[American Institute of Aeronautics and Astronautics 49th AIAA Aerospace Sciences Meeting including...

American Institute of Aeronautics and Astronautics

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Modeling of Streamer Discharges in Supersonic Flows for Combustion Applications

Doug Breden1 and Laxminarayan Raja2

University of Texas at Austin, Austin, Texas, 78712

Nanosecond pulsed plasma discharges can significantly reduce ignition delay time in supersonic fuel-oxidizer mixtures. While it is generally believed that such plasmas enhance combustion through fast production of radicals, there is still some uncertainty over the detailed kinetics which takes place during the pulse along with the importance of mechanisms such as gas heating. In this work, simulations of single 10 ns pulses in supersonic O2-H2 and argon flows are presented. Different polarities are investigated at voltages ranging from 4 kV to 8 kV. Results indicate that the anodic pulse plasma forms in filamentary streamers while the cathodic pulse plasma forms above the dielectric surface due to charge trapping. The bulk plasma is weakly ionized with O radical densities on the order of 1021 m-3 (~0.5% of the mixture) observed in addition to metastables such as O(1D), O2(a1Δg) and O2(b1Σg

+). The O2-H2 plasma is highly electronegative in the bulk, while the argon plasma is electropositive. Increasing peak voltages increase plasma volume, peak species densities, and peak gas temperatures. Rapid gas heating on the order of hundreds of Kelvin is observed within the streamer channels and at the electrode edges of the O2-H2 plasma, which results in the formation of “micro blast” waves which propagate into the flow. For the electronegative argon plasma, gas heating is confined primarily to the electrode edges while gas heating in the bulk plasma is negligible.

Nomenclature Zk = species charge number

kn = species number density μk = species mobility coefficient Dk = species diffusion coefficient

k = species particle flux

0 = permittivity of free space

= electrostatic potential kiE = inelastic collision energy transfer

k = secondary electron emission coefficient

bkkv , = mean momentum transfer collision frequency

bkkg , = mean relative speed of species k with respect to bulk species

bkk , = mean momentum cross section of species k with respect to bulk species

sn = wall outward unit normal vector

1 Graduate Research Assistant, Aerospace Engineering and Engineering Mechanics, 210 East 24th Street, W. R. Woolrich Laboratories, 1 University Station, C0600 Austin, Texas 78712-0235, AIAA Student Member. 2 Associate Professor, Aerospace Engineering and Engineering Mechanics, 210 East 24th Street, W. R. Woolrich Laboratories, 1 University Station, C0600 Austin, Texas 78712-0235, AIAA Member.

49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition4 - 7 January 2011, Orlando, Florida

AIAA 2011-909

Copyright © 2011 by Doug Breden and Laxminarayan L. Raja. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.


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I. Introduction

Non-equilibrium plasmas produced by high-voltage nanosecond pulses have shown significant promise in applications such as flow actuation [1] [2] [3] [4], stabilization of lean air flames [5] [6], and ignition of supersonic flows [7]. Nanosecond pulse discharges are of great interest due to their ability to efficiently ionize gases at high pressures compared to glow and rf discharges [8]. The high reduced electric fields (E/N) created by the discharge preferentially heat the high energy tail of the electron energy distribution function where electrons efficiently ionize and dissociate the gas. By truncating the pulse to tens of nanoseconds or less the plasma does not have time to thermalize, which minimizes power lost due to bulk heating of the gas. The discharge is then pulsed at a frequency which allows the plasma density to be maintained.

There have been numerous experiments and numerical simulations [9] [10] [11] [12] [13] [14] [15] which have investigated nanosecond pulsed plasmas for combustion enhancement. The primary means by which such plasma is believed to enhance flow ignition is through production of combustion enhancing radicals such as O, H and OH. Plasmas can produce radicals by thermal dissociation, electron impact dissociation or electronic excitation of metastable states. Electron impact dissociation occurs on much shorter (nanosecond) time scales than thermal dissociation and therefore has the ability to significantly reduce ignition delay. Another mechanism by which the plasma can enhance combustion of the mixture is through electronic excitation of the bulk gas (oxygen or nitrogen) into long lived metastable excited states. The electron energy essentially gets stored by these metastable molecules which are then advected downstream of the discharge region. Experiments and simulations [15] [16] [17] have demonstrated that metastable oxygen produced by non-equilibrium plasma can reduce ignition delay of fuel-air mixtures by 1-2 orders of magnitude. Other experiments [18] and simulations [19] have demonstrated that metastable species produced by the discharge (such as metastable nitrogen) can play a dominant role in the dissociation of oxygen molecules into O radicals. An important step to understanding how non-equilibrium plasmas enhance ignition is to accurately model gas heating, radical species production, and metastable species production which take place within a pulse.

The primary goal of this paper is to provide a comprehensive understanding of the plasma dynamics and radical production mechanism in a single nanosecond pulse applied to a premixed supersonic flow stream. We simulate a single nanosecond pulse in premixed oxygen-hydrogen and model the production of combustion enhancing species and gas heating due to the plasma. To simulate the high-voltage nanosecond pulses, we utilize a non-equilibrium plasma solver with finite-rate chemistry coupled with a compressible Navier-Stokes solver. The simulations utilize a high-pressure oxygen-hydrogen chemistry to model the production of combustion enhancing radicals such as O atoms and the excited metastables O(1D), O2(a1Δg), and O2(b1Σg

+) at different voltages and polarities. We also perform simulations with a high-pressure argon chemistry for the purpose of comparing the effects of different chemistries on plasma formation for an identical pulse and flow configuration.

Section II presents the governing equations and discretization scheme utilized by the plasma and flow solver. Section III discusses the oxygen-hydrogen and argon chemistries and provides a discussion of the rationale behind the inclusion of the different species and reactions. Section IV presents the simulation domain and pulse configuration. Section V presents a discussion of the results obtained from all simulations along with figures. Section VI concludes this paper with a summary of the results and conclusions.

