This thesis aimed at developing multi-scale models and computational methods for aerother-modynamics applications. The research on multi-scale models has focused on internal energy excitation and dissociation of molecular gases in atmospheric entry flows. The scope was two-fold: to gain insight into the dynamics of internal energy excitation and dissociation in the hydrodynamic regime and to develop reduced models for Computational Fluid Dynamics applications. The reduced models have been constructed by coarsening the resolution of a detailed rovibrational collisional model developed based on ab-initio data for the N2 (1Σ+g)-N (4Su) system provided by the Computational Quantum Chemistry Group at NASA Ames Research Center. Different mechanism reduction techniques have been proposed. Their appli-cation led to the formulation of conventional macroscopic multi-temperature models and vi-brational collisional models, and innovative energy bin models. The accuracy of the reduced models has been assessed by means of a systematic comparison with the predictions of the detailed rovibrational collisional model. Applications considered are inviscid flows behind normal shock waves, within converging-diverging nozzles and around axisymmetric bodies, and viscous flows along the stagnation-line of blunt bodies. The detailed rovibrational colli-sional model and the reduced models have been coupled to two flow solvers developed from scratch in FORTRAN 90 programming language (SHOCKING_F90 and SOLV-ER_FVMCC_F90). The results obtained have shown that the innovative energy bin models are able to reproduce the flow dynamics predicted by the detailed rovibrational collisional model with a noticeable benefit in terms of computing time. The energy bin models are also more accurate than the conventional multi-temperature and vibrational collisional models. The research on computational methods has focused on rarefied flows. The scope was to formu-late a deterministic numerical method for solving the Boltzmann equation in the case of multi-component gases with internal energy by accounting for both elastic and inelastic collisions. The numerical method, based on the weighted convolution structure of the Fourier trans-formed Boltzmann equation, is an extension of an existing spectral-Lagrangian method, valid for a mono-component gas without internal energy. During the development of the method, particular attention has been devoted to ensure the conservation of mass, momentum and en-ergy while evaluating the collision operators. Conservation is enforced through the solution of constrained optimization problems, formulated in a consistent manner with the collisional in-variants. The extended spectral-Lagrangian method has been implemented in a parallel com-putational tool (best; Boltzmann Equation Spectral Solver) written in C programming lan-guage. Applications considered are the time-evolution of an isochoric gaseous system initially set in a non-equilibrium state and the steady flow across a normal shock wave. The accuracy of the proposed numerical method has been assessed by comparing the moments extracted from the velocity distribution function with Direct Simulation Monte Carlo (DSMC) method predictions. In all the cases, an excellent agreement has been found. The computational results obtained for both space homogeneous and space inhomogeneous problems have also shown that the enforcement of conservation is mandatory for obtaining accurate numerical solutions.

During atmospheric entry, a spacecraft's aeroshell uses a thermal protection system (TPS) to withstand severe thermal loads. Heating to the vehicle surface arises as convective, catalytic and radiative heat flux due to the high temperature of the shockwave compressed gases surrounding the aeroshell. The problem for the TPS designer is that the heat load estimates are based on phenomenological models which have questionable validity and, thus, large uncertainty. As an example, recent analyses of heat loads for a proposed aerocapture vehicle designed for Titan differ by up to an order of magnitude. This uncertainty stems from the complexity of the blunt body flow field and the associated physical effects: thermochemical nonequilibrium; ablation and vehicle surface catalycity; and radiating flow. The motivation for this thesis is to develop computational tools that give accurate estimates of vehicle heat transfer as an input for design calculations. With that goal in mind, this thesis work has focussed on one aspect of this problem and that is the modelling of thermochemical nonequilibrium. The longer term goal is to produce tools which can be used to compute the high-temperature, radiating flow fields about aeroshell configurations; the modelling work presented here on thermochemical nonequilibrium effects is a foundation for tackling the radiating flow problem. The modelling work was implemented in an existing flow solver which solves the compressible Navier-Stokes equations with a finite volume method. As part of this work, the flow solver was verified by two methods: the Method of Manufactured Solutions to verify the spatial accuracy for purely supersonic flow; and the Method of Exact Solutions --- the flow problem being an oblique detonation wave --- to verify the spatial accuracy for