ХИМИЧЕСКАЯ ФИЗИКА, 2004, том 23, № 9, с. 3-8
ГОРЕНИЕ И ВЗРЫВ
YÑK 541.126
PLASMA-SURFACE INTERACTIONS FOR LANGMUIR PROBE IMMERSED IN HYDROCARBON COMBUSTION FRONT
© 2004 A. Cenian1' *, A. Chernukho2, A. Bogaerts3, C. Leys4
1 Institute of Fluid-Flow Machinery, Polish Academy of Sciences, 80-952 Gdansk, Fiszera 14, Poland 2Heat and Mass Transfer Institute, PBrovki Street 15, 220072 Minsk, Belarus 3 Department of Chemistry, University of Antwerp, Universiteitsplein 1, B-2610 Antwerp-Wilrijk, Belgium 4Department of Applied Physics, Ghent University, B-9000 Gent, Rozier 44, Belgium
Received 01.10.2003
Langmuir-probes immersed in a combustion front are effective tools of flame-plasma diagnostics, including determination of flame-front arrival, ion temperature or ionization density. Particle-in-cell Monte-Carlo models, combined with computational fluid-dynamics and ion-kinetics codes may be very helpful in providing some additional information useful in interpretation of probe data. The results of the first particle-in-cell simulation of current-voltage characteristic of Langmuir probe are presented here.
1. INTRODUCTION
Langmuir probe is a well-established diagnostic tool of a low pressure, stationary plasma [1]. It allows determining the electron and ion densities, temperatures, etc. Moreover, a procedure of charge currier identification was discussed e.g. by Studniarz [2]. The electrical probe was already applied as an indicator of combustion-front arrival [3-5]; however, serious problems arise when more detailed characteristics of "combustion" plasma i.e. high-pressure, non-stationary, multi-ion medium, are investigated. Series of experiments on electric-probe diagnostics of combustion plasma were performed by MacLatchy et al. (see e.g. [6-8]) and Hirano et al. (e.g. [9, 10]). Lately Labuda et al. have done some experiments for probe immersed in combustion front propagating through a closed vessel - see e.g. [11].
The standard models of Langmuir probe (see e.g. [1]) as well as the Bohm criterion of sheath formation [12, 13] cannot be straightforward applied [14]. The realistic probe models (based e.g. on Fluid or Particle-in-cell approach) should take into account plasma-probe interactions in a multi-collisional sheath. The Fluid Models are based on a solution of the Boltzmann (or its moments i.e. continuity, momentum and energy conservation-equations) and Poisson equations. In the Par-ticle-In-Cell Monte-Carlo (PIC-MC) models the Bolt-zmann equation and the averaging procedure using a derived EEDF, are substituted by a numerical integration of an observable along the "quasi-particle" trajectories. Each "quasi-particle" represents large number (~105-1010) of electrons, positive and negative ions
* Corresponding author - e-mail: cenian@imp.gda.pl
moving in the electric field determined by a solution of Poisson's equation. A simulation box is divided by computational grid, with spacing (1/4)^D often assumed. The number of grids points considered varies between few hundreds and few thousands (e.g. 200 [15] or 2560 [16]). The particles crossing the simulation box boundaries are removed (or specular-reflected), whereas the particles injected at the boundaries are added to the simulations. The collisions are treated by MC methods as instantaneous processes, governed by the probability law related to the measured cross sections. Some approximations are applied, in order to make the problem computationally treatable.
The plasma-wall interactions have lately been investigated by using various PIC-MC models, e.g. [15, 17, 18]. For example, an important fundamental issue of multiple-sheath formation in electronegative discharges was discussed.
Kono [15] has proposed the spherical 1d2v (1D displacement 2D velocity) PIC-MC model for the probe immersed in the plasma. It determines the MC trajectories of all charged particles (including electrons), which gradually fills the empty simulation box due to the thermal particle flux from ambient plasma. The particles passing the boundaries of the simulation box are lost (absorbed on the wall or into ambient plasma). All particles move in the determined electric field. The ion collisions are treated in a simplified manner i.e. the velocity of the colliding particle is replaced by the random thermal velocity corresponding to the temperature of that species and T+ = T- = Te/100 is assumed. The stationary particle-density and potential profiles are determined.
Probe signal, rel .u. 1.0
2.5 3.0 Time, ms
Fig. 1. Langmuir probe signal in propane-butane/air stoichiometric mixture flame.