II. Description of Model The governing equations, numerical discretization schemes, and boundary conditions utilized by both solvers

are presented in this section. A self-consistent, two-temperature plasma solver with finite rate chemistry developed by our group [20] [21] is utilized to simulate the high voltage pulses and resulting plasma discharge. To model the effects of the plasma on the supersonic bulk flow and vice versa, a Navier-Stokes flow solver developed by Mahadevan [21] was coupled to the plasma solver by passing electrostatic forcing and plasma heating source terms from the plasma solver to the flow solver and then passing the resulting pressure, temperature and velocity fields to the plasma solver.


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A. Plasma Governing Equations

The governing equations consist of species continuity equations coupled with Poisson’s equation. Individual continuity equations are solved for each species modeled by the plasma and the species fluxes are determined using the drift-diffusion approximation. A two temperature model is used where the heavy species are assumed to have one temperature, Tg, and the electrons are assumed to have a separate temperature, Te. The full electron energy equation is solved by the plasma solver, while the gas energy equation with plasma heating source terms is solved using the Navier-Stokes solver.

i. Continuity

The number density for each species is obtained by solving a separate continuity equation with source terms for each species.

kkk Rt

n, )(,...2,1 bg kkKk (1)

The source terms are found using finite rate chemistry reactions such as ikkik GnnR for two-body reactions and

ijkkjik GnnnR for three-body reactions. The reaction rate coefficients are tabulated in Table 1 and Table 2. The background species number density (O2 or argon for the simulations) is obtained using the ideal gas law

kBk Tknp and the bulk gas pressure, which is obtained from the flow solver.

ii. Drift-Diffusion

The charged and neutral species number flux is found using a drift-diffusion approximation with a bulk convection term.

VnnDnZun kkkkkkkkk (2)

Zk is the charge number (e.g. -1 for electrons and +1 for positive ions). The ion species mobilities are found using

the formulabkk

kk vm

eZ

,

where the electron mobility coefficients are obtained using BOLSIG+ (22) and tabulated

as a function of the mean electron temperature. The diffusion coefficients for all species are obtained using Einstein’s relation. The momentum transfer collision frequency is found using the formula

bbbb kkkkkkk gnv ,,, . Bulk convection due to the supersonic flow field obtained from the Navier-Stokes solver is taken into account by the third term.

iii. Poisson Equation

The Poisson’s equation, shown below in Eq. (3), is solved to obtain the self-consistent electrostatic potential required by the drift-diffusion approximation and energy equations.

kkk nZ

e

0

2

(3)


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iv. Electron Energy

Electron temperatures, which are obtained from the mean electron energy, are calculated directly by solving the

complete electron energy equation, shown below in Eq. (4).

ikege

k

eebi

eieeeeee

eb

b

vTTmm

nkrEeeTkupet

e,)(

223))((

(4)

The total electron energy is assumed to be approximately equal to the mean electron energy ee 3/2 nekbTe while the pressure is found using the ideal gas law. The right hand side incorporates three source terms: electron Joule heating, inelastic collisional energy loss and elastic collisional energy loss respectively. ΔEi

e is the energy lost by an electron in eV due to a collision with heavy species i. B. Fluid Flow Governing Equations

The 2-D compressible Navier-Stokes equations with heating and electrostatic forcing source terms are shown below.

SFFdt

dUviscousinviscid

tevu

U

(5)

Where ρ is the bulk fluid density obtained from adding all the species densities, u and v are the x and y components of the bulk fluid velocity respectively, and et is the gas energy.

The two dimensional in viscid and viscous flux terms of the Navier-Stokes equations are shown below.

j

vPePv

vu

v

i

uPeuv

Pu

u

F

tt

inviscid

)()(

2

2

j

qvu

i

qvu

F

yyyx

yy

yx

xxyxx

xy

xxviscous

0

ˆ

0

The viscous flux terms are given by i

j

j

ixx x

x

xx

ji. The heat flux q is obtained using Fourier’s law.

The total fluid energy is )( 2221

)1( vue Pt where у is the ratio of specific heats. The gas energy is assumed

to be for all heavy species (ions and neutrals) and is solved separately from the electron energy.

The source terms for the momentum and energy equations are obtained from the plasma solver. xf and yf are the electrostatic forcing (momentum source) terms due to the self-consistent electric fields and Sg is the plasma gas heating (energy source) term.


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VfS

ff

S

ESg

y

x

0

ikege

k

eebi

kikkthg b

vTTmm

nkrEeeZS ,)(223

(6)

The first term in the gas heating source term represents ion Joule heating, where an ion Joule heating

thermalization factor, ηth , is included to account for energy loss to the walls. The thermalization factor will be

smaller at lower pressures and shorter length scales. Unfer and Boeuf [1] assume all the ion Joule energy is

transferred to gas heating (ηth=1.0) at pressures of one atmosphere. For the simulations in this work, it is assumed

approximately 75% of ion Joule energy is transferred to gas heating while the rest is lost to the wall (ηth=0.75). The

second and third terms represent transfer of energy between electrons and heavy species due to inelastic and elastic

collisions respectively.

C. Boundary Conditions

Flux boundary conditions are specified for all plasma and flow equations that are solved on the domain. Dirichlet boundary conditions can be specified for all inflow, outflow, and wall boundaries in the form of fixed flux quantities or symmetry (zero flux).

All electrons, ions, and neutrals are assumed to have a Maxwellian flux component at solid walls. The electron flux into the wall is given by Eq. (7). The second term in Eq. (7) is due to secondary emission of electrons at the wall due to ion bombardment.

k

kke

ebese

mTk

nn21

841

(7)

For ions and neutrals, the flux is given by the Eq. (8), where the second term accounts for the flux of species k

due to the electric field.

)(8

41 2

1

nnZm

Tkn kkk

k

gbkk

(8) The electron energy flux towards a solid surface is given by Eq. (9).


