Maximum entropy modeling of oxygen vibrational excitation and dissociation

The vibrational excitation and dissociation of oxygen are modeled using different approaches with a range of fidelity, including the conventional two-temperature model, the state-specific method, and two variations of a model based on the maximum entropy principle. Comparison of the post-shock predictions with recent shock tube experimental data shows that the maximum entropy quadratic model predicts similar trends to the state-specific method and the experimental data. Although the maximum entropy quadratic model has significantly fewer equations than the state-specific method, no gain in computational efficiency is seen. Hence, the former model is further simplified by assuming that the vibrational relaxation can be described by the Landau-Teller formulation, with the corresponding relaxation times for ${\mathrm{O}}_2\text{−}{\mathrm{O}}_2$ and ${\mathrm{O}}_2\text{−}\mathrm{O}$ interactions determined from state-specific calculations of relaxation in a heat bath. The post-shock simulations indicate that the modified maximum entropy quadratic model maintains sufficient prediction accuracy while significantly improving computational efficiency. The proposed model could be used in computational fluid dynamics solvers for hypersonic nonequilibrium flow simulations.

Figure 1

Post-shock profiles for case 1 (a) Translationalrotational temperature, (b) Vibrational temperature, (c) Mass fraction of O, and (d) Mixture density.

Figure 2

Post-shock profiles for case 2 (a) Translationalrotational temperature, (b) Vibrational temperature, (c) Mass fraction of O, and (c) Mass fraction of O.

Figure 3

Post-shock profiles for case 3 (a) Translationalrotational temperature, (b) Vibrational temperature, (c) Mass fraction of O, and (d) Mixture density.

Figure 4

Specific vibrational energy profiles for different cases (a) Case 1, (b) Case 2, and (c) Case 3.

Figure 5

Post-shock profiles for case 3 showing the effects of a larger number of internal groups (a) Translationalrotational temperature, and (b) Mass fraction of O.

Figure 6

Evolutions of $e_{\mathrm{v}}$ and $f_{\mathrm{v}}$ for ${\mathrm{O}}_2\text{−}\mathrm{O}$ interactions at heat bath temperature of 10 000 K.

Figure 7

Post-shock profiles for case 3 (a) Translationalrotational temperature, (b) Mass fraction of O, (c) Mixture density, and (d) Specific vibrational energy.

Figure 8

Vibrational energy level populations for case 3 (a) $t=0.01\mu \mathrm{s}$, (b) $t=0.5\mu \mathrm{s}$.