approach on the same computational domain. The generation and dissipation of the wakes and vortices are significantly different on the two simulations, and thus impact the creation of aerodynamic losses. Finally, URANS simulations enable to better understand the interaction effects between the different blade rows. First, the unsteady phase-lagged approaches that take into account a single rotor and stator assess the important unsteady effects in the inter-turbine channel. They finally lead to the implementation of a multipassages phase-lagged computation that takes into account the two stators and the rotor in order to model all the existing determinist interactions. In order to quantify them accurately, a modal decomposition of the unsteady flow field is set up. The interaction levels linked to the different blade rows are therefore quantified and the impact of the aerodynamic losses is evaluated.

<p align="justify">This work deals with the development of numerical methods for compressible flow simulation with application to the interaction of fluid flows and structural bodies.</p> <p align="justify">First, we develop numerical methods based on multidimensional upwind residual distribution (RD) schemes. Theoretical results for the stability and accuracy of the methods are given. Then, the RD schemes for unsteady problems are extended for computations on moving meshes. As a second approach, cell centered and vertex centered finite volume (FV) schemes are considered. The RD schemes are compared to FV schemes by means of the 1D modified equation and by the comparison of the numerical results for scalar problems and system of Euler equations. We present a number of two and three dimensional steady and unsteady test cases, illustrating properties of the numerical methods. The results are compared with the theoretical solution and experimental data.</p> <p align="justify">In the second part, a numerical method for fluid-structure interaction problems is developed. The problem is divided into three distinct sub-problems: Computational Fluid Dynamics, Computational Solid Mechanics and the problem of fluid mesh movement. The problem of Computational Solid Mechanics is formulated as a system of partial differential equations for an anisotropic elastic continuum and solved by the finite element method. The mesh movement is determined using the pseudo-elastic continuum approach and solved again by the finite element method. The coupling of the problems is achieved by a simple sub-iterative approach. Capabilities of the methods are demonstrated on computations of 2D supersonic panel flutter and 3D transonic flutter of the AGARD 445.6 wing. In the first case, the results are compared with the theoretical solution and the numerical computations given in the references. In the second case the comparison with experimental data is presented.</p>

Ce travail de thèse s’appuie sur une étude expérimentale en tube à choc, plus précisément, c’est une approche expérimentale de l'étude de l'interaction fluide-structure. Considérons un solide indéformable auquel on laisse un degré de liberté en rotation autour d'un axe. Cette structure ferme un espace clos. Si le contenu de l'espace clos subit le passage d'une onde de choc, ce solide va être mis mouvement et tourner autour de son axe. Concrètement, l'onde de choc va augmenter les caractéristiques physiques, en particulier sa pression, du fluide en contact avec la face impactée de cette porte. La face opposée de la porte ne subissant pas ou que très peu l'influence de l'onde de choc, une seule de ses faces est soumise à la surpression. Au moment de l'impact, le déséquilibre ainsi créé impose une action mécanique sur la porte qui va la faire accélérer et tourner autour de son axe de rotation. Jusqu'à ce stade tout est relativement simple. La difficulté intervient à l'instant où la porte commence à s'ouvrir, car les frontières du volume dans lequel le fluide évolue sont modifiées. Des fuites apparaissent et le gaz qui était maintenu dans un volume clos peut maintenant s'écouler vers un milieu libre. Une communication entre les gaz agissant de chaque coté de la porte est créée modifiant leurs propriétés et par conséquent la pression agissant sur chaque côté de la porte. Les actions mécaniques qui s'appliquent sur la porte ne sont plus les mêmes, et par conséquent l'accélération que la porte subit aussi. Au fur et à mesure que la porte change de position, le problème fluide continue d'être modifié et change en retour son action sur la porte. Cette interaction perdure soit jusqu'à ce que les limites du problème cessent d'être modifiées, la porte ne peut plus bouger, ou bien lorsque les actions mécaniques agissant sur la porte s'équilibrent, les fluides de chaque côté de la porte étant dans le même état physique. Le travail présenté ici est une étude des paramètres du fluide ou du solide en mouvement qui sont les acteurs de la loi comportementale gérant ce système complexe. Pour ce faire, nous avons réalisé une maquette expérimentale mettant en action la physique que nous venons de décrire et nous l'avons adaptée à un tube à choc. En éprouvant de nombreuses configurations expérimentales, nous avons pu déterminer comment l'écoulement interne d'un tube à choc évolue lorsqu'il est plus ou moins ouvert à son extrémité. Comment une porte fermée réagit-elle à l'impact d'une onde de choc et