Cryogenic propellants are going to be the cornerstone for effective future human space exploration. These propellants need to be stored and maintained at really low temperatures for a long duration. Accurate phase change modeling is necessary for characterizing the thermal state of future cryogenic propellant tanks and for designing systems to alleviate the self pressurization problem. Better understanding about how to properly store and manage cryogenic propellants would help greatly with In-Situ Resource Utilization (ISRU) strategies for future missions to Mars and further. Predicting the fluid flow, heat transfer, and phase change mass transfer in long term cryogenic storage using CFD models is greatly affected by our understanding of the accommodation coefficient. The kinetically limited phase change model governed by the Hertz-Knudsen-Schrage equation is the model of choice for such calculations. The value of the accommodation coefficient required for the model is unknown for cryogenic propellants. Even in the case of water, the value of the accommodation coefficient has been found to vary over three orders of magnitude based on 80 years of measurements. Experiments specifically built to study accommodation coefficient are needed to estimate the value of the accommodation coefficient and understand some of the uncertainties surrounding these models. <div><br></div><div>Two phase change models, viz. the thermally limited and the kinetically limited phase change model are implemented in OpenFOAM. Different approaches to implement the Hertz-Knudsen-Schrage equation in a sharp interface conjugate heat transfer solver are studied. Evaporation and condensation calculations for a liquid hydrogen meniscus inside an aluminum container are compared with experimental measurements. The effect of accommodation coefficient on phase change is then studied with the kinetically limited model by comparing with the thermally limited model and the experimental measurements. The uncertainties associated with the temperature and pressure measurements in the experiment are quantified to show their effect on computational predictions. Since cryogenic propellants are perfectly wetting fluids, modeling the thin-film region close to the contact line leads to a multi-scale computational problem. However, the phase change contribution from the thin-film region is approximated in these computations to show the importance of modeling the contact line region accurately to adequately capture the small local thermodynamics in that region.</div>

In most applications concerning a fluid flowing over a solid surface, the no-slip velocity condition was widely used because it is simple and produces the results in agreement with experiments. However, this dynamical boundary condition is not appropriate when the flow under consideration is at a micro or nano length scale.In order to model this effect at the macroscopic scale, the Navier boundary conditions have been introduced, with the slip length as a parameter. When the fluid is a gas, this length is related to the tangential momentum accommodation coefficient (TMAC) and the mean free path, according to the Maxwell model. The aim of this work is to systematically address this model using a multi-scale approach and to extend it by incorporating both the morphology and the anisotropy of a surface. The thesis consists of five chapters. In Chapter 1, the basics of the kinetic theory of gases, the Boltzmann equation and related solutions (Navier-Stokes-Fourier, Burnett, Grad, Direct Simulation Monte Carlo ...) are briefly presented. The models of gas-wall interaction and slip models introduced in the fluid mechanics are also recalled. The chapter ends with a description of the computational method used for the molecular dynamics simulations performed in this work. Chapter 2 is dedicated to the development of a simple technique to simulate the pressure driven flows. The principle is to rely on the atomistic formulas of the stress tensor (Irving Kirkwood, Method of Plane, Virial Stress) and to modify the periodic conditions by maintaining the difference between the kinetic energy of the ingoing and outgoing particles of the simulation domain. Several types of channels are studied with this technique. The results (temperature, velocity ...) are discussed and compared. Chapter 3 deals with the study of the gas-wall interaction potential by the ab-initio method. The code CRYSTAL 09 is used to obtain the potential between an atom of argon (Ar) and a surface of platinum (Pt) <111> as a function of distance. Then the gas-wall potential is decomposed into binary potential and approached by an analytic function. This function is then implemented in a MD code to simulate the gas-wall collisions and determine the TMAC coefficient. In Chapter 4, the effect of morphology is studied. The multi-body Quantum Sutton Chen (QSC) potential is used for Pt <100> solid and the binary potential proposed in the previous chapter for the Ar-Pt couple is employed. The QSC potential is needed to reproduce the surface effects that affect the final results. Different surfaces are treated : smooth, nanostructured surface and, random surface obtained by Chemical vapor deposition (CVD). The TMAC is determined using a generalized approach, i.e. depending on the angle of incident flux of gas atoms on the surface. The surface anisotropy and the scattering kernel are also examined. In Chapter 5, we propose a model of anisotropic slip for fluids based on accommodation tensor. The model is obtained by the analytical approximate calculations developed in the framework of the kinetic theory. We thus generalize Maxwell's equation by showing that the slip length tensor is directly related to the accommodation tensor. The model is in good agreement with the MD results. Thanks to our MD simulations, we develop a suitable technique for reproducing the anisotropy of the accommodation tensor. The thesis ends with a conclusion section in which we suggest some perspectives for a continuation of this work