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k

kksee

e

ebeebse Ee

mTk

nTknQ21

841

25

(9)

For dielectric surfaces, charged species can be trapped at the surface due to a local surface charge induced

electric field which can be modeled by solving the ODE in Eq. (10) to determine surface charge density ρs.

kskk

s nZet

(10)

The potential at the dielectric boundary can then be found analytically using Gauss’ Law shown by Eq. (11),

where φb is the potential at the dielectric surface, φc is the potential in the solution at a distance Δx from the boundary, εd and d are the dielectric constant and thickness of the dielectric respectively, and φback is the potential on the other side of the dielectric.

dx

dx

d

backd

sc

b

0

0

1 (11)

D. Numerical Scheme

The individual species fluxes are discretized in space using a first-order accurate hybrid-power law scheme described by Patankar [23]. The Joule heating source term is discretized using a flux reconstruction approach described by Deconinck et al [24]. The species continuity and electron energy equation are discretized in time using first-order backward Euler and solved implicitly using the PETSc Krylov solver package [25]. The electrostatic Poisson equation is solved semi-implicitly using an explicit predictor step for the electron number densities.

The inviscid flux terms of the Navier-Stokes equations are discretized using a second-order accurate advection upwind splitting scheme (AUSM) and the viscid flux terms are discretized using the method of Hasselbacher. A fourth-order Runge-Kutte time discretization scheme is used to obtain a time accurate solution of the flow variables.

The governing plasma and flow equations are solved on the same unstructured two-dimensional mesh in a time accurate manner. The plasma solver time steps utilized for the following simulations are on the order of picoseconds or less during the pulse. Because the flow timescales are typically much larger (microseconds) than the plasma timescales (picoseconds), we use flow solver time steps on the order of nanoseconds to speed up the simulations.

III. Chemistry A. Oxygen-Hydrogen Chemistry

The primary chemistry utilized for the simulations performed herein is a reduced oxygen-hydrogen mechanism consisting of 16 species: electrons, O2, H2, O, H, OH, O+, O2

+, O4+, O-, O2

-, H+, H2+, O(1D), O2(a1Δg) and O2(b1Σg

+). The mechanism consists of 87 reversible and irreversible reactions which include electron ionization, electron dissociation, electronic excitation of metastables, attachment, ion-ion, ion-neutral, metastable quenching, as well as metastable and neutral combustion reactions which are compiled in Table 1. Electron impact reaction rates were calculated using BOLSIG+ [22] using cross-sectional data compiled by [26]. The two-body electron impact reaction rates with oxygen calculated from BOLSIG+ are plotted in Figure 1. The remaining reaction rate coefficients were compiled from a variety of sources and are tabulated in Table 1 of the appendix in the form Gi = ATBexpC/T. The units for all tabulated reaction rates are in molecules, meters and Kelvin.

Our primary focus is to accurately model the production of radical and metastable species. Most experiments of nanosecond pulse plasmas for ignition enhancement investigate formation of combustion enhancing radicals such as O, H, and OH. Other experiments such as [27] [17] and numerical simulations such as [15] have investigated the effects of metastables on combustion enhancement, primarily the oxygen metastables O(1D), O2(a1Δg), and


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O2(b1Σg+). We model these metastables as separate species while the higher energy electronically excited states such

as the Herzberg state (4.5 eV) are combined into the reaction rates G7 and G8 which act to remove energy from the electrons.

In early simulations [28] we included combustion reactions with species such as H2O, H2O2, and HO2 from the GRI 3.0 mechanism. None of these species except for O, H and OH radicals were observed in significant amounts during the microsecond timescales of those simulations. We therefore neglect all the combustion reactions and species except those involving O, H and OH for the simulations performed in this work. To model the plasma itself, we include O+, O2

+, O4+, O-, and O2

- ions in our chemistry. From previous simulations it is known that O2+ is the

dominant ion in the plasma. O4+ is produced by three-body reactions involving O2

+ and can be significant at higher pressures. O+ is produced by electron-impact dissociation and has also been included. Oxygen discharges are typically electronegative; therefore we include O- and O2

- ions. Ion-neutral, ion-ion, metastable-ion and quenching reactions for all ion species are included.

The energetics of the plasma discharge are taken into account by including reactions G5-G11 which account for

energy lost due to rotational, vibrational and electronic excitation of oxygen and hydrogen. We assume that rotationally excited oxygen and hydrogen are immediately de-excited and return their energy to the bulk gas. We make the assumption that the relaxation rates for vibrational and the electronically excited oxygen and hydrogen are much greater than the nanosecond time scales of a single pulse. We therefore assume that all electron energy that goes into vibrational and electronic excitation (G6, G7,G8, G10, G11) is advected out of the system. The exception is the electronic excitation of the metastable species included in the chemistry. Energy transfer between electrons and metastables is taken into account by excitation reactions and quenching reactions are included to account for inelastic heating of the bulk gas.

Figure 1 – Two-body electron-O2 impact reaction rates from BOLSIG+

B. Argon Chemistry

The purpose of the argon simulations is to provide a comparison between the plasma discharges in an electropositive gas (argon) with that in an electronegative gas (oxygen). The argon simulations utilize a high pressure chemistry mechanism used in previous work to model micro-cavity discharges [20]. It consists of 6 species and 14 irreversible reaction rates tabulated in Table 2 in the form Gi = ATBexpC/T where T is the temperature of the bulk gas or the electrons. Electron-impact reaction rates and electron motilities where obtained using the BOLSIG+ [22] external program and tabulated as a function of mean electron temperature. The units for all tabulated reaction rates are in molecules, meters and Kelvin.


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IV. Simulation Configuration A configuration similar to that used in the experiments by the Mungal-Cappelli group at Stanford was chosen

for all simulations performed in this work [11]. The experiments involved a supersonic O2-H2 mixture at atmospheric pressures and temperatures flowing over a flat plate with two pin-electrodes (0.8 mm diameter) flush mounted to the surface. High-voltage repetitive pulses (8 kV peak voltage and 20 ns pulse duration) were applied which resulted in the observation of flow ignition downstream of the discharge. A similar configuration to the experiments in [11] is chosen, with a flat plate geometry with pin electrodes and supersonic O2-H2 flow. Unlike the experiments, a smaller electrode is modeled (0.2 mm) and a much higher circuit ballast resistance is used to limit particle current densities. From the experiments, the resulting pulse peak current draw is on the order of 50 A which requires time steps on the order of pico to femtoseconds to resolve. Simulating a pulse on a single processor using such small time steps would require unacceptably long computational run times. For the simulations presented herein, a ballast resistance of 30 kΩ was used to limit the particle current draw to tens of mA, allowing larger plasma solver time steps.

