The prediction of transient phenomena inside Liquid Rocket Engines (LREs) has not been feasible until now because of the many challenges posed by the operating conditions inside the combustion chamber. Especially, the departure from ideal gas because of the cryogenic injection in a high-pressure chamber is one of the ma jor hurdle for such simula- tions. In order to begin addressing these issue, a real-gas model has been implemented in a massively parallel flow solver. This solver is capable of performing Large-Eddy Simula- tions (LES) in geometrical configurations ranging from an axisymmetric slice to a 3D slice up to a full 3D combustor. We present here the results from an investigation of unsteady combustion inside a small-scale, multi-injectors LRE. Both thermally perfect gas (TPG) and real gas (RG) approaches are evaluated for this LOX-GH2 system. The Peng-Robinson cubic equation of state (PR EoS) is used to account for real gas effects associated with the injection of cryogenic oxygen. Realistic transport properties are computed but simplified chemistry is used in order to achieve a reasonable turnaround time. Results show the impor- tance of the unsteady dynamics of the flow, especially the interaction between the different injectors. The role of the equation of state is assessed and the real gas model, despite a limited zone of application, seems to have a strong influence on the overall chamber behav- ior. Although several features in the simulated results agree well with past experimental observations, the prediction of heat flux using a simplified flux boundary condition is not completely satisfactory. This work also reviews in details the state of our knowledge on supercritical combustion in a coaxial injector configuration, stressing issues where numeri- cal modeling could provide new insights. However, many developments and improvements are required before an LES modeling of such a flow is both feasible and valid. We finally propose a comprehensive roadmap towards the completion of this goal and the possible use of CFD as a design tool for a modern liquid rocket engine.

L’allumage est un point essentiel dans le dimensionnement des moteurs-fusées, et il nécessite de prendre en compte plusieurs phénomènes physiques très distincts qui sont autant de challenges numériques. Le premier point abordé pendant cette thèse est la modélisation et la simulation par Simulation aux Grandes Échelles d’un allumeur de type VINCI. Des gaz chauds, riches en oxygène, sont délivrés de façon supersonique dans une chambre remplie d’hydrogène faisant apparaître un jet fortement sous-détendu et de multiples interactions choc/choc ou choc/flamme. Les premiers instants du processus d’allumage sont ici détaillés. Le second point abordé est la modélisation et la simulation numérique de la combustion H2/O2 à haute pression. En particulier, les effets d’une diffusion non-idéale sont étudiés dans le cas de flammes de prémélange 1D et sur la configuration 2D de type ‘splitter plate’. Un impact de la modélisation sur les espèces produites et le champ de température est ici mis en lumière. / Ignition is a key point in the design of liquid rocket engine (LRE), and it requires to take into account several distinct physical phenomena that constitute numerical challenges. The first point addressed during this thesis is the modeling and simulation using Large Eddy Simulation of a LRE igniter in a configuration close to VINCI rocket engine. The hot gases from the igniter, rich in oxygen, are delivered at supersonic speeds in a chamber filled with hydrogen. Such configuration creates under-expanded jets with multiple shock/shock or shock/flame interactions. A focus is done on the ignition process. The second point addressed is the modeling and simulation of high pressure H2/O2 combustion which occurs. In particular, the effects of non-ideal diffusion are studied through a 1D premixed flames and a 2D splitter plate configuration. An impact of modeling on the species produced and the temperature field is highlighted.