quelles en sont les conséquences sur l'évolution des fluides mis en jeu? Quelles sont les conséquences d'une position différente de la porte au moment de l'impact avec l'onde de choc? Ou encore, quel rôle joue l'intensité de l'onde de choc incidente ou l'inertie de la porte sur toute cette dynamique? / This thesis is based on an experimental study carried out in shock tube; in particular, this is an experimental approach to the study of fluid-structure interaction. Consider a rigid body which is allowed to rotate only around an axis and which closes a confined space. If a shock wave crosses the content of the confined space, the body will accelerate and rotate around its axis. Specifically, the shock wave will increase the physical characteristics, especially its pressure, of the fluid acting on the impacted face of the door. The opposite side of the door is not influenced by the incident shock wave, only one of its faces is subjected to overpressure. Following the first impact, the resulting imbalance imposes a mechanical action on the door that will increase its speed and make it turn around its rotation axis. The difficulty comes when the door begins to open: the volume boundaries in which the fluid is contained are modified. Leaks occur and the gas kept in this closed volume can now flow to the atmosphere. Communication between the gas acting on each side of the door is created modifying their properties and consequently the pressure acting on each side of the door.The mechanical actions that apply to the door are no more the same with time, and therefore the acceleration of the door is changing. As the door moves, the fluid problem continues to be changed and in turn it changes its action on the door. This interaction process continues until either the limits of the problem ceases to be changed, the door cannot move, or when the mechanical actions acting on the door are in equilibrium, fluids on each side of the door are in the same physical state. The presented work is a study of the parameters of the fluid or the solid motion which are main actors in the behavioral law managing this complex system. In this aim, we designed an experimental device involving the physics that we have described and we have adapted it to a shock tube. Testing many experimental configurations, we could determine how the internal flow of a shock tube evolves when the end of this shock tube is more or less open.How a closed door reacts to the impact of a shock wave and what are the implications for the evolution of the involved fluids? What are the consequences of a different position of the door at the instant of the impact with the incident shock wave? What role plays the intensity of the incident shock wave or the inertia of the door on this dynamic?

Dans ce travail, on s'intéresse au développement d'une méthode hybride qui couple spatialement les schémas d'intégration temporelle explicite et implicite. Afin de répondre aux contraintes du solveur industriel FLUSEPA, les schémas explicite Heun et implicite Crank-Nicolson ont été hybridés via un paramètre de transition : l'approche mise en place est appelée schéma AION. Cette dernière est étudiée en détails avec une attention particulière sur son comportement spectral et sa capacité à maintenir l'ordre de précision. On montre que le traitement hybride a d'intéressants comportements dissipatif et dispersif tout en empêchant la réflexion d'ondes parasites et en maintenant la précision attendue. De plus, l'approche hybride est validée sur plusieurs cas académiques à la fois pour les flux convectifs et pour les flux diffusifs. Et comme espéré, la méthode est plus intéressante en terme de temps de calcul que les méthodes standards d'intégration temporelle. Pour l'extension de cette approche à la méthode temporelle adaptative présente dans FLUSEPA, il a été nécessaire d'améliorer le traitement qui permet à la méthode d’être conservative tout en obtenant des propriétés spectrales acceptables. Finalement l'approche hybride a été aussi étendue pour la modélisation RANS/LES de la turbulence avec des temps de calcul intéressants tout en capturant la physique de l'écoulement / This work deals with the design of a hybrid time integrator that couples spatially explicit and implicit time integrators. In order to cope with the industrial solver of Ariane Group called FLUSEPA, the explicit scheme of Heun and the implicit scheme of Crank-Nicolson are hybridized using the transition parameter : the whole technique is called AION time integration. The latter is studied into details with special focus on spectral behaviour and on its ability to keep the accuracy. It is shown that the hybrid technique has interesting dissipation and dispersion properties while maintaining precision and avoiding spurious waves. Moreover, this hybrid approach is validated on several academic test cases for both convective and diffusive fluxes. And as expected the method is more interesting in term of computational time than standard time integrators. For the extension of this hybrid approach to the temporal adaptive method implemented in FLUSEPA, it was necessary to improve some treatments in order to maintain conservation and acceptable spectral properties. Finally the hybrid time integration was also applied to a RANS/LES turbulent test case with interesting computational time while capturing the flow physics.

