Anne Bourdon

Efficient models for photoionization produced by non-thermal gas discharges in air based on radiative transfer and the Helmholtz equations

This paper presents formulation of computationally efficient models of photoionization produced by non-thermal gas discharges in air based on three-group Eddington and improved Eddington (SP3) approximations to the radiative transfer equation, and on effective representation of the classic integral model for photoionization in air developed by Zheleznyak et al (1982) by a set of three Helmholtz differential equations. The reported formulations represent extensions of ideas advanced recently by S´ egur et al (2006) and Luque et al (2007), and allow fast and accurate solution of photoionization problems at different air pressures for the range 0.1 <p O2 R< 150 Torr cm, where pO2 is the partial pressure of molecular oxygen in air in units of Torr (pO2 = 150 Torr at atmospheric pressure) and R in cm is an effective geometrical size of the physical system of interest. The presented formulations can be extended to other gases and gas mixtures subject to availability of related emission, absorption and photoionization coefficients. The validity of the developed models is demonstrated by performing direct comparisons of the results from these models and results obtained from the classic integral model. Specific validation comparisons are presented for a set of artificial sources of photoionizing radiation with different Gaussian dimensions, and for a realistic problem involving development of a double-headed streamer at ground pressure. The reported results demonstrate the importance of accurate definition of the boundary conditions for the photoionization production rate for the solution of second order partial differential equations involved in the Eddington, SP3 and the Helmholtz formulations. The specific algorithms derived from the classic photoionization model of Zheleznyak et al (1982), allowing accurate calculations of boundary conditions for differential equations involved in all three new models described in this paper, are presented. It is noted that the accurate formulation of boundary conditions represents an important task needed for a successful extension of the proposed formulations to two- and three-dimensional physical systems with obstacles of complex geometry (i.e. electrodes, dust particles, aerosols, etc), which are opaque for the photoionizing UV photons.

Ignition of Propane–Air Mixtures by a Repetitively Pulsed Nanosecond Discharge

Results of an experimental study of the efficiency of the ignition of propane-air mixtures by a high voltage repetitively pulsed nanosecond gas discharge (10 kV, 10 ns, 30 kHz) are presented for the pressure range 0.35-2.0 bar. The measured minimal energy for ignition is found to decrease with the pressure. A significant reduction of the ignition delay and a decrease of the overall combustion duration were obtained by using a train of high-voltage pulses. Spectroscopic measurements in a 1-bar air just after a 10-pulse train (300 mus) of about 10 mJ in total energy show the presence of N, N+, O, and O+ atomic species and a gas temperature increase up to 3000 K

Fire II Flight Experiment Analysis by Means of a Collisional-Radiative Model

We study the behavior of the excited electronic states of atoms in the relaxation zone of one-dimensional airflows obtained in shock-tube facilities. A collisional-radiative model is developed, accounting for thermal nonequilibrium between the translational energy mode of the gas and the vibrational energy mode of individual molecules. The electronic states of atoms are treated as separate species, allowing for non-Boltzmann distributions of their populations. Relaxation of the free-electron energy is also accounted for by using a separate conservation equation. We apply the model to three trajectory points of the Fire II flight experiment. In the rapidly ionizing regime behind strong shock waves, the electronic energy level populations depart from Boltzmann distributions because the high-lying bound electronic states are depleted. To quantify the extent of this nonequilibrium effect, we compare the results obtained by means of the collisional-radiative model with those based on Boltzmann distributions. For the earliest trajectory point, we show that the quasi-steady-state assumption is only valid for the high-lying excited states and cannot be extended to the metastable states.

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...

Overview of the coordinated ground-based observations of Titan during the Huygens mission

Coordinated ground-based observations of Titan were performed around or during the Huygens atmospheric probe mission at Titan on 14 January 2005, connecting the momentary in situ observations by the probe with the synoptic coverage provided by continuing ground-based programs. These observations consisted of three different categories: (1) radio telescope tracking of the Huygens signal at 2040 MHz, (2) observations of the atmosphere and surface of Titan, and (3) attempts to observe radiation emitted during the Huygens Probe entry into Titans atmosphere. The Probe radio signal was successfully acquired by a network of terrestrial telescopes, recovering a vertical profile of wind speed in Titans atmosphere from 140 km altitude down to the surface. Ground-based observations brought new information on atmosphere and surface properties of the largest Saturnian moon. No positive detection of phenomena associated with the Probe entry was reported. This paper reviews all these measurements and highlights the achieved results. The ground-based observations, both radio and optical, are of fundamental importance for the interpretation of results from the Huygens mission.

