The paper presents a comparative study of vibrational-chemical kinetics and heat transfer in carbon dioxide flows under Mars entry conditions for two classes of models: the state-to-state and multitemperature models. The state-to-state approach treats each vibrational state of a molecule as a separate chemical species, thus providing a very detailed flow description. Reduced multitemperature models are based on nonequilibrium quasi-stationary Boltzmann distributions over vibrational energy with vibrational temperatures of different modes. Implementation of multitemperature models requires much less computational effort, making them rather attractive for engineering applications. Simulations have been performed for the upper part of the Mars Pathfinder entry trajectory. Comparisons between different models demonstrate a good agreement for the flowfield variables obtained using the state-to-state and multitemperature approaches, except some discrepancies for the species mole fractions prediction. This conclusion is encouraging for computational fluid dynamics, since it confirms that multitemperature models, while not being so much detailed as state to state, are still able to capture the main peculiarities of thermal and chemical nonequilibrium flows. The transport and thermochemical models have been validated using experimental data obtained in the NASA Hypersonic Pulse ground test facility. It is shown that both state-to-state and advanced multitemperature transport models used in the present simulations provide a better agreement for the heating predictions compared to traditional models.

The modeling of atmospheric gas, interacting with the space vehicles in re-entry conditions in planetary exploration missions, requires a large set of scattering data for all those elementary processes occurring in the system. A fundamental aspect of re-entry problems is represented by the strong non-equilibrium conditions met in the atmospheric plasma close to the surface of the thermal shield, where numerous interconnected relaxation processes determine the evolution of the gaseous system towards equilibrium conditions. A central role is played by the vibrational exchanges of energy, so that collisional processes involving vibrationally excited molecules assume a particular importance. In the present paper, theoretical calculations of complete sets of vibrationally state-resolved cross sections and rate coefficients are reviewed, focusing on the relevant classes of collisional processes: resonant and non-resonant electron-impact excitation of molecules, atom-diatom and molecule-molecule collisions as well as gas-surface interaction. In particular, collisional processes involving atomic and molecular species, relevant to Earth (N-2, O-2, NO), Mars (CO2, CO, N-2) and Jupiter (H-2, He) atmospheres are considered.

State-to-state vibrational kinetics and transport properties of a mixture containing carbon dioxide molecules are studied. Theoretical models are developed and implemented in a hypersonic boundary layer solver. Various vibrational relaxation channels are considered, and the influence of complex kinetic processes on the flow parameters and heat flux is evaluated. A simpler reduced model is developed to keep the computational cost reasonable.

In the inner part of the dissociated boundary layer of hypersonic bodies, a vibrational freezing zone has been observed. This freezing region takes place even if, in the outer part of the boundary layer, translation and vibration temperatures are in equilibrium and even if the surface is catalytic. This phenomenon can be attributed to the diffusion towards the wall of the vibrational energy; consequently the dissociation rate constantsin this region can increase. Advanced physical models taking into account the vibration-chemistry interaction are required for the description of such flows. State-to-state and statistical global models are described in this paper and used in the computation of hypersonic boundary layers. All methods can predict the general features of the freezing phenomenon and present a qualitative agreement, as far as similar assumptions are used. Applications to boundary layers behind a reflected shock wave and along a hemispherical body are also presented.

A recent complete set of oxygen atom-molecule collision rate coefficients, calculated by means of a quasiclassical trajectory (QCT) method, has been used to evaluate the vibrational non-equilibrium in hypersonic boundary layer flows. The importance of multiquanta transitions has been demonstrated. Moreover a new 'direct dissociation-recombination' (DDR) model has been adopted and the corresponding results differ from the ones obtained with the Ladder-Climbing (LC) model, characterized by the extrapolation of bound-to-bound transitions to the continuum. The heat flux through the boundary layer and at the surface have been calculated too.

The state-to-state vibrational kinetics of a CO2/O-2/CO/C/O/e(-) mixture in a hypersonic boundary layer under conditions compatible with the Mars re-entry is studied. The model adopted treats three CO2 modes (the two degenerated bending modes are approximated as a unique one) as not independent ones. Vibrational-translational transitions in the bending mode, inter-mode exchanges within CO2 molecule and between molecules of different chemical species as well as dissociation-recombination reactions are considered. Attention is paid to the electron-CO2 collisions that cause transitions from the ground vibrational state, CO2(0,0,0), to the first excited ones, CO2(1,0,0), CO2(0,1,0) and CO2(0,0,1). The corresponding processes rate coefficients are obtained starting from the electron energy distribution function, calculated either as an equilibrium Boltzmann distribution at the local temperature or by solving the Boltzmann equation.Results obtained either neglecting or including in the kinetic scheme the electron-CO2 collisions are compared and explained by analysing the rate coefficients of the electron-CO2 collisions.