Analysis of unsteady flows is a very challenging topic of research. A decade ago, potential flow equations were used to predict unsteady pressures on oscillating bodies. Recognising the fact that nonlinear aerodynamics is essential to analyse unsteady flows accurately, particularly in transonic and supersonic flows, different Euler formulations operating on moving grids have emerged recently as important CFD tools for unsteady aerodynamics. Numerical solution of Euler equations on moving grids based on upwind schemes such as the ones due to van Leer and Roe have been developed for the purpose of numerical simulation of unsteady transonic and supersonic flows. In the present work, Euler computations based on yet another recent robust upwind scheme (for steady flows) namely Kinetic Flux Vector Splitting (KFVS) scheme due to Deshpande and Mandal is chosen for further development of a time accurate Euler solver to operate on problems involving moving boundaries. The development of an Euler code based on this scheme is likely to be highly useful to analyse problems of unsteady aerodynamics and computational aeroelasiticity especially when it is noted that KFVS has been found to be an extremely robust scheme for computation of subsonic, transonic, supersonic and hypersonic flows. The KFVS scheme, basically exploits the connection between the linear scalar Boltzmann equation of kinetic theory of gases and the nonlinear vector conservation law, that is, Euler equations of fluid dynamics through moment method strategy. The KFVS scheme has inherent simplicity in splitting the flux even on moving grids due to underlying particle model. The inherent simplicity of KFVS for moving grid problems is due to its relationship with the Boltzmann equation. If a surface is moving with velocity w and a particle has velocity v, then it is quite reasonable to do the splitting based on (v-w)<0 or >0. Only particles having velocity v greater than w will cross the moving surface from left to right and similar arguments hold good for particles moving in opposite direction. It is therefore quite natural to extend KFVS by splitting the Maxwellian velocity distribution at Boltzmann level based on the sign of the normal component of the relative velocity. The relative velocity is the difference between the molecular velocity (v) and the velocity of the moving surface(w). This inherent simplicity of the Kinetic Flux Vector Splitting scheme on Moving Grids (KFMG) method has prompted us to extend the same ideas to 2-D and 3-D problems leading to the present KFMG method. If w is set to zero then KFMG formulation reduces to the one corresponding to KFVS. Thus KFMG formulations axe generalisation of the KFVS formulation. In 2-D and 3-D cases, in addition to the KFMG formulation, the method to move the grids, the appropriate boundary conditions for treating moving surfaces and techniques to improve accuracy in space and time are required to be developed. The 2-D and 3-D formulations based on Kinetic Flux Vector Splitting scheme on Moving Grids method have been developed for computing unsteady flows. Between two successive time steps, the body changes its orientation in case of an oscillation or it deforms when subjected to, aerodynamic loads. In either of these cases the grid corresponding to the first time step has to be moved or regenerated around the displaced or deformed body. There are several approaches available to generate grids around moving bodies. In the present work, the 'spring analogy method' is followed to obtain grid around deflected geometries within the frame work of structured grid. Using this method, the grids are moved from previous time to the current time. This method is capable of tackling any kind of aeroelastic deformation of the body. For oscillating bodies, a suitable boundary condition enforcing the flow tangency on the body needs to be developed. As a first attempt, the body surface has been treated as an 1-D piston undergoing compression and expansion. Then, a more general Kinetic Moving Boundary Condition(KMBC) has been developed. The KMBC uses specular reflection model of kinetic theory of gases. In order to treat fixed outer boundary, Kinetic Outer Boundary Condition(KOBC) has been applied. The KOBC is more general in the sense that, it can treat different type of boundaries (subsonic, supersonic, inflow or out flow boundary). A 2-D cell-centered finite volume KFMG Euler code to operate on structured grid has been developed. The time accuracy is achieved by incorporating a fourth order Runge-Kutta time marching method. The space accuracy has been enhanced by using high resolution scheme as well as second order scheme using the method of reconstruction of fluxes. First, the KFMG Euler code has been applied to standard test cases for computing steady flows around NACA 0012 and NACA 64AQ06 airfoils in transonic flow. For these two airfoils both computational and experimental results are available in literature. It is thus possible to verify (that is, prove the claim that code is indeed solving the partial differential equations + boundary conditions posed to the code) and validate(that is, comparison with experimental results) the 2-D KFMG Euler code. Having verified and validated the 2-D KFMG Euler code for the standard test cases, the code is then applied to predict unsteady flows around sinusoidally oscillating NACA 0012 and NACA 64A006 airfoils in transonic flow. The computational and experimental unsteady results are available in literature