Two subdomains are utilized for all simulations: a gas subdomain upstream of the electrode where only the flow solver is activated and a plasma sub domain in the region downstream of the gas sub domain where both the plasma and flow solvers are activated.

Figure 2 - The two sub domains utilized by the simulations. Both solvers are used in the plasma sub domain, while only the

flow solver is used in the gas sub domain.

For all flow simulations, an incoming Mach 3 flow with a static pressure of 225 Torr (30 kPa) and static temperature of 300 K was chosen. The gas subdomain is included to capture the initial oblique shock that forms at the front edge of the flat plate and to give the boundary layer sufficient time to reach a relatively uniform thickness near the powered electrode region as seen below in Figure 3.

Figure 3 - Pressure and x-velocity contours for steady state flow before the voltage pulses are applied.

The plasma subdomain is 2.5 mm across, 0.5 mm high, and consists of 8,000 cells. It is centered on a single powered electrode that measures 0.2 mm across. The electrode is indicated by a black box while the surrounding dielectric is shown in red. For all simulations, it is assumed that the grounded electrode is downstream of the powered electrode outside of the computational domain. In previous simulations, a two-electrode configuration with 0.8 mm electrodes separated by a 6.2 mm gap identical to the Mungal-Cappelli experiments was used. From these simulations we found that for short pulses, the plasma formed primarily in the vicinity of the powered electrode as seen below in Figure 4. By focusing on a single electrode in the simulations, the mesh can be refined around this region to obtain better resolution of the plasma discharge.


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Figure 4 - Sample image of the plasma forming over the electrode. Subsequent results will focus on the electrode near field

region.

For all simulations, a 10 ns trapezoidal pulse with 2.5 ns rise and fall time is applied. The power supply is modeled as a voltage source in series with a ballast resistor as seen in the figure below. As mentioned above, the ballast resistance for all simulations was set to 30 kΩ. This value is much higher than that used in the experiments in [11] and was chosen for numerical reasons as it limits current densities within the plasma which in turn allows for larger time steps. The electrode is assumed to be made of tungsten with a secondary electron emission coefficient of 0.015 taken from Lieberman and Lichtenberg [29]. The wall is modeled as a thin dielectric layer with a thickness of 1 mm and a dielectric constant of 8.0. The gas boundaries are modeled using inflow/outflow boundary conditions and symmetry boundary conditions are used for the voltage. An initial electron density of 1014 m-3 was assumed for all simulations.

Figure 5 – Overall configuration showing incoming flow conditions and the power supply arrangement. Note that most of the

mesh cells have been clustered near the electrode edges.

V. Simulation Results In this section, the results are presented and discussed. At the voltages utilized by the simulations the reduced

electric fields (E/N where E is the electric field and N is the number density of the O2-H2 mixture) can reach levels as high as 103 Townsend or more (1 Townsend equals 10-17 V cm-2). The resulting discharges are characterized by cathode-directed streamers which originate at the edges of the electrode for positive pulses and charge trapping with reverse breakdown streamer for negative pulses. A discussion of the physics of streamer discharges can be found in the book by Raizer [35].

There have been several computational studies in recent years which have modeled 2-D and 3-D streamer discharges in air mixtures [30] [31] [32] [33] [34] and for applications involving actuators [1] [2]. For this work, the focus is on the production of combustion enhancing species and gas heating within the plasma. Comparisons are made between simulations with different voltage polarities, different voltage magnitudes (4-8 kV), different chemistries (O2-H2 versus argon), and simulations with and without the flow. The primary results of interest are the


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formation of the plasma and its composition, the amount of combustion radicals and metastable oxygen produced by the discharge, and thermal phenomena such as gas heating and pressure waves due to the plasma.

A. Voltage Polarity a. Anodic Pulse (4000 V)

Figure 6 illustrates the formation of the plasma at different time intervals during the pulse. For positive polarity voltage pulses, the resulting plasma is produced in two cathode directed streamers which propagate away from the powered electrode, parallel to the dielectric surface. Streamer propagation takes place entirely within the fluid mechanical boundary layer, and the two streamers are essentially symmetric in the upstream and downstream directions.

Figure 6 – anodic (+4 kV) pulse streamer formation

From Figure 7 it is seen that gas breakdown occurs at approximately 3000 V. Power is deposited into the gas only during the ramping phases at the beginning and end of the pulse when the electric fields are strongest. During the gas breakdown phase, most of the power draw is due to electron conduction current into the anode which drives the production of the plasma. At the down-ramp of the pulse, the conduction current and power deposition is due to ion current, primarily O2

+, which deposits energy as heat.

Figure 7 – Voltage and particle conduction power at electrode and dielectric surfaces for anodic pulse (4 kv). Dashed line

represents voltage while solid lines are particle conduction power per unit meter depth into the surface.


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Most streamer propagation takes place during the first 3-5 ns of the pulse. The reduced electric field in the streamer head is on the order of 104 Townsend or higher as the streamers propagate outwards as seen below in Figure 8. Within the streamer channels, the reduced electric field is on the order of 102 Townsend. At such high reduced electric fields, dissociation and ionization reactions are dominant. Electrons are only present in significant quantities (1019 m-3) during streamer propagation and only within the streamer heads. In the streamer channels, the reduced electric field is much lower and electrons are lost due to attachment reactions which form O2

-. The competing processes of ionization and electron attachment at high versus low E/N essentially sets a floor on the minimum E/N for which the streamers will propagate, as discussed in Raizer [35].

Figure 8 - Reduced electric field, electron density and electron temperature 3 nanoseconds after the start of the pulse.

Figure 9 indicates the dominant positive ion in the plasma is O2+

(peak ~5 x 1020 m-3), followed by O+ (peak ~1 x 1020 m-3) and H2

+ (peak 1 x 1019 m-3). The resulting plasma is highly electronegative with the dominant charged particle being O2

- (peak ~5 x 1020 m-3) followed by O- (peak ~1 x 1020 m-3). Negative ion charge buildup can be observed above the dielectric and electrode surface. The remaining ions that were included in the chemistry mechanism (H+, O4

+) are present in negligible quantities.

