O trabalho desenvolvido nesta tese propõe a aplicação do método da expansão em funções hierárquicas elaborado por Zienkiewics e Morgan (1983), para a solução das equações de conservação da massa (continuidade), conservação da quantidade de movimento (Navier-Stokes) e conservação da energia, para fluidos compressíveis em duas dimensões e em alta velocidade. Esse método consiste no emprego do método de elementos finitos utilizando a formulação Petrov-Galerkin, conhecido como SUPG (“Streamline Upwind Petrov-Galerkin"), desenvolvido por Brooks e Hughes (1982), aplicado em conjunto com uma expansão das variáveis em funções hierárquicas. A fim de testar e validar o método numérico proposto, assim como o programa computacional elaborado, foram simulados alguns casos conhecidos da literatura. Os casos estudados foram os seguintes: teste de Continuidade; teste de convergência e estabilidade; problema do degrau de temperatura e problema do choque oblíquo, onde o objetivo desse último caso era, basicamente, verificar a captura da onda de choque pelo método numérico desenvolvido. Através dos casos estudados e em função dos resultados obtidos nas simulações realizadas, conclui-se que o objetivo desse trabalho foi alcançado de maneira satisfatória, pois os resultados obtidos com o método desenvolvido nesse trabalho foram qualitativamente e quantitativamente bons, quando comparados com os resultados teóricos. / The Thesis develops a new application for the Hierarchical Function Expansion Method, proposed by Zienkiewics and Morgan (1983), for the solution of the Navier-Stokes equations for compressible fluids in two dimensions and in high velocity. This method is based on the finite elements method using the Petrov-Galerkin formulation, know as, SUPG (Streamline Upwind Petrov-Galerkin) developed by Brooks and Hughes (1982), and applied in conjunction with the expansion of the variables into hierarchical functions. To test and validate the numerical method proposed as well as the computational program developed some cases whose theoretical solution are known simulated. These cases are the following: continuity test; stability and convergence test; temperature step problem; and several oblique shocks. The objective of the last cases is basically to verify the capture of the shock wave by the method developed. The results obtained in the simulations of the cases performed with the proposed method were good both qualitatively and quantitatively when compared with the teorethical solutions. This allows us to conclude that the objective of this Thesis was satisfactorily reached.

Dans de nombreuses régions du monde, d’immenses réserves gazéifères dites non conventionnelles sont piégées dans des roches faiblement perméables qui ne peuvent pas être exploitées par des méthodes de forage classiques. Bien que très controversée, la seule méthode d’exploitation de ces gisements repose actuellement sur la technique de fracturation hydraulique. Pour ces raisons, une collaboration de recherche a débuté en 2007 entre la société TOTAL et le Laboratoire de Génie Electrique de l’université de Pau (récemment devenu le laboratoire SIAME), visant à étudier l’opportunité d’utiliser la fracturation électrique comme solution alternative à la fracturation hydraulique. Cette méthode repose sur un procédé dynamique de fracturation de la roche par application d’une onde de pression créée suite à l’initiation d’un arc électrique dans un liquide. Ce travail, financé par TOTAL dans le cadre d’une bourse CIFRE, s’inscrit dans la continuité de travaux déjà engagés sur cette thématique et vise particulièrement à approfondir les connaissances concernant le cœur du procédé de fracturation : la décharge électrique dans l’eau et la caractérisation de l’onde de pression résultante. Dans cette optique, l’importance du circuit et des paramètres électriques de l’arc a été démontrée en termes d’injection de courant et de transfert de puissance. Une formule empirique permettant de prévoir la valeur de la pression dynamique a, par conséquent, été établie. Afin d’optimiser le rendement électro-acoustique, une étude spécifique a été menée sur l’effet du mode de rupture diélectrique du fluide. Ces travaux ont également permis de proposer des solutions concernant le contrôle de la dynamique de l’onde de pression. Enfin, les effets des propriétés thermodynamiques du fluide sur sa rigidité diélectrique, sur la consommation