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1 Contents Nomenclature xiii 1. Introduction Objectives of this Thesis Outline Test Configurations and Literature Review Cooling Gas Injection Motivation LiteratureReview TestConfiguration Edney Type IV and Type VII Shock-Shock Interaction Motivation LiteratureReview TestConfiguration Physical and Mathematical Modeling FlowRegimes FlowEquations Nonequilibrium Gas Models ClassificationofGases EnergyModes Practical Use of Nonequilibrium Modes Overview RelaxationCharacteristics Equilibrium Assumptions for Practical Usage Mathematical Modeling of Nonequilibrium Models in QUADFLOW MixtureProperties TransportProperties Viscosity(MomentumTransport) ViscousStressTensor Sutherland s Law BlottnerViscosityModel ViscosityCurveFit vii

2 Wilke s Semi-Empirical Mixing Rule Diffusion(MassTransport) Fick slaw BinaryDiffusionCurveFit Conduction (Energy Transport) HeatFlux Thermal Conductivity Chemical Nonequilibrium Model Chemical Nonequilibrium ReactionKinetics ChemicalSourceTerm ForwardReactionRates Equilibrium Constant BackwardReactionRates ConservationofChemicalElements Computation of the Equilibrium Constant Thermal Nonequilibrium Models Overview Vibrational-Translational Energy Exchange Ω VT (VT) Millikan and White (VT.1) KlomfaßCurveFit(VT.2) Vibrational-Vibrational Energy Exchange Ω VV (VV) KlomfaßCurveFit(VV.1) Candler (VV.2) Vibration-Dissociation Coupling (VD) Park Average Temperature Model (VD.1) Coupled Vibration Dissociation Vibration Model (VD.2) Numerical Methods Overview:QUADFLOWsolver GridGeneration GridAdaptation Finite Volume Discretization DiscretizationofFluxes InviscidFluxes ViscousFluxes Boundary Conditions Wall Symmetry Subsonic Injection Far-field viii

3 4.6. TimeIntegration Explicit Method Explicit-Implicit Method Implicit Method CFLEvolutionandConvergenceCriteria Model Validation and Evaluation ThermodynamicProperties CalculationMethod Validation of Results Evaluation of the Park CO 2 Model TransportProperties CalculationMethod Validation of Results Equilibrium Constant CalculationMethod Validation and Evaluation of Results RelaxationofaClosedSystem SimulationMethod Chemical Equilibrium Composition AirModel Additional Reaction Models Thermal Equilibrium State Relaxation Behind Shock Waves SimulationMethod AirModel Air Model: Energy Exchange and Coupling Models AirModel:TemperatureModels Simulation of Air with Jachimowski Model Validation of the QUADFLOW solver Chemical and Thermochemical Nonequilibrium Flow over a Cylinder ProblemSetup GridConvergenceandGridAdaptation EfficientSolutionStrategy FlowField StagnationLine WallQuantities Comparison of Chemical and Thermochemical Nonequilibrium Thermochemical Nonequilibrium Flow over a Cylinder (Hornung) ProblemSetup ix

4 ComparisonofResults NozzleFlow ProblemSetup Results Cooling Gas Injection Theoretical Description of the Cooling Gas Injection Validation of Boundary Layer Flows Computational Setup ResultsandDiscussion ExperimentalTestCase Computational Setup ResultsandDiscussion GridAdaptationandEfficiency Modeled vs. Simulated Injection MixingProcesses InfluenceofDifferentCoolants Edney Type IV and VII Interaction Experimental Test Case of Edney Type IV Interaction Computational Setup Nitrogen Flow: Edney Type IV Interaction Grid Adaptation and Dependency w.r.t. Space and Time Dependency of the Unsteady Mechanism w.r.t. Spatial Order FlowField WallQuantities Logarithmic Temperature Model Martian Atmosphere: Edney Type VII Interaction GridAdaptationandDependency FlowField WallQuantities Conclusion and Outlook 183 Bibliography 187 Appendix 199 A. Nondimensional Coefficients 199 A.1.SkinFriction A.2.StantonNumber B. Physical Constants and Model Parameters 201 x

5 B.1. Thermodynamic Properties of Flows in Thermal Nonequilibrium B.1.1. Energy Models: Translational and Rotational Energy Models B.1.2. EnergyModels:VibrationalEnergyMode B.1.3. Limits of Vibrational Energy Models and Derivatives B Unbounded Harmonic Oscillator Model B Bounded Harmonic Oscillator Model B.1.4. EnergyModels:ElectronicEnergyMode B.1.5. EnergyModels:Zero-pointEnergy B.1.6. EnergyModelDataforAir B.1.7. Curve Fit Data for the Park CO 2 Model B.2.TransportCoefficients B.2.1. Sutherland s Law for Air B.2.2. BlottnerViscosityModel B.2.3. Lennard-JonesParameters B.3. Implemented Reaction Models B.3.1. AirModel B.3.2. AirModelwithCoolant B.3.3. NitrogenModel B.3.4. Reduced Evans and Schexnayder Model (Hydrogen-Oxygen) B.3.5. Jachimowski Model (Hydrogen-Oxygen-Nitrogen) B.3.6. HydrogenModel B.3.7. Park CO 2 Model(Oxygen-Nitrogen-Carbon) B.4. Thermal Nonequilibrium Models B.4.1. Millikan and White (VT.1) B AirModel B Park CO 2 Model B.4.2. KlomfaßCurveFit(VT.2andVV.1) B.4.3. Candler (VV.2) xi

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