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Combustion and Flame 184 (2017) 208–232
Contents lists available at ScienceDirect
Combustion and Flame
journal homepage: www.elsevier.com/locate/combustflame
Plasma-combustion coupling in a dielectric-barrier discharge actuated
fuel jet
Luca Massa
a , ∗, Jonathan B. Freund
b
a Aerospace and Ocean Engineering, Virginia Tech, Blacksburg, VA,United States b Mechanical Science & Engineering and Aerospace Engineering, University of Illinois at Urbana–Champaign, Urbana, IL, United States
a r t i c l e i n f o
Article history:
Received 26 November 2016
Revised 8 January 2017
Accepted 14 June 2017
Available online 1 July 2017
Keywords:
Ignition
Plasma-assisted combustion
a b s t r a c t
A plasma-combustion coupling mechanism is proposed and applied to the laser-induced atmospheric-
pressure ignition and combustion of a hydrogen jet as assisted by a dielectric-barrier discharge (DBD).
The specific configuration matches corresponding experiments, and the proposed coupling mechanism
leads to an improvement of the prediction for ignition probability and explains the observed electrical
power increase during burning conditions. To realize this, the model includes the key effects of the fast
DBD microflimentary plasma structure on combustion time scales, which would not be included in a sim-
pler quasi-steady approximation. It also explains observed plasma emission patterns and the dependence
of the DBD power absorbed on the cross-flow velocity. The main conclusion of the present computa-
tional analysis is that the interaction of plasma and combustion supports a two-way coupling rooted in
the electron and neutral energy equations. The coupling selectively amplifies the energy and radical con-
tributions by the discharge at the ignition hot spot. These contributions dominate the evolution of hot
spots interacting with the local electric field over dielectric surfaces and are a key ingredient of predictive
ignition models. Results are discussed in the context of the lower pressure, lower equivalence ratio and
lower dimensional (often premixed and quasi-one-dimensional) studies that provide insights for develop-
ing this integrated model while illuminating the important differences of the coupling in non-premixed
conditions at atmospheric pressure.
© 2017 The Combustion Institute. Published by Elsevier Inc. All rights reserved.
s
t
1. Introduction
It is well-understood that plasma can accelerate combustion
rates [1–6] . While most of this work has focused on how the
electrical discharg e can affect chemical kinetics, Savelkin et al.
[7] have recently shown a strong reverse coupling effect: combus-
tion and mixing can affect the discharge leading to an increase of
the electrical power absorbed and a broadening of the plasma’s ex-
tent. Yet the mechanisms of this two-way coupling are not fully
understood, and it remains uncertain what factors are important
in any particular configuration. We develop a model to analyze the
mechanisms that are active in the laser-induced ignition of a round
fuel jet in a turbulent cross-flow in the presence of a dielectric-
barrier discharge (DBD) plasma. Our goal is to identify and rep-
resent in a simulation how the plasma-combustion interaction af-
fects the ignition probability. Experimental observations for this
∗ Corresponding author.
E-mail addresses: lmassa@vt.edu (L. Massa), jbfreund@illinois.edu (J.B. Freund).
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http://dx.doi.org/10.1016/j.combustflame.2017.06.008
0010-2180/© 2017 The Combustion Institute. Published by Elsevier Inc. All rights reserved
ame configuration are recently reported [8,9] ; observations of par-
icular interest are summarized here:
• The DBD plasma enhances ignition above a threshold, although
it also slightly hinders is probability for low applied voltages.
A two-stage ignition and associated blow-off process has been
identified in the regime when the DBD supports ignition.
• Although the actuator is axisymmetric, the plasma light emis-
sion is not once the jet is burning. The absorbed electrical
power is significantly increased by the flame, and, more inter-
estingly, decreases when the flame is in a cross-flow. Both of
these observations indicate coupling between the flow, plasma,
and flame.
• Light emissions at 720 nm (near the water vapor infrared band)
are more intense and more spatially distributed with DBD-
actuation, pointing to additional coupling.
To explain these observations we develop a model for the in-
eraction of plasma and combustion on the time scales of turbu-
ent combustion ( ∼ 10 −2 s). These are fast relative to the flow,
et around 10 6 times slower than the characteristic time for
lectron transport and ionization in atmospheric air ( ∼ 10 −8 s ),
.
L. Massa, J.B. Freund / Combustion and Flame 184 (2017) 208–232 209
Fig. 1. DBD setup with the electrodes drawn in brown. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this
article.)
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hich occurs for reduced electric field strength E / N � 100 Td.
herefore, we anticipate at the outset that a detailed resolu-
ion of the electron transport is unneeded and would likely be
omputationally infeasible. However, despite this time-scale dif-
erence, we can also anticipate that an only weak coupling of
uid and plasma dynamics [10] , whereby the fluid would be
pproximated as unchanging on the plasma time scale, would
iss essential interactions that are tightly coupled at atmospheric
ressure [11, ch. 9] . The primary two-way coupling can be an-
icipated to arise from a decrease in specific collisional loss
ith increasing temperature and Joule heating [ 11 , p. 223]. Be-
ause the ratio between electron drift is expected to far exceed
uid velocity for our conditions ( v d / U ∞
� 10 4 ), the avenue of
uch a coupling is anticipated to be through the relatively slow
hange of the target state that the electrons impact in the their
rift.
The quantitative description of the coupling mechanism we de-
elop is based on the microstructure of DBD plasma, particularly
hat it is supported by many quasi-periodic microstreamers, each
ccurring on a ∼ 10 −9 s time scale. Surface charging provides these
ith an effective memory, so that they recur in the same locations
t each change of the voltage polarity [12] . Our specific model
s motivated by the observed intensification in the presence of
he flame as well as the corresponding electric power absorption
hanges.
At low gas temperature and large electric frequencies, mi-
rostreamers are inefficient and Joule heating is negligible [10] .
owever recent measurements show a dramatic change when
here is a sustained flame, presumably due to the high tempera-
ures supported by turbulent combustion. In this case it is seen
hat the filament coverage of the dielectric surface increases, has
ow intermittency, and tracks the flame location [8] . We propose
hat this coupling is due to the linear decrease in three-body at-
achment to oxygen with increasing temperature. Our analysis re-
ults in a criterion for the formation of self-sustained plasma fila-
ents, which bypass the random avalanche phase [ 11 , p. 328] and
orm in the pre-ionized gas of previous microstreamers. This is de-
eloped to explain these observations and plasma–flame interac-
ions primarily in Section 4.4.3 .
Recent analysis of the effect of plasma and combustion in
ow-dimensional configurations has led to the improvement of ki-
etic models and the coupling between the Boltzmann equation
ith trusted models for neutral chemistry [13,14] . Yet studying
lasma-combustion coupling in one-dimension is difficult. Thermal
oupling between the discharge and the fluid enthalpy contracts
he plasma column [11] and selectively amplifies the energy and
adical production at distinct locations [8] . Experiments demon-
trate the difficulty in obtaining a one-dimensional ignition front,
ven at very low pressure [14] . Realistic, higher-pressure condi-
ions accentuate this [7,8] . Our current target is thus intrinsically
hree-dimensional, and mechanism are integrated into a model
f a genuinely three-dimensional configuration with correspond-
ng experimental observations. Because the time scales of the elec-
ron drift are small and thus neglected, this comparison depends
toremost upon the coupling model. Lower-dimensional simulations
ave been used to determine some model parameters, though in a
ay such that the three-dimensional results are true predictions.
The following Section 2 provides a description of the target
onfiguration and measurements. Then, Section 3 provides addi-
ional detailed motivation and reviews the specific assumptions
nvoked in crafting the integrated model. Section 4 describes
he ion-chemistry model, Section 5 the practical tabulation strat-
gy to include the plasma sources in the governing equations,
ection 6 the governing equations, Section 7 the simulation strat-
gy, and Section 8 the results. Conclusions are revisited with addi-
ional discussion in Section 9 .
. Experiments
.1. Apparatus
The experiments were conducted in a subsonic windtunnel
ith a test section of 0.4 m × 0.4 m cross section and 1.19 m
ong. A 40-grit sandpaper roughness strip of total height 1.64 and
0.8 mm width trips the boundary layer turbulent 333 mm up-
tream of the center of the fuel port. PIV measurements confirm
hat a fully-developed turbulent boundary layer was obtained [9] .
The hydrogen fuel enters vertically through the windtunnel
oor through a port with diameter D H = 4 . 83 mm at flow rate Q =7 . 83 cm
3 / s . The Reynolds number in the tube is Re D = 4 Q /νD
2 H
=4 . 5 , so the fuel flow is laminar. A laser-induced optical break-
own with measured power P int = 17 . 64 ± 6 . 12 mJ was used to ig-
ite the fuel.
The DBD actuator shown in Fig. 1 was operated with a 12 kV,
0 kHz sine-wave. The dielectric material is quartz; the exposed
lectrode is a coaxially aligned copper tube with wall thickness
.51 mm and is recessed 4.8 mm from the top surface of the
uartz, which in turn is flush with the windtunnel floor. The other
lectrode is buried 4.425 mm below the exposed quartz surface.
t is a ring of thickness 0.4 mm that extends radially from r i = . 375 mm r e = 19 . 05 mm.
.2. Measurements
A complete description the measurements used to support the
nalysis in the present study is reported elsewhere [8,9] . The prob-
bility of igniting the H 2 jet was measured as the position of a
aser spark varied. For each breakdown position, 50 independent
xperiments were conducted, in which the laser energy and flame
gnition status were determined. Ignition was determined based on
oth schlieren imaging and water emission spectra from the ro-
ovibrational bands at 717 nm [15,16] using a lens with a 720 nm
10 nm FWHM) bandpass filter. The discharges were analyzed with
ight emission and power measurements to ascertain their contri-
ution of streamers to the current and electric power coupled into
he fluid.
210 L. Massa, J.B. Freund / Combustion and Flame 184 (2017) 208–232
Fig. 2. Flattening of standburner flame with increasing voltage �V filtered emis-
sions (water ∼ 720 nm) for �V = 0 , �V = 5 kV, �V = 7 kV, and �V = 8 . 8 kV.
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3. Model design: motivation and main assumptions
3.1. Motivation
As listed in Section 1 , even the visible-light emissions suggest
that a coupling occurs between the plasma, combustion, and flow.
The obvious emissions without cross-flow have a distinct cylindri-
cal symmetry ( Fig. 3 a); when the H 2 is burning in a 15 m/s cross-
flow, the corresponding emissions are skewed downstream, and
the region of brightest plasma glow overlaps the plume, as seen
in ( Fig. 3 b). A corresponding 10-fold increase in the electric power
is required to maintain the plasma [8] . An H 2 flame increases the
power at all voltages by a factor of approximately 1.5, indicating
additional coupling [8] . Retter et al. [8] also show that the pres-
ence of the flame, or even just the heating of the dielectric sur-
face, cause a transition between highly intermittent microstream-
ers to a diffuse, repetitive filamentary plasma. This transition is ac-
companied by an increase of the anodic current and a flattening
of the flame, anticipated to be caused by Coulombic body forces.
The flame flattening substantially intensifies emissions, which we
anticipate to be due to the overlapping of the flame and the elec-
tric field layer. An example of this flattening is shown in Fig. 2 .
Flame-on measurements also manifest an increase in frequency
and magnitude of the current pulses when the exposed electrode
acts as the anode. Therefore, this effect would be consistent with
the flame energizing the anode-directed microstreamers formed
near the dielectric wall, as seen in Figs. 7 and 8 of Retter et al. [8] .
