Speaker
Description
Background
Upcoming missions to Mars considered by JAXA generate strong motivation in designing advanced thermal protection systems (TPSs) with low design margins, in an effort to reduce the launching costs and increase the scientific value of the mission by embedding larger payloads and to enhance the reliability and safety of the reentry systems. The sizing of the TPSs relies on the knowledge of the physico-chemical processes heating the spacecraft on its front and back covers using a combined approach based on ground experiments and numerical simulations. For entries into CO2-based atmospheres, measurements contributed to mitigate the uncertainties in front shell TPS. The back shell received little attention since the heating loads, especially the radiative heating, were deemed negligible. However, recent numerical studies demonstrated that the radiative heating encountered by a spacecraft on its back shell was dominated CO2 infrared (IR) radiation (at 2.3, 2.7, 4.3 and 15$\mu$m) and was of the order of magnitude of the convective heating. These findings triggered measurement campaigns of CO2 IR radiation under nonequilibrium and during expansion.
This paper aims at assessing the various radiation models with respect to the works of, to strengthen the predictive capabilities of the current simulation tools, and to compute the radiative heating withstand by a Martian reentry spacecraft.
Methodology
In this work, we want to reproduce absorption and emission spectra obtained through various experiments (nozzles, shock-tubes, expansion-tubes). The radiation emitted from a CO2-based mixture is computed with the in-house Structured Package for Radiation Analysis (SPRADIAN) code and the Carbon Dioxyde Spectroscopic Databank (CDSD). This database was selected after the works of Lemal et al. (2018). In this work, we use a multi-temperature model for the calculation of the populations of the different rovibrational levels.
The present work considers the complete expression of the effective Hamiltonian to compute the rovibrational energy levels. The Hamiltonian is built using the same parameters as Tashkun, and the rovibrational levels' energy are obtained through its diagonalization. It is possible to extract the contributions of the different couplings and interactions by decomposing the Hamiltonian before diagonalization, and applying the change of basis to the different parts of the Hamiltonian. This allows to use the rovibrational levels' energies in within the multi-temperature model for nonequilibrium conditions.
Once the Hamiltonian built, it is possible to calculate the levels' populations. Using a 5-temperature model, we need to consider a pseudo-temperature applied to the coupling and interaction part of the levels' energy. In order to investigate multiple cases, we chose to use $T_{\text{coupling}} = T_{v_1}^a T_{v_2}^b T_{v_3}^c T_{\text{rot}}^d$ with $a+b+c+d=1$ : by choosing appropriate exponents, we will be able to investigate the impact on the populations of considering the coupling and interactions' part of the levels' energy with some particular vibrational mode.
Results
A database of approximately 7.3M states has been computed using Python's numpy, pandas and multi-threading libraries (with a maximum polyad number of 40, a maximum rotational number of 300 and an energy cutoff of 55000cm$^{-1}$).
The correctness of the calculated energies was checked thanks to equilibrium simulations in the 2.7 and 4.3$\mu$m regions. We compared SPRADIAN's results to Depraz's EM2C database, Depraz's use of CDSD [Depraz et al. (2014)] and Vargas's results [Vargas et al. (2018)]. Better agreements with CDSD were obtained than the former EM2C database and Vargas's results.
Other tests were performed by trying to reproduce EAST experimental emission spectra for a 3.12km.s$^{-1}$ shock wave. We observed the same behaviour than Cruden et al. (2014) and RADIS [Pannier et al. (2018)], ie that the frozen chemistry describes the emission spectra better than the equilibrium chemistry. Nonetheless, some discrepancies were observed with RADIS simulations, for the same input temperatures and pressures.
Other simulations investigated the influence of the pseudo-temperature on the absorption and emission spectra, under nonequilibrium conditions. The first results show a small impact of the choice of the pseudo-temperature, especially on the absorption coefficients.
The absorption and emission spectral shapes are very sensitive to nonequilibrium conditions. Future shock-tube experiments at Chofu Aerospace Center will be investigated through the spectral fitting method, using these new simulation tools.
Conclusion
The first simulations made thanks to the improved radiative solver give good agreement at equilibrium, and an useful spectral shape sensitivity for nonequilibrium conditions. The coupling and interactions part of the levels' energies thus seems to have a non-negligible impact on absorption and emission spectra.
It will also be possible to perform spectral fitting on the future experimental spectra obtained with JAXA experimental facilities. Investigations of previous expansion-tube experiments are also planned, using CFD (with JAXA in-house code JONATHAN) and radiative simulations.
Summary
This paper presents the efforts in simulating the infrared radiation emitted by CO2 under nonequilibrium conditions, such as encountered in shock waves and wakes, when CO2 undergoes dissociation and recombination, respectively. This paper addresses the modelling and computation of CO2 spectral properties with the Carbon Dioxide Spectral Databank (CDSD-4000) under thermal nonequilibrium, under the multi-temperature formalism. Schemes to split the level energy into its pure vibrational, rotational and vibration-rotation coupling and interactions contributions are proposed and implemented into JAXA in-house solver to compute nonequilibrium spectral properties. Available experimental data under equilibrium and nonequilibrium conditions were used to evaluate the correctness of the implementation and the performances of the spectral code. The influence of the energy splitting model on CO2 infrared radiation is discussed.