for these airfoils for verification and validation of the present results. The unsteady lift and normal force coefficients have been predicted fairly accurately by all the CFD codes. However there is some difficulty about accurate prediction of unsteady pitching moment coefficient. Even Navier-Stokes code could not predict pitching moment accurately. This issue needs further in depth study and probably intensive computation which have not been undertaken in the present study. Next, a two degrees of £reedom(2-DOF) structural dynamics model of an airfoil undergoing pitch and plunge motions has been coupled with the 2-D KFMG Euler code for numerical simulation of aeroelastic problems. This aeroelastic analysis code is applied to NACA 64A006 airfoil undergoing pitch and plunge motions in transonic flow to obtain aeroelastic response characteristics for a set of structural parameters. For this test case also computed results are available in literature for verification. The response characteristics obtained have showed three modes namely stable, neutrally stable and unstable modes of oscillations. It is interesting to compare the value of airfoil-to-air mass ratio (Formula) obtained by us for neutrally stable condition with similar values obtained by others and some differences between them are worth mentioning here. The values of \i for neutral stability are different for different authors. The differences in values of (Formula) predicted by various authors are primarily due to differences which can be due to grid as well as mathematical model used. For example, the Euler calculations, TSP calculations and full potential calculations always show differences in shock location for the same flow problem. Changes in shock location will cause change in pressure distribution on airfoil which in turn will cause changes in values of \L for conditions of neutral stability. The flutter speed parameter(U*) has also been plotted with free stream Mach number for two different values of airfoil - to - air mass ratio. These curves shown a dip when the free stream Mach number is close to 0.855. This is referred as "Transonic Dip Phenomenon". The shock waves play a dominant role in the mechanism of transonic dip phenomenon. Lastly, cell-centered finite volume KFMG 3-D Euler code has been developed to operate on structured grids. The time accuracy is achieved by incorporating a fourth order Runge-Kutta method. The space accuracy has been enhanced by using high resolution scheme. This code has 3-D grid movement module which is based on spring analogy method. The KMBC to treat oscillating 3-D configuration and KOBC for treating 3-D outer boundary have also been formulated and implemented in the code. The 3-D KFMG Euler code has been first verified and validated for 3-D steady flows around standard shapes such as, transonic flow past a hemisphere cylinder and ONERA M6 wing. This code has also been used for predicting hypersonic flow past blunt cone-eylinder-flare configuration for which experimental data are available. Also, for this case, the results are compared with a similar Euler code. Then the KFMG Euler code has been used for predicting steady flow around ogive-cylinder-ogive configuration with elliptical cross section. The aerodynamic coefficients obtained have been compared with those of another Euler code. Thus, the 3-D KFMG Euler code has been verified and validated extensively for steady flow problems. Finally, the 3-D KFMG based Euler code has been applied to an oscillating ogive-cylinder-ogive configuration in transonic flow. This test case has been chosen as it resembles the core body of a flight vehicle configuration of interest to DRDO,India. For this test case, the unsteady lift coefficients are available in literature for verifying the present results. Two grid sizes are used to perform the unsteady calculations using the present KFMG 3-D Euler code. The hysteresis loops of lift and moment coefficients confirmed the unsteady behaviour during the oscillation of the configuration. This has proved that, the 3-D formulations are capable of predicting the unsteady flows satisfactorily. The unsteady results obtained for a grid with size of 45x41x51 which is very close to the grid size chosen in the reference(Nixon et al.) are considered for comparison. It has been mentioned in the reference that, a phase lag of (Formula) was observed in lift coefficients with respect to motion of the configuration for a free stream Mach number of 0.3 with other conditions remaining the same. The unsteady lift coefficients obtained using KFMG code as well as those available in literature are plotted for the same flow conditions. Approximately the same phase lag of (Formula) is present (for (Formula)) between the lift coefficient curves of KFMG and due to Nixon et al. The phase lag corrected plot of lift coefficient obtained by Nixon et al. is compared with the lift coefficient versus time obtained by 3-D KFMG Euler code. The two results compare well except that the peaks are over predicted by KFMG code. It is nut clear at this stage whether our results should at all match with those due to Nixon et al. Further in depth study is obviously required to settle the issue. Thus the Kinetic Flux Vector Splitting on Moving Grids has been found to be a very good and a sound method for splitting fluxes and is a generalisation of earlier KFVS on fixed grids. It has been found to be very successful in numerical simulation of unsteady aerodynamics and computational aeroelasticity.