flows with embedded shocks. Validation of the flow solver, without any of the complexity of thermochemical nonequilibrium, was performed by comparing numerical simulation results to experiments which measured shock detachment on spheres fired into noble gases. A model for chemical nonequilibrium based on the Law of Mass Action and using finite-rate kinetics was coupled with the flow solver. The implementation was verified on two test problems. The first treated a closed-vessel reactor of a hydrogen-iodine mixture, and the second computed the chemically relaxing flow behind a normal shock in air. For validation, the implementation was tested by computing ignition delay times in hydrogen-air mixtures and comparing to experimental results. It was found that the selection of a chemical kinetics scheme can complicate validation, that is, a poor choice of reaction scheme leads to poor computational results yet the implementation is correct. As further validation, a series of experiments on the shock detachment distance on spheres fired into air was compared against numerical simulations based on the present work. Two models for species diffusion were also implemented: Fick's first law approximation and the Stefan-Maxwell equations. These models were verified by comparison to an exact solution for binary diffusion of two semi-infinite slabs. The more general problem of thermochemical nonequilibrium was also pursued. A multi-temperature model, one translational/rotational temperature and multiple vibrational temperatures, was developed as appropriate for hypersonic flows. The model uses the Landau-Teller expression to compute the rate of vibrational-translational energy exchange and the Schwartz-Slawsky-Herzfeld expression for vibrational-vibrational energy exchange. The time constants for the rate expressions are estimated by a number of methods such as the use of SSH theory and the Millikan-White correlation. The coupling of vibrational nonequilibrium effects with the fluid dynamics was tested by computing the flow of nitrogen over an infinite cylinder. The simplified problem of a vibrationally relaxing flow behind a shock, without reactions, was compared to other calculations in the literature. This case tested the multi-temperature formulation, with oxygen and nitrogen each being ascribed their own vibrational temperatures. The coupling of chemistry and vibrational nonequilibrium uses the model by Knab, Fruehauf and Messerschmid. The complete model for thermochemical nonequilibrium was verified by calculating the relaxation of oxygen behind a strong shock. The models developed provide a basis for computing radiating flow fields, however the radiating flow problem cannot be attempted based on this work alone. Instead, a more immediate application of the modelling work was the simulation of expansion tube operation. It is desirable to simulate an impulse facility to give the experimenters access to aspects of experiment that are not directly attainable by experiment; especially a complete characterisation of the test flow properties. The modelling work and code development, as part of this thesis, addresses this need of experimenters. Two large-scale simulations are presented as a demonstration of the modelling work: (a) a simulation of an expansion tube in expansion mode; and (b) a simulation of an expansion tube in nonreflected shock tube mode.

During atmospheric entry, a spacecraft's aeroshell uses a thermal protection system (TPS) to withstand severe thermal loads. Heating to the vehicle surface arises as convective, catalytic and radiative heat flux due to the high temperature of the shockwave compressed gases surrounding the aeroshell. The problem for the TPS designer is that the heat load estimates are based on phenomenological models which have questionable validity and, thus, large uncertainty. As an example, recent analyses of heat loads for a proposed aerocapture vehicle designed for Titan differ by up to an order of magnitude. This uncertainty stems from the complexity of the blunt body flow field and the associated physical effects: thermochemical nonequilibrium; ablation and vehicle surface catalycity; and radiating flow. The motivation for this thesis is to develop computational tools that give accurate estimates of vehicle heat transfer as an input for design calculations. With that goal in mind, this thesis work has focussed on one aspect of this problem and that is the modelling of thermochemical nonequilibrium. The longer term goal is to produce tools which can be used to compute the high-temperature, radiating flow fields about aeroshell configurations; the modelling work presented here on thermochemical nonequilibrium effects is a foundation for tackling the radiating flow problem. The modelling work was implemented in an existing flow solver which solves the compressible Navier-Stokes equations with a finite volume method. As part of this work, the flow solver was verified by two methods: the Method of Manufactured Solutions to verify the spatial accuracy for purely supersonic flow; and the Method of Exact Solutions --- the flow problem being an oblique detonation wave --- to verify the spatial accuracy for flows with embedded shocks. Validation of the flow solver, without any of the complexity of thermochemical