In the present paper, detailed state-to-state model of vibrational-chemical kinetic and transport processes is applied to study fluid dynamics and heat transfer in a non-equilibrium flow of a five-component mixture containing CO2 molecules and products of their dissociation near the surface of the Mars Sample Return Orbiter. For several test cases, vibrational distributions, chemical composition, specific vibrational energy profiles as well as the transport coefficients and different contributions to the heat flux are calculated along the stagnation line. For a non-catalytic surface, the role of thermal diffusion process is found to be important. Prandtl and Schmidt numbers are calculated along the stagnation line, and their influence on the diffusion velocities and heat flux is evaluated.

In the present chapter some prototype gas and gas-surface processes occurring within the hypersonic flow layersurrounding spacecrafts at planetary entry are discussed. The discussion is based on microscopic dynamical calculationsof the detailed cross sections and rate coefficients performed using classical mechanics treatments for atoms, moleculesand surfaces. Such treatment allows the evaluation of the efficiency of thermal processes (both at equilibrium and nonequilibrium distributions) based on state-to-state and state specific calculations properly averaged over the population ofthe initial states. The dependence of the efficiency of the considered processes on the initial partitioning of energy amongthe various degrees of freedom is discussed.

The NO formation in a hypersonic boundary layer is investigated by solving a numerical code that couples fluid dynamics and state-to-state vibrational kinetics. An N2/N/O2/O/NO mixture is considered to simulate the space vehicle Earth re-entry problem. Two new sets of state-to-state rate coefficients of the processes O + N2(v) <-> NO(w) + N and N + O2(v) <-> NO(w) + O are used, calculated in our research group by means of a molecular dynamics approach.Particular attention is payed to rescale the rates of different kinetic processes in order to have a unique vibrational scale for each molecular species (N2, O2, NO). This is not obvious because vibrational levels, obtained from asymptotics of three-body potential of different collisional systems, often do not match, particularly for high-lying vibrational states. The reactions involving NO affect the mass fractions, the molecular vibrational distributions and the heat flux in the boundary layer.

In the present paper, state-to-state model of vibrational-chemical kinetic and transport processes is applied to study heat and mass transfer in non-equilibrium flows of CO2 and air mixtures under atmospheric entry conditions. Different contributions to the heat flux typical for the state-to-state approach are considered: fluxes due to heat conduction, mass diffusion, thermal diffusion, and diffusion of vibrational energy. For several test cases, vibrational distributions, chemical composition, temperature profiles as well as the transport coefficients and heat flux are calculated along the stagnation line. Various models for diffusion velocities are considered. For a non-catalytic surface, the role of thermal diffusion process is found to be important in some test cases. Prandtl and Schmidt numbers are calculated along the stagnation line, and it is shown that they are essentially non-constant. The influence of Prandtl and Schmidt numbers on the diffusion velocities and heat flux is evaluated

We present the quantum mechanical (QM) and quasiclassical trajectory (QCT) dynamics of the title reac- tion on two uncoupled surfaces, using a wavepacket (WP) method and considering some N2(v, j) vibra- tional and rotational states. The reaction is investigated by calculating initial-state-resolved reaction probabilities, cross sections, and rate constants, which are explained in terms of energy profiles and col- lision mechanisms. These properties reflect the large endo-thermicity of the reaction and the features of the surfaces. Indeed, at low v values we obtain large thresholds and the lower surface is more reactive than the higher one, whereas at high v the thresholds decrease or disappear and the upper surface becomes more reactive. QM and QCT results are in satisfactory agreement, except some differences at low or high collision energy and temperature. QCT rate coefficients agree also with some published results. WP snapshots and movies of QCT time evolution show clearly abstraction and insertion mecha- nisms depending on the initial conditions. Insertion proceeds via a reaction complex and we observe a QM Feshbach resonance for a specific initial condition. On the overall, the dynamical observables are con- sistent with the collision mechanisms.