Figure 9 - Dominant plasma ion species density contours after 10 ns (end of pulse).

The dominant combustion radical is atomic oxygen (peak ~2 x 1021 m-3), followed by atomic hydrogen (peak ~1 x 1020 m-3) and OH (peak ~1 x 1019 m-3). Note that the O radical densities due to electron-impact dissociation exceeds the peak density of the plasma itself by approximately one order of magnitude indicating that dissociation is the dominant reaction. During the pulse, O(1D) number densities exceed O2(a1Δg) and O2(b1Σg

+) due to the high electric fields which favor dissociation reactions. Note that O2(b1Σg

+) is present in larger quantities after the pulse than O2(a1Δg), despite the reaction rate for O2(a1Δg) being higher (Figure 1). This is most likely due to rapid quenching of O(1D) into O2(b1Σg

+). For our simulations, the peak O mole fraction is 4 x 10-3 or approximately 0.5%. It is believed that increased O

radical densities, even in quantities as low as 0.5%, are the primary means which lead to a faster initiation of chain reactions and a reduced ignition delay [19]. It is difficult to compare our results with those from experiments and simulations in the literature, as most data is for air-fuel mixtures where nitrogen contributes significantly to O radical production. Experiments and simulations such as [36] and [19] using methane-air mixtures detected O radical densities on the order of 10-4-10-3.


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Figure 10 - Radical and metastable species contours after 10 ns (end of pulse).

Most gas heating is due ion Joule heating which takes place during the ramping stages of the pulse. Inelastic heating due to quenching reactions takes place within the plasma, but at an order of magnitude lower than ion Joule heating. Elastic collisional heating is negligible compared to the other two source terms.

Figure 11 illustrates the time evolution of the temperature and pressure fields over the 200 ns simulation time of the anodic pulse. The peak gas temperature is approximately 1200 K, which amounts to an increase of about 400 K over the wall recovery temperature which is approximately 800 K. The most intense heating takes place at the cathode edges where the reduced electric fields are greatest, but heating on the order of 10s of Kelvin also occur within the streamer channels. The rapid increase in temperature at the electrode edges and within the streamer filaments results in compression waves which propagate into the free stream as in Figure 11. Such micro blast waves were observed experimentally from Adamovich et al [10] and Starikovskii et al [37] as well as numerically by Unfer et al [1].

Figure 11 - Temperature and Pressure contours from end of anodic pulse (10 ns) to 200 ns after pulse.

b. Cathodic Pulse (4000 V)

Figure 12 illustrates the formation of the plasma at different time intervals during the pulse. Compared to the anodic pulse plasma which forms entirely within streamer channels, we see two different types of plasma form. Electron charge trapping takes place on the dielectric adjacent to the electrode over which plasma forms. At the electrode edges, two reverse breakdown streamers form much like those seen in the DBD actuator simulations from [2].


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Figure 12 – Cathodic (-4 kV) pulse plasma formation

The voltage and particle conduction power for the cathodic pulse are shown in Figure 13. Gas breakdown occurs at a voltage magnitude of about 3500 V. The electrode particle conduction power is due to ions while the electrode power deposition is due to electrons. The peak power and the duration of power deposition are greater than that seen in the anodic pulse which results in greater ion Joule heating of the gas for the cathodic pulse.

Figure 13 – Voltage and particle conduction power at electrode and dielectric surfaces for anodic pulse (4 kv). Dashed line

represents voltage while solid lines are particle conduction power per unit meter depth into the surface.

Figure 14 displays the electron density, electron temperature and reduced electric field 3 nanoseconds into the pulse. Electrons are present only during the ramping phases of the pulse in the surface plasma and the heads of the two small streamers which propagate. The magnitudes of the electron density, electron temperature, and reduced electric fields are comparable to the anodic pulse, although they are more intense in the vicinity of the electrode edges.


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Figure 14 - Electron density, electron temperature and reduced Electric field 3ns after the start of the pulse.

Figure 15 shows the densities of the dominant at the end of the pulse (10ns). Like the anodic pulse, the plasma is

highly electronegative with O2+ and O2

- forming the dominant positive and negative charged species, respectively.

Figure 15 - Dominant plasma ion species contours after 10 ns (end of pulse).

Figure 16 shows the densities of the radical and metastable species after 10 ns. The magnitudes are comparable to those seen in the anodic pulse, with most of the radicals and metastables produced within the reverse breakdown streamers. The surface plasma produces radicals and metastable at densities approximately one order of magnitude lower than those seen in the reverse breakdown streamers.

Figure 16 - Radical and metastable species contours after 10 ns (end of pulse).


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Figure 17 illustrates the time evolution of the temperature and pressure fields over the 200 ns simulation time of the cathodic pulse. Gas heating in cathodic pulses is more intense compared to anodic the pulse. The peak temperature is over 2000 K at the electrode edge, which is an increase of over 1200 K compared to the wall recovery temperature in that region. For comparison, the max temperature increase in the anodic pulse is on the order of 400 K. Most of the gas heating is due to ion Joule heating which is a consequence of the ion conduction current observed during the first half of the pulse. The rapid increase in temperature in a small volume results in blast waves which emanate from the electrode edges.

Figure 17 - Temperature and Pressure contours from end of pulse (10 ns) to 200 ns after pulse

B. Voltage Magnitude : Comparison of Pulses from 4-8 kV

For anodic and cathodic pulses, increasing the voltage increases the volume of gas which is ionized by the discharge. For anodic pulses, the streamer propagation distance approximately triples as seen in Figure 18. For cathodic pulses (not shown), increasing the voltage increases the distance from the electrode over which plasma forms on the dielectric surface but has little effect on the streamers which form at the electrode edges. Note the formation of plasma on the surface of the dielectric for the 8 kV anodic case during the down ramp phase of the pulse (7-10 ns). This is due to the reversal of the electric field, discussed by Macheret et al [8], which takes place at the end of the pulse due to the low mobility of the positive ions in the streamer channels and the rapid change in electrode voltage. This electric field acts much like a cathodic pulse which is why we see plasma formation on the dielectric surface like in the cathodic pulse case.