nonequilibrium, was performed by comparing numerical simulation results to experiments which measured shock detachment on spheres fired into noble gases. A model for chemical nonequilibrium based on the Law of Mass Action and using finite-rate kinetics was coupled with the flow solver. The implementation was verified on two test problems. The first treated a closed-vessel reactor of a hydrogen-iodine mixture, and the second computed the chemically relaxing flow behind a normal shock in air. For validation, the implementation was tested by computing ignition delay times in hydrogen-air mixtures and comparing to experimental results. It was found that the selection of a chemical kinetics scheme can complicate validation, that is, a poor choice of reaction scheme leads to poor computational results yet the implementation is correct. As further validation, a series of experiments on the shock detachment distance on spheres fired into air was compared against numerical simulations based on the present work. Two models for species diffusion were also implemented: Fick's first law approximation and the Stefan-Maxwell equations. These models were verified by comparison to an exact solution for binary diffusion of two semi-infinite slabs. The more general problem of thermochemical nonequilibrium was also pursued. A multi-temperature model, one translational/rotational temperature and multiple vibrational temperatures, was developed as appropriate for hypersonic flows. The model uses the Landau-Teller expression to compute the rate of vibrational-translational energy exchange and the Schwartz-Slawsky-Herzfeld expression for vibrational-vibrational energy exchange. The time constants for the rate expressions are estimated by a number of methods such as the use of SSH theory and the Millikan-White correlation. The coupling of vibrational nonequilibrium effects with the fluid dynamics was tested by computing the flow of nitrogen over an infinite cylinder. The simplified problem of a vibrationally relaxing flow behind a shock, without reactions, was compared to other calculations in the literature. This case tested the multi-temperature formulation, with oxygen and nitrogen each being ascribed their own vibrational temperatures. The coupling of chemistry and vibrational nonequilibrium uses the model by Knab, Fruehauf and Messerschmid. The complete model for thermochemical nonequilibrium was verified by calculating the relaxation of oxygen behind a strong shock. The models developed provide a basis for computing radiating flow fields, however the radiating flow problem cannot be attempted based on this work alone. Instead, a more immediate application of the modelling work was the simulation of expansion tube operation. It is desirable to simulate an impulse facility to give the experimenters access to aspects of experiment that are not directly attainable by experiment; especially a complete characterisation of the test flow properties. The modelling work and code development, as part of this thesis, addresses this need of experimenters. Two large-scale simulations are presented as a demonstration of the modelling work: (a) a simulation of an expansion tube in expansion mode; and (b) a simulation of an expansion tube in nonreflected shock tube mode.

<div>High speed flow problems of practical interest require a solution of nonequilibrium aerothermochemistry to accurately predict important flow phenomena including surface heat transfer and stresses. As a majority of these flow problems are in the continuum regime, Computational Fluid Dynamics (CFD) is a useful tool for flow modeling. This work presents the development of a nonequilibrium add-on solver to ANSYS Fluent utilizing user-defined-functions to model salient aspects of nonequilibrium flow in air. The developed solver was verified for several benchmark nonequilibrium flow problems and compared with the available experimental data and other nonequilibrium flow simulations. <br></div><div><br></div><div>The rate of dissociation behind a strong shock in thermochemical nonequilibrium depends on the vibrational excitation of molecules. The Macheret-Fridman (MF) classical impulsive model provides analytical expressions for nonequilibrium dissociation rates. The original form of the model was limited to the dissociation of homonuclear molecules. In this work, a general form of the MF model has been derived and present macroscopic rates applicable for modeling dissociation in CFD. Additionally, some improvements to the prediction of mean energy removed in dissociation in the MF-CFD model has been proposed based on the comparisons with available QCT data. In general, the results from the MF-CFD model upon investigating numerous nonequilibrium flows are promising and the model shows a possibility of becoming the standard tool for investigating nonequilibrium flows in CFD.</div><div><br></div><div>The aerodynamic deorbit experiment (ADE) CubeSat has dragsail to accompany accelerated deorbiting of a CubeSat post-mission. A good estimation of the aerothermal load on a reentry CubeSat is paramount to ensure a predictable reentry. This study investigates the aerothermal load on an ADE CubeSat using the direct simulation Monte Carlo (DSMC) methods and Navier-Stokes-Fourier continuum based methods with slip boundary conditions. The aerothermal load on an ADE CubeSat at 90 km altitude from the DSMC and continuum methods were consistent with each other. The continuum breakdown at a higher altitude of 95 km resulted in a strong disagreement between the continuum and DSMC solutions. Overall, the continuum methods could offer a considerable computational cost saving to the DSMC methods in predicting aerothermal load on an ADE CubeSat at low altitudes.<br> </div>

