Arnaud Bultel

Collisional-radiative model in air for earth re-entry problems

A nonlinear time-dependent two-temperature collisional-radiative model for air plasma has been developed for pressures between 1kPa and atmospheric pressure to be applied to the flow conditions of space vehicle re-entry into the Earth’s atmosphere. The model consists of 13 species: N2, O2, N, O, NO, N2+, O2+, N+, O+, NO+, O2−, O− in their ground state and major electronic excited states and of electrons. Many elementary processes are considered given the temperatures involved (up to 10 000K). Time scales to reach the final nonequilibrium or equilibrium steady states are derived. Then we apply our model to two typical re-entry situations and show that O2− and O− play an important role during the ionization phase. Finally, a comparison with existing reduced kinetic mechanisms puts forward significant discrepancies for high velocity flows when the flow is in chemical nonequilibrium and smaller discrepancies when the flow is close to chemical equilibrium. This comparison illustrates the interest of using a ti...

Electronic Excitation of Atoms and Molecules for the FIRE II Flight Experiment

An accurate investigation of the behavior of electronically excited states of atoms and molecules in the postshock relaxation zone of a trajectory point of the Flight Investigation of ReentryEnvironment 2 (FIRE II) flight experiment is carried out bymeans of a one-dimensional flow solver coupled to a collisional-radiativemodel. Themodel accounts for thermal nonequilibrium between the translational energy mode of the gas and the vibrational energy mode of individualmolecules. Furthermore, electronic states of atoms andmolecules are treated as separate species, allowing for non-Boltzmann distributions of their populations. In the rapidly ionizing regime behind a strong shockwave, the high-lying bound electronic states of atoms are depleted. This leads to the electronic energy level populations of atoms departing from the Boltzmann distributions. For molecular species, departures from Boltzmann equilibrium are limited to a narrow zone close to the shock front. A comparison with the recent model derived by Park (Park, C., “Parameters for Electronic Excitation of Diatomic Molecules 1. Electron-Impact Processes,” 46th AIAAAerospace Sciences Meeting and Exhibit, Reno, NV, AIAA Paper 2008-1206, 2008.) shows adequate agreement for predictions involving molecules. However, the predictions of the electronic level populations of atoms differ significantly. Based on the detailed collisional-radiative model developed, a reduced kinetic mechanism has been designed for implementation into two-dimensional or three-dimensional flow codes.

Modeling of non-equilibrium phenomena in expanding flows by means of a collisional-radiative model

The effects of non-equilibrium in a quasi-one-dimensional nozzle flow are investigated by means of a collisional-radiative model. The gas undergoing the expansion is an air plasma and consists of atoms, molecules, and free electrons. In the present analysis, the electronic excited states of atomic and molecular species are treated as separate pseudo-species. Rotational and vibrational energy modes are assumed to be populated according to Boltzmann distributions. The coupling between radiation and gas dynamics is accounted for, in simplified manner, by using escape factors. The flow governing equations for the steady quasi-one-dimensional flow are written in conservative form and discretized in space by means of a finite volume method. Steady-state solutions are obtained by using a fully implicit time integration scheme. The analysis of the evolution of the electronic distribution functions reveals a substantial over-population of the high-lying excited levels of atoms and molecules in correspondence of the nozzle exit. The influence of optical thickness is also studied. The results clearly demonstrate that the radiative transitions, within the optically thin approximation, drastically reduce the over-population of high-lying electronic levels.

Analysis of the FIRE II Flight Experiment by Means of a Collisional Radiative Model

An accurate investigation of the behavior of electronically excited states of atoms and molecules in the post shock relaxation area is carried out by means of the Collisionalradiative model. The model is applied to a 1D shock tube code and the operating conditions are taken from three points in the trajectory of the FIRE II flight experiment. We account for thermal nonequilibrium between the translational and vibrational energy modes of individual molecular species and treat the electronic states of atoms and molecules as separate species. Relaxation of free-electrons is also accounted for by making use of a separate conservation equation for their energy. Non-Boltzmann distributions of the electronic state populations of atoms and molecules are allowed. Deviations from Boltzmann distributions are expected to occur in a rapidly ionizing regime behind a strong shock wave, due to the depletion of the high lying bound electronic states. In order to quantify the extent of departure from equilibrium of the electronic state populations, results are compared with those obtained assuming a Boltzmann distribution.

Global rate coefficients for ionization and recombination of carbon, nitrogen, oxygen, and argon

The flow field modeling of planetary entry plasmas, laser-induced plasmas, inductively coupled plasmas, arcjets, etc., requires to use Navier-Stokes codes. The kinetic mechanisms implemented in these codes involve global (effective) rate coefficients. These rate coefficients result from the excited states coupling during a quasi-steady state. In order to obtain these global rate coefficients over a wide electron temperature (Te) range for ionization and recombination of carbon, nitrogen, oxygen, and argon, the behavior of their excited states is investigated using a zero-dimensional (time-dependent) code. The population number densities of these electronic states are considered as independent species. Their relaxation is studied within the range 3000  K≤Te≤20 000  K and leads to the determination of the ionization (ki) and recombination (kr) global rate coefficients. Comparisons with existing data are performed. Finally, the ratio ki/kr is compared with the Saha equilibrium constant. This ratio increases more rapidly than the equilibrium constant for Te>15 000  K.The flow field modeling of planetary entry plasmas, laser-induced plasmas, inductively coupled plasmas, arcjets, etc., requires to use Navier-Stokes codes. The kinetic mechanisms implemented in these codes involve global (effective) rate coefficients. These rate coefficients result from the excited states coupling during a quasi-steady state. In order to obtain these global rate coefficients over a wide electron temperature (Te) range for ionization and recombination of carbon, nitrogen, oxygen, and argon, the behavior of their excited states is investigated using a zero-dimensional (time-dependent) code. The population number densities of these electronic states are considered as independent species. Their relaxation is studied within the range 3000  K≤Te≤20 000  K and leads to the determination of the ionization (ki) and recombination (kr) global rate coefficients. Comparisons with existing data are performed. Finally, the ratio ki/kr is compared with the Saha equilibrium constant. This ratio increases ...

