A series of shock tube experiments performed in the 1970s at the Institute for Aerospace Studies, University of Toronto, led in the discovery of instabilities in relaxing shock structures in noble gases under hypervelocity conditions. The instabilities were oscillatory in nature and found to affect the entire shock structure including the translational front, induction zone, and electron avalanche. Theoretical models were first developed in order to reproduce the length and time scales of the observed quasi-equilibrium state, and later extended to include unsteady plasmadynamic simulations that verified the influence of pressure oscillations in one dimension. Despite these attempts, a complete explanation for the oscillations nor a quantitative analysis of the multi-dimensional shock structure has been provided to date.
This dissertation builds upon previous modeling efforts, extending the numerical simulations to a high level of accuracy and detail so that coupling of complex wave phenomena and nonequilibrium effects can be well resolved. This has necessitated the development of a numerical capability aimed at relaxing shock layers and other unsteady, high-enthalpy nonequilibrium plasmas and is the focus of much of this work. The plasma is described as a two-temperature, single fluid with the electronic states convected as separate species. Solution of the convective transport is handled via upwind shock-capturing techniques, extended to third-order on general curvilinear meshes. A collisional-radiative model describing the kinetics of excitation and ionization and reverse processes allows for a non-Boltzmann distribution of the excited levels. The solver is developed within a parallelized software architecture, implemented entirely in Java and capable or execution on distributed memory machines.
The numerical solver is developed in a systematic fashion with much emphasis placed on code validation. The transport schemes are benchmarked using standard test cases. The collisional-radiative model is benchmarked as well on a steady flow fields before considering unsteady calculations.
Numerical simulations of ionizing shocks in argon are conducted to gain insight to the shock structure and help determine the source of the oscillations observed in the experiment. Solutions presented in the form of simulated interferograms provide a direct comparison with experimental interferograms enabling identification of key wave structures. Results show that the instabilities are caused by a resonance pattern of longitudinal and transverse waves that give rise to ionization cells that are analogous to detonation cells. Furthermore, a mechanism is proposed for the oscillations which takes into account the unsteady wave phenomena coupled with the collisional-radiative kinetics.
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