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.