Certaines missions d'astrophysique embarquent des détecteurs infrarouges ou X qui sont refroidis à des températures subkelvin via un système cryogénique qui comporte soit un bain d'hélium (comme pour Herschel), soit un réfrigérateur Joule-Thomson (comme pour Planck) pour le pré-refroidissement de l'étage subkelvin. Un doigt froid à tube à gaz pulsé ayant les mêmes performances qu'un Joule-Thomson pourrait offrir un certain nombre d'avantages pour les futures chaines cryogéniques (pas de pré-refroidissement nécessaire, simplicité d'intégration, fiabilité accrue).L'objectif de cette thèse concerne l'étude et la réalisation d'un doigt froid à tube à gaz pulsé 4K qui pourrait remplacer une machine Joule-Thomson. Deux principaux axes d'étude ont été menés parallèlement : des études sur les matériaux régénérateur et des études de performances. Des développements technologiques portant sur le régénérateur (étude et mise en forme de différents matériaux ayant des anomalies de chaleur spécifique à basse température) ont été menés afin d'améliorer les performances d'un doigt froid à tube à gaz pulsé haute fréquence (30Hz) travaillant avec de l'hélium 4.Cette thèse a permis d'obtenir la meilleure performance mondiale en terme de température limite en utilisant de l'hélium 4 et avec un pré-refroidissement à 20K. Une température limite de 3,86K a été obtenue et une puissance froide de 25mW est disponible à 5K. Cette thèse a également permis d'étudier l'effet du gaz réel sur le comportement de la machine, en particulier grâce à des mesures de profils de température du régénérateur. Cinq configurations différentes de régénérateur (variation de la répartition de chaleur spécifique le long du régénérateur froid) ont été testées. Elles ont permis de mieux comprendre le rôle de la répartition de la chaleur spécifique dans le régénérateur. Ces différentes mesures ont été complétées avec des études de fluctuations de températures pariétales réalisées à l'aide d'une centrale d'acquisition rapide (toutes les millisecondes). / Some astrophysics missions embark infrared or X detectors which are cooled down to subkelvin temperatures using a cryogenic cooling system that features helium bath (like for the Herschel satellite) or a Joule-Thomson cryocooler (like for the Planck satellite) for the precooling of the subkelvin cooling stage. A pulse tube cold finger which would have the same performances as a Joule-Thomson cryocooler could offer some advantages for future cryogenic chains (no need of precooling, simplicity of integration, increased reliability).The goal of this PhD is the making and the study of a pulse tube cold finger working at temperature around 4K which could replace a Joule-Thomson cryocooler. Two main lines have been worked on simultaneously : studies on materials for the cold regenerator and studies on the cold finger performances. Technological developments on the cold regenerator (including study and shaping of different materials with specific heat anomalies at low temperature) have been performed to enhance the performances of a cold finger working at high frequency (30Hz) with helium 4.The work done during this PhD led to the best no-load temperature never achieved using helium 4 and with a precooling of 20K. A no-load temperature of 3.86K has been obtained and 25mW of cooling power are available at 5K. In addition the effect of real gas on the cryorefrigerator operation has been studied in particular thanks to the measurement of regenerator thermal profiles. Five configurations with different regenerator fillings (variation of the distribution of the specific heat along the cold regenerator) have been tested. These five tests led to a better understanding of the role of the distribution of the specific heat in the regenerator. These measurements have been completed with studies of regenerator wall temperature fluctuations recorded thanks to a fast data acquisition system (each millisecond).

A combined experimental and numerical study of multidimensional viscous flows at speeds exceeding 8 km/s is reported. Experiments were performed in the X3 superorbital expansion tube with air and nitrogen test flows at a Mach number and total enthalpy of 10 and 40 MJ/kg, respectively. Laminar skin friction, heat flux and pressure measurements were obtained at regular intervals along one wall of a rectangular duct. The spatial resolution of the transducers was chosen to capture the multidimensional flow phenomena within the duct. Quasi-steady flow periods were established along the entire length of the duct in the test times offered by the expansion tube. Direct skin friction measurements were accomplished through the use of ‘in house’ acceleration compensated transducers. The successful operation of these skin friction transducers in a high performance expansion tube was demonstrated. Furthermore, the systematic uncertainty in measured shear stress was significantly reduced with the development of a new pressure calibration technique. For the conditions tested, Reynolds analogy was shown to be valid to within experimental uncertainty. The experimental data was in excellent agreement with numerical estimates. Three-dimensional numerical simulations of the diverging duct revealed that the flowfield structure in the vicinity of the corners differs from that of an unbounded corner or a constant area duct. Real gas effects other than those present in the residual nonequilibrium levels of freestream dissociation were negligible for the conditions tested. A computational study of two waverider configurations recently tested in the X3 superorbital expansion tube was conducted to assist in the interpretation of past results. The off-design aerodynamic performance was also analyzed and showed that blunting the leading edges dramatically degraded the performance by increasing drag and decreasing lift for the conditions considered.

A combined experimental and numerical study of multidimensional viscous flows at speeds exceeding 8 km/s is reported. Experiments were performed in the X3 superorbital expansion tube with air and nitrogen test flows at a Mach number and total enthalpy of 10 and 40 MJ/kg, respectively. Laminar skin friction, heat flux and pressure measurements were obtained at regular intervals along one wall of a rectangular duct. The spatial resolution of the transducers was chosen to capture the multidimensional flow phenomena within the duct. Quasi-steady flow periods were established along the entire length of the duct in the test times offered by the expansion tube. Direct skin friction measurements were accomplished through the use of ‘in house’ acceleration compensated transducers. The successful operation of these skin friction transducers in a high performance expansion tube was demonstrated. Furthermore, the systematic uncertainty in measured shear stress was significantly reduced with the development of a new pressure calibration technique. For the conditions tested, Reynolds analogy was shown to be valid to within experimental uncertainty. The experimental data was in excellent agreement with numerical estimates. Three-dimensional numerical simulations of the diverging duct revealed that the flowfield structure in the vicinity of the corners differs from that of an unbounded corner or a constant area duct. Real gas effects other than those present in the residual nonequilibrium levels of freestream dissociation were negligible for the conditions tested. A computational study of two waverider configurations recently tested in the X3 superorbital expansion tube was conducted to assist in the interpretation of past results. The off-design aerodynamic performance was also analyzed and showed that blunting the leading edges dramatically degraded the performance by increasing drag and decreasing lift for the conditions considered.