d’énergie, ainsi que sur la propagation de l’onde de pression ont été analysés afin d’établir une série de conclusions permettant d’optimiser le procédé. / Numerous parts of the world contain huge unconventional gas reserves which are located in low permeability rocks, and consequently, cannot be produced by classical drilling techniques. Besides its numerous detractors, the only currently available method to exploit these reservoirs relies on hydraulic fracturing. For these reasons, a research collaboration was started in 2007 between the Total Company and the Electrical Engineering Laboratory of Pau university (recently renamed SIAME Laboratory). The main goal was to study the potential concerning the use of the electrical fracturing technique as an alternative to hydraulic fracturing. This method is based on a dynamic rock fracturing process through the applying of a pressure wave enhanced by the generation of an electrical arc into a liquid. This work, which is financed by TOTAL through a CIFRE funding, follows the track initiated on this topic and mainly intends to improve the knowledge concerning the critical part of the fracturing process: the electrical discharge in water and the resulting pressure wave characterization. In this purpose, the importance of the circuit and of the arc electrical parameters was demonstrated in terms of current injection and power transfer. An empirical formula used to predict the dynamic pressure value has consequently been established. In order to optimize the electro acoustic efficiency, a specific study was performed on the liquid dielectric breakdown modus. This work allowed us to suggest new solutions concerning the dynamic pressure wave control. Finally, the fluid thermodynamic properties effects on its dielectric strength, on the energy consumption, and on the pressure wave propagation were analyzed in order to draw conclusions for the process optimization.

Cette étude a été l'occasion d'étudier les effets liés à la présence d'un cisaillement particulier de l'écoulement moyen sur le phénomène d'interaction choc/turbulence. Dans un premier temps, un outil de calcul performant et modulaire fondé sur une approche orientée objet a été développé afin de réaliser des simulations numériques directes de ce type d'écoulement. L'utilisation de schémas numériques à capture de choc et d'ordre élevé de type WENO ont permis une résolution fidèle des équations de Navier-Stokes compressibles. Dans un deuxième temps, une analyse poussée des effets de ce type de cisaillement sur la turbulence en l'absence de choc a été réalisée. Cette première étude a été l'occasion de dégager l'influence de plusieurs paramètres influents pour cette configuration d'écoulement. Enfin, dans un dernier temps, l'étude du phénomène d'interaction choc/turbulence cisaillée en présence de gradients moyens de température et de masse volumique a permis de souligner l'activation de phénomènes physiques caractéristiques à cette configuration. Ce travail permet également d'apporter une base de données de résultats susceptible d'être confrontée avec les modèles de turbulence et constitue un point de vue intéressant pour l'étude du phénomène d'interaction choc/couche limite. / This study sheds some light on the effects of a specific sheared flow over the shock / turbulence interaction phenomenon. An efficient and modular computational tool using an oriented object approach has first been developed in order to carry out direct numerical simulations of this configuration. The use of high order shock capturing schemes allows to solve accurately the turbulent flow, even in presence of physical discontinuities. A detailed study concerning the effects of this specific mean shear on the turbulent flow has then been conducted in a shock-free configuration. This preliminary study emphases some significant parameters of this flow configuration. In a second step, DNS of the interaction between the turbulent shear flow and a normal shock ware are performed. These simulations are compared to the isotropic turbulence / shock interaction situation, which allows to underline the activationof specific mechanisms due to the presence of the mean shear in the upstream flow. An interesting database is now available and can be used to assess and improve turbulence models. This is also an interesting point of view for studying the shock/boundary layer interaction phenomenon.