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Figure 18 - Snapshots of O2

+ ion illustrating streamer propagation for 4 kV, 6 kV and 8 kV pulses respectively.

Figure 19 compares the temperature and pressures profiles of the anodic pulse simulations after 50 ns. Increasing voltage from 4 – 6 kV doubles the peak temperature due to gas heating, from 1200 K to 2400 K. In addition, a much larger volume of gas is heated due to heating taking place within the streamer channels. Gas temperatures are also observed to increase with increasing voltage in the cathodic pulses. Increasing the voltage from 6-8 kV did not result in a noticeable increase in peak temperature compared to the 6 kV case, although the volume of gas which is heated increased.


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Figure 19 - Comparison of temperature and pressure fields 50 ns into simulations (40 ns after end of pulse)

Increasing voltages also results in an increase in peak species densities for anodic and cathodic pulses. Increasing the voltage has the most dramatic effect on peak O radical densities, which nearly triple as the voltage is increased from 4 kV to 8kV. The peak densities of the plasma species on the other hand, only increase moderately as the voltage increases. This is because dissociation reactions become more dominant as the reduced electric field is increased. C. Chemistry : Argon versus O2-H2

The simulations performed using argon and O2-H2 demonstrate that chemistry makes a dramatic difference. Although the general features of plasma formation are the same for both chemistries, such as positive streamer formation for anodic pulses and charge trapping for cathodic pulses, there are significant differences. The biggest difference between these two chemistries is the presence of negative ions which results in differences in streamer propagation distance at comparable voltages. Even between various O2-H2 mechanisms such as the simplified mechanism used in previous work by our group, including or neglecting certain species or reactions, particularly negative ions, can dramatically change the characteristics of the plasma. In previous simulations, electron densities were comparable to positive ion densities much like the argon plasma. In the current simulations, the inclusion of negative ions results in a plasma which is highly electronegative, with negligible amounts of electrons in the streamer channels.

Figure 20 and Figure 21 illustrate the formation of the argon plasma for a 4000 V anodic and cathodic pulse respectively. Like the O2-H2 test cases, the anodic pulse plasma forms in cathode directed streamers which propagate away from the electrode. The cathodic pulse plasma initially forms above the dielectric due to charge trapping, from which two streamers can be seen propagating above the electrode. Compared to the O2-H2 simulations, voltage breakdown occurs at a lower voltage and the electrons are not consumed by any attachment processes, allowing the streamers to propagate much farther compared to the highly electronegative O2-H2 plasma. Note that the argon streamers for both anodic and cathodic pulses propagate above the flow boundary layer. The O2-H2 streamers on the other hand, propagate entirely within the thickness of the boundary layer.


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Figure 22 shows the particle conduction power for both anodic and cathodic pulses per unit meter extrusion depth. It can be seen that power deposition for the anodic pulse is approximately an order of magnitude greater than the cathodic pulse. The disparity in power deposition into the plasma results in a peak cathodic pulse plasma density approximately one order of magnitude lower than the anodic pulse peak plasma density. Most of the ion Joule gas heating in the anodic pulse takes place after the pulse, indicated by (ion) particle current flux into the electrode in (a). There is no noticeable gas temperature increase for the cathodic pulse.

Figure 22 – Anodic (a) and cathodic (b) pulse instantaneous particle conduction current. The dashed line represents voltage at the electrode while solid lines represent power due to particle fluxes at the electrode and dielectric surfaces.

This difference in power deposition translates into dramatically different heating profiles between the two cases. For the anodic pulse, most gas heating takes place after the pulse, as seen below in Figure 23. Peak gas temperatures for the 4 kV anodic pulse (~5000 K) are more than double the peak gas temperature of the O2-H2 4 kV anodic pulse (~1200 K) . For the argon cathodic pulse on the other hand, the negligible power deposition results in virtually no gas heating. This trend is opposite that seen for O2-H2 where cathodic pulses produce higher gas temperatures.

Figure 20 - Anodic anodic (+4 kV) pulse electron density

Figure 21 - Argon cathodic (-4kV) pulse electron density


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Figure 23 - gas temperature profile for argon anodic (4 kV) pulse 10 ns and 20 ns after start of pulse.

D. Flow Effects

The primary effect that the flow has on the formation of the plasma is the decrease in number density within the boundary layer due to increasing temperature and pressure. This results in a relative increase in the reduced electric field which encourages plasma formation within the boundary layer. When there is a flow present, the O2-H2 gas will breakdown and form plasma entirely within the lower density region of the boundary layer. When there is no flow present, the gas is unable to breakdown for either the 4 kV or the 6 kV simulations.

The timescale for the plasma formation (1-5 ns) is much smaller than the timescale of bulk convection. As a result, the flow is essentially frozen during the pulse phase of the simulations. It is only after the pulse has terminated that the effects of the flow are felt by the plasma. Over a timescale of microseconds, radicals such as O are convected downstream of the discharge as seen in Figure 24.

Figure 24 – Convection of atomic oxygen radicals over 200 ns for the 4 kV anodic pulse.

VI. Conclusion

In the previous section, we compared anodic and cathodic pulses at voltages ranging from 4 kV to 8 kV. In addition, we compared the formation of plasma in pure argon with that in O2-H2 with all other parameters such as geometry, voltage and flow held constant.

For both chemistries, the anodic pulse plasma forms in positive streamers which propagate away from the electrode. The cathodic pulse plasma forms above the dielectric due to charge trapping, with streamer like discharges emanating from the electrode edges. The O2-H2 plasma formed by both pulse types is highly electronegative. Oxygen radicals with peak densities on the order of 2x1021 m-3 (mole fraction of 4x10-3) are the dominant species produced in both anodic and cathodic pulses. O radicals are convected downstream of the discharge region over microsecond timescales.

