The non-equilibrium aerothermal environment during hypersonic flows is determined by the interaction between a multitude of disparate physical phenomena with varying characteristic time scales. The multi-physics nature of this flight regime renders the task of accurately estimating vehicular characteristics both theoretically and computationally challenging. The rapid dissipation of flow velocity into thermal energy in the post-shock region drives collisional-radiative processes that alter the chemical and energy composition of the flowfield. Traditional thermochemical and radiative models often introduce ad-hoc simplifications and rely on model parameters calibrated for a limited range of experimental conditions. Recent advances in computing power have allowed non-equilibrium internal state population distributions of gaseous species to be precisely determined using ab-initio quantum-chemistry calculations, referred to as the state-to-state (StS) approach. Similarly, first-principles based databases for different chemical species are now available that can characterize radiative behavior by accounting for millions of individual radiative transitions, referred to as line-by-line (LBL) modeling. Although exceedingly accurate, both StS and LBL approaches are computationally expensive and cannot be viably applied for solving practical physical problems. This thesis is aimed at developing a unified reduced-order framework for describing non-equilibrium thermochemistry and radiative heating which retains the physical fidelity of the aforementioned approaches but at dramatically lowered computational costs.
A computationally tractable description of non-Boltzmann thermochemistry is obtained using the multi-group maximum-entropy (MGME) framework. This involves dividing individual internal states into bins and then reconstructing the state population distribution using the maximum entropy principle. The current work introduces an adaptive grouping methodology that incorporates state-specific kinetics for further improving the MGME method. Two strategies are considered —Modified Island Algorithm and Spectral Clustering Method — for identifying clusters of states that are likely to equilibrate faster with respect to each other and then lumping them together into bins. The efficacy of MGME-based model reduction is assessed by studying non-equilibrium characteristics of two chemical systems, molecular nitrogen and carbon-dioxide, in a homogeneous chemical reactor. The introduction of adaptive binning which correctly accounts for localized thermalization due to preferential transition pathways allows the complex dynamics of about 9,000 internal states to be modeled using only 10-30 bins.
The multi-variate nature of radiative transfer is tackled by breaking it down into two components: geometric transfer and spectral modeling. A combination of discrete-ordinate method and finite-volume discretization with mesh sweeping is used to resolve generalized three-dimensional radiation fields in the angular and spatial domains. A reduced-order representation of the spectral variation in absorption/emission behavior is obtained through multi-group Planck-averaging. A formal interpretation for Planck-averaging is obtained based on maximum entropy closure in frequency space which allows a direct equivalence to be drawn with the MGME framework. Furthermore, a new generalized grouping strategy for non-equilibrium radiation is proposed that considers both absorption and emission coefficients while defining reduced-order groups. A detailed line-of-sight analysis for various Earth and Jovian entry problems indicates that Planck-averaging combined with the new grouping procedure allows reliable predictions while achieving a two orders-of-magnitude speed-up with respect to narrow-band methods (and three to four orders with respect to full LBL modeling).
The new simulation framework, with its focus on minimizing computational outlays, is ideally suited for realizing flow-radiation coupled simulations on large computational meshes. This is demonstrated by investigating, in conjunction with the US3D flow solver, the impact of vibrational non-equilibrium on carbon dioxide wake flows and resultant infrared radiation around NASA's Mars 2020 vehicle. Predictions for flowfield properties and radiative transfer are obtained using the conventional two-temperature model, bin-based StS model, and for decoupled/coupled flow-radiation calculations. Conventional two-temperature models overestimate the rate of thermal equilibration in the near-wake region resulting in the population of mid-lying and upper carbon dioxide vibrational levels being underpredicted by multiple orders of magnitude. Additionally, the two-temperature approach (in comparison to bin-based StS) overpredicts the rate of carbon dioxide dissociation thereby leading to erroneous estimates for flow properties in the post-shock region (primary source of afterbody radiative emission). This results in inflated values for surface radiative heat flux with conventional two-temperature modeling, although overall differences in radiative behavior are moderated by factors such as fast characteristic relaxation times for ground vibrational levels
