Speaker
Description
\section{Background of the study}
\label{sec:intro}
The planned NASA missions to the ice-giants, i.e. Uranus and Neptune, push the space exploration to the edge of the solar system and commit to new challenges the research activities meant to address all the related engineering issues. Fluid-dynamic models of hypersonic entry conditions allows the estimation of heat load at the surface of the vehicle and represent the most valuable tool to perform virtual experiments and assist the design of thermal protection systems.
The reliable modelling of hypersonic entry of bodies in the atmosphere of the ice giants needs information relevant to the thermodynamics and transport properties of the plasma formed in the shock layer. The chemistry of the major atmosphere-components, i.e. H$_2$ and He, is affected by the presence of CH$_4$ as minority though not-negligible chemical species, furthermore the region close to the vehicle surface is complicated by the contamination of carbon-oxygen-compounds from the surface, thus requiring their characterisation in terms of single-species thermodynamic quantities and collision integrals for binary interactions.
This contribution focusses on the derivation of these properties within an hybrid theoretical framework and on the assessment of their accuracy for the construction of a database to be included in CFD codes.
\section{Methodology}
\label{sec:method}
The calculation of chemical equilibrium, thermodynamics and transport is performed with the web-access tool EquilTheTA (EQUILibrium for plasma THErmodynamics and Transport Applications)~\cite{d2018equiltheta} designed and implemented in the framework of the cooperation between the CNR ISTP Bari and University of Basilicata. The tool, accurate, stable and reliable in wide temperature and pressure ranges, derives the quantities from core databases of atomic and molecular energy levels and collision integrals, in the frame of the classical theory of statistical thermodynamics and the Chapman-Enskog theory, respectively.
The creation of a complete database of collision integrals for binary heavy-particle interactions in complex mixtures including large number of species has been successfully tackled adopting a hybrid procedure that combines the traditional {\sl multi-potential} with the {\sl phenomenological} approaches~\cite{capitelli2007possibility,laricchiuta2007classical,pirani2023intermolecular}. In the multi-potential method the effective collision integrals for a given interaction results from the averaging procedure of terms corresponding to each allowed interaction between the two colliding partners. The phenomenological approach, allowing the derivation of complete and consistent datasets of collision integrals for possibly any interaction, is very attractive, estimating the interaction potential on a physically sound basis. In fact, the average interaction is modeled by an Improved Lennard Jones (ILJ) potential whose features (depth and position of the well) are derived by correlation formulas given in terms of fundamental physical properties of interacting partners (dipole polarizability, charge, number of electrons effective in polarization). These approaches combined with the asymptotic approach for the estimation of the resonant charge-exchange contribution to odd-order collision integrals, represent a powerful strategy to extend the collision integral database. The electron-neutral interactions require the integration of the quantum differential elastic cross section for electron scattering.
\section{Results}
\label{sec:results}
The single-species thermodynamic properties are based on partition functions in a direct-level-summation scheme for diatomic molecules and within a RRHO (rigid rotator-harmonic oscillator) approximation for polyatomic molecules. The upgraded database of EquilTheTA, including the newly-calculated partition functions, has been compared with the most recent references in the literature~\cite{barklem2016partition,gamache2021total}, this last relying on experimental (HITRAN database) compilation of levels, finding a good agreement.
The transport cross sections for binary interactions, involving neutral-neutral and neutral-ion collision systems, have been derived within the hybrid approach, while for electron-neutral interactions the knowledge about the energy dependence of the differential elastic cross section has been constructed combining experimental and theoretical information in the literature. For interactions relevant to a dissociation regime, the comparison with the NASA results~\cite{bellas2022transport} shows a substantial agreement of the empirical formula for the estimation of phenomenological parameters, namely the effective number of electrons~\cite{cambi91}, with respect to the ab-initio approach adopted in the NASA study~\cite{bellas2022transport}.
The extended core databases for the H$_2$/He/C/O system allowed to perform a systematic comparison of the EquilTheTA results, in terms of equilibrium composition, thermodynamics and transport coefficients, with a number of papers in the literature discussing H/O and H/C/O subsystems~\cite{aubreton2009transport,kvrenek2008thermophysical,wang2012thermophysical,wang2012thermophysical_2}.
\section{Conclusions}
\label{sec:Conclusions}
The databases for H$_2$/He system developed for the atmosphere of the gas giants (Jupiter and Saturn) of the solar system have been extended to allow the thermodynamic and transport characterisation of the ice giants in presence of carbon-oxygen contaminants.
\subsection*{\sc acknowledgements}
This research has been funded under ESA Contract No. 4000139351/22/NL/MG "Development of a state-to-state CFD code for the characterization of the aerothermal environment of Ice Giants planets entry capsules".
%\bibliographystyle{IEEEbib}
%\bibliography{refs}
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Summary
Thermodynamic properties and transport coefficients, for the characterisation of the plasma generated during the entry phase in the atmosphere of ice giants, are calculated from first principles. The strategies adopted in the construction of the core databases of the tool EquilTheTA, for energy levels and collision integrals of binary interactions, are discussed and reviewed. Results are compared with the literature.