Rapid gas temperature increase on the order of hundreds of Kelvin due to ion Joule heating at the electrode edges was observed, which results in blast waves for both anodic and cathodic O2-H2 pulses. Gas heating was higher for


20

the cathodic pulse. Gas heating due to inelastic collisions was also observed within the plasma during and after the pulse, but at an order of magnitude lower than ion Joule heating. Increasing voltage resulted in an increase in the volume of plasma formed, peak species number densities, and gas heating for anodic and cathodic pulses. For argon, gas heating on the order of thousands of Kelvin was observed for the argon 4 kV anodic pulse, but no heating at all was observed in the 4 kV cathodic pulse. Increasing peak voltage results in greater gas heating, but also leads to an increase in peak O radical densities due to greater rates of dissociation at high E/N. It is only during the ramping phases of the pulse that power is deposited into the gas and plasma formation takes place. Increasing the peak voltage of a fixed width pulse should result in much greater radical production than would be seen by increasing the pulse width. From the previously presented results, it can be seen that most of the radicals and metastables are produced within the streamers, while the peak densities in the surface plasma due to charge trapping are approximately an order of magnitude less. This combined with the fact that streamers penetrate further into the flow region which prevents losses to the wall suggests that anodic pulses are best suited for combustion applications.

Appendix

Table 1 – High pressure O2-H2 reduced chemistry mechanism.

O2-H2 Chemistry (molecules-meters-Kelvin) Electron Impact Excitation/Dissociative Excitation

Rxn Reaction A B C Activation energy ref G1 E + O -> O(1D) + E BOLSIG+ 2.0 (22) G2 E + O2 -> O + O(1D) + E BOLSIG+ 7.12 (22) G3 E + O2 -> O2(a1Δg) + E BOLSIG+ 0.98 (22) G4 E + O2 -> O2(b1Σg

+) + E BOLSIG + 1.63 (22) G5 E + O2 -> E + O2 rotational BOLSIG + 0.02 (22) G6 E + O2 -> E + O2 vibrational BOLSIG + 0.19 (22) G7 E + O2 -> E + O2 electronic (Herzberg) BOLSIG+ 4.5 (22) G8 E + O2 -> E + O2 electronic (other) BOLSIG+ 1.0 (22) G9 E + H2 -> E + H2 rotational BOLSIG+ 1.0 (22) G10 E + H2 -> E + H2 vibrational BOLSIG+ 1.0 (22) G11 E + H2 -> E + H2 electronic BOLSIG+ 1.0 (22) G12 E + O2(a1Δg) -> O + O(1D) + E BOLSIG+ 6.34 (22) G13 E + O2(a1Δg) -> O2(b1Σg

+) + E BOLSIG+ 0.64 (22) G14 E + O2(b1Σg

+) -> O + O(1D) + E 1.8e-13 0.0 2.12628e5 5.44 (38)

Metastable Quenching G15 O2(a1Δg) + O2(a1Δg) -> O2(b1Σg

+) + O2 6.992e-35 3.8 -700.0 -0.33 (39) G16 O2(a1Δg) + O2 -> O2 + O2 1.694e-24 0.0 0.0 -0.98 (40) G17 O2(a1Δg) + H2 -> O2 + H2 4.483e-24 0.0 0.0 -0.98 (40) G18 O2(a1Δg) + O -> O2 + O 6.974e-22 0.0 0.0 -0.98 (40) G19 O2(a1Δg) + H -> O2 + H 6.974e-22 0.0 0.0 -0.98 (40) G20 O2(b1Σg

+) + O2 -> O2(a1Δg) + O2 4.583e-23 0.0 0.0 -0.65 (40) G21 O2(b1Σg

+) + H2 -> O2(a1Δg) + H2 8.17e-19 0.0 0.0 -0.65 (40) G22 O2(b1Σg

+) + O -> O2(a1Δg) + O 7.97e-20 0.0 0.0 -0.65 (40) G23 O2(b1Σg

+) + H -> O2(a1Δg) + H 7.97e-20 0.0 0.0 -0.65 (40) G24 O(1D) + O2 -> O + O2(a1Δg) 6.31e-18 0.0 -67.0 -1.02 (40) G25 O(1D) + O2 -> O + O2(b1Σg

+) 2.557e-17 0.0 -67.0 -0.37 (40) G26 O(1D) + O2(a1Δg) -> O + O2(b1Σg

+) 4.982e-17 0.0 0.0 -1.35 (40) G27 O(1D) + H2 -> O + H2 5.48e-18 0.0 0.0 -2.0 (40) G28 O(1D) + O -> O + O 3.188e-17 00 -67.0 -2.0 (40) G29 O(1D) + H -> O + H 3.188e-17 0.0 -67.0 -2.0 (40) G30 O(1D) + O2 -> O + O2 3.188e-17 0.0 -67.0 -2.0 (40) G31 O2(b1Σg

+) + O2 ->2 O2 1.0e-24 0.0 0.0 -1.63 (39) G32 O2(b1Σg

+) + O -> O2 + O 8.0e-20 0.0 0.0 -1.63 (39)

Metastable De-Excitation G33 E + O2(a1Δg) -> O2 + E 5.6e-15 0.0 2.552e4 -0.98 (38) G34 E + O2(b1Σg

+) -> O2 + E 5.6e-15 0.0 2.552e4 -1.63 (38) G35 E + O(1D) -> O + E 8.0e-15 0.0 0.0 -2.0 (41)


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Electron Impact Dissociation G36 E + O2 -> O + O + E BOLSIG+ 5.12 (22) G37 E + H2 -> E + 2H (combined) BOLSIG+ 1.0 (22) G38 E + O2(a1Δg) -> 2O + E 4.2e-15 0.0 5.336e4 4.14 (38) G39 E + O2(b1Σg

+) -> 2O + E 7.1e-15 0.0 9.976e4 3.44 (38)

Electron Impact Ionization/Dissociative Ionization G40 E + O2 -> O2

+ + 2E BOLSIG+ 12.06 (22) G41 E + O -> O+ + 2E BOLSIG+ 13.61 (22) G42 E + H2 -> H2

+ + 2E BOLSIG+ 15.4 (22) G43 E + H -> 2E + H+ BOLSIG+ 13.6 (22) G44 E + O2 -> O + O+ + 2E BOLSIG+ 19.5 (22) G45 E + O2 -> O+ + O- + E 7.1e-17 0.5 1.97268e5 17.81 (41) G46 E + O(1D) -> O+ + 2E 1.95e-17 0.6 1.4e5 11.61 (42) G47 E + O2(a1Δg) -> O2