O trabalho desenvolvido nesta tese propõe a aplicação do método da expansão em funções hierárquicas elaborado por Zienkiewics e Morgan (1983), para a solução das equações de conservação da massa (continuidade), conservação da quantidade de movimento (Navier-Stokes) e conservação da energia, para fluidos compressíveis em duas dimensões e em alta velocidade. Esse método consiste no emprego do método de elementos finitos utilizando a formulação Petrov-Galerkin, conhecido como SUPG (“Streamline Upwind Petrov-Galerkin”), desenvolvido por Brooks e Hughes (1982), aplicado em conjunto com uma expansão das variáveis em funções hierárquicas. A fim de testar e validar o método numérico proposto, assim como o programa computacional elaborado, foram simulados alguns casos conhecidos da literatura. Os casos estudados foram os seguintes: teste de Continuidade; teste de convergência e estabilidade; problema do degrau de temperatura e problema do choque oblíquo, onde o objetivo desse último caso era, basicamente, verificar a captura da onda de choque pelo método numérico desenvolvido. Através dos casos estudados e em função dos resultados obtidos nas simulações realizadas, conclui-se que o objetivo desse trabalho foi alcançado de maneira satisfatória, pois os resultados obtidos com o método desenvolvido nesse trabalho foram qualitativamente e quantitativamente bons, quando comparados com os resultados teóricos. / The Thesis develops a new application for the Hierarchical Function Expansion Method, proposed by Zienkiewics and Morgan (1983), for the solution of the Navier-Stokes equations for compressible fluids in two dimensions and in high velocity. This method is based on the finite elements method using the Petrov-Galerkin formulation, know as, SUPG (Streamline Upwind Petrov-Galerkin) developed by Brooks and Hughes (1982), and applied in conjunction with the expansion of the variables into hierarchical functions. To test and validate the numerical method proposed as well as the computational program developed some cases whose theoretical solution are known simulated. These cases are the following: continuity test; stability and convergence test; temperature step problem; and several oblique shocks. The objective of the last cases is basically to verify the capture of the shock wave by the method developed. The results obtained in the simulations of the cases performed with the proposed method were good both qualitatively and quantitatively when compared with the teorethical solutions. This allows us to conclude that the objective of this Thesis was satisfactorily reached.

An obvious reason for studying unsteady flows is the prediction of the effect of unsteady aerodynamic forces on a flight vehicle, since these effects tend to increase the likelihood of aeroelastic instabilities. This is a major concern in aerodynamic design of aircraft that operate in transonic regime, where the flows are characterised by the presence of adjacent regions of subsonic and supersonic flow, usually accompanied by weak shocks. It has been a common expectation that the numerical approach as an alternative to wind tunnel experiments would become more economical as computers became less expensive and more powerful. However even with all the expected future advances in computer technology, the cost of a numerical flutter analysis (computational aeroelasticity) for a transonic flight remains prohibitively high. Hence it is vitally important to develop an efficient, cheaper (in the sense of computational cost) and physically accurate flutter simulation tech nique which is capable of reproducing the data, which would otherwise be obtained from wind tunnel tests, at least to some acceptable engineering accuracy, and that it is essentially appropriate for industrial applications. This need motivated the present research work on exploring and developing efficient and physically accurate computational techniques for steady, unsteady and time-linearised calculations of transonic flows over an aircraft wing with moving shocks. This dissertation is subdivided into eight chapters, seven appendices and a bibliography listing all the reference materials used in the research work. The research work initially starts with a literature survey in unsteady transonic flow theory and calculations, in which emphasis is placed upon the developments in these areas in the last three decades. Chapter 3 presents the small disturbance theory for potential flows in the subsonic, transonic and supersonic regimes, including the required boundary conditions and shock jump conditions. The flow is assumed irrotational and inviscid, so that the equation of state, continuity equation and Bernoulli's equation formulated in Appendices A and B can be employed to formulate the governing fluid equation in terms of total velocity potential. Furthermore for transonic flow with free-stream Mach number