Speaker
Description
This work aims to improve the prediction of CN electronic state populations in high temperature $\text{N}_2/\text{CH}_4$ plasmas, an essential prerequisite for robust radiative flux modeling during Titan entry [1], [2], [3]. We develop a comprehensive collisional radiative (CR) model that tracks all relevant global species as well as the ground state $\text{CN}(X^2\Sigma^+)$ and the first four excited states: $\text{CN}(A^2\Pi)$, $\text{CN}(B^2\Sigma^+)$, $\text{CN}(a^4\Sigma^+)$, and $\text{CN}(D^2\Pi)$. The global species reactions of the CR model are based on the modified mechanism of Gökçen [4], [5]. The reactions involving CN excited states include heavy particle/electron-impact dissociation, heavy particle/electron-impact excitation, and spontaneous emission. The corresponding rate coefficients are taken from Ref. [4], while adding processes that were not included in the initial set.
The CR model predictions are compared against two independent data sets:
(i) absorption/emission measurements of the CN red ($A-X$) and violet ($B-X$) bands in a recombination plasma experiment, and
(ii) emission measurements of the same bands in a dissociating plasma obtained with the Low Density Shock Tube (LDST) of NASA Ames Research Center [6], [7].
The model is coupled to a one dimensional space marcher (1D SM) for comparison with LDST measurements.
The recombination experiment consists of generating a plasma using an inductively coupled plasma (ICP) torch that subsequently recombines in a water cooled tube. Initial CR model predictions of $\text{CN}(X^2\Sigma^+)$, $\text{CN}(A^2\Pi)$ and $\text{CN}(B^2\Sigma^+)$ number densities underpredict the measurements by up to a factor five at 37.5-cm tube length. A kinetic analysis, combined with One At a Time and Sobol' sensitivity studies revealed that the $\text{N}_2$ recombination reaction is by far the dominant source of variance of the densities of CN electronic states. The next-most important contributor to the total variance is the recombination reaction into $\text{CN}(A^2\Pi)$. CN electronic states densities are also sensitive to the exchange reaction $\text{CN}(A^2\Pi) + \text{N} \leftrightarrow \text{N}_2 + \text{C}$, along with the heavy particle excitation/deexcitation reactions between the three electronic states. Guided by these insights, we perform a quasi Monte Carlo (QMC) optimization of the rate coefficients corresponding to the reactions identified by the sensitivity analysis within their respective uncertainty domains. This analysis showed that good agreement with the measured CN densities in the recombination tube can only be achieved if we increase the $\text{CN}(A^2\Pi)$ recombination rate coefficient by a factor of at least 200. A separate QMC study performed on one LDST dataset showed that reducing the $\text{CN}(A^2\Pi) \leftrightarrow \text{CN}(B^2\Sigma^+)$ heavy particle excitation rate by at least a factor 30 brings the LDST predictions within 20% of experiment.
Finally, a global QMC optimization that respects both experiments is performed. Based on this analysis, we recommend a final set of modifications to the reaction rate coefficients of the baseline model that allows for reasonable agreement with both datasets. Good agreement can only be obtained if the $\text{CN}(A^2\Pi)$ recombination/dissociation rate ($\text{C} + \text{N} + \text{M} \leftrightarrow \text{CN}(A^2\Pi) + \text{M}$) is allowed to be different for the LDST and recombination experiments, indicating that the chemical pathways – dissociation in the case of LDST and recombination for the recombination experiment – are not the same for these two experiments.
[1] A. M. Brandis, R. G. Morgan, and T. J. McIntyre, “Analysis of Nonequilibrium CN Radiation Encountered During Titan Atmospheric Entry,” Journal of Thermophysics and Heat Transfer, vol. 25, no. 4, pp. 493–499, Oct. 2011, doi: 10.2514/1.50966.
[2] T. E. Magin, L. Caillault, A. Bourdon, and C. O. Laux, “Nonequilibrium radiative heat flux modeling for the Huygens entry probe,” J. Geophys. Res., vol. 111, no. E7, p. 2005JE002616, Jul. 2006, doi: 10.1029/2005JE002616.
[3] M. Wright, “The Dragonfly Entry and Descent System”.
[4] C. O. Johnston, T. K. West, and A. M. Brandis, “Features of Afterbody Radiative Heating for Titan Entry,” in AIAA Aviation 2019 Forum, Dallas, Texas: American Institute of Aeronautics and Astronautics, Jun. 2019. doi: 10.2514/6.2019-3010.
[5] T. Gökçen, “N2-CH4-Ar Chemical Kinetic Model for Simulations of Atmospheric Entry to Titan,” Journal of Thermophysics and Heat Transfer, 2007.
[6] A. Fagnani, A. M. Brandis, and B. A. Cruden, “Characterization of Titan Entry Radiative Heating in the Low Density Electric Arc Shock Tube,” in AIAA SCITECH 2025 Forum, in AIAA SciTech Forum. American Institute of Aeronautics and Astronautics, Jan. 2025. doi: 10.2514/6.2025-0448.
[7] A. Fagnani, D. L. Drescher, J. W. Streicher, R. Hanson, A. M. Brandis, and B. A. Cruden, “Assessment of CN Non-Boltzmann Kinetics Against Low Density Shock Tube Data,” in AIAA SCITECH 2026 Forum, Orlando, FL: American Institute of Aeronautics and Astronautics, Jan. 2026. doi: 10.2514/6.2026-1677.
Summary
This work aims to develop and validate a collisional-radiative model for high-temperature N₂/CH₄ plasmas, suitable for both recombining and dissociating flows. First, we start with a CR model based on previous models by Gökçen [1] and Johnston [2], with updates. Model predictions are evaluated against two different flow configurations: a recombining plasma experiment performed at EM2C, and shock tube data from experiments performed at NASA Ames Research Center by Fagnani et al. [3]. Finally, we recommend adjustments to the baseline model, based on the previous comparison.
[1] T. Gökçen, “N2-CH4-Ar Chemical Kinetic Model for Simulations of Atmospheric Entry to Titan,” Journal of Thermophysics and Heat Transfer, 2007.
[2] C. O. Johnston, T. K. West, and A. M. Brandis, “Features of Afterbody Radiative Heating for Titan Entry,” in AIAA Aviation 2019 Forum, Dallas, Texas: American Institute of Aeronautics and Astronautics, Jun. 2019. doi: 10.2514/6.2019-3010.
[3] A. Fagnani, A. M. Brandis, and B. A. Cruden, “Characterization of Titan Entry Radiative Heating in the Low Density Electric Arc Shock Tube,” in AIAA SCITECH 2025 Forum, in AIAA SciTech Forum. American Institute of Aeronautics and Astronautics, Jan. 2025. doi: 10.2514/6.2025-0448.