The 1d3v (1D displacement 3D velocity) PIC-MC model for electropositive plasma systems of cylindrical geometry was proposed by Kawamura et al. [18]. The 3D trajectories are calculated, however, only radial (1D) dependence of charge distribution is taken into account in Poisson's equation (due to radial symmetry). The axial component of charged particle velocity, introduced to the model, enables determination of self-sustained electric field corresponding to the chosen current density. The assumption about the charge loss and gain balance is used here i.e. at steady state electron ionization processes should balance electron losses (in volume and at the wall). The gas temperature (T), gas density (Ng), discharge tube radius (R) and axial currents are treated as the initial parameters. The rest including axial field (Ez), spatial and velocity distribution of electrons and ions are calculated from the first principles, assuming Ez(r) = const. The initial distribution of charged particles is spatially uniform, while velocities are determined using fixed energy (for electrons) or Maxwellian distribution (for ions). Already introductory investigations [14] proved that this model could be useful to study fundamental problems of plasma-wall interaction, including plasma neutrality, Bohm criterion and sheath formation.
Both, the process of sheath generation and sheath structure depend on ion identities and concentrations. It is generally accepted that the primary ion in hydrocarbon flames (CHO+) is produced during the well-known Calcote mechanism [19]. However, there are
some fast charge transfer and electron attachment processes, which lead soon to appearance of great variety of other ions. And so, Egsgaard and Carlsen [20] have
found (using mass-spectroscopy) that H3O+ and C3 H+ ions prevail during combustion of CH4, C3H8, CH4/C2H4 and CH4/C2H2 mixtures with oxygen. Fialkov [21] has reported, however, that the second ion plays major role only in fuel-rich flames.
Among the negatively charged species, produced in stoichiometric, low pressure methane flames, OH- and
CH3 ions prevail according to Feugier and van Tiggelen
[22], but HCO-, CO3, C2H3O-, OH-, C6H- and C2H-were found by Sugden et al. (1976) [23] in fuel-rich flames, with O2 as the primary negative ion.
The presence of nitrogen (air) in the combustion chamber significantly influences ion composition - see
e.g. [24-26]. In that case, NO+, NH+, NCO-, CN- and
NO2 ions play major role. Finally, Starik and Titova [27] have found from simulations of hydrocarbon/air combustion, that the main ion species, which should be taken into account to simulate the real combustion plasma, are NO+, H3O+, C2H3O+, NO-, NO- and CO-.
2. TIME EVOLUTION OF LANGMUIR-PROBE SIGNAL
Figure 1 presents the time evolution of a current signal for the spherical probe (rp = 0.1 mm, positively polarized) immersed in a combustion front propagating in stoichiometric LPG(propane-butane)/air mixture [28]. The signal rise-time lies in the range 0.12-0.2 ms. A double structure observed indicates that at least two negatively-charged species take part in the process of sheath formation. Taking into account, a significant decrease of the probe-current after changing voltage polarization, one might conclude that one of these negatively charged species are electrons.
The decay time of the first peak - related to the "electron" current - is smaller than 0.55 ms. This corresponds fairly well with the combustion-front thickness. As the chemi-ionization (and electron formation) takes place mainly in the combustion front (see e.g. [21]) it supports the idea that the first peak is related to the electron current. The following plateau and the second decay time (~1.4 ms) of the current signal are determined by the negative ion kinetics (probably by
the recombination of NO- [27]).
3. MODELING OF PLASMA-SURFACE INTERACTION
The modeling of combustion-plasma and probe interactions should include considerations related to the gasdynamic flows, chemical kinetics and plasma-dynamics. Here we investigate only the last stage i.e. the plasma-dynamic. The results of simulations will be later included into general combustion model. The 1d3v PIC-MC model (related to these of Kono [15], Kawa-mura et al. [18] and Cenian et al. [14]) will be used in order to check the possibility to derive probe characteristic. Because of model complexity and lack of data relative to the ions listed above, only 1-ion approximation will be used at this stage. The (positive) ion will be described by the mass to charge (m/z) ratio and the set of cross sections described in [14, 29, 30].
The plasma-probe interactions are studied in the system with the radial symmetry (related to the infinitely long cylindrical probe, 2rp in diameter, immersed in a continuum, non-flowing, electro-positive plasma - see Fig. 2). The whole space is separated (for the sake of simplification) into three different zones: Sheath-Pre-Sheath (SPS) zone, ring-shaped volume around it (called later "buffer zone") and the infinite rest (equilibrium "bulk plasma"), which serve as a particle-source or particle-sink for the buffer zone. The MC trajectories are calculated only for the charged particles present in SPS and buffer zones. The neutral plasma outside the pre-sheath is described by the electron (Te) and ion (T) temperatures. There is a cont
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