close to unity, we show in Appendix C that the shocks that appear are weak enough to allow us to neglect the flow rotationality. The formulations are based on the main assumption that aerofoil slopes are everywhere small, and the flow quantities are small perturbations about their free-stream values. In Chapter 4, we developed an improved approximate factorisation algorithm that solves the two-dimensional steady subsonic small disturbance equation with nonreflecting far-field boundary conditions. The finite difference formulation for the improved algorithm is presented in Appendix D, with the description of the solver used for solving the system of difference equations described in Appendix E. The calculation of steady and unsteady nonlinear transonic flows over a realistic aerofoil are considered in Chapter 5. Numerical solution methods, based on the finite difference approach, for solving the two-dimensional steady and unsteady, general-frequency transonic small disturbance equations are presented, with the corresponding finite difference formulation described in Appendix F. The theories and solution methods for the time-linearised calculations, in the frequency and time domains, for the problem of unsteady transonic flow over a thin planar wing undergoing harmonic oscillation are presented in Chapters 6 and 7, respectively. The time-linearised calculations include the periodic shock motion via the shock jump correction procedure. This procedure corrects the solution values behind the shock, to accommodate the effect of shock motion, and consequently, the solution method will produce a more accurate time-linearised solution for supercritical flow. Appendix G presents the finite difference formulation of these time-linearised solution methods. The aim is to develop an efficient computational method for calculating oscillatory transonic aerodynamic quantities efficiently for use in flutter analyses of both two- and three-dimensional wings with lifting surfaces. Chapter 8 closes the dissertation with concluding remarks and future prospects on the current research work.

Modern turbomachines are designed towards thinner, lighter and highly loaded blades. This gives rise to increased sensitivity to flow induced vibrations such as flutter, which leads to structure failure in a short period of time if not sufficiently damped. Although numerical tools are more and more reliable, flutter prediction still depends on a large degree on simplified models. In addition, the critical nature of flutter, resulting in poor well-documented real cases in the open literature, and the lack of experimental database typical of engine flows make its apprehension even more challenging.  In that context, the present thesis is dedicated to study flutter in recent turbines through aerodynamic analysis of subsonic or supersonic flows in response to a prescribed vibratory mode of the structure. The objective is to highlight some mechanisms potentially responsible for flutter in order to be in better position when designing blades. The strategy consists in leading both experimental and numerical investigations.  The experimental part is based on a worldwide unique annular turbine sector cascade employed for measuring the aeroelastic response by means of the aerodynamic influence coefficient technique. The cascade comprises seven low pressure gas turbine blades one of which can oscillate in a controlled way as a rigid body. Aeroelastic responses are measured at various mechanical and aerodynamic parameters: pure and combined modeshapes, reduced frequency, Mach number, incidence angle. In addition to turbulence level measurements, the database aims at assessing the influence of these parameters on the aerodynamic damping, at validating the linear combination principle and at providing input for numerical tools. The numerical part is based on unsteady computations linearized in the frequency domain and performed in the traveling wave mode. The focus is put on two industrial space turbines: 2D computations are performed on an integrally bladed disk, also called blisk; its very low viscous material damping results in complex motions with combined modes and extremely high reduced frequency. The blisk operates at low subsonic conditions without strong non-linearities. Although the blades have been predicted aeroelastically stable, an original methodology based on elementary decompositions of the blade motion is presented to identify the destabilizing movements. The results suggest that the so-called classical flutter is surprisingly prone to occur. Moreover, the aerodynamic damping has been found extremely sensitive to the interblade phase angle and cut-on/cut-off conditions. 3D computations are then performed on a supersonic turbine, which features shock waves and boundary layer separation. In contrast, the blade motion is of elementary nature, i.e. purely axial. The blades have been predicted aeroelastically unstable for backward traveling waves and stable for forward traveling waves. The low reduced frequencies allow quasi-steady analysis, which still account for flutter mechanisms: the shock wave motion establishes the boundary between stable and unstable configurations. / <p>QC 20111209</p>