Application of photoionization models based on radiative transfer and the Helmholtz equations to studies of streamers in weak electric fields

Recent advances in development of photoionization models in air based on radiative transfer and Helmholtz equations open new perspectives for efficient solution of nonthermal gas discharge problems involving complex geometries. Many practical applications require accurate modeling of streamer discharges developing in weak electric fields, in which the photoionization process significantly contributes to discharge dynamics. This paper (1) reports original studies, which demonstrate the validity and accuracy of the recently proposed photoionization models for studies of streamers in weak electric fields, and (2) introduces efficient boundary conditions for the photoinization models based on radiative transfer theory.

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.

The use of an improved Eddington approximation to facilitate the calculation of photoionization in streamer discharges

In the simulation of streamer discharge propagation, classical integral methods used to calculate the photoionization source term are computationally very expensive. In this work, a new approach based on the direct solution of an approximate radiative transfer equation is developed. Different approximations of the radiative transfer equation are discussed and tested for typical conditions encountered in streamer discharges. An improved Eddington approximation is shown to be very accurate to calculate the photoionization term for a Gaussian emission source term with a half-width length of the order of 0.02 cm when the absorption coefficient of the gas is higher than or equal to 50 cm−1. For steeper gradients of the source term, good agreement is obtained for higher values of the absorption coefficient. Furthermore, the computation time of the improved Eddington method is four orders of magnitude less than with the usual integral method. For streamer propagation in air at atmospheric pressure, the absorption coefficient is shown to be of the order of 130 cm−1 which validates the use of the improved Eddington approximation to calculate the photoionization term. Finally, two-dimensional calculations of a positive streamer discharge in air at atmospheric pressure in plane–plane geometry with the improved Eddington approximation are presented.

The use of the ghost fluid method for Poisson's equation to simulate streamer propagation in point-to-plane and point-to-point geometries

This paper presents the application of the ghost fluid method (GFM) to solve Poissons equation for streamer discharge simulations between electrodes of complex geometries. This approach allows one to use a simple rectilinear grid and nevertheless take into account the influence of the exact shape of the electrode on the calculation of the potential and the electric field. First, the validity of the GFM approach concerning the computation of the electric field is demonstrated by performing direct comparisons in a point-to-plane geometry of the Laplacian potential and electric field calculated with this method and given by the analytical solution. Second, the GFM is applied to the simulation of a positive streamer propagation in a hyperboloid-to-plane configuration studied by Kulikovsky (1998 Phys. Rev. E 57 7066–74). Very good agreement is obtained with the results of Kulikovsky (1998) on all positive streamer characteristics during its propagation in the interelectrode gap. Then the GFM is applied to simulate the discharge in preheated air at atmospheric pressure in point-to-point geometry. The propagation of positive and negative streamers from both point electrodes is observed. After the interaction of both discharges, the very rapid propagation of the positive streamer towards the cathode in the volume pre-ionized by the negative streamer is presented. This structure of the discharge is in qualitative agreement with the experiment.

Simulation of the discharge propagation in a capillary tube in air at atmospheric pressure

This paper presents simulations of an air plasma discharge at atmospheric pressure initiated by a needle anode set inside a dielectric capillary tube. We have studied the influence of the tube inner radius and its relative permittivity ?r on the discharge structure and dynamics. As a reference, we have used a relative permittivity ?r = 1 to study only the influence of the cylindrical constraint of the tube on the discharge. For a tube radius of 100??m and ?r = 1, we have shown that the discharge fills the tube during its propagation and is rather homogeneous behind the discharge front. When the radius of the tube is in the range 300?600??m, the discharge structure is tubular with peak values of electric field and electron density close to the dielectric surface. When the radius of the tube is larger than 700??m, the tube has no influence on the discharge which propagates axially. For a tube radius of 100??m, when ?r increases from 1 to 10, the discharge structure becomes tubular. We have noted that the velocity of propagation of the discharge in the tube increases when the front is more homogeneous and then, the discharge velocity increases with the decrease in the tube radius and ?r. Then, we have compared the relative influence of the value of the tube radius and ?r on the discharge characteristics. Our simulations indicate that the geometrical constraint of the cylindrical tube has more influence than the value of ?r on the discharge structure and dynamics. Finally, we have studied the influence of photoemission processes on the discharge structure by varying the photoemission coefficient. As expected, we have shown that photoemission, as it increases the number of secondary electrons close to the dielectric surface, promotes the tubular structure of the discharge.