Modeling plasma-combustion coupling in a turbulent field is
challenging because of the inherent three-dimensionality of tur-
bulence, the separation between chemical induction and electron
drift temporal and spatial scales, and the stochastic character of
the electric field supported by the dielectric barrier discharge. The
following observations are deemed to be particular important in
developing a predictive model [8] :
• The axial symmetry of the electrodes leads to a primarily ra-
dial inhomogeneity in electric field. Retter et al. [8] report that
changing the size of the ring electrode significantly changes the
distribution of the microdischarges in the flame-on measure-
ments. Thus, the radial geometry must be accounted for, which
is done by solving an axisymmetric Poisson equation for the
electrostatic potential.
• Plasma is localized near the electrodes and orifice, and its cou-
pling with the flow and combustion is only in the sheath layer
( λ ≈ 1 mm), which is thinner than the momentum boundary
layer ( δ∗ ≈ 2 mm) [17] .
• Plasma exists in a region where we anticipate there to be a
mixture of air and H 2 . These have significantly different at-
tachment cross sections (electro-positivity), so it is expected
that mixing affects the plasma formation, which will likely be
spatially dependent. This is supported by the observation that
flowing H 2 enlarges the region where microdischarges occur
[8] , consistent with the weaker electropositivity of H and thus
2lower ionization breakdown potential. This effect is not due
to plasma advection because a comparable Q of air does not
change the plasma emissions [8] .
• These same measures show that an increase in temperature re-
duces the electric field necessary to sustain the plasma, with
greater sensitivity at lower gas temperature. A reduction of
collisional losses is expected to provide this phenomenology.
Molecular oxygen, in particular, has a strong three-body attach-
ment, which might be anticipated to lead to the linear reduc-
tion of attachment rate with the temperature and a consequent
reduction of the breakdown threshold. This translates in a re-
duction of the specific collisional energy loss per electron-ion
pair produced [ 18 , p. 81].
• The laser-induced breakdown is intense and forms a localized
overvoltage on the dielectric surface that induces the genera-
tion of microstreamers on a time-scale much faster than that of
ignition. Plasma-ignition coupling is therefore due to the low-
ering of the particle density N and corresponding increase in
reduced electric field E / N .
• At the atmospheric pressure, most ionization is expected to oc-
cur at peak electric-field strength because of the fast decrease
in electronic temperature after the micro discharge extinguish-
ment (see Section 1 ). Subsequent production of electrons, in
the afterglow of this nominal event, is expected to be bal-
anced by recombination in the microdischarge remnant [19] . A
quasi-steady approximation, which is deemed accurate in some
regimes [ 20 , p. 228], would therefore risk mis-representation of
key features of such a process.
Based on these observation and anticipate underlying effects,
e identify three main modeling needs. (1) The first is the quan-
itative representation of the pressure, temperature, composition
nd external electric-field conditions for microdischarge existence,
ince this will so affect the extend and intensity of the plasma.
iven the plasma character, it is also important to represent both
he (2) plasma-to-fluid energy transfer rates and (3) chemical rates
f radical production. The specific assumptions invoked to develop
hese models are discussed in the following subsection.
.2. Assumptions
To develop a model for the effect of the microdischarges [12] ,
e invoke the filamentary plasma structure as proposed by Frid-
an et al. [19] . This is predicated on the assumption that a slow
urface-charge relaxation leads to microdischarges reforming on
he same spot with each change of polarity. The electric field in
he microdischarges can be considered the superposition of three
ontributions: an external component supported by the electrodes,
n internal component due to the polarization space charge at the
treamer head, and a surface component due to charge deposi-
ion on the dielectric walls [21] . Because the fields nearly can-
el after a microdischarge, and assuming that the local field fol-
ows the external value (see justification below), we propose to
odel a filament with a duty cycle that reflects the local elec-
ric field. We note that this is an alternative approach to that pro-
osed by Goldberg et al. [22] , who determine the field by solving
f a decoupled one-dimensional discharge with the drift-diffusion
pproximation.
.2.1. External field
The external field is deemed that which is present in sheaths
lose to the boundaries, governed by a screened Poisson equation
· (ε∇ φ)
= F ( φ) ,
here F is assumed to be independent of the combustion and
ixing events and is evaluated as described at the beginning of
L. Massa, J.B. Freund / Combustion and Flame 184 (2017) 208–232 211
Fig. 3. Visible-light plasma emissions in the DBD actuator [8] at 12 kV.
S
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f
ection 8 . Thus, the local charge F depends only on the local po-
ential, which is an established approximation [23,24] . In essence,
t follows from three principal assumptions: (1) the region with
ignificant charge is localized in thin sheets along the boundary,
2) the plasma is in a Boltzmann equilibrium, and (3) the Poisson–
oltzmann equation can be linearized. This view is supported by
he analysis in Section 8 , where the body forces and sheath ex-
ension are deduced based on the measured velocity field over an
ctuated stand-burner without cross-flow.
.2.2. Space and surface charge fields
Within microstreamers, the (combined) electric field will in-
lude both the influence of the polarization space charge, which
esponds quickly to reduce the field after the ionization wave,
nd of the transfer of charge to the dielectric surface, which
loses the conductive channel, thus extinguishing the discharge.
his scenario is fundamentally multi-dimensional, whereby trans-
erse derivatives of the polarization space charge create a non-
lanar wave with a strong peak [25] . We assume a wave-
orm based on similarity, based on the lack of geometrical
ength scale, the slow time-dependence of the external field,
nd a negligible Peclet number dependence [26,27] . In this
imit, the reactive time and the drift velocity provide the rel-
vant scales [26,27] . Insensitivity to initial conditions has been
stablished [28] .
In many combustion conditions, the variation of fluid transport
oefficients with the mixture fraction is small compared to their
emperature dependence [29] . We assume this also for the drift-
iffusion equations, with relatively low sensitivity of transport to
eutral particle density N . Using μ0 and χ0 to denote respec-
ively the mobility and Townsend coefficient at the reference state,
ives time scale τ ≡ 1 μ0 χ0 E 0
and length scale ≡ 1 χ0
. Based on first-
rinciples arguments (e.g., Hagelaar and Pitchford [30] ), χ∝ N and
∝ N
−1 , so ∝ N
−1 , and τ∝ E 0 .
There are two possible limits that provide an E 0 : it can match
he field ahead of the wave E ∞
, and so be independent of N , or the
haracteristic field of the space charge E sc ≡ n 0 e /( χ0 ɛ 0 ), where n 0 s the plasma density and e the unit charge. If the wave propaga-
ion is driven by photo-ionization, n 0 ∝ N
2 [26] and the time scale
ased on the space charge is τsc ∝ N
−1 . There are three situations
hen E 0 ≈ E ∞
, and for our purposes we can neglect the quadratic
ependence on n 0 : (1) short-lived streamers, for which the space
harge is set by the initiation condition, giving E sc = E ∞
[31,32] ; (2)
treamers driven by pre-ionization, for which n 0 is constant and
atches the pre-breakdown density [33] ; and (3) streamers that
re well-described by a one-dimensional ionization waves [21] . We
ake E 0 ≈ E ∞
because conditions (1) and (2) are both satisfied.
he success of similitude based on E 0 describing the experiments
nd computations of Pancheshnyi et al. [25] provides additional
upport.
With E 0 ≈ E ∞
time scale is independent of N (and thus evolu-
ion of the combustion), we assume
ˆ ≡ | ∇ φ| , E(r, y, t)
=
ˆ E ( r, y )
⎡
⎣
tanh
(δc −2 t m
2 t f
)+ tanh
(δc +2 t m
2 t f
)2
⎤
⎦ | sin ( ω act t ) | ,
ith t m
≡ mod (t − δD + T act / 4 , T act / 2) − T act / 4 . The time-period is
act ≡ 1 / f = 2 π/ω act . The parameters δD , t f , δc are set to match the
ower in cold flow in Section 4.6 based on the same anticipated
emperature independence of the pulse form.
With the approximation ∝ T established, the fast ionization
ave thickness �a that can exceed 1 cm [34] for high temper-
tures and low densities. When the characteristic thickness ex-
eeds the geometrical scale of the actuator �g , quenching of sur-
ace charge is expected to introduce an dependence on �g / �a . To
ccount for such an effect, we limit the wave thickness in (3.2.2)
ith the cut-off wave-length
∗c = min ( δc , �g / ( μ0 E 0 θ ) )
n place of δc . The electron mobility μ0 is evaluated at the refer-
nce electric field E 0 , and θ is the ratio between wave velocity and
lectron mobility, which is taken to be θ = 10 based on fast-wave
xperiments [21] . The reference length of the actuator is the ra-
ial extent of the covered electrode, �g = 1 . 9 cm (cf. Section 2.1 ).
he use of (3.2.2) also limits Joule heating and radical generation
or large E / N . Overall, for plasma-combustion coupling, it reduces
he thermal instability of atmospheric plasmas induced by the mu-
ual reinforcement of Joule heating and temperature [ 11 , p. 222].
therwise, it does not affect the scaling at low temperature and,
herefore, parameters can be selected to match baseline cold-flow
ower data.
.2.3. Charged particle transport
Because plasma time scales so exceed those of the flow, elec-
ron and ion transport are not resolved. Here we confirm that in
he fast-wave limit θ � 1 their contribution to the overall ioniza-
ion budget will be small, especially when compared to the colli-
ional source terms. First, ion transport in the remnants is negli-
ible compared to ion production and destruction in the pulse be-
ause the Bohm velocity in the afterglow is expected to be small.
his assertion follows from δc / T act 1 and the fast electron tem-
erature relaxation time (as discussed in Section 1 ), so that the
lectron energy drops quickly after the pulse, the Bohm velocity
t the sheath edge is small, and plasma ion losses are small [ 18 ,
p. 376–380]. Second, in an ionization wave propagating at several
imes the electron drift velocity, electron transport is important
nly in determining the polarization space charge, while collisions
ominate particle production in the wave, as supported by planar
elf-similar theory [21, ch. 3] and considered in more detail in the
ollowing. Taking θ ≡ V / μE , α = μ| E | χ the ionization frequency,
0212 L. Massa, J.B. Freund / Combustion and Flame 184 (2017) 208–232
Fig. 4. Contributions to the electron density change across a planar ionization wave.
p
b
R
s
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N
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i
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h
e
i
i
r
d
i
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o
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o
H
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X
e
e
p
ρ
t
t
e
t
c
c
b
c
l
B
t
s
e
d
t
c
T
S
g
i
(
i
e
χ ≡ A exp
(− ˆ E / ̃ E
)the Townsend coefficient, μ the constant elec-
tron mobility, ˜ E ≡ | E | /E 0 the scaled electric field, then the change
in electron density ( n e ≡ N e − ) across an anode-directed wave is
n e, −∞
− n e, ∞
=
∫ ∞
−∞
χ ˜ E − ∂ ̃ E ∂ξ
θ − ˜ E n e d ξ .
Because the two members in the numerator of the integrand do
not change sign, the two terms
T 1 ≡∫ ∞
−∞
χ ˜ E
θ− ˜ E n e d ξ
n e, −∞
− n e, ∞
T 2 ≡∫ ∞
−∞
∂ ̃ E ∂ξ
θ− ˜ E n e d ξ
n e, −∞
− n e, ∞
(1)
represent the contributions of collisional process and drift relative
to the particle production. They are plotted against θ in Fig. 4 for
three values of the ionization parameter ˆ E . We confirm that for
realistic values θ ≈ 10 [21] , the contribution of drift is negligible
in the determination of the particle production. We will use this
result to remove the electron transport terms and obtain the cou-
pling terms through an ODE solution illustrated in Section 4.4 .