Dans la plupart des applications concernant un fluide s'écoulant sur une surface solide, la condition de non-glissement est largement utilisée car elle est simple et produit des résultats en accord avec les expériences. Toutefois, cette condition de limite n'est plus appropriée lorsque l'écoulement considéré est à l'échelle micro ou nano-métrique. Pour modéliser cet effet à l'échelle macroscopique, les conditions aux limites de Navier ont été introduites, avec la longueur de glissement comme paramètre. Lorsque le fluide est un gaz, cette longueur est liée au coefficient d'accommodation tangentiel (TMAC) et au libre parcours moyen, selon le modèle de Maxwell. Le but de ce travail est de traiter systématiquement ce modèle par une approche multi échelle et de l'étendre en incorporant la morphologie et l'anisotropie de la surface. La thèse est composée de cinq chapitres. Après l'Introduction, les notions de base de la théorie cinétique des gaz, l'équation de Boltzmann et les solutions associées (Navier-Stokes-Fourier, Burnett, Grad, Direct Simulation Monte Carlo…) sont rappelées dans le chapitre 1. Les modèles d'interaction gaz-paroi ainsi que les modèles de glissement introduits dans le cadre le la mécanique des fluides sont aussi rappelés. Le chapitre se termine par la description de la méthode de calcul par dynamique moléculaire (MD) utilisée dans ce travail. Le chapitre 2 est dédié au développement d'une technique simple afin de simuler les écoulements induits par la pression. Le principe est de se baser sur les formules atomistiques du tenseur des contraintes (Irving Kirkwood, Méthode de Plan, Contraintes Virielles) et de modifier les conditions périodiques, tout en maintenant la différence entre l'énergie cinétique des atomes à l'entrée et à sortie du domaine de calcul. Plusieurs types de conduite sont étudiés avec cette technique. Les résultats (température, vitesses, …) sont discutés et comparés. Le chapitre 3 concerne l'étude du potentiel d'interaction gaz-paroi par la méthode ab-initio. Le code CRYSTAL 09 est utilisé pour obtenir le potentiel entre un atome d'argon (Ar) et une surface de platine (Pt) <111> en fonction de la distance. Ensuite, le potentiel atome/surface est décomposé en potentiel binaire et approché par une fonction analytique. Cette fonction est ensuite implémentée dans un code MD pour simuler les collisions gaz-paroi et déterminer le coefficient TMAC.Dans le chapitre 4, l'effet de morphologie est étudié. Le potentiel multi-corps Quantum Sutton Chen(QSC) est utilisé pour le solide Pt <100> et un des potentiels binaires étudié dans le chapitre précédent pour le couple Ar-Pt. Le potentiel QSC est nécessaire pour reproduire l'effet de surface qui affecte le résultat final. Différentes surfaces sont traitées : surface lisse, surface nanostructurée, surface aléatoire obtenue par déposition de vapeur (CVD). Le coefficient TMAC est déterminé de façon généralisée, c.à.d en fonction de l'angle du flux d'atomes incidents sur la surface. Les anisotropies de surface et le noyau de collision sont également examinés. Dans le chapitre 5, on propose un modèle de glissement anisotrope pour les fluides en fonction du tenseur d'accommodation. Le modèle est obtenu par les calculs analytiques approchés développés dans le cadre de la théorie cinétique. On a ainsi généralisé l'équation de Maxwell en montrant que le tenseur de longueur de glissement est directement lié au tenseur d'accommodation. Le modèle est en bon accord avec les résultats de la méthode MD. Concernant la simulation MD, on a développé une technique pour reproduire l'anisotropie du tenseur d'accommodation. Le mémoire de thèse se termine par une synthèse des résultats obtenus. Des perspectives pour de futures études sont proposées / In most applications concerning a fluid flowing over a solid surface, the no-slip velocity condition was widely used because it is simple and produces the results in agreement with experiments. However, this dynamical boundary condition is not appropriate when the flow under consideration is at a micro or nano length scale.In order to model this effect at the macroscopic scale, the Navier boundary conditions have been introduced, with the slip length as a parameter. When the fluid is a gas, this length is related to the tangential momentum accommodation coefficient (TMAC) and the mean free path, according to the Maxwell model. The aim of this work is to systematically address this model using a multi-scale approach and to extend it by incorporating both the morphology and the anisotropy of a surface. The thesis consists of five chapters. In Chapter 1, the basics of the kinetic theory of gases, the Boltzmann equation and related solutions (Navier-Stokes-Fourier, Burnett, Grad, Direct Simulation Monte Carlo ...) are briefly presented. The models of gas-wall interaction and slip models introduced in the fluid mechanics are also recalled. The chapter ends with a description of the computational method used for the molecular dynamics simulations performed in this work. Chapter 2 is dedicated to the development of a simple technique to simulate the pressure driven flows. The principle is to rely on the atomistic formulas of the stress tensor (Irving Kirkwood, Method of Plane, Virial Stress) and to modify the periodic conditions by maintaining the difference between the kinetic energy of the ingoing and outgoing particles of the simulation domain. Several types of channels are studied with this technique. The results (temperature, velocity ...) are discussed and compared. Chapter 3 deals with the study of the gas-wall interaction potential by the ab-initio method. The code CRYSTAL 09 is used to obtain the potential between an atom of argon (Ar) and a surface of platinum (Pt) <111> as a function of distance. Then the gas-wall potential is decomposed into binary potential and approached by an analytic function. This function is then implemented in a MD code to simulate the gas-wall collisions and determine the TMAC coefficient. In Chapter 4, the effect of morphology is studied. The multi-body Quantum Sutton Chen (QSC) potential is used for Pt <100> solid and the binary potential proposed in the previous chapter for the Ar-Pt couple is employed. The QSC potential is needed to reproduce the surface effects that affect the final results. Different surfaces are treated : smooth, nanostructured surface and, random surface obtained by Chemical vapor deposition (CVD). The TMAC is determined using a generalized approach, i.e. depending on the angle of incident flux of gas atoms on the surface. The surface anisotropy and the scattering kernel are also examined. In Chapter 5, we propose a model of anisotropic slip for fluids based on accommodation tensor. The model is obtained by the analytical approximate calculations developed in the framework of the kinetic theory. We thus generalize Maxwell's equation by showing that the slip length tensor is directly related to the accommodation tensor. The model is in good agreement with the MD results. Thanks to our MD simulations, we develop a suitable technique for reproducing the anisotropy of the accommodation tensor. The thesis ends with a conclusion section in which we suggest some perspectives for a continuation of this work