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.

The results from computer simulations of the gas-dynamic processes that occur during and after the rupture of diaphragms within shock tubes and expansion tubes are presented. A two-dimensional and axisymmetric finite-volume code that solves the unsteady Euler equations for inviscid compressible flow, was used to perform the simulations. The flow domains were represented as unstructured meshes of triangular cells and solution-adaptive remeshing was used to focus computational effort in regions where the flow-field gradients were high. The ability of the code to produce accurate solutions to the Euler equations was verified by examining the following test cases: supersonic vortex flow between two arcs, an ideal shock tube, and supersonic flow over a cone. The ideal shock tube problem was studied in detail, in particular the shock speed. The computed shock speed was accurate when the initial pressure ratio was low. When the initial pressure ratio was high the ow was dificult to resolve because of the large density ratio at the contact surface where significant numerical diffusion occurred. However, solution- adaptive remeshing was used to control the error and reasonable estimates for the shock speed were obtained. The code was used to perform multi-dimensional simulations of the gradual opening of a primary diaphragm within a shock tube. The development of the flow, in particular the contact surface was examined and found to be strongly dependent on the initial pressure ratio across the diaphragm. For high initial pressure ratios across the diaphragm, previous experiments have shown that the measured shock speed can exceed the shock speed predicted by one- dimensional models. The shock speeds computed via the present multi-dimensional simulation were higher than those estimated by previous one-dimensional models and were closer to the experimental measurements. This indicates that multi- dimensional ow effects were partly responsible for the relatively high shock speeds measured in the experiments. The code also has the ability to simulate two-dimensional fluid-structure interac- tions. To achieve this the Euler equations are solved for a general moving frame of reference. Mesh management during a simulation is important. This includes the ability to automatically generate a new mesh when the current mesh becomes distorted (due to the motion of the structures) and the transfer of the solution from the old mesh to the new. The shock induced rupture of thin diaphragms was examined. Previous one dimen- sional models are awed because they do not simultaneously consider the diaphragm mass and allow the upstream gas to penetrate the diaphragm mass. Two multi- dimensional models which allow the upstream gas to penetrate are described. The first model assumes the diaphragm vaporises immediately after the arrival of the incident shock. The second model assumes the diaphragm shatters into a number of pieces which can be treated as rigid bodies. The results from both models are compared with experimental data.

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.