4. Ion chemistry and plasma model
4.1. Overview and parameterization
The objective of the ion chemistry model is to represent
plasma-combustion of our weakly ionized H 2 /O 2 /N 2 /H 2 O mixtures
for temperatures T = 300 to 30 0 0 K and pressures near atmo-
spheric. Because the ionization is weak, collisions between elec-
trons and radicals are neglected during the pulse. Likewise, with
only one exception (reaction 6 in (2) ) the bimolecular reactions
between ions and radicals are assumed not to affect the radical
production and energy transfers supported by the plasma.
Parameters for the ion chemistry scheme for the plasma are
based on six main sources: (1) Tawara et al. [35] for the cross sec-
tions of the collisions between hydrogen molecules and ions with
electrons, (2) Itikawa [36] for the cross section of oxygen molecules
and ions, (3) Itikawa and Mason [37] for the cross sections of wa-
ter molecules, (4) Buckman and Phelps [38] for the cross sections
of nitrogen molecules, (5) Aleksandrov et al. [39] for the ther-
mal rates of plasma decay in the afterglow (remnant) period of
the microdischarge, and (6) the UMIST database [40] (and refer-
ences therein) for the other reactions induced by collisions be-
tween heavy particles. Additional data [41] have also been used to
extend viable temperature ranges of some of the bimolecular rates
to the high temperatures in the flame and igniter.
All collisions leading to excitation, ionization and attachment
are included, and all associated energy transfers affect electron
energy distribution function and the energy coupled in the gas
hase (see Section 8.4 ). However, not all excited states affect com-
ustion through non-equilibrium initiation of the chain branching.
adical generation from from vibrationally excited nitrogen was
hown to be unimportant at low pressure (50 Torr) [42] ; we ex-
ect their effect to be smaller in the current conditions. Radical
roduction by electronically excited (triplet) nitrogen was shown
o be comparable to the electron impact dissociation of H 2 by
agaraja et al. [43] at low pressure (25 Torr) and low equiva-
ence ratios (premixed mixture with φ ≈ 0.1). Their relative impor-
ance is smaller at atmospheric pressure because (1) the quench-
ng decay-time is ∝ 1/ P [44] , while the microdischarge interval
25] and the electric (actuation) period do not scale with the pres-
ure; (2) strong non-linear effects [45] result in the peak concen-
ration of N
∗2 behind a fast ionization wave to be substantially
igher at lower pressure, while the electron number density and
nergy are weakly affected. The equivalence ratio plays also a role
n determining relevant radical production paths: the direct path
s dominant in non-premixed combustion because the majority of
adicals are produced close or above stoichiometric conditions, as
iscussed in more details in Appendix A. Thus, triplet nitrogen
s assumed in a quasi-steady state with equilibrium statistics for
ollisions.
Electronic excitations of oxygen states include the transitions
o O 2 (a 1 �g ), O 2 ( b
1 �+ g ) , O 2 (
1, 3 �g ), O 2 ( B
3 �−u
) , O 2 ( 1 �u ). The first
wo states are also discussed in Appendix A, while the other
hree lead via pre-dissociation to corresponding excited states
f atomic oxygen [46] . Atomic oxygen can also be assumed in
hemical quasi-equilibrium [47] because (1) the time scales of
are fast compared to other processes in the reaction layer
f H 2 / Airflames , and (2) the chain-branching initiation of the
2 /O 2 system depends, to the leading order in X H 2 /X O 2
, on
he concentration of H only [47] . Corrections of higher order in
H 2 /X O 2
are implemented using the scaling described by Boivin
t al. [47] . We also remark that in our conditions the fuel en-
rgy density ρH 2 �HHV is much larger than that coupled by the
lasma,
H 2 Q �HHV ≈ 250 W �
∫ ˙ ω E d V ≈ 25 W,
hus the radical production by the flame pool is much stronger
han that of the discharge. This is different from the low-pressure
xperiments of Nagaraja et al. [43] , where the power coupled by
he plasma accounts for ≈ 50% of the heat of combustion. In our
onditions, the DBD-produced radicals are relevant only during the
hain-initiation. For these reasons, we focus on the plasma contri-
utions to H production.
The rate constants and branching ratios of all dissociative re-
ombination reactions were obtained using the cross section data
isted below and the electron density distribution function from a
oltzmann equation solution, as described in Section 4.3 . The to-
al cross section for dissociative excitation of H 2 is evaluated by
umming the contributions of predissociation and dissociation via
xcitation to Lyman, Werner and metastable states [35] . The pre-
issociation cross section is in turn the sum of the excitation to
he lowest repulsive state H 2 ( b 3 �u
+) , and to H 2 ( a 3 �g +) that de-
ays to H 2 ( b 3 �u
+) via fast radiative-collisional exchange [4 8,4 9] .
he dissociative recombination cross section for H
+ 2 (reaction 4 in
ection 4.2 ) is that of Tawara et al. [35] , for O
+ 2 (reaction 10) is
iven by Peverall et al. [50] , the cross section for N
+ 2 (reaction 17)
s from Sheehan and St-Maurice [51] , the cross section for H 2 O
+
reaction 21) is from Rosén et al. [52] , that for H 3 O
+ (reaction 25)
s from Neau et al. [53] , that for N 2 H
+ (reaction 26) is from Vigren
t al. [54] .
L. Massa, J.B. Freund / Combustion and Flame 184 (2017) 208–232 213
4
4
.
t
w
y
n
s
d
f
4
.
T
e
o
t
o
e
h
a
t
t
t
a
a
a
t
r
p
o
G
c
i
4
T
s
w
t
n
4
w
g
h
[
l
e
.
4
B
.2. Reactions
.2.1. Hydrogen reactions
The represented reactions primarily involving hydrogen are
1. Ionization: e − + H 2 − > H
+ 2 + 2 e −
2. Dissociative attachment: e − + H 2 − > H
− + H
3. Ion–ion recombination: H
− + H
+ 2 − > H 2 + H
4. Dissociative recombination: H
+ 2 + e −− > 2 H
5. Electron collision detachment: H
− + e −− > H + 2 e −
6. Associative detachment: H
− + H − > H 2 + e −
7. Dissociation: H 2 + e −− > 2 H + e −
(2)
Associative detachment has a limited but consistent effect on
he model. The H concentration in reaction 6 is assumed constant
ithin the ion chemistry solution based on the time-scale anal-
sis reported below in Section 4.4.1 , thus its value is set by the
eutral chemistry evolution with reported rate parameters [55] . A
ensitivity analysis of the other reaction paths for the associative
etachment from H
− [40] suggest at most secondary importance
or to present configuration.
.2.2. Oxygen reactions
The represented reaching primarily involving oxygen are
8. Ionization: e − + O 2 − > O
+ 2 + 2 e −
9a. 3B attachment: e − + O 2 + O 2 − > O
−2 + O 2
9b. 3B attachment: e − + O 2 + N 2 − > O
−2 + N 2
9c. 3B attachment: e − + O 2 + H 2 O − > O
−2 + H 2 O
9d. 2B attachment: e − + O 2 − > O + O
−
10. Dissociative recombination: O
+ 2 + e −− > O + O
11a. Detachment: O
−2 + O 2 − > e − + 2 O 2
11b. Detachment: O
−2 + N 2 − > e − + O 2 + N 2
11c. Hydration: O
−2 + H 2 O + M − > H 2 O
−3 + M
12a. 3B ion–ion: O
−2 + O
+ 2 + M − > 2 O 2 + M
12b. 2B ion–ion: O
−2 + O
+ 2 − > 2 O 2
13. Ion–ion: O
− + H
+ 2 − > O + H 2
14. Detachment: H 2 + O
−− > H 2 O + e −
15. Charge transfer: O 2 + O
−− > O
−2 + O
(3)
he first six reactions are evaluated by integrating the electron en-
rgy distribution function (eedf; see Section 4.3 ). Two reported sets
f cross sections have been used: The electron impact cross sec-
ions of Itikawa and Mason [37] yield essential the same results as
thers that are available in other sources [38,56] . Following Skalny
t al. [57] , the rates for processes 9a, 9b and 9c are assumed to
ave identical third-body efficiency. Pack and Phelps [58] report
significantly higher efficiency for the attachment rate when wa-
er is the third body and a significantly lower efficiency when ni-
rogen acts as the third body, but the corresponding changes in
he cross sections are unknown. The formation of cluster ions O
−4
nd N
−4 having higher dissociative recombination rates than the di-
tomic analogs is estimated to be unimportant at the high temper-
ture of hydrogen/air ignition [39] . The ions are assumed to be in
hermal equilibrium, so the corresponding temperature dependent
ates are taken directly from the UMIST data [40] with reported
arameter [39] . The hydration reaction rate of the anion super-
xide radical and water (reaction 11.c above) is that suggested by
ravendeel and De Hoog [59] . The temperature dependence is un-
ertain, and we consider its effect on plasma-combustion coupling
n Section 8.4 .
.2.3. Nitrogen and water reactions
The reactions primarily involving nitrogen and water are
16. Ionization: e − + N 2 − > N
+ 2 + 2 e −
17. Dissociative recombination: N
+ 2 + e −− > 2 N
18. Charge transfer: N
+ 2 + O 2 − > O
+ 2 + N 2
19. Ionization: e −+ H 2 O − > H 2 O
+ +2 e −
20. Charge transfer: H 2 O
+ + O 2 − > O
+ 2 + H 2 O
OH + H γ1
21. Dissociative recombination: H 2 O
+ + e −− > O + H 2 γ2
O + 2 H γ3
22. Dissociative attachment: e − + H 2 O − > H
−+ H + O
23a. Charge transfer: H
+ 2 + H 2 O − > H 2 O
+ + H 2
23b. Ion-neutral: H
+ 2 + H 2 O − > H 3 O
+ + H
24. Charge transfer: N
+ 2 + H 2 O − > H 2 O
+ + N 2
(4)
he cross section and the normalized branching ratios of the dis-
ociative recombination of H 2 O
+ are those of Rosén et al. [52] ,
ho suggests γ1 = 0 . 20 , γ2 = 0 . 09 , γ3 = 0 . 71 . The parameters of
he charge transfer rate are those suggested by Rakshit and War-
eck [60] .
.2.4. Ion clusters
Ion clustering with water are known to alter the discharge in
et air [61,62] . To account for such clusters and generally investi-
ate the effect of hydration on plasmas in hydrogen–air flames we
ave included the relevant reactions for H 3 O
+ H 3 O
+ [53] and N 2 H
+
54] . Rates of ion–ion recombination in local thermodynamic equi-
ibrium (LTE) are from the UMIST data [40] . The reactions consid-
red are
25. Dissociative recombination: H 3 O
+ + e −− > OH + 2 H
26. Dissociative recombination: N 2 H
+ + e −− > N 2 + H
27. Ion-neutral: H 2 O + H 2 O
+ − > H 3 O
+ + OH
28. Ion-neutral: H 2 + H 2 O
+ − > H 3 O
+ + H
29. Ion–ion: H
− + H 3 O
+ − > 2 H + H 2 O
30. Ion–ion: O
−2 + H 3 O
+ − > O 2 + H + H 2 O
31. Ion-neutral: H 2 O + N
+ 2 − > N 2 H
+ + OH
32. Ion-neutral: H 2 + N
+ 2 − > N 2 H
+ + H
33. Ion–ion: H
− + N 2 H
+ − > 2 H + N 2
34. Ion–ion: O
−2 + N 2 H
+ − > O 2 + H + N 2
35. Ion–ion: O
− + H 3 O
+ − > O + H + H 2 O
36. Ion–ion: O
− + N 2 H
+ − > O + H + N 2
37. Ion–ion: N 2 H
+ + H 2 O − > N 2 + H 3 O
+
(5)
.3. Electron Energy distribution function
The electron energy distribution function is governed by a
oltzmann equation, which is crafted in a common form as [30] ,
∂
∂ε
(˜ W F 0 − ˜ D
∂ F 0 ∂ε
)=
˜ S . (6)
214 L. Massa, J.B. Freund / Combustion and Flame 184 (2017) 208–232
W
C
Table 1
Rate parameters for (10) .