Elaboration of collisional–radiative models for flows related to planetary entries into the Earth and Mars atmospheres

The most relevant way to predict the excited state number density in a nonequilibrium plasma is to elaborate a collisional–radiative (CR) model taking into account most of the collisional and radiative elementary processes. Three examples of such an elaboration are given in this paper in the case of various plasma flows related to planetary atmospheric entries. The case of theoretical determination of nitrogen atom ionization or recombination global rate coefficients under electron impact is addressed first. The global rate coefficient can be implemented in multidimensional computational fluid dynamics calculations. The case of relaxation after a shock front crossing a gas of N2 molecules treated in the framework of the Rankine–Hugoniot assumptions is also studied. The vibrational and electronic specific CR model elaborated in this case allows one to understand how the plasma reaches equilibrium and to estimate the role of the radiative losses. These radiative losses play a significant role at low pressure in the third case studied. This case concerns CO2 plasma jets inductively generated in high enthalpy wind tunnels used as ground test facilities. We focus our attention on the behaviour of CO and C2 electronic excited states, the radiative signature of which can be particularly significant in this type of plasma. These three cases illustrate the elaboration of CR models and their coupling with balance equations.

Reactive collisions between electrons and NO+ ions: rate coefficient computations and relevance for the air plasma kinetics

Extensive calculations of the rate coefficients for dissociative recombination (DR), elastic collisions, inelastic collisions (ICs) and superelastic collisions of NO+ ions on initial vibrational levels, , with electrons of energy between 10−5 and 10 eV have been performed, with a method based on multichannel quantum defect theory. Comparisons of the DR rate coefficients with the plasma experimental results give a good agreement, confirming that the vibrationally excited NO+ ions recombine more slowly than those in the ground state. Also, our ground state IC rate coefficients are very similar to previously computed R-matrix data. The rate coefficients have been fitted to a modified Arrhenius law, and the corresponding parameters are given, in order to facilitate the use of the reaction data in kinetical plasma modelling.

Collisional-Radiative Modeling Behind Shock Waves in Nitrogen

Nonequilibrium plasma, produced by the propagation of a shock wave in a shock tube or behind a shock front detached from a body entering a planetary atmosphere, requires the development of state-to-state models. The collisional-radiative model for N2 has been elaborated on in this framework for pure nitrogen flows. Its elaboration is reported in this paper. The model includes N2, N2+, N, N+, and free electrons in thermochemical nonequilibrium. The model is vibrationally and electronically specific insofar as the vibrational states of the electronic ground state of N2 and the electronic excited states of N2; and the electronic ground and excited states of N2+, N, and N+ are individually treated. These states are involved in collisional and radiative elementary processes, forming a set of around 40,000 basic data. This model is implemented in a one-dimensional flow, numerical code based on an Eulerian approach. Two test cases are treated at Mach numbers of around 30 and 40, the conditions of which relate to...

Measurement of the ground state and metastable atomic nitrogen number density in a low-pressure plasma jet

The radial profiles of metastable and ground state atomic number densities at numerous sections of a supersonic nitrogen plasma jet have been derived from UV absorption and emission spectroscopy. An original method that provides the ground state number density from the ratio of the intensities of the 119.955, 120.022 and 120.071 nm resonance lines has been developed. Along the jet axis direction, and similarly to the N and N2+ excited states, the N ground state density decreases more steeply at the centre of the jet than at its border. At the exit of the plasma source, our results throw doubt upon the nitrogen dissociation rate usually considered in the literature.

Numerical Simulation of Stagnation Line Nonequilibrium Airflows for Reentry Applications

We study the stagnation point boundary layer of high enthalpy subsonic flows obtained in inductively coupled plasma torches, aiming at determining the catalytic properties of materials for reentry applications. Simple recombination processes are often considered with the same recombination probability at the wall. In this work, a phenomenological model has been used to describe more accurately the gas-surface interaction. This model shows that the recombination processes are strongly dependent on the wall temperature, the concentration of the different species close to the wall, and the free sites available on the surface. Moreover, the wall is found to be noncatalytic at low temperatures. Then, up to a temperature T w ≃ 1400 K, the catalytic properties of the wall increase. For higher temperatures, thermal desorption becomes very efficient and the catalytic properties of the wall decrease. For the typical flow conditions studied, the gas kinetic mechanism has a small influence on the calculated wall heat flux obtained at high pressures, and a higher influence at decreasing pressures. Besides, the results show that small differences in the calculated wall heat fluxes may correspond to significant discrepancies in the profiles of species concentrations in the boundary layer.