A combined experimental and numerical study of multidimensional viscous flows at speeds exceeding 8 km/s is reported. Experiments were performed in the X3 superorbital expansion tube with air and nitrogen test flows at a Mach number and total enthalpy of 10 and 40 MJ/kg, respectively. Laminar skin friction, heat flux and pressure measurements were obtained at regular intervals along one wall of a rectangular duct. The spatial resolution of the transducers was chosen to capture the multidimensional flow phenomena within the duct. Quasi-steady flow periods were established along the entire length of the duct in the test times offered by the expansion tube. Direct skin friction measurements were accomplished through the use of ‘in house’ acceleration compensated transducers. The successful operation of these skin friction transducers in a high performance expansion tube was demonstrated. Furthermore, the systematic uncertainty in measured shear stress was significantly reduced with the development of a new pressure calibration technique. For the conditions tested, Reynolds analogy was shown to be valid to within experimental uncertainty. The experimental data was in excellent agreement with numerical estimates. Three-dimensional numerical simulations of the diverging duct revealed that the flowfield structure in the vicinity of the corners differs from that of an unbounded corner or a constant area duct. Real gas effects other than those present in the residual nonequilibrium levels of freestream dissociation were negligible for the conditions tested. A computational study of two waverider configurations recently tested in the X3 superorbital expansion tube was conducted to assist in the interpretation of past results. The off-design aerodynamic performance was also analyzed and showed that blunting the leading edges dramatically degraded the performance by increasing drag and decreasing lift for the conditions considered.

A combined experimental and numerical study of multidimensional viscous flows at speeds exceeding 8 km/s is reported. Experiments were performed in the X3 superorbital expansion tube with air and nitrogen test flows at a Mach number and total enthalpy of 10 and 40 MJ/kg, respectively. Laminar skin friction, heat flux and pressure measurements were obtained at regular intervals along one wall of a rectangular duct. The spatial resolution of the transducers was chosen to capture the multidimensional flow phenomena within the duct. Quasi-steady flow periods were established along the entire length of the duct in the test times offered by the expansion tube. Direct skin friction measurements were accomplished through the use of ‘in house’ acceleration compensated transducers. The successful operation of these skin friction transducers in a high performance expansion tube was demonstrated. Furthermore, the systematic uncertainty in measured shear stress was significantly reduced with the development of a new pressure calibration technique. For the conditions tested, Reynolds analogy was shown to be valid to within experimental uncertainty. The experimental data was in excellent agreement with numerical estimates. Three-dimensional numerical simulations of the diverging duct revealed that the flowfield structure in the vicinity of the corners differs from that of an unbounded corner or a constant area duct. Real gas effects other than those present in the residual nonequilibrium levels of freestream dissociation were negligible for the conditions tested. A computational study of two waverider configurations recently tested in the X3 superorbital expansion tube was conducted to assist in the interpretation of past results. The off-design aerodynamic performance was also analyzed and showed that blunting the leading edges dramatically degraded the performance by increasing drag and decreasing lift for the conditions considered.