Reaction No. α cm
3 /s β γ
3 7 . 51 × 10 −8 –1/2 0
6 4 . 32 × 10 −9 –0.39 39.40
11a 2 . 7 × 10 −10 1/2 5590
11b 1 . 9 × 10 −12 1/2 4990
11c 2 × 10 −28 M –3 0
12a 2 × 10 −25 M –3/2 0
12b 4 . 2 × 10 −7 –1/2 0
13 2 × 10 −7 –1/2 0
14 7 × 10 −10 0 0
15 7 . 3 × 10 −10 0 890
18 1 . 704 × 10 −11 0.934 –973
20 4 . 6 × 10 −10 0 0
23a 3 . 9 × 10 −9 –1/2 0
23b 3 . 4 × 10 −9 –1/2 0
24 2 . 3 × 10 −9 –1/2 0
27 2 . 1 × 10 −9 –1/2 0
28 6 . 4 × 10 −10 0 0
29 7 . 51 × 10 −8 –1/2 0
30 7 . 51 × 10 −8 –1/2 0
31 5 × 10 −10 –1/2 0
32 2 × 10 −9 0 0
33 7 . 51 × 10 −8 −1/2 0
34 7 . 51 × 10 −8 −1/2 0
35 7 . 51 × 10 −8 −1/2 0
36 7 . 51 × 10 −8 −1/2 0
37 2 . 60 × 10 −9 −1/2 0
a
c
t
t
n
t
c
Z
a
w
c
t
R
w
s
t
p
T
e
c
[
R
f
t
r
r
t
w
w
r
This is deemed active where E / N > 1 Td; thermal equilibrium is
assumed elsewhere. In (6) , ε is the electron energy, ˜ W is the flux
coefficient in the energy coordinate, the diffusion coefficient ˜ D in-
cludes the effect of the heating field | E ( x )/ N | 2 , and
˜ S the reac-
tion source modeled as cross sections of the electron collisions
with neutrals (H 2 , O 2 , N 2 , H 2 O). The low-concentration radicals are
neglected. Mixture rules are based on particle number averaging,˜ =
∑ 4 k =1 x k W k , where x are the mole fractions of the background
species. The 78 cross sections used were taken from the sources
listed in Section 4 .
The electron energy distribution function (eedf) is represented
with a two-term spherical harmonic expansion dependent on the
local electric field. Such a representation is acceptable in the limit
of uniform electric field and collision probabilities over a mean
free-path [63] . The mean free path is l ≡ k B T √
2 πd 2 p � 1 × 10 −7 m,
which is smaller than any essential scales of advection, diffusion,
and reaction of the neutrals. Per the discussion of Section 3.2 , we
neglect transport in (6) , which leads to exponential growth of the
electron number density at a rate reflecting the difference between
ionization and attachment, each weighted by the particle fraction
of each target species. The popular BOLSIG+ package makes this
same approximation [30] , which has been examined critically in
previous plasma-coupled combustion studies [4,5] .
Our implementation was confirmed to reproduce measured
Townsend coefficients for electron impact ionization of pure N 2 ,
H 2 and O 2 [63] . We note one difference from the BOLSIG+ [30] for-
mulation: For the case with equal sharing of energy between the
created pair, our implementation sets
˜ 0 ,k d ε = −γ x k [ εσk ( ε) F 0 ( ε) d ε − 2 ( ε1 ) σk ( ε1 ) F 0 ( ε1 ) d ε1 ] ,
with ε1 = 2 ε + u k for constant energy loss u k . Expanding the dif-
ferential d ε1 = 2 d ε, we find that a factor 4, rather than 2 [30] ,
multiplies the last term in the normalized source term. With this
correction, the relative difference
�ν ≡ 2
νi, BLSG − νi, PLSCM
νi, BLSG + νi, PLSCM
, (7)
in the ionization coefficient obtained using the BOLSIG+ formula
ν i , BLSG is of the same magnitude as the error between measure-
ments and the present theory: relative errors between 10 and 20%
in the interval 100 Td ≤ E / N ≤ 200 Td and insensitivity to the ion-
ization degree α.
4.4. Numerical solution
4.4.1. Ionization rates and chemical time scales
The Boltzmann analysis shows that relevant ion production
1 /νi � 10 −8 s (for E / N � 100 Td) and destruction 1 /νr � 10 −6 (for
E / N ≈ 0) are much faster than the induction time of hydrogen-air
explosions, which have τi ≈ 1 × 10 −5 s [47] . Similarly, flame resi-
dence time over the dielectric surface is approximately equal to
the flow residence time τ r ≈ 1 ms, which is slower still and also
much longer than the electric period T act = 0 . 03 ms , which in turn
is much smaller than the gas heating time [ 11 , p. 219]. Thus, the
neutral concentration and temperature are taken to be fixed during
any particular microdischarge. More specifically, the simulations of
Section 8 suggest ˙ ω E ≈ 5 × 10 8 W / m
3 , thus the gas heating time
is approximately 50 times the electric half-period. Thus, the ion
chemistry can be represented as a system of ordinary differential
equations with coefficients dependent on the slow-varying neutral
chemistry.
4.4.2. Coupled kinetic system
The previous subsection shows that mixing and combustion
times are much longer than the 30 kHz DBD actuation period, so
these concentrations are effectively static with regard to ionization
nd recombination. The ion chemistry reactions do couple with the
ombustion reactions as sources of radicals and energy in the neu-
ral species and energy conservation equations.
The ion reactions of Sections 4.2.1 –4.2.4 lead, as usual, to a sys-
em of ordinary differential rate equations with temperature and
eutral target species compositions approximately constant over
he electric half-period. The represented particle-per-volume ion
oncentrations are
≡[N e − , N H − , N O − , N O −
2 , N O +
2 , N N +
2 , N H 2 O + , N N 2 H + , N H 3 O + , N H +
2
], (8)
nd governed by
d Z k dt
=
∑
j
(ν ′′
j,k − ν ′ j,k
)R j
∏
i
Z ν ′
j,i
i ,
here ν is the stoichiometric matrix and R i are the rate coeffi-
ients. The R i for reactions with electrons depend on the local elec-
ron energy distribution function,
i = x p i N γ
∫ εσi F 0 d ε, (9)
here the N accounts for the neutral concentrations, which is as-
umed constant within the ion system per our time scale separa-
ion. Additionally, in (9) , σ i are the cross sections, γ ≡√
2 e/m , and
i references the corresponding target neutral species for process i .
he eedf F 0 depends upon the time-dependent electric field and
lectron density and upon the effectively time-invariant chemical
omposition and temperature.
Rates not involving electrons are written with the UMIST
40] schema
i = αi
(T
300 K
)βi
exp
[ −γi
T
] . (10)
or parameters summarized in Table 1 , where M in 11c and 12a is
he concentration of the target species expressed in cm
−3 . All pa-
ameters are from UMIST, with two exceptions. The reaction 18 pa-
ameters were determined by directly minimizing the deviation of
he fit (10) from the data of Dotan et al. [64] . The reaction 13 rates
ere developed by Sakiyama et al. [65] , who assumed the rates
ithout citing detailed measurements. We note, however, that our
esults are insensitive to these particular reaction rates.
L. Massa, J.B. Freund / Combustion and Flame 184 (2017) 208–232 215
4
t
m
l
c
[
s
t
p
c
o
ν[
d
c
t
E
d
p
f
fi
a
t
o
n
p
v
T
Z
w
n
N
s
c
O
d
�
n
s
s
4
fl
r
b
s
s
S
i
m
c
t
s
n
t
t
s
〈
T
l
p
w
[
l
t
〈w
t
ω
w
b
c
t
ω
4
e
[
s
δ
m
c⟨w
N
d
w
d
a
1
5
t
t
d
a
o
d ∑
1
r
.4.3. Initial condition and the breakdown criterion
The final model component is the breakdown condition
hat governs the transition from the seemingly intermittent
icrodischarge initiation on the DBD surface, typical of the
ow-temperature experiments, to the apparently repetitive mi-
rostreamers supporting significant anodic current with the flame
8] . The definition of breakdown electric field at atmospheric pres-
ure is imprecise [ 11 , p. 135], because it can occur either by ei-
her a low-pressure route (i.e., the Townsend criterion) or by by-
assing this to a filamentary plasma. The high-pressure breakdown
ondition for an electronegative gas is typically assigned in terms
f a local balance between attachment and ionization frequencies
i = νa with an overvoltage factor on the resulting electric field E k 11,27] . Here, we introduce a self-sustained high-pressure break-
own condition that obviates initiation via wall emissions and ac-
ounts for the ratio between electric half-period and characteris-
ic particle removal rate by attachment. This leads to a breakdown
k dependent on temperature and concentrations appropriate con-
ition for a self-sustained pulsed discharge in the current high-
ressure, short-pulse regime. Particle losses and emissions to and
rom the surface are neglected. Functionally, it yields breakdown
elds that share characteristics with both the Paschen condition
nd a local balance between ionization and attachment.
The description is motivated, in part, by the common observa-
ion that microstreamers recur at the same location at each change
f polarity [19] . Even in the absence of secondary emission and
eglecting photoionization, a recurrence can be supported if the
lasma density reduction in the afterglow is slow compared to the
oltage period, which seeds the opposite polarity streamers.
Streamer recurrence justifies solution of (4.4.2) with periodicity
act /2
(0) = Z(T act / 2) ≡ B, (11)
here the half-period is sufficient since this particular system has
o symmetry breaking in the exposed versus covered electrode.
umerical solutions confirm that periodic solutions are indeed
trongly attracted to the periodic cycles supported by (11) , with
onvergence to three significant digits in three half periods.
These assumption and the condition (11) allow us to solve the
DE system independently with an adaptive fifth-order backward
ifferentiation formula method [66] . The requisite time step is
t � 10 −12 s. Still, this solution does depend on the time-evolving
eutral field, thus (11) is solved for a range of target state compo-
itions and temperatures and approximated (accurately) with the
ource term maps described in Section 5 .
.5. Source terms
Fast, non-LTE plasma effects are represented in the slow, LTE
ow and transport equations as source terms in the energy and
adical mass conservation equations. Corresponding terms in the
ackground species are determined by imposing atomic mass con-
ervation, yet they are found to be unimportant because of the
mall degree of ionization (cf. [ 67 , p. 281]). As discussed in
ection 4.1 , only non-equilibrium H radicals are considered in the
gnition of hydrogen in air at atmospheric condition. This does not
ean that the processes leading to molecular excitation and disso-
iation of other species are ignored. They are represented, though
heir products (vibrationally, electronically and rotationally excited
pecies, atomic oxygen, etc.) and assumed to equilibrate with the
eutral thermochemistry quickly on the ignition time scale. Thus,
hese processes provide an energy source in the flow equations.
Consistent with the T act τ r assumption of Section 4.4.1 (ac-
uation periods are slower than flow/flame residence times), any
ource f is applied as period averages
f (t) 〉 T ≡ 1
T act
∫ T act
0
f (t ) d t . (12)
his neglects any direct effect of the microdischarges on turbu-
ent fluctuations, which is justified based on the anticipated weak
ower coupled by any particular micro-pulse. Schlieren images
ith and without DBD actuation at 15 m/s supports this assertion
9] .