We report the results of detailed calculations of reactive, inelastic, and dissociative processes in collisions of atomic oxygen with molecular nitrogen in their respective electronic ground states. Cross sections are calculated as a function of collision energy in the range 0.001-10 eV, considering the whole rovibrational ladder. Some problems related to the vibrational energy levels of the asymptotes of 3A" and 3A' potential energy surfaces used in this work are solved by an appropriate scaling at the level of cross sections. The results are compared with data in the literature, obtaining excellent agreement with experimental thermal data for reactive processes on a very large temperature range, and reasonable agreement with indirect dissociative data. Significant discrepancies are observed with previous reactive state-to-state results calculated on less detailed potential energy surfaces. Inelastic results are compatible with extrapolation of experimental thermal rate coefficient for temperatures higher than 4500 K but completely fail to reproduce experimental data at room temperature. The issue is discussed, indicating the reasons and possible solutions to the problem, and a resonable rate coefficient is obtained combining experimental and theoretical results in the range 300-20000 K. Complete, accurate fits are provided for both reactive and dissociative state-to-state rate coefficients to use them in applicative numerical codes concerning air kinetics.

Collisions of atomic oxygen and nitrogen with nitrogen and oxygen molecules respectively have been sistematically studied with respect to initial and final vibration of the diatoms by the quasiclassical method, using the best potential energy surfaces available. Cross sections for dissociation, vibrational energy exchange and reaction have been calculated, in a translational energy range up to 10 eV. Comparisons with available thermal data are generally good. Special emphasis has been given to the inclusion of rotation in these calculations, for its importance in dissociation-recombination kinetics.

Kinetics and heat transfer in a CO2/CO/O2/O/C mixture in a hypersonic boundary layer is studied using a state-to-state vibrational-chemical kinetic model. The CO2 molecule is detailed in its symmetric stretching, bending and asymmetric stretching modes, which are strongly coupled through inter-mode vibrational energy transfers. Two sets of rate coeficients for the vibrational energy transitions are used. Different kinetic schemes including various physical and chemical processes are assessed. The heat flux is calculated, in the framework of the modified Chapman-Enskog theory, accounting for the vibrational states of involved molecules. Comparisons with results obtained using a simplified model, including mainly vibrational levels of the asymmetric stretching mode, are carried out. It is shown that VT transitions in the symmetric and asymmetric modes do not alter the flow and can be neglected. The heat flux is not sensitive to the rates of vibrational energy transitions but depends noticeably on the processes implemented to the kinetic scheme. Using the simplified model yields under-predicted surface heat fluxes; nevertheless we can recommend it for fast estimates of the fluid dynamic variables and heat transfer in hypersonic flows since its implementation essentially reduces computational costs.

State-to-state vibrational kinetics and transport models of a mixture containing triatomic CO2 molecules are developed. The models are implemented into a hypersonic boundary layer solver specially upgraded for this purpose. Although at the moment only vibrational-translational transitions in the bending mode (VT2), inter-mode exchanges within CO2 molecule (VV1-2-3), and inter-mode exchanges between mole- cules of different chemical species (VV1-2-CO) are taken into account, the approach can be generalized to include more complete kinetics.In order to overcome problems caused by the computational load of the state-to-state vibrational kinetics of a triatomic molecule, a Reduced Model is proposed and compared with the Full one.

The paper deals with kinetic theory methods modelling of reacting gas flows near spacecrafts entering the Mars atmosphere. For mixtures containing CO2 molecules, the complete kinetic scheme including all vibrational energy transitions, dissociation, recombination and exchange chemical reactions is proposed. For the prediction of gas dynamic parameters and heat transfer to the surface of a spacecraft, a detailed approach taking into account state-to-state CO2 vibrational and chemical kinetics as well as multi-temperature approaches based on quasi-stationary vibrational distributions are used. A more accurate but complicated and time consuming state-to-state model is applied for the numerical simulation of a one-dimensional flow in a boundary layer near the entering body surface. More simple quasi- stationary three-temperature, two-temperature and one-temperature approaches are used for the numerical study of a 2-D viscous shock layer under entry conditions. The vibrational distributions near the surface are far from the local vibrational and chemical equilibrium and a noticeable difference is found between the values of CO2 vibrational-specific energies at the surface obtained by means of the state-to-state and quasi-stationary approaches. At the same time, for all considered approaches, the kinetic model for vibrational distributions and chemical reactions has a weak influence on the heat transfer to the non-catalytic vehicle surface.