Ce travail de recherche s’intéresse au problème de la stabilisation de flammes, et du transfert de chaleur résultant, dans les moteurs fusées cryogéniques. La stabilisation de flamme dans un moteur fusée est un phénomène critique, et toute instabilité peut conduire à des dégâts importants, voire à la destruction du lanceur et des satellites embarqués. Les moteurs (Vulcain 2 et Vinci) qui équipent Ariane 5, et la future Ariane 6, utilisent le couple hydrogène / oxygène, dont la grande impulsion spécifique permet, en minimisant la masse des ergols par rapport à la masse de la charge, une meilleure performance du lanceur. Pour réduire le volume de stockage, les ergols sont refroidis à des températures très basses de l’ordre de quelques dizaines de Kelvin. Ils alimentent une flamme dont la température maximale peut atteindre 3500K, générant de très forts gradients de température dans le fluide, et des flux de chaleur extrêmes dans les parties solides de l’injecteur. Pour prédire les flux de chaleur entre la flamme, l’injecteur et les ergols froids, l’approche de Simulation aux Grandes Echelles (SGE), pour reproduire l’écoulement réactif turbulent instationnaire, est couplée au calcul de thermique du solide dans l’injecteur. Cette approche est d’abord validée par comparaison à une expérience en conditions ambiantes, menée au Laboratoire EM2C (Paris). L’interaction flamme-paroi en présence de transfert de chaleur, qui est un mécanisme de base de la stabilisation de flamme, est ensuite étudiée pour différents niveaux de pression. Finalement une configuration représentative d’un injecteur coaxial de moteur fusée est simulée pour étudier la structure et les mécanismes de stabilisation de la flamme, ainsi que les flux de chaleur reçus par l’injecteur, en vue d’évaluer la fatigue thermique du système. / This research work deals with the problem of the flame stabilization in the context of high pressure liquid rocket engines. Flame stabilization in a rocket engine is a critical feature. An instability can lead to important damages of the engine or the destruction of the launcher and the satellite. The engines (Vulcain 2 and Vinci) of the Ariane 5, and the future Ariane 6, use the hydrogen/oxygen propellants. One characteristic of this couple is its high specific impulse. The launcher performance is linked to the ratio of the payload to the total mass of propellants. For volume reasons the propellants are stored at low temperature of the order of a few tens of Kelvin. When injected in the combustion chamber, their combustion releases a huge amount of heat leading to temperature of 3500K. In order to predict the heat transfer between the flame, the solid injector and the cold propellants the Large Eddy Simulation, which allows to capture the unsteady features of the flow, is used in association with a thermal solver for the injector. This approach is validated with a low pressure experiment conducted at Centrale Paris, then a basic 1D configuration allows to understand the phenomena of high pressure flame-wall interaction. Finally a configuration representative of a coaxial rocket engine injector allows to evaluate the structure and the stabilization mechanisms of a cryogenic flame, the heat flux and the temperature of the injector.

Mass flow models for gaseous media describe the relationship between gas flow through throttle elements depending on pressure, temperature and type of medium. These models are used to calculate pneumatic components, to simulate pneumatic systems or to plan facilities. The known flow models are verified for ideal gases, such those as according to ISO 6358-1 (International Standard ISO 6358- 1: pneumatic fluid power – Determination of flow-rate characteristics of components using compressible fluids: General rules and test methods for steady-state flow, 2013). But they fail with real gases, especially at higher pressures. The objective of this contribution is to recommend a simple-touse model for the mass flow calculation of real gases. The advantage of the C and b model is the use of only two parameters. A testbench for high pressure up to 300 bar was used for model verification with air and hydrogen. The Library for standard dry air and hydrogen up to 1000 bar was used for the state variables of the real gases. The parameters C and b are obtained, applied and verified in the state space of real gas. With the C and b parameter it is possible to simulate not only the single component (valve, throttle, nozzle and so on) but also the whole system with a complete system simulation, like such as hydrogen filling stations.

Au cours de l’utilisation de certains systèmes propulsifs, tels que les moteurs fusées cryotechniques ou les moteurs Diesel, le point de fonctionnement peut varier sur une large plage de pressions. Ces variations de pression peuvent conduire à un changement de régime thermodynamique si la pression critique du fluide est franchie, l’injection initialement diphasique devenant alors transcritique. Ce changement modifie la topologie de l’écoulement, ainsi que la dynamique du mélange, ce qui impacte le comportement de la flamme. L’objectif de cette thèse est de développer une méthodologie originale capable de traiter au sein du même solveur des écoulements sous-critiques ainsi que supercritiques. Pour cela, une extension du solveur AVBP-RG aux écoulements diphasiques sous-critiques est proposée, basée sur des modèles d’interface diffuse. Les développements nécessaires à l’intégration de ces modèles dans le cadre du solveur aux éléments finis sont effectués. Des simulations numériques multidimensionnelles sont ensuite proposées de manière à confronter le modèle à des données exprérimentales, vis-à-vis desquelles un bon accord est observé. Cesrésultats offrent des perspectives encourageantes vers de futures améliorations du modèle et des applications à des configurations industrielles complexes. / In various industrial combustion devices, such as liquid rocket engines at ignition or Diesel engines during the compression stage, the operating point varies over a wide range of pressures. These pressure variations can lead to a change of thermodynamic regime when the critical pressure is exceeded, switching from two-phase injection to transcritical injection. This change modifies the topology of the flow and the mixing, thereby impacting the flame dynamics. The objective of the present Ph.D thesis is to develop an original methodology able to address both subcritical and supercritical flows within the same solver. To achieve this, an extension of the real gas solver AVBP-RG to subcritical two-phase flows is provided, based on diffuse interface models. The required developments for the integration of such models into the finite-element framework of the solver are provided. Multidimensional numerical simulations are led in order to confront the model with experimental data, with which good agreement is observed. These results offer encouraging perspectives regarding further enhancements of the model and applications to complex industrial cases.