The energy dissipated and the species produced by electron col-
isions are convolutions of the corresponding cross sections σ i with
he eedf F 0 ,
σi ( ε) 〉 n ≡ γ
∫ εn σi ( ε) F 0 ( ε) d ε, (13)
here n = 1 for species and n = 2 for energy. The radical produc-
ion source term is thus
˙ H =
∑
j| ν ′ j,e
=1
x p j x H 2
ν ′′ j,H
− ν ′ j,H
2
⟨⟨σ j
⟩1 N e −
⟩T
+
∑
j| ν ′ j,e
=0
1
Nx H 2
ν ′′ j,H 2
− ν ′ j,H 2
2
⟨
R j
∏
i
Z ν ′
j,i
i
⟩
T
, (14)
here the number densities Z i are functions of time as determined
y solving (4.4.2). The corresponding mass source in the species
onservation equations is ˙ ω H ρH 2 . Similarly, the energy transfer be-
ween plasma and gas leads to the power density source term
˙ E = Ne
⟨
N e −
( ∑
k = inelastic
x k 〈 σk ( ε) 〉 2 +
∑
k = elastic
2
m e
M k
x k 〈 σk ( ε) 〉 2 ) ⟩
T
.
(15)
.6. Pulse waveform parameters
The waveform (3.2.2) contains three principal empirical param-
ters. The first, δD , adjusts the phase of the actuator. Experiments
8] show that microdischarges are formed between the times of
witching polarity and the peak voltage, which is reflected by
D = 0 . 15 × T act . The other parameters ( δc and t f ) are calibrated by
atching the measured absorbed power per cycle for cold, zero-
ross-flow conditions, ∫ ∞
−∞
∫ ∞
0
˙ ω E d y 2 π r d r
⟩T
= W exp = 8 W , (16)
here y and r are the axial and radial coordinate, respectively.
ote, the cold, zero-cross-flow conditions are axisymmetric. In ad-
ition, we impose a consistency condition based on observations:
hen increasing the air temperature without cross-flow, break-
own occurs for surface temperature T ≈ 750 K [8] . This constraint
nd (16) lead to δc = 1 × 10 −4 T act = 10 / 3 ns and t f = 1 × 10 −5 T act = / 3 ns.
. Energy and radical production maps
Practical implementation of the model in a large-scale simula-
ion depends upon multidimensional maps for the ions–neutrals
ime-scale separation model motivated in Section 4.4.1 and intro-
uced in Section 4.5 . Their goal is to provide ˙ ω Radical from (14) (for
ll radicals in chemical non-equilibrium) and ˙ ω E from (15) based
n local conditions. This is a six-parameter map with indepen-
ent variables x O 2 , x O 2 /x N 2 , x H 2 O , x H , T , and E / N , with constraints
x i = 1 and p = 1 atm . The present simulations used 16, 16, 16, 4,
6, and 30 entries to represent x O 2 , x O 2 /x N 2 , x H 2 O , x H , T , and E / N ,
espectively.
216 L. Massa, J.B. Freund / Combustion and Flame 184 (2017) 208–232
Fig. 5. Energy source (15) map: log 10 ˙ ω E
W / m 3 for the local conditions as indicated in the titles and x H = 0 , P = 1 atm plus x H 2 + x O 2 + x N 2 + x H 2 O = 1 . Note: the vertical axis
scale changes between plots, while the color scale is fixed and ranges between −5 (blue) and 12 (yellow). (For interpretation of the references to color in this figure legend,
the reader is referred to the web version of this article.)
Fig. 6. Dimensionless price per radical: log 10 ( P ) (see (17) ) for the local conditions as indicated in the titles and x H = 0 , P = 1 atm plus x H 2 + x O 2 + x N 2 + x H 2 O = 1 . Note: the
vertical axis scale changes between plots, while the color scale is fixed and ranges between 1 (blue) and 4 (yellow). (For interpretation of the references to color in this
figure legend, the reader is referred to the web version of this article.)
i
i
t
b
t
t
Example maps are shown in Figs. 5 and 6 to illustrate the gen-
eral behavior of (15) and (14) and their sensitivity the local con-
ditions. The conditions in Fig. 5 were selected to illustrate three
key sensitivities: (1) a notable increase in ˙ ω E with decreasing x O 2 for x H 2 O = 0 , showing oxidizer sensitivity; (2) a decrease in ˙ ω E with x H 2 O reflecting a decreasing region of filament coverage with
ncreasing water content; and (3) an only weak effect of x O 2 /x N 2 n the E / N –T plane. The radical coupling term ˙ ω H 2
follows closely
he energy coupling: each plot shows a threshold-like increase of
oth ˙ ω E and radical coupling ˙ ω H with increasing E / N and T due
o the reduction of the electron-molecule collision frequency with
he increase of target gas temperature. In Fig. 6 we show the
L. Massa, J.B. Freund / Combustion and Flame 184 (2017) 208–232 217
d
a
P
w
o
e
i
(
c
a
6
t
d
T
v
Q
w
i
m
f
a
o
N
O
w
c
i
s
r
d
s
p
F
φ
w
p
7
e
j
a
s
i
b
u
a
t
s
t
p
p
Fig. 7. Schematic of the simulation domain matching a corresponding wind tunnel
configuration [9] , which includes a section of the flat windtunnel wall, a sandpaper
turbulence trip, a turbulent cross-flow, 4.826 mm diameter hydrogen jet, and a DBD
plasma actuator. The simulation domain width is 4.76 cm, with spanwise periodicity
used to model as section of wind tunnel. The domain is 50.8 cm long.
F
T
8
u
a
e
t
l
s
t
a
p
l
m
t
8
m
v
s
i
o
a
d
s
(
j
t
d
1
i
e
e
s
F
i
t
a
c
e
imensionless price P per H radical generated by the electric actu-
tion, which is defined
≡ ˙ ω E ρH 2 ˙ ω H 2 �H
◦f , H
, (17)
here �H
◦f , H
is the specific (i.e., mass based) heat of formation
f the radical. The price is lowest for pure H 2 at high reduced
lectric field and low temperature (top-right panel), and largest
n H 2 O −rich mixtures at low reduced field and large temperature
bottom-left panel). The price is consistently lowered by an in-
rease of the reduced electric field, while an increase in temper-
ture at constant E / N has an opposite (though weaker) effect.
. Governing equations and neutral chemistry
The source terms developed in the previous sections carry
he effect of the plasma and plasma chemistry into the three-
imensional chemically reacting compressible flow equations.
hese are expressed in general curvilinear coordinates for the state
ariables
= [ ρ ρu 1 ρu 2 ρu 3 ρE ρY 1 ρY 2 . . . ρY N ] � , (18)
here ρ is the gas density, ρu i is the momentum density in the
th direction, ρE is the total energy density, and ρY k is the species
ass density for k = 1 , 2 , . . . , N. Additional details regarding this
ormulation and its discretization with high-order finite differences
re available elsewhere [68] .
Neutral chemistry is modeled with the 12-steps H 2 –O 2 model
f Boivin et al. [47] , which includes 9 species H 2 , O 2 , H, H 2 O, HO 2 ,
2 , OH, O, and H 2 O 2 and invokes a quasi-steady state reduction for
H, O, H 2 O 2 .
The computational mesh is formed by the overlap of three grids
ith interpolation conditions at the mutual boundaries. The grid
ontains approximately 30 millions nodes. Resolution insensitivity
s established for both the turbulence and the ignition [17] .
The electric field is evaluated as a solution of a screened Pois-
on equation. A linearized approximation for the charge on the
ight-hand side of the Poisson equation leads to a sinusoidal time-
ependence of the electric field, so that the Poisson equation is
olved once per simulation. The right-hand side of (3.2.1) is ex-
ressed following Corke et al. [23] ,
( φ) =
φ − φ0
λ2 N
, (19)
0 = V exposed +
V covered − V exposed
K
for K ∈ [1 , ∞ ) (20)
ith K = 4 and model parameter λN evaluated as previously re-
orted [17] .
. Flow configuration
The specific ignition experiment for which we demonstrate and
valuate our model is report on in full elsewhere [9] . It is a fuel
et in a for 15 m/s crossflow with a developed turbulent bound-
ry layer. The turbulence was seeded with the sandpaper trip
hown on the left-hand side of Fig. 7 , which was represented
n model geometric detail by 1600 randomly Gaussian-shaped
umps on the same scale as the sandpaper grains [17] making
p a 1.64 mm thick strip on the windtunnel floor. The inter-
ction of the trip with the step affects the bypass process and
he turbulence characteristics at the hydrogen jet. A compari-
on between computed and measured Reynolds stress shows that
his model well reproduces turbulence at the hydrogen injection
ort [9] .
The flow is ignited by a thermal hot spot, deposited in the ex-
eriment via the optical breakdown of a focused laser, as shown in
ig. 10 . The focal point is h i above the bottom of the wind tunnel.
he igniter is described in more detail elsewhere [17] .
. Results
We first consider some essential components of the full config-
rations: the DBD plasma and the igniter gas hot spot, the inter-
ction of the flame front with the plasma, and the non-symmetric
missions from the plume. In Section 8.2, we demonstrate the con-
ributions of plasma-combustion coupling to the ignition of the
aminar jet in the turbulent cross-flow, then in Section 8.3 we
how that including the plasma-combustion contribution improves
he prediction of the ignition probability data. In Section 8.4 , we
nalyze the effect of the coupling on the spatially integrated power
redictions and plasma extension, in Section 8.5 we analyze the
ink between plasma-combustion coupling and the filtered experi-
ental light emissions, and, finally, in Section 8.6 we discuss how
he coupling can support two-stage ignition.
.1. DBD body force
Although they lack the direct comparison of direct electric-field
easurements, PIV data allow for the validation of the body-force
ector, which is proportional to the divergence of the electrostatic
tress tensor [69] . The flow is compared with the correspond-
ng stand burner experiment [8] in Fig. 8 . The major uncertainty
f the experiments is due to thermophoretic effects in the flame
nd the correction of the particle velocities due to thermal gra-
ients. No correction has been applied to the experimental data
hown in Fig. 8 , therefore particle velocities in the flame sheet
i.e., where thermal gradients are large) are not reported. The ma-
or uncertainty of the computations relates to modeling the vor-
icity added by the discharge. A streamline representation of the
ata in Fig. 8 shows significant vorticity at the flame edge ( r ≈0 mm). A model like the one proposed in (20) introduces vortic-
ty only due to misalignment of electric field and density gradi-
nt, ˙ �DBD ∝ −F
′ /ρ2 ∇ φ × ∇ ρ, which is concentrated at the flame
dge. Computational analyses with vorticity corrections [70] have
hown that the disagreement between data and simulations in
ig. 8 at y = 10 mm and y = 5 mm is likely due to lack of vorticity
n the model due to its irrotational specific force.
The same standburner configuration also allows us to validate
he computational model by comparing the predicted thermal field
gainst CARS wave spectroscopy measurements [71] . The flat-flame
ase obtained with a DBD forcing of 8 kV was selected for this
xperiment because the strong body forces appear to remove the
218 L. Massa, J.B. Freund / Combustion and Flame 184 (2017) 208–232
Fig. 8. PIV measurement and current prediction for the DBD stand burner operated at 5 kV. The curves marked as “no-model” refer to computed results without a body-force
model.
Fig. 9. Unperturbed reduced electric field ˆ E /N 0 1 Td
: the solution of the screened Pois-
son equation (3.2.1). The red rectangle is the exposed electrode, while the black one
is the covered analog; the quartz dielectric is white. (For interpretation of the ref-
erences to color in this figure legend, the reader is referred to the web version of
this article.)
Fig. 10. The laser breakdown height h i .
