State-resolved modeling of electronic excitation in weakly ionized oxygen mixtures

Electronic excitation and ionization in oxygen-argon mixtures are analyzed using a three-temperature electronic state-resolved model and evaluated using recent experimental data from reflected shock experiments. A detailed description of the model formulation and parameter selection is provided. Excellent agreement is obtained between model predictions and experimental measurements of ${\mathrm{O}}_2$ number density during dissociation in mixtures of 2%–5% ${\mathrm{O}}_2$ dilute in argon. Next, electron number density measurements are leveraged to infer a rate constant for the heavy particle impact excitation of argon, facilitating improved modeling of net ionization and a clearer understanding of the electronic excitation kinetics of oxygen. The electronic state-resolved model is then assessed using measured data for three electronic states of atomic oxygen. The model successfully reproduces the multistage behavior observed in the measured time histories and yields new insights into the multistage behavior that revises previous interpretations. For several experiments, the modeling choices involved in the calculation of escape factors significantly influence the predicted time histories. A global sensitivity analysis considering nearly 300 parameters is then conducted to identify which model parameters most sensitively influence the predicted excited state populations. Excitation of the measured states from the metastable levels and collisional excitation between the three measured states are important across all conditions. The excited state populations demonstrate complex sensitivities involving a large number of collisional and radiative processes, highlighting the importance of adopting a detailed modeling approach when interpreting excited state measurements.

Figure 1

Grotrian diagram of O I with absorption transitions leveraged for number density measurements marked with orange upward arrows. Wavelengths of the illustrated transitions are given in nm.

Figure 2

Space-time diagram of the reflected shock experiments being analyzed. Regions are labeled using numbers, and dominant wave systems are labeled using colored lines.

Figure 3

Available and selected experimental conditions for measurements of excited atomic oxygen and ground-state molecular oxygen.

Figure 4

${\mathrm{O}}_2$ number density predictions using the present collisional-radiative model alongside predictions from a two-temperature model using parameters from [22].

Figure 5

Electron number density predictions by the collisional radiative model using the inferred rate constant expressions for Ar(1) $+$ Ar $\leftrightharpoons \mathrm{Ar}(i$) $+$ Ar.

Figure 6

Comparison of rate constants available for the electronic excitation of Ar($1\to 5$) in Ar $+$ Ar collisions.

Figure 7

Model predictions compared with experimental data from Nations-16 using two values of the cross-sectional scale factor ${\sigma }_0$ for the HP-CIE reaction $\mathrm{O}({}^3\mathrm{P}$) $+$ Ar $\to \mathrm{O}({}^5\mathrm{S}^{\circ }$) $+$ Ar.

Figure 8

Temperature predictions for the Li-21-1 experiment, including the electronic temperature for the fourth and sixth excited states of O as calculated from the measured data and the model predictions.

Figure 9

Rate constants for the excitation of O($4\to 6$) in collisions with argon and electrons. The E-CIE rate constant from Li et al. [10] is the baseline rate constant in that study. The HP-CIE rate from Li et al. is the optimized rate constant obtained by multiplying their baseline value by 6,200.

Figure 10

Comparison of collisional-radiative model predictions with measured data from the Li-21-2 experiment. Agreement with the experimental data is representative of other experiments in the Li-21 data set.

Figure 11

Boltzmann plot showing the electronic state distribution of oxygen atoms at three different time points in the Li-21-2 experiment.

Figure 12

Comparison between measured data and model predictions for the number density of $\mathrm{O}({}^5\mathrm{S}^{\circ }$) in the Li-20-L1 and Li-20-L4 experiments.

Figure 13

Comparison between model predictions and measured data for the number density of $\mathrm{O}({}^5\mathrm{S}^{\circ }$) in the Minesi-1920 and Minesi-2037 experiments.

Figure 14

Comparison between model predictions and measured data for the number density of $\mathrm{O}({}^5\mathrm{S}^{\circ }$) in the Li-20-H2 experiment at 9,161 K and 0.95 atm in 1% ${\mathrm{O}}_2$-Ar.

Figure 15

Total Sobol' indices for the number density of (a) $\mathrm{O}({}^5\mathrm{S}^{\circ }$) and (b) $\mathrm{O}({}^3\mathrm{S}^{\circ }$) in the Nations-16 experiment at 7,250 K and 0.61 atm in 1% ${\mathrm{O}}_2$-Ar.

Figure 16

Total Sobol' indices for the prediction of electron number density in the Li-21-1 case at 10,153 K and 0.49 atm in 1% ${\mathrm{O}}_2$-Ar.

Figure 17

Normalized total Sobol' indices for the number density of (a) $\mathrm{O}({}^5\mathrm{S}^{\circ }$) and (b) $\mathrm{O}({}^5\mathrm{P}$) in the Li-21-1 experiment at 10,153 K and 0.49 atm in 1% ${\mathrm{O}}_2$-Ar.

Figure 18

Normalized total Sobol' indices for the number density of $\mathrm{O}({}^5\mathrm{S}^{\circ }$) in the Minesi-2037 experiment at 12 199 K and 0.23 atm in 1% ${\mathrm{O}}_2$-Ar.

Figure 19

Convergence metrics for the sensitivity analyses.