Sensitivity Analysis of Ionization in Two-Temperature Models of Hypersonic Airflows

Abstract

Plasma generation in hypersonic flows is analyzed using a two-temperature model of nonequilibrium air. The uncertainties in electron number density predictions are assessed for flow scenarios that correspond to both strongly shocked and strongly expanded flows, and the dependencies of the calculated uncertainties on individual input parameters are quantified. Ionization levels behind 5 and 7 km/s normal shocks are found to be most sensitive to the associative ionization reactions producing ${\mathrm{O}}_2^{+}$ and ${\mathrm{NO}}^{+}$ in the region of peak electron number density, with nitric oxide kinetics dominating the uncertainty downstream. The higher levels of ionization behind a 9 km/s shock are found to strongly depend on the electron impact ionization of atomic nitrogen as well as the charge exchange between ${\mathrm{N}}_2^{+}$ and N. Recombining flow scenarios depend on many of the same processes that influence the shocked flows, with the notable addition of the reassociation reaction ${\mathrm{O}}^{+}+{\mathrm{N}}_2\leftrightarrow {\mathrm{NO}}^{+}+\mathrm{N}$, which is responsible for large uncertainties in electron number density in net recombining flows. The results provide valuable insight into the typical magnitude of uncertainty associated with plasma formation predictions in hypersonic flows and identify the parameters that should be targeted in efforts to reduce those uncertainties.