8
o
S
c
c
c
t
g
b
e
a
w
v
i
t
o
t
o
i
n
n
t
t
t
n
i
flickering instability flames [72] . The errors in the temperature pre-
diction
∫ 2 D H −2 D H
| T (r, y ) − T CARS (r, y ) | d r
max r ( T CARS (r, y ) ) 4 D H
,
is 4%, 3%, 2%, and 6% at the measurement locations above the
dielectric surface of 1.5 mm, 2 mm, 3 mm and 4 mm, respectively.
This disagreement is comparable to the measurement uncertainty
quantified estimated based upon deviation of the data from axial
symmetry.
The unperturbed reduced electric field magnitude ˆ E /N 0 corre-
sponding to this comparison is shown in Fig. 9 for a value of
N 0 = P atm
/ (k B T ∞
) and T ∞
= 300 K. Because the model parameters
were chosen independently and a priori of the data measurement,
they suggest that the predicted distribution of the unperturbed
electric field
ˆ E is correct.
.2. Coupling at ignition
This section describes the effect of plasma combustion coupling
n the ignition of the hydrogen jet in a cross-flow introduced in
ection 7 . It is shown that the DBD actuation of the ignition pro-
ess is more efficient in the temperature regime where the dis-
harge is thermally coupled to the combustion. When plasma and
ombustion are decoupled, which is the condition typical of gas
emperatures significantly lower than those supported by hydro-
en flames, the augmentation of ignition by plasma is inefficient
ecause energy and radical addition to the flow occur (in gen-
ral) away from the ignition kernel. However, when the discharge
nd ignition are coupled, power is selectively added to the region
here both fuel concentration and temperature are high, in the
icinity of the induction region. This selective process is especially
mportant in cross-flow configurations because the advection of
he kernel moves the induction zone away from where breakdown
ccurs in the cold flow.
The computational setup is that described in Fig. 10 . The con-
rol variable is the laser-induced breakdown height h i and we focus
n successful ignition, for which a flame anchors itself at the lead-
ng edge of the fuel port. The size and shape of the ignition ker-
el have been deduced from luminosity measurements [17] . Those
umerical experiments have shown that if total energy transfer to
he fluid and the first moment of its distribution with respect to
he stoichiometric surface are maintained constant, this parame-
er does not play a significant role in the determination of the ig-
ition boundary. For h i = 2 . 68 mm, we predict no such sustained
gnition. Moreover, this is close to the predicted ignition bound-
L. Massa, J.B. Freund / Combustion and Flame 184 (2017) 208–232 219
Fig. 11. Ignition of the jet in cross-flow without DBD: red surface showing T = 1500 K and blue surface showing X H 2 = 0 . 1 . The labeled times are relative to the laser-induced
breakdown. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
a
t
o
s
t
k
t
t
b
m
d
w
t
t
s
c
n
d
g
o
t
s
i
t
o
n
c
ry discussed in Section 8.3 , thus this is a useful case for testing
he marginal influence of the radical model. The thermal history
f this unsuccessful ignition is visualized in Fig. 11 . High-speed
chlieren movies of failed ignition experiments similarly close to
he sustained-ignition boundary show a similar dynamics for the
ernel: the heat addition by the DBD distorts the interface be-
ween low- and high-density gases, but does not penetrate inside
he slow boundary layer flow. It thus cannot propagate upstream
ecause the laminar flame speed of hydrogen S L ≈ 3 m/s is so
uch slower than the free-stream velocity 15 m/s [9] .
In order to analyze the proposed coupling mechanism in more
etail, we compare to an artificially decoupled ignition model
ithout the fundamental coupling mechanism of Section 4.5 . To do
his we simply evaluate the source terms at T = 298 K even though
he gas temperature of the laser igniter exceeds 50 0 0 K [73] . This
fiuppresses energy and radical transfers because of both the in-
reased three-body attachment cross section and the increased
umber density leading to a smaller reduced electric field and a
iminished electron energy. Thus, the majority of the radicals are
enerated by the plasma close to the electrode, where breakdown
ccurs (because of the lower breakdown potential of hydrogen and
he higher electric field; see Fig. 9 ). The H radical concentration
upported by the DBD in the cold flow is visualized on the X H 2
so-surface in Fig. 12 . This figure shows a large radical concentra-
ion close to the electrode, and the computations agree with the
bserved emissions presented in Fig. 3 a showing no plasma lumi-
escence above the dielectric surface in cold conditions.
The radical and energy fields supported by the artificially de-
oupled model do not affect the ignition probability. The thermal
eld supported is shown in Fig. 13 , and is similar to the no-DBD
220 L. Massa, J.B. Freund / Combustion and Flame 184 (2017) 208–232
Fig. 12. H radical stream generated by the DBD in a cold flow: the X H 2 = 0 . 1 isosur-
face is colored by the H radical molar fraction. The scale limit at 5 × 10 −6 highlights
the important region outside the fuel tube. The DBD turns on at t = 0. (For inter-
pretation of the references to color in this figure legend, the reader is referred to
the web version of this article.)
[
e
q
[
t
s
d
a
a
i
t
b
a
t
a
m
w
c
d
b
T
a
I
r
8
s
c
t
d
S
e
t
n
e
s
A
f
6
fi
d
b
S
n
p
a
a
h
t
t
s
b
y
q
t
t
p
c
w
c
t
case Fig. 11 . Such a result might be expected based upon the power
densities involved. The laser igniter transfers approximately 18 mJ
to a fluid volume that at ignition covers approximately 1 mm
3 ac-
cording to measurements [17] , whereas the DBD transfers approx-
imately 8 W to a volumetric flow rate of 1070 cm
3 /min, leading
to an energy density of only about 1/40th that of the laser. Thus,
without thermal coupling, we would indeed expect no direct effect
of the DBD-generated radicals.
Including the full coupling leads to the significant changes and
successful ignition visualized in Fig. 14 . Although the initial phase
is similar to the DBD-off analog (i.e., panels with t < 1 ms in
Figs. 11 and 14 ), the ignition kernel becomes wider as it advects
downstream and interacts with the external electric field seen in
Fig. 9 . The electric breakdown and Joule heating forms a region of
sustained heat release. The subsequent penetration of the hot gas
into the boundary layer ( t ≈ 1.47 ms) allows the ignition front to
propagate upstream ( t > 1.5 ms). The continued increased temper-
ature in the high electric field layer induces stronger energy and
radical concentration production by the electron impact collisions,
leading to a two-way coupled propagation of the ignition front.
Such thermally-coupled discharges are particularly efficient in sup-
porting thermo-chemical induction because the discharge current
density is selectively concentrated where the temperature and fuel
concentration are large, as they are in the ignition kernel. Such a
selective amplification is also responsible for the plasma filament
formation in the experiments of Savelkin et al. [7] : the tempera-
ture increase caused by the direct current discharge augments the
conductivity in selective locations of the flow field, which reduces
the gap voltage below the cold breakdown value, which in turn
concentrates current density in the filaments.
Therefore, the coupled ignition process is aided by the transfer
of energy to the gas by the discharge. The predicted spatial distri-
bution of the energy transferred ˙ ω E is shown in Fig. 15 , where the
surface ˙ ω E = 1 W / m
3 is superimposed to the hydrogen concentra-
tion surface X H 2 = 0 . 1 . Figure 15 shows that the ignition hot spot
generates a plasma kernel that is advected by the flow in synchro-
nized motion with the hot gas. The synchronization between ther-
mal and plasma fields is due to their two-way coupling so that
plasma can exist only where the temperature is large and the hot
spot is sustained by the presence of the plasma. This mechanism
is, in our opinion, also the underlying physics that controls the ad-
vection of plasma filaments in the experiments of Savelkin et al.
7] . Our model neglects the plasma time-scales associated with
lectron drift and diffusion. Although this assumption yields results
ualitatively similar to those from the analysis of Savelkin et al.
7] , the physics underlying our simulation is very different from
hat hypothesized by the authors of that study. Here the plasma
cales are much faster than the fluid scales, so that the electron/ion
ensity immediately adjusts to the background gas temperature
nd concentration, there the assumption of “local ionization bal-
nce” [7] in a spatially varying electric field effectively translates
n plasma being advected as a passive scalar, i.e., decoupled from
he thermal state of the fluid.
When the flame anchors ( t � 2 ms in Figs. 14 and 15 ), the com-
ined energy budget of combustion and discharge is locally bal-
nced by thermal losses, with statistically stationary plasma condi-
ions. Once this occurs, these visualizations of the coupled energy
re qualitatively similar to the emissions measured in the experi-
ents (see Fig. 3 b). The widening of region with plasma emission
hen the flame is on (compare Fig. 3 a and 3 b) is due to the de-
rease in breakdown electric field due to temperature increase in-
uced by the combustion, consistent with the obvious breakdown
oundary in Fig. 5 . A similar effect was noted by Savelkin et al. [7] .
his is also tied with the power coupled in the fluid and the time-
veraged plasma extension which will be analyzed in Section 8.4 .
n the next section we consider the ability of the coupled model to
eproduce the measured sustained-ignition boundary.
.3. Ignition probability predictions
Here we apply plasma-combustion coupling mechanism de-
cribed in Section 8.2 on the ignition probability of the jet in a
ross-flow Fontaine et al. [9] . While the measured ignition dis-
ance is a stochastic variable such that the associated probability
ensity function is obtained by ensemble-averaging 50 trials (cf.
ection 2.2 ), the simulations indicate that the stochasticity inher-
nt with the computed turbulent field has a marginal effect on
he ignition of the jet [17] . We, therefore, infer that the random-
ess of the measurements is mainly due to the variation in laser
nergy absorbed by the gas, which is estimated to be nearly Gaus-
ian with 95% of the data within ± 6.12 mJ of the average 17.64 mJ.
s a consequence, the simulations obtain a (for our purposes) ef-
ectively deterministic ignition boundary, as confirmed with up to
repeated attempts. The representative snapshot of the turbulent
eld used as the initial state for all the simulations discussed in
etail in this section is visualized in Fig. 16 .
A comparison between the computed and measured ignition
oundaries is shown in Fig. 17 . The uncoupled plasma model of
ection 8.2 is again used here for comparison, and shifts the ig-
ition boundary towards lower values of h i . The body forces sup-
orted by the discharge act to “flatten” the stoichiometric surface
t the edge of the H 2 −Air mixing layer. Such a flattening causes
reduction of the chemical reactions close to the port and, thus,
inders the ability of the ignition kernel to propagate upstream.
The coupled model shifts the ignition boundary of an amount
hat is consistent with the measurements [9] . The major uncer-
ainties of the experiments are related to the previously discussed
hot-to-shot variability of the power deposition and the distance
etween optical focal point and laser breakdown location. An anal-
sis of the schlieren images immediately after breakdown leads to
uantify such distance as 0.2 mm [9] . The experiments show that
he DBD-on case ignites with probability greater than 0 at a dis-
ance 0.6 mm greater than the DBD-off case. The computations
redict 0.4 mm. The experiments predict that the maximum lo-
ation of the slope of the curve P ( h i ) is displaced by 0.32 mm
hen the DBD is on. The computations still predict 0.4 mm. Be-
ause the radicals are generated in close proximity to the dielec-
ric surface, one of the possible causes of the over-prediction of P
L. Massa, J.B. Freund / Combustion and Flame 184 (2017) 208–232 221
Fig. 13. Ignition of the jet in cross-flow with thermally uncoupled DBD sources: red surface showing T = 1500 K and blue surface showing X H 2 = 0 . 1 . (For interpretation of
the references to color in this figure legend, the reader is referred to the web version of this article.)
i
t
M
f
8
W
i
m
p
c
I
p
T
t
fl
i
w
“
a
c
l
F
r
p
c
t
s
d
a
f
e
g
n the DBD-on case is the absence of the radical recombination at
he quartz surface. These effects have been recently quantified by
ackay et al. [74] . Future analysis by the authors will include sur-
ace effects.