Injury from blast is significant in both military and civilian environments. Although injuries from blast are well-documented, the mechanisms of injury are not well understood. Developing better protection requires knowledge of injury mechanisms and material response to blast loading. The importance of understanding how soft materials such as foams and fabrics behave under blast loading is further apparent when one realizes the capacity for some of these materials, frequently used in protective ensembles, to increase the potential for injury under some conditions. The ability for material configurations to amplify blast pressure and injury has been shown experimentally by other researches, and numerically in this study. Initially, 1-D finite element and mathematical models were developed to investigate a variety of soft materials commonly utilized in ballistic and blast protection. Foams, which have excellent characteristics in terms of energy absorption and density, can be used in conjunction with other materials to drastically reduce the amplitude of the transmitted pressure wave and corresponding injury. Additionally, a more fundamental examination of single layers of fabric was undertaken to investigate to the effects of parameters such as fabric porosity and density. Shock tube models were developed and validated against experimental results from the literature. After the models were validated, individual fabric properties were varied independently to isolate the influence of parameters in ways not possible experimentally. Fabric permeability was found to have the greatest influence on pressure amplification. Kevlar, a ballistic fabric, was modelled due to its frequent use for fragmentation protection (either stand-alone or in conjunction with a hard ballistic plate). The developed fabric and foam material models were then utilized in conjunction with a detailed torso model for the estimation of lung injury resulting from air blast. It was found that the torso model predicted both amplification and attenuation of injury, and all materials investigated as a part of the study had the capacity for both blast amplification and attenuation. The benefit of the models developed is that they allow for the evaluation of specific protection concepts.

Injury from blast is significant in both military and civilian environments. Although injuries from blast are well-documented, the mechanisms of injury are not well understood. Developing better protection requires knowledge of injury mechanisms and material response to blast loading. The importance of understanding how soft materials such as foams and fabrics behave under blast loading is further apparent when one realizes the capacity for some of these materials, frequently used in protective ensembles, to increase the potential for injury under some conditions. The ability for material configurations to amplify blast pressure and injury has been shown experimentally by other researches, and numerically in this study. Initially, 1-D finite element and mathematical models were developed to investigate a variety of soft materials commonly utilized in ballistic and blast protection. Foams, which have excellent characteristics in terms of energy absorption and density, can be used in conjunction with other materials to drastically reduce the amplitude of the transmitted pressure wave and corresponding injury. Additionally, a more fundamental examination of single layers of fabric was undertaken to investigate to the effects of parameters such as fabric porosity and density. Shock tube models were developed and validated against experimental results from the literature. After the models were validated, individual fabric properties were varied independently to isolate the influence of parameters in ways not possible experimentally. Fabric permeability was found to have the greatest influence on pressure amplification. Kevlar, a ballistic fabric, was modelled due to its frequent use for fragmentation protection (either stand-alone or in conjunction with a hard ballistic plate). The developed fabric and foam material models were then utilized in conjunction with a detailed torso model for the estimation of lung injury resulting from air blast. It was found that the torso model predicted both amplification and attenuation of injury, and all materials investigated as a part of the study had the capacity for both blast amplification and attenuation. The benefit of the models developed is that they allow for the evaluation of specific protection concepts.

