Novel approach for CO₂ state-to-state modeling and application to multi-dimensional entry flows

This paper presents a physics-based macroscopic model for the description of non- equilibrium effects in CO₂ flows. The starting point is the development of a vibrational state-to-state kinetic model including both vibrational excitation and dissociation processes for CO₂ internal states. A reduced-order representation is formulated by grouping the vibrational states into a set of macroscopic bins. The novel aspect of this work is to use both the levels’ energy and the magnitude of their transition rates to generate these bins of vibrational states. The state population is then reconstructed from the macroscopic variables using bin-wise distribution functions based on the maximum entropy principle. A reduced system of governing equations is derived by taking successive moments of the fundamental microscopic equations without any ad-hoc assumptions. In order to fulfill the needs of practical multi-dimensional simulations, a set of kinetic and thermodynamic databases are constructed. The accuracy of the grouping strategy is assessed by analyzing the error introduced by the reduced-order models. It is found that the reduced-order state- to-state model can accurately reproduce the internal population and various macroscopic quantities, even for strong non-equilibrium conditions and a reduced number of bins. The reduced-order state-to-state model has been implemented in the US3D code and is applied to the Mars Science Laboratory entry. The conventional Boltzmann and the newly developed state-specific model are compared using a pure CO₂ gas mixture. Both approaches shows very similar results in the forebody region of the spacecraft, while large discrepancies are observed in the backshell region, where non-Boltzmann effects become significant.