Modelling of radiating shock layers for atmospheric entry at Earth and Mars

This thesis investigates the modelling of radiating shock layers encountered during atmospheric entry from space. Specifically, the conditions relevant to entry at Earth and Mars from hyperbolic trajectories are considered. Such trajectories are characteristic of the interplanetary transits that would be required for the human exploration of Mars, for example. A set of computational tools for the simulation of radiating shock layers is presented, and then applied to simulate shock tube and expansion tunnel experiments performed in both the EAST facility at NASA Ames and the X2 facility at the University of Queensland. Appropriate thermodynamic, transport and spectral radiation models for the species of interest in the Ar–C–N–O elemental system have been developed. Expressions for multitemperature thermodynamic coefficients for 11 species air and 22 species Mars gas are derived from statistical mechanics. Viscosity, conductivity and diffusivity coefficients are calculated by applying the Gupta-Yos mixture rules. A complete set of binary collision integrals are compiled from critically selected sources in the literature, where preference is given to data based on computational chemistry and experimental measurements. A spectral radiation model describing atomic and diatomic bound-bound transitions via a line-by-line approach is presented, while continuum transitions are approximated by hydrogenic and step models. Collisional-radiative models for Ar, C, N, O, C2, CN, CO, N2 and N2+ are implemented for calculating the non-Boltzmann electronic level populations of these species in a temporally decoupled manner. For the simulation of shock tube experiments, two- and three-temperature formulations of the one-dimensional post-shock relaxation equations are implemented. The chemical kinetic and thermal energy exchange processes are fully coupled with the gas dynamics, and the radiation source term is modelled in the optically thin and thick limits that bound the solution space. Prior to the comparison with experimental data, the one-dimensional post-shock relaxation equations are applied to simulate flow conditions representative of hyperbolic entry at Earth and Mars; specifically, the Fire II t = 1634 s and t = 1636 s trajectory points and hypothetical 8.5 and 9.7 km/s Mars aerocapture conditions are considered. For these conditions comparisons are made with published solutions to verify the code implementation, and various physical models are applied to assess the sensitivity of the solutions to the underlying physics. The one-dimensional post-shock relaxation equations are then applied to simulate shock tube experiments performed in the EAST and X2 facilities. For the EAST facility, nominally 10 km/sair conditions and a 8.5 km/s Mars condition are considered. For the X2 facility, an 11 km/s air condition is considered. Comparisons with both ultraviolet and infrared spatially resolved spectra are made for all experiments. For the air conditions, good agreement (within the limits of experimental uncertainty) is observed for the higher pressure conditions considered (40 Pa), while some discrepancies emerge for the lower pressure conditions considered (13.3 and 16 Pa). For the 8.5 km/s Mars condition, certain spectral features such as the the important CO Fourth Positive band system, CN Violet band system and atomic C lines in the infrared are well described, while others such as and atomic C lines in the ultraviolet and atomic O lines are overestimated. Overall, shock tube comparisons show the total measured radiation is able to be estimated within 30% for N2–O2 mixtures and within 50% for CO2–N2 mixtures. In contrast to shock tube experiments where the flow is well described by a one-dimensional variation of properties, expansion tunnel experiments are inherently multidimensional. For simulating these experiments, modifications to an existing time-accurate Navier–Stokes code have been made to allow the calculation of radiating, partially ionised plasmas. The governing equations for a two-temperature multi-species gas are implemented. The tangent-slab model and a ray-tracing based model are implemented for computing the radiation source term. Radiation-flowfield coupling is treated in a loosely coupled manner. The chemical kinetic and thermal energy exchange source terms are applied in an ‘operator split’ fashion; this approach is validated by comparisons with solutions from the fully coupled post-shock relaxation equations. Two expansion tunnel experiments are then considered: (1) a 47 MJ/kg N2–O2 condition with a 1:10 scale Hayabusa model, and (2) a 37 MJ/kg CO2–N2 condition with a 25mm diameter cylinder model. For both experiments, the freestream conditions generated by the X2 facility are firstly estimated by a novel, simplified strategy based on one-dimensional simulations of the secondary diaphragm rupture and Navier–Stokes simulation of the test gas expansion through the hypersonic nozzle. The freestream conditions so determined are then applied to simulate the radiating shock layer formed by the test gas recompression over the models. From these radiatively-coupled simulations, spatially resolved spectral intensity fields are post-processed and compared with the experimental measurements. For the 47 MJ/kg N2–O2 condition, comparisons with both ultraviolet and infrared spectra are made, while for the 37 MJ/kg CO2–N2 ultraviolet spectra are compared. While good qualitative agreement is found for the CO2–N2 condition, the intensity profiles for the N2–O2 condition show substantial discrepancy. Reasons for the difference between calculation and experiment are discussed. Finally, the binary scaling hypothesis is numerically assessed by comparing simulations of the subscale Hayabusa model with an effective flight equivalent. While similitude in the surface radiative flux is demonstrated for radiatively uncoupled simulations, the consideration of radiation-flowfield coupling is found to reduce the flight radiative flux disproportionally to the subscale radiative flux. The flight radiative flux at the stagnation point is calculated to be reduced by 80% when radiation coupling is considered, while the reduction is only 23% for the subscale radiative flux.