Cette thèse porte sur le développement de modèles multi-échelles et de méthodes de calcul pour les applications aérothermodynamiques. Le travail de recherche sur les modèles multi-échelles met l’accent sur l’excitation énergétique et la dissociation. L’objectif était double : mieux comprendre la dynamique des processus d'excitation énergétique et dissociation et développer des modèles réduits en diminuant la résolution d’un modèle détaillé de collisions rovibrationnelles. Les résultats obtenus ont montré que les modèles réduits permettent de reproduire avec précision la dynamique d’écoulement prédites par le modèle détaillé de collisions rovibrationnelles. Le travail de recherche sur les méthodes de calcul a porté sur les écoulements raréfiés. L’objectif était de formuler une méthode numérique de type déterministe pour résoudre l’équation de Boltzmann dans le cas de gaz à plusieurs composants y compris l’énergie interne. La méthode numérique est basée sur la structure de convolution pondérée de la transformée de Fourier de l’équation de Boltzmann. La précision de la méthode numérique proposée a été évaluée en comparant les moments extraits de la fonction de distribution de vitesse avec les prédictions de la méthode de simulation directe Monte Carlo (DSMC). Dans toutes les applications étudiées, un excellent accord a été trouvé. / This thesis aimed at developing multi-scale models and computational methods for aerother-modynamics applications. The research on multi-scale models has focused on internal energy excitation and dissociation of molecular gases in atmospheric entry flows. The scope was two-fold: to gain insight into the dynamics of internal energy excitation and dissociation in the hydrodynamic regime and to develop reduced models for Computational Fluid Dynamics applications. The reduced models have been constructed by coarsening the resolution of a detailed rovibrational collisional model developed based on ab-initio data for the N2 (1Σ+g)-N (4Su) system provided by the Computational Quantum Chemistry Group at NASA Ames Research Center. Different mechanism reduction techniques have been proposed. Their appli-cation led to the formulation of conventional macroscopic multi-temperature models and vi-brational collisional models, and innovative energy bin models. The accuracy of the reduced models has been assessed by means of a systematic comparison with the predictions of the detailed rovibrational collisional model. Applications considered are inviscid flows behind normal shock waves, within converging-diverging nozzles and around axisymmetric bodies, and viscous flows along the stagnation-line of blunt bodies. The detailed rovibrational colli-sional model and the reduced models have been coupled to two flow solvers developed from scratch in FORTRAN 90 programming language (SHOCKING_F90 and SOLV-ER_FVMCC_F90). The results obtained have shown that the innovative energy bin models are able to reproduce the flow dynamics predicted by the detailed rovibrational collisional model with a noticeable benefit in terms of computing time. The energy bin models are also more accurate than the conventional multi-temperature and vibrational collisional models. The research on computational methods has focused on rarefied flows. The scope was to formu-late a deterministic numerical method for solving the Boltzmann equation in the case of multi-component gases with internal energy by accounting for both elastic and inelastic collisions. The numerical method, based on the weighted convolution structure of the Fourier trans-formed Boltzmann equation, is an extension of an existing spectral-Lagrangian method, valid for a mono-component gas without internal energy. During the development of the method, particular attention has been devoted to ensure the conservation of mass, momentum and en-ergy while evaluating the collision operators. Conservation is enforced through the solution of constrained optimization problems, formulated in a consistent manner with the collisional in-variants. The extended spectral-Lagrangian method has been implemented in a parallel com-putational tool (best; Boltzmann Equation Spectral Solver) written in C programming lan-guage. Applications considered are the time-evolution of an isochoric gaseous system initially set in a non-equilibrium state and the steady flow across a normal shock wave. The accuracy of the proposed numerical method has been assessed by comparing the moments extracted from the velocity distribution function with Direct Simulation Monte Carlo (DSMC) method predictions. In all the cases, an excellent agreement has been found. The computational results obtained for both space homogeneous and space inhomogeneous problems have also shown that the enforcement of conservation is mandatory for obtaining accurate numerical solutions.