Rovibrational grouping for N₂(¹Σ_g⁺)-N₂(¹Σ_g⁺) energy transfer using state-to-state model

The present work discusses the development of a reduced-order model to describe N₂(¹Σ_g⁺)-N(⁴S_u) and N₂(¹Σ_g⁺)-N₂(¹Σ_g⁺) inelastic and reactive interactions. Following the main ideas of previous works by the authors and coworkers, the kinetic mechanism reduction is realized by lumping the rovibrational states of N₂(¹Σ_g⁺) in energy groups. However, owing to the large number of channels in N₂(¹Σ_g⁺)-N₂(¹Σ_g⁺) collisions, the grouped rate coefficients are now evaluated when performing QCT calculations. This innovative approach avoids the explicit storage of the whole set of elementary rate coefficients, leading to large savings in terms of both memory and CPU time. The effectiveness of the proposed methodology is first verified by comparing the grouped rate coefficients for the N₂ (¹Σ_g⁺)-N(⁴S_u) system with those obtained directly from the rovibrational State-to-State data (which are in this case available). As a second verification step, the macroscopic dissociation rate coefficient in N₂(¹Σ_g⁺)-N₂(¹Σ_g⁺) collisions is evaluated and compared with the predictions obtained in the past years, and with the calculations by other research groups. The proposed reduced-order model is finally applied to a constant temperature heat-bath simulation where the results are compared with those of conventional multi-temperature models (e.g. Park).