+ + 2E 9.0e-16 2.0 1.3456e5 11.08 (38) G48 E + O2(b1Σg

+) -> O2+ + 2E 9.0e-16 0.0 1.4616e5 10.43 (38)

G49 E + O2(b1Σg+) -> O+ + O + 2E 5.3e-16 0.9 2.32e5 17.1 (38)

Electron Attachment G50 E + O2 -> O + O- BOLSIG+ 4.2 (22) G51 E + O2(a1Δg) -> O + O- BOLSIG+ 3.22 (22) G52 E + O2(b1Σg

+) -> O + O- BOLSIG+ 2.57 (22) G53 E + O2 + M-> O2

- + M BOLSIG+ -0.43 (22) G54 E + O + O2 -> O- + O2 1.0e-43 0.0 0.0 -0.92 (41) G55 E + O + O2 -> O + O2

- 1.0e-43 0.0 0.0 -0.43 (41)

Electron-Ion G56 E + O2

+ -> 2O BOLSIG+ -6.91 (22) G57 E + O4

+ -> 2 O2 BOLSIG + -12.07 (22) G58 E + O2

+ -> O(1D) + O 3.6546e-12 -0.7 0.0 -10.06 (41) G59 E + O- -> O + 2E 2.1e-16 0.5 3.9434e4 0.92 (42)

Ion-Neutral G60 O- + O -> O2 + E 1.4e-16 0.0 0.0 -4.2 (42) G61 O2

- + O -> O- + O2 5.733e-15 -0.5 0.0 -0.49 (41) G62 O+ + O2 -> O2

+ + O 2.1e-17 0.0 0.0 -1.55 (42) G63 O2

+ + O2 + M -> O2+ + M 2.03e-34 -3.2 0.0 0.01 (43)

Ion-Metastable G64 O2(a1Δg) + O- -> O2

- + O 1.905e-16 -0.5 0.0 -0.48 (41) G65 O2(a1Δg) + O2

- -> 2O2 + E 4.6765e-16 -0.5 0.0 -0.55 (41) G66 O(1D) + O2

+ -> O2(a1Δg) + O 1.732e-17 -0.5 0.0 -13.08 (41)

Ion-Ion G67 O- + O+ -> O + O 4.6765e-12 -0.5 0.0 -12.69 (41) G68 O- + O+ -> O + O(1D) 8.487e-15 -0.5 0.0 -10.69 (41) G69 O- + O2+ -> O + O2 3.46e-12 -0.5 0.0 -10.61 (43) G70 O2

- + O2+ + M <-> 2 O2 + M 3.12e-31 -2.5 0.0 -11.64 (43)

G71 O2- + O4

+ <-> 3O2 1.0e-13 0.0 0.0 -11.64 (43) G72 O2

- + O4+ + M <-> 3O2 + M 3.12e-31 -2.5 0.0 -11.64 (43)

G73 O2- + O+ -> O2 + O 3.464e-12 -0.5 0.0 -13.18 (41)

Neutral Combustion Reactions G74 2O + M <-> O2 + M 3.31e-43 -1.0 0.0 - (44) G75 O + H + M <-> OH + M 1.38e-42 -1.0 0.0 - (44) G76 O + H2 <-> OH + H 6.43e-26 2.7 3.143e3 - (44) G77 O + OH <-> O2 + H 4.4e-14 -0.6707 8.555e3 - (44) G78 2H + M <-> H2 + M 2.76e-42 -1.0 0.0 - (44) G79 H2 + 2H <-> H2 + H2 2.48e-43 -0.6 0.0 - (44)

Metastable Combustion Reactions G80 O2(a1Δg) + M -> 2O + M 8.967e-12 -1.0 4.8008e4 - (40) G81 O2(b1Σg

+) + M -> 2O + M 8.967e-12 -1.0 4.0415e4 - (40) G82 H2 + O(1D) -> OH + H 1.0412e-16 0.0 0.0 - (40) G83 O2(a1Δg) + H -> OH + O 1.827e-16 0.0 3.188e3 - (40) G84 OH + O -> O2(a1Δg) + H 9.6312e-18 0.0 6.224e3 - (40)


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G85 O2(b1Σg+) + H -> OH + O 1.827e-16 0.0 1.62e3 - (40)

G86 H2 + O2(a1Δg) -> 2OH 2.823e-15 0.0 1.7906e4 - (40) G87 H2 + O2(b1Σg

+) -> 2OH 2.823e-15 0.0 1.4657e4 - (40)

Table 2 - High pressure argon reduced chemistry mechanism.

Argon Chemistry (molecules-meters-Kelvin) Rxn Reaction A B C Activation energy ref G1 E + Ar -> E + Arm 1e-14 0.1 1.3856e5 11.56 (20) G2 E + Ar -> 2E + Ar+ BOLSIG+ 15.8 (22) G3 E + Arm -> 2E + Ar+ BOLSIG+ 4.43 (22) G4 E + Arm -> E + Ar BOLSIG+ -11.5 (22) G5 2Arm -> E + Ar + Ar+ 5e-16 0.0 0.0 -7.2 (20) G6 E + Ar2

m -> 2E + Ar2+ 1.29e-16 0.7 0.42456e5 3.66 (20)

G7 E + Ar2m -> E + 2Ar 1e-13 0.0 0.0 -10.9 (20)

G8 Arm + 2Ar -> Ar2m + Ar 1.14e-44 0.0 0.0 -0.6 (20)

G9 Ar+ + 2Ar -> Ar2+ + Ar 2.5e-43 0.0 0.0 -1.3 (20)

G10 Ar2m -> 2Ar 6e7 0.0 0.0 -10.9 (20)

G11 2Ar2m -> E + Ar2

+ + 2Ar 5e-16 0.0 0.0 -7.3 (20) G12 E + Ar+ ->Arm 4.3e-17 -0.5 0.0 -4.3 (20) G13 2E + Ar+ -> E + Arm 9.75e-15 -4.5 0.0 -4.3 (20) G14 E + Ar2

+ -> Arm + Ar 2.59e-11 -0.66 0.0 -3.0 (20)

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