The present thesis is an experimental study of some aspects of unsteady two dimensional boundary layers subject to adverse pressure gradient. An adverse pressure gradient usually leads to boundary layer separation or an instability which may result in transition to turbulence. Unsteady boundary layer separation is not yet fully understood and there is no specific criterion proposed in literature for its occurrence. The details of separation depend on the Reynolds number, the geometry of the body (streamlined or bluff) and the type of imposed unsteady motion (impulsive, oscillatory etc.). Similarly there are many unknowns with respect to instability and transition in unsteady boundary layers, especially those having a streamwise variation. For unsteady flows it is useful to break up the pressure gradient term in the unsteady boundary layer equation into two components:(Formula) is the velocity at the edge of the boundary layer. The first term of the right hand side of this equation may be called the temporal component (Πt) which signifies acceleration or deceleration in time of the free stream and the second term is the spatial component (Πx) which represents the spatial or convective acceleration of the free stream. Many of the studies on instability in unsteady flows found in literature are carried out in straight tubes or channels, where the Πx term is absent. However, in many cases, especially in biological systems both terms are present. An example is the unsteady flow over the moving body of a fish. To study the effects of Πt and Πx on unsteady separation and instability we have built an unsteady water tunnel where the two components can be systematically varied. The flow is created by a controlled motion of a piston. By a suitable combination of the geometry of the model and the piston motion, different types of separation bubbles may be generated. In our studies the piston motion follows a trapezoidal variation: constant acceleration from rest, followed by constant velocity and then deceleration to zero velocity. We have chosen two geometries. One is a bluff body and thus has a high value of Πx and other is a small angle diffuser with a divergence angle 6.2° and thus having a small value of Πx. Upstream and downstream of the diffuser are long lengths of constant cross section. We have performed experiments with the above mentioned geometries placed in the tunnel test section. Flow is visualized using the laser induced fluorescence technique by injecting a thin layer of fluorescein dye on the test wall. Numerical simulations have been done using the software FLUENT. Boundary layer parameters like boundary layer, displacement and momentum thicknesses are calculated from the simulations and used to analyze the experimental results. For the flow in the diffuser, quasi-steady stability analysis of the instantaneous velocity profiles gives a general idea of stability behavior of the flow. Two types of experiments have been done with the bluff body. One is the unsteady boundary layer separation and the formation of the initial vortex for a flow that is uniformly accelerated from rest. We have found some scalings for the formation time (tv) of the separation vortex. The second type of experiment was to study the vortex shedding from the separating shear layer after the boundary layer has fully separated. At high enough Reynolds number shear layer vortices are seen to shed from the separation bubble. The Strouhal number based on the momentum thickness and the velocity at the edge of the boundary layer just upstream of the separation point is found to vary between 0.004 and 0.008. This value is close to the Strouhal number value of 0.0068 found in laminar separation bubbles on a flat plate. The second part of the study concerns with the evolution of the flow in the small angle diffuser with a mild variation of the spatial component of the pressure gradient. From the experimental visualizations we have found that the ratio of Πx and Πt at the start of the deceleration phase of the piston motion is an important parameter that determines the type of instability. This value of Πx/Πt is controlled by controlling the piston deceleration: a large deceleration gives a low Πx/Πt value and a low deceleration gives a large Πx/Πt value. Three types of instabilities have been observed in our experiments. In Type I, the first vortex forms at the maximum pressure gradient point (MPGP) and which grows disproportionately with time. However, instability vortices are seen later at other locations around the MPGP. In type II an array of vortices over a certain length are observed; the vortices grow with time. In Type III, which we observe for low decelerations, we observe initial vortices only in the diffuser section in the deceleration phase of the piston motion. Type III instability is similar to the one observed in dynamic stall experiments. In all cases the instability is very localized - it occurs only over some length of the boundary layer. Transition to turbulence, which is also localized, is observed at higher Reynolds numbers. The non-dimensional time for vortex formation is not very different from that found in straight channel experiments. Quasi-steady linear stability analyses for the boundary layer at the MPGP both for the top and the bottom walls show that the flow is absolutely unstable for some cases. In summary, the thesis looks at in a unified way the separation and instability of unsteady boundary layers with reverse flow. It is hoped that the results will be useful in predicting and understanding onset of separation and instability in practically occurring unsteady flows.