.4. Power predictions
The total power coupled into the gas phase per DBD cycle,
˙ ≡
∫ ˙ ω E d V. (21)
s shown in Fig. 18 , as it depends on time and compared with the
easured (using the monitor-capacitor method) averaged over ap-
roximately 100 periods. The measurements are shown for both
old (before ignition) and hot (after flame anchoring) conditions.
nterestingly, Retter et al. [8] indicate that the measured power-
er-cycle varies significantly during the anchored-flame timeframe.
he simulations indicate a qualitatively similar result, which is due
o the action of the turbulence in changing the position of the
ame in the electric field layer.
Figure 18 shows the “Total” power, which is sum of the value
ntegrated above the dielectric surface and in the hydrogen tube,
hich would better correspond to the experiment, as well as the
Above the Surface” power that includes only the amount absorbed
bove the dielectric. The simulation results indicate a strong in-
rease in the latter value between t = 1 . 5 and 2.5 ms from the
aser breakdown. This “peak-energy” time-frame corresponds (see
ig. 14 ) to the advancement of the flame-front in the hydrogen-
ich gas. After the ignition front reaches the port at t ≈ 2 ms, the
roduction of water in the flame significantly reduces the power
oupled as discussed with regard to the maps in Section 5 .
The predicted, time-averaged power slightly exceeds 30 W in
he hot-period ( t > 2.5 ms). Contrasted with cold value of 8 W, this
hows the substantial contribution of the flame in changing the
ischarge structure. We note that also Savelkin et al. [7] measured
substantial increase in power absorbed by the gas when injecting
uel in the combustion chamber (burning cases), also noting the
xtension of the plasma filaments and consequently increases the
ap voltage. Our model supports the link between power absorbed
222 L. Massa, J.B. Freund / Combustion and Flame 184 (2017) 208–232
Fig. 14. Ignition of the jet in cross-flow with thermally coupled DBD sources: red surface showing T = 1500 K and blue surface showing X H 2 = 0 . 1 . (For interpretation of the
references to color in this figure legend, the reader is referred to the web version of this article.)
t
t
t
t
p
a
t
i
r
b
r
d
t
r
m
t
and plasma extension. Yet, our model does not account for the
solid-state electrical circuit, thus the gap voltage is constant. Our
model is, instead, based on a similarity law for the microstream-
ers, whereby the main limiting mechanism to the power coupled
is the quenching effect of the charge deposited by the microdis-
charges on the dielectric surface.
The proposed model is complex and was parameterized inde-
pendently of the current measurements, which makes this level of
agreement acceptable. Limiting the spatial scale of the pulses at
high temperature as described in (3.2.2) is an important ingredi-
ent of this prediction, without which the simulated power signif-
icantly overestimates the measurements. However the current pa-
rameterization does somewhat overpredict the measured power in
Fig. 18 . We can anticipate potential causes, but leave refinement of
it to future studies, likely with additional supporting experiments.
Because the model was calibrated in low temperature hydrogen, a
possible missing mechanism is that of water vapor on the power
ransferred to the gas in the hot burnt plume. Water increases
he rate of electron attachment at high E / N ; the hydration reac-
ion helps this process by reducing the detachment from O
−2 [75] ,
hus increasing the production of anions in the high temperature
lume. The kinetics of the superoxide anion in high temperature
tmospheric flames is not well understood.
We can estimate the potential effect of water vapor increasing
he exponent of the hydration reaction 11.c in (3) from its nom-
nal value of ζ = −3 . 5 to the upper-end value of −2.5. It indeed
educes power, as shown in Fig. 19 . However, the ignition proba-
ility prediction (i.e., Fig. 17 ) is only marginally dependent on the
ate constant of this reaction, because water concentration is small
uring both the advection of the ignition kernel and the propaga-
ion of the front ( t < 2 ms in Figs. 14, 15 and 18 ) . We find that the
elationship between coupled power and hydration exponent is al-
ost linear in the interval of interest. We have selected the hydra-
ion reaction for this test because its temperature dependence is
L. Massa, J.B. Freund / Combustion and Flame 184 (2017) 208–232 223
Fig. 15. Ignition of the jet in cross-flow with thermally coupled DBD sources: red surface showing ˙ ω E = 1 W / m
3 and blue surface showing X H 2 = 0 . 1 . (For interpretation of
the references to color in this figure legend, the reader is referred to the web version of this article.)
p
i
o
f
u
c
d
o
i
v
d
b
a
r
fl
m
t
s
D
a
t
o
c
l
m
e
a
8
p
c
t
articularly uncertain and the sensitive derivative with respect to
ts temperature exponent is the largest component of the gradient
f the coupling source-terms (cf. Fig. 5 ) in parameter space, there-
ore the variation in Fig. 19 provides an estimate for the parametric
ncertainty of the power predictions.
The substantial effect of the hydration exponent on the power
oupled is thus due to the quenching effect of water on the plasma
ensity. The results of Fig. 19 help us explain the marked variation
f the measured power against the cross-flow velocity discussed
n [ 9 , Fig. 10]: an increase in cross-flow velocity bends the water
apor plume and increases its interaction with the plasma at the
ielectric wall downstream of the port. Conversely, in the standing-
urner experiments [8] the water vapor is removed by buoyancy
nd discharged vertically. In fact, the contribution of buoyancy in
emoving hot products from the flame region is highlighted by the
ickering motion observed in the actuated stand-burner experi-
ents. Therefore, the interaction of the water vapor plume and
he dielectric walls explains why the standing burner supports a
ignificantly more energetic coupling between the plume and the
BD plasma.
Figure 20 shows the spatial distribution of power coupled aver-
ged in time over an interval of 2 ms within the quasi-stationary
urbulent flame ( t > 2.5 ms). Of particular note is that the plasma
nly marginally shrinks with the hydration reaction exponent in-
rease. Thus, as the intensity of the energy coupling increases,
eading to a larger power transfer, the overall plasma extension re-
ains approximately constant. The scope of this conclusion will be
xpanded in the next section by comparing the simulation results
gainst the brightness and size of the experimental emissions.
.5. Temperature profiles
The marked influence of the hydration exponent ζ on the
ower transferred to the fluid is due to the strong two-way
oupling between plasma and thermal processes. Chemical reac-
ions increase the gas temperature, which increases the reduced
224 L. Massa, J.B. Freund / Combustion and Flame 184 (2017) 208–232
Fig. 16. The Q-criterion Q = 300 s −2 isosurface colored by the vorticity magnitude using a colormap linear color map between 0 (blue) and 100 s −1 (red). (For interpretation
of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 17. Comparison between prediction and experiment for the ignition distance
probability h i .
Fig. 18. Power coupled in the gas by the DBD plasma.
Fig. 19. Power coupled in the gas by the DBD plasma plotted versus the hydration
reaction exponent ζ for (3) , reaction 11.c.
e
s
p
t
w
o
t
s
i
n
g
d
fl
fi
t
g
l
a
n
lectric field leading to a larger electron temperature and thus
tronger collisional energy transfers. The reduced momentum loss
er electron-pair produced (see Section 3.1 ) only partially offset
his bootstrapping mechanism and the exothermal reactions in the
eakly ionized plasma can “launch” the system. The nonlinearity
f the temperature change versus the gap voltage is rooted in the
hermal budget of the gas phase. Temperature is, therefore, a very
ensitive indicator of coupling and will be analyzed in more details
n this section.
Measured thermal emissions from water molecules at 720
m [ 9 , Fig. 10] show that the actuated flames support two re-
ions of significant emissions. A first one is elongated in the
ownstream direction and is associated with a H 2 /O 2 diffusion
ame, the second, located immediately downstream of the ori-
ce, is wider, shorter and brighter. Anticipating that the lat-
er region is due to plasma-combustion coupling, we investi-
ate the ability of the model to simulate its spatial extent and
ocation.
The computed thermal field supported by the actuated flames
re shown in Fig. 21 for values of the hydration reaction expo-
ent equal to −3.5, −3.0 and −2.5; the top left panel also shows
L. Massa, J.B. Freund / Combustion and Flame 184 (2017) 208–232 225
Fig. 20. Energy coupling versus the hydration reaction temperature exponent ζ : red surface showing the energy coupled in the gas by the plasma ˙ ω E = 1 × 10 −2 W / mm
3
and blue surface showing the hydrogen molar fraction for X H 2 = 0 . 1 . (For interpretation of the references to color in this figure legend, the reader is referred to the web
version of this article.)
Fig. 21. Mean temperature in the electric field layer versus the hydration reaction rate temperature exponent.
Fig. 22. Integrated temperature versus the radial distance from the orifice center
for three values of the hydration reaction exponent. The ordinate for the “emission
peak location” has been selected based on ease of visualization.
t
t
3
e
T
w
s
a
a
c
o
t
s
t
t
p
t
i
b
c
w
a
[
t
c
he unactuated analog for reference. In these plots the tempera-
ure has been averaged in the wall normal direction over a layer
mm thick, corresponding, approximately, to the thickness of the
lectric-field layer over the dielectric in Fig. 9 ,
ˆ ( x, y ) ≡
∫ 3 mm
0 T ( x, y, z ) d z
3 mm
,
here z = 0 corresponds to the windtunnel wall.
The simulations predict the formation of a well-defined hot
pot starting approximately 10 mm downstream of the injection
xis. On the one hand, the size and shape of this high temper-
ture region is weakly dependent on the power coupled, as we
an infer by its variation against the hydration exponent. On the
ther hand, the maximum temperature is roughly proportional to
he power coupled. This result agrees qualitatively with the mea-
urements described by Fontaine et al. [9] , who correlated the in-
ensity of the water vapor emissions from the region directly above
he dielectric surface and downstream of the jet with the electrical
ower absorbed by the DBD. That experimental study reports that
he “characteristic” spanwise half-width of the thermal emissions
s equal to 5.84 mm for a DBD power of 26.80 W. The horizontal
lack, thick line superimposed to the colormaps in Fig. 21 indi-
ates the extension of the experimental measurements; the thin
avy line is a reconstruction of the experimental emission im-
ge at ˙ W = 26 . 80 using a morphological reconstruction algorithm
76] with pixel threshold set equal 0.5. This result, together with
he observed weak correlation of plasma extension against power
oupled in Fig. 20 , supports the idea that hot-spot brightness not
226 L. Massa, J.B. Freund / Combustion and Flame 184 (2017) 208–232
Fig. 23. Upstream propagation of the flame in actuated conditions: red surface showing the energy coupled in the gas by the plasma ˙ ω E = 1 W / mm
3 and blue surface
showing the hydrogen molar fraction for X H 2 = 0 . 1 . (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this
article.)
T
v
p
c
a
i
t
c
t
t
8
i
c
size correlates with the absorbed power, which agrees with the
trend shown in the experiments [9] .
The streamwise location of the strongest plasma–gas energy ex-
change depends on various factors, including the unperturbed elec-
tric field, the water content and the temperature in the plume.
The experiments [9] have shown a distinct peak in thermal emis-
sions located approximately 15 mm from the port axis. We test the
model by analyzing the variation of the temperature field against
the radius. In order to that, the temperature is averaged in the cir-
cumferential direction by integrating ˆ T defined in (8.5) over the
angle θ ∈ [ − arctan ( 5 . 84 / 10 ) , arctan ( 5 . 84 / 10 ) ] ≈ [ −π/ 6 , π/ 6 ] , i.e.,
evaluating
˜ T ( r ) ≡∫ π/ 6
−π/ 6 ˆ T ( r cos θ, r sin θ ) d θ
1 / 3 π. (22)
he values of ˜ T ( r ) are plotted against the radius in Fig. 22 for three
alues of the hydration exponent. Although the variation in tem-
erature is markedly dependent on the power absorbed, the lo-
ation of the peak is marginally affected by it, and it is located
round 15 mm from the port, in good agreement with the exper-
ments. The peak temperature in the simulations is located near
he maximum of the external electric field in Fig. 9 . Therefore, this
omparison confirms that the use of the screened Poisson equation
o determine the reference electric in the pulse approximation of
he microstreamer, i.e., Eq. (3.2.2), is correct.