A pulsed-plasma jet (called a "spark-jet" by other researchers), is a high-speed synthetic jet that is generated by striking an electrical discharge in a small cavity. The gas in the cavity pressurizes owing to the heating and is allowed to escape through a small orifice. A series of experiments were conducted to determine the characteristics of the pulsed-plasma jet issuing into stagnant air at a pressure of 45 Torr. These results show that typical jet exit velocities of about 250 m/s can be induced with discharge energies of about 30 mJ per jet. Furthermore, the maximum pulsing frequency was found to be about 5 kHz, because above this frequency the jet begins to misfire. The misfiring appears to be due to the finite time it takes for the cavity to be recharged with ambient air between discharge pulses. The velocity at the exit of the jet is found to be primarily dependent on the discharge current and independent of other discharge parameters such as cavity volume and orifice diameter. Temperature measurements are made using optical emission spectroscopy and reveal the presence of considerable non-equilibrium between rotational and vibrational modes. The gas heating efficiency was found to be 10% and this parameter is shown to have a direct effect on the plasma jet velocity. These results indicate that the pulsed-plasma jet creates a sufficiently strong flow perturbation that is holds great promise as a supersonic flow actuator. An experimental study is conducted to characterize the performance of a pulsed-plasma jet for potential use in supersonic flow control applications. To obtain an estimate of the relative strength of the pulsed-plasma jet, the jet is injected normally into a Mach 3 cross-flow and the penetration distance is measured by using schlieren imaging. These measurements show that the jet penetrates 1.5 [delta], where [delta] is the boundary layer thickness, into the cross-flow and the jet-to-crossflow momentum flux ratio is estimated to be 0.6. An array of pulsed-plasma jets was issued from different locations upstream of a 30-degree compression ramp in a Mach 3 flow. Furthermore, two different jet configurations were used: normal injection and pitched and skewed injection. The pitched and skewed configuration was used to see if the jets could act as high-bandwidth pulsed vortex generators. The interaction between the jets and the separation shock was studied using phase-locked schlieren imaging. Results show that the plasma jets cause a significant disturbance to the separation shock and clearly influence its unsteadiness. While all plasma jet configurations tested caused an upstream motion of the separation shock, pitched and skewed plasma jets caused an initial downstream shock motion before the upstream motion, demonstrating the potential use of these plasma jets as vortex generator jets. The effect of the plasma jet array on the separation shock unsteadiness is studied in a time-resolved manner by using 10 kHz schlieren imaging and fast-response wall pressure measurements. An array of three pulsed-plasma jets, in a pitched and skewed configuration, is used to force the unsteady motion of the interaction formed by a 24° compression ramp in a Mach 3 flow. The Reynolds number of the incoming boundary layer is Re[theta]=3300. Results show that when the pulsed jet array is placed upstream of the interaction, the jets cause the separation shock to move in a quasi-periodic manner, i.e., nearly in sync with the pulsing cycle. As the jet fluid convects across the separation shock, the shock responds by moving upstream, which is primarily due to the presence of hot gas and hence the lower effective Mach number of the incoming flow. Once the hot gases pass through the interaction, the separation shock recovers by moving downstream, and this recovery velocity is approximately 1% to 3% of the free stream velocity. With forcing, the low-frequency energy content of the pressure fluctuations at a given location under the intermittent region decreases significantly. This is believed to be a result of an increase in the mean scale of the interaction under forced conditions. Pulsed-jet injection are also employed within the separation bubble, but negligible changes to the separation shock motion were observed. These results indicate that influencing the dynamics of this compression ramp interaction is much more effective by placing the actuator in the upstream boundary layer. / text

The purpose of this thesis is to perform numerical solutions of hypersonic, high temperature, perfect gas flows over various geometries. Three dimensional, thin layer, compressible, Navier-Stokes equations are solved. An upwind finite difference approach with Lower Upper-Alternating Direction Implicit (LU-ADI) decomposition is used. Solutions of laminar, hypersonic, high temperature, perfect gas flows over flat plate and compression corners (qw=5&deg / , 10&deg / , 14&deg / , 15&deg / , 16&deg / , 18&deg / and 24&deg / ) with eight different free-stream and wall conditions are presented and discussed. During the analysis, air viscosity is calculated from the Sutherland formula up to 1000&deg / K, for the temperature range between 1000 &ordm / K and 5000 &ordm / K a curve fit to the estimations of Svehla is applied. The effects of Tw/T0 on heat transfer rates, surface pressure distributions and boundary layer characteristics are studied. The effects of corner angle (&amp / #952 / w) on strong shock wave/boundary layer interactions with extended separated regions are investigated. The obtained results are compared with the available experimental data, computational results, and theory.