State-Resolved Analysis of Recombinative O₂ and N₂ Mixtures in Hypersonic Boundary Layers

A master equation model resolving individual vibrational states is coupled to the Lees-Dorodnytsin (LD) boundary layer flow equations for stagnation-line flow. The master equation model leverages a database of rate coefficients of ab-initio accuracy, marking a significant advancement over previous boundary layer modeling efforts using the LD-transformed boundary layer equations. Using the developed code, a parametric analysis of N2 and O2 boundary layers covering pressures from 0.001 to 10 atm and nose radii from 1 mm to 10 m is performed, with the wall being modeled as non-catalytic. Marked differences between Tvib and Ttr occur at the wall for small nose radii and at low pressures, indicating incomplete vibrational thermalization at the surface. Overpopulation of high-lying vibrational levels due to recombination is observed in all calculations, even when the bulk vibrational temperature is in equilibrium with the translational-rotational temperature. This overpopulation slows the net formation rate of molecules due to recombination to between 15% and 70% of the equilibrium rate, depending on the geometry and flow conditions. Greater suppression of the recombination rate is observed in oxygen flows than in nitrogen. Finally, formal sensitivity analysis of atomic mass fraction and convective heating are performed in O2 and N2 boundary layers, considering 498 and 630 uncertain parameters, respectively. The Sobol' index results indicate that the rate coefficients for recombination to intermediate vibrational levels most sensitively influence the atomic mass fraction and the convective heating.