.6. Two-stage ignition
One of the most interesting aspects of the plasma-combustion
nteraction, is that it leads to a closed-loop feedback pro-
ess, whereby a larger temperature leads to a stronger energy
L. Massa, J.B. Freund / Combustion and Flame 184 (2017) 208–232 227
Fig. 24. Effect of direct and indirect paths on H radical production: log 10 ˙ ω H
1kg / m 3 −s for the local conditions as indicated in the titles and P = 1 atm plus x H 2 + x O 2 + x N 2 + x H 2 O =
1 .
a
t
i
o
o
i
F
t
w
p
t
r
i
9
a
c
j
p
d
T
a
c
t
a
e
c
p
c
t
a
n
t
d
t
o
s
p
t
o
T
s
l
a
n
l
e
b
t
p
s
t
t
p
t
m
l
m
f
i
i
t
t
R
c
i
p
c
g
t
s
i
i
bsorption from the discharge, thus resulting in an increase in the
emperature. This means by which the discharge can sustain itself
n an electric field that is below the cold-flow breakdown thresh-
ld is the probable mechanism the underlying physical mechanism
f the observed two-stage ignition process [9] .
In order to illustrate this process we consider the DBD-actuated
gnition close to the sustained flame boundary, h i = 3 . 07 mm in
igs. 17 and 10 . Six solution snapshots are shown in Fig. 23 where
he energy absorbed by the fluid is superimposed to a surface
ith constant hydrogen molar fraction equal to 0.1. High tem-
erature plasma self-sustains with small localized power absorp-
ion, ˙ W ≈ 16 W, for several milliseconds, before H 2 –Air chemistry
eaches the chemical runaway condition, which, then, leads to an
gnition kernel propagating upstream.
. Conclusions
Based upon independent measurements, we have designed
model to analyze the mechanisms of the observed plasma-
ombustion coupling in a DBD-mediated ignition and combustion
et in cross-flow system. We show that plasma-combustion cou-
ling is a two-way interaction rooted in the temperature depen-
ent terms appearing in the electron and neutral energy equations.
here are two aspects of the coupling. An increase in gas temper-
ture due to exothermal neutral reactions reduces the plasma spe-
ific collisional energy loss and leads to a larger electron tempera-
ure and number density. Likewise, an increase in electron temper-
ture increases the Joule heating contribution to the neutral en-
rgy by thermalization of the energy released in electron impact
ollisions. Because the neutral energy is proportional to the tem-
erature, this coupling creates a closed-loop feedback process that
an yield a nonlinear, super-adiabatic temperature increase against
he gap voltage. Because the coupling results in a selective mech-
nism that concentrates the absorbed power to the region of high
eutral temperature, it is an important, beneficial contribution of
he interaction of ignition hot spots with electric field layers over
ielectric surfaces.
The two-way mechanism supports non-LTE energy and radical
ransfers to the neutrals, which we model by solving a quasi-steady
ne-dimensional Boltzmann equation and corresponding charged
pecies mass conservation with an imposed electric field. The
lasma generated by an atmospheric DBD is sustained by stochas-
ic, recurrent, self-similar microstreamers that occur on a nanosec-
nd timescale in the gas pre-ionized by previous microdischarges.
he electric field supported by this microstructure is the superpo-
ition of the external, space charge and surface charge components,
eading to a pulses in the field strength. We assume that the time
nd length scales of the pulses affect the coupling terms but ig-
ore the details of its shape to obtain an assumed-shape scaling
aw. The periodicity of the streamers and the smallness of the en-
rgy relaxation time compared to the electric period lead to the
reakdown condition being imposed in terms of the balance be-
ween time-integrated attachment and ionization with no trans-
ort losses. Thus, the plasma-fluid coupling depends on the gas
tate, for which we presented a practical tabulation map.
The neutral composition and temperature significantly modify
he coupling. Three-body attachment dominates ionization in low
emperature air (see Figs. 5 and 6 ), which effectively limits the
lasma extension to the envelope of the diffusion flame and leads
o the non-symmetric plasma emissions observed in the experi-
ents. Because the three-body attachment cross section increases
inearly with the pressure, we expect that the plasma enhance-
ent will be more important at a reduced pressure, while the ef-
ect of plasma-combustion coupling will be less pronounced lead-
ng to a quasi-one-dimensional ignition [14] . The energy coupled
n the plasma is also sensitive to the degree of mixing between
he weakly electro-positive hydrogen and the strongly electronega-
ive oxygen. This effect was also observed in the experiments [71] .
esults presented in Figs. 21 and 22 show that changes in plasma-
ombustion coupling due to temperature are dominant over mix-
ng because the fluid internal energy supports a two-way cou-
ling with the electron energy. Yet, our computations show that
omposition has a non-marginal effect: H 2 supports a more ener-
etic interaction than mixtures of air and H 2 O in agreement with
he experiments of Yin et al. [42] . This is demonstrated by the
trong peak in power during the advancement of the ignition front
n Fig. 18 . Therefore, we expect that more energetic turbulence
ntensities will introduce a similar level of power augmentation
228 L. Massa, J.B. Freund / Combustion and Flame 184 (2017) 208–232
Fig. 25. Fractional contributions of elementary processes to the time-integrated radical maps at X O 2 = 0 . 15 X H 2 O
= 0 . Frame (a) includes only predissociation to H 2 ( b 3 �u +) ,
the contribution of Lyman, Werner, and metastable transitions is smaller.
Fig. 26. Effect branching ratio γ c in on H radical production: log 10 ˙ ω H
1kg / m 3 −s for P = 1 atm and x H 2 + x O 2 + x N 2 + x H 2 O = 1 .
r
fl
t
s
i
t
during the flame period and a decreased coupling during ignition
due to better mixing. This might best be considered in a configu-
ration such at that of Bedat and Cheng [77] .
Water production in the atmospheric hydrogen flames supports
a strong removal rate of the superoxide anion through the hydra-
tion reactions, leading to an increase in the energy absorbed per
adical produced and a sharp decrease in energy coupled after the
ame anchors. This phenomenon controls the interaction between
he flame-plume and the electric field layer, and explains the mea-
ured decrease of power absorbed when the cross-flow velocity
s increased. The present model predicts the electrical power in
he anchored-flame period satisfactorily, with most of the power
L. Massa, J.B. Freund / Combustion and Flame 184 (2017) 208–232 229
c
t
h
p
t
h
r
n
u
w
D
f
s
v
a
w
t
n
c
A
G
p
d
A
o
a
n
e
m
n
H
t
t
(
e
t
I
fi
c
a
e
m
≡N
O
t
s
t
s
t
c
a
t
s
i
n
fi
b
4
b
t
a
v
p
a
a
p
(
r
r
t
b
h
H
(
t
i
j
l
t
t
e
S
e
o
i
f
d
w
t
[
e
H
a
[
r
t
H
g
b
[
w
h
c{
w
t
t
a
X
t
i
l
oupled in burning conditions away from the exposed electrode
ube through which the hydrogen is delivered.
Plasma-combustion coupling plays a role in the ignition of the
ydrogen jet in the cross-flow. The temperature and species de-
endence of the amplification mechanism selectively concentrates
he energetic and chemical plasma contributions to the region with
igh temperature and low water content, essentially the induction
egion. This mechanism is responsible for the penetration of the ig-
ition kernel in the slow boundary layer fluid and the consequent
pstream flame propagation; its inclusion improves the agreement
ith the measured augmentation of the ignition probability by the
BD. Moreover, our simulations have shown that the closed-loop
eedback process at the root of plasma-combustion interaction can
elf-sustain high-temperature kernels in fuel-lean air flows with
elocities larger than the local adiabatic flame speed. This mech-
nism enables the two-stage ignition in DBD assisted conditions,
here high temperature kernels were observed to anchor above
he covered electrode for time intervals long compared to the ig-
ition time, and then slowly move upstream due to velocity and
oncentration fluctuations in the turbulence eddies.
cknowledgments
We thank Ryan Fontaine, Jon Retter, Greg Elliott and Nick
lumac for providing and discussing their experimental results.
This material is based in part upon work supported by the De-
artment of Energy, National Nuclear Security Administration , un-
er Award Number DE-NA0 0 02374 .
ppendix A. Effect of excited nitrogen on radical production
The chemistry scheme of Section 4 includes the contribution
f electronic excitation of nitrogen and oxygen molecules, but
ssumes that these energy exchanges are thermalized instanta-
eously, thus they cannot affect radical production through non-
quilibrium kinetics. Nagaraja et al. [43] shows that a similar ther-
alization of all the electron impact collisions has a small but not
egligible effect on ignition of H 2 at very low pressures (25 Torr).
ere, we analyze the non-equilibrium paths of N
∗2 , and confirm
hat their omission is justified for our condition. This is impor-
ant to consider because nitrogen has a large dissociation enthalpy
about twice that of oxygen), and a discharge can load significant
nergy in its bound electronic states. These states in turn poten-
ially support production of H via dissociative quenching [43,49] .
n the following, we generalize the model to include this, and con-
rm that in our system the large peak reduced field in the mi-
rodischarges in flames and the high pressure makes this mech-
nism small compared to the direct dissociation of hydrogen by
lectron impact.
For this assessment, we include ten levels of excited
olecular nitrogen N 2 , two levels each for O 2 , O and N : Z e [ N 2 (A
3 �u
+) , N 2 (B
3 �g ) , N 2 (W
3 �u
) , N 2 ( B
′ 3 �−u
) , N 2 ( a ′ 1 �−
u
) ,
2 ( a 1 �g ) , N 2 ( w
1 �u
) , N 2 ( C
3 �u
) , N 2 (E 3 �+ g ) , N 2 ( a
′′ 1 �+ g ) ,
2 ( a 1 �g ) , O 2 ( b
1 �+ g ) , N( 2 D) , N( 2 P) , O( 1 S) , O( 1 D) ] . The reac-
ion set used in this test includes contributions from several
ources [49,78,79] and is shown in Table A.2 .
The implementation matches that described in Section 4.4.3 for
he charged species, periodicity is imposed on Z e . The charged
pecies Z in (11) is computed independently because the concen-
ration of the targets does not change during a periodic microdis-
harge. In fact, the peak mole fraction of excited species produced
re of the order of 1 × 10 −8 . Therefore, the electron concentra-
ion from the Boltzmann analysis ( Section 4 ) provides a set of
ource terms independent of Z e . The solution of Z e (0) = Z e (T act / 2)
s straightforward because the quenching rates are only weakly
on-linear with the concentration of the excited states. We use a
xed point iteration to solve for the periodic Z e .
Radical production is shown in Fig. 24 for different neutral
ackground conditions with the nitrogen to oxygen ratio fixed at
. We designate direct path production of H as the one supported
y (14) , rather the indirect path is supported primarily by reac-
ions A80, A84, A85 and A86 in Table A.2 . In pure H 2 ( Figs. 24 a
nd 24 d), radical production through the indirect path is zero (ob-
iously) and the direct path production is the strongest among the
lots on the first row. The addition of O 2 ( Fig. 24 b and 24 c) causes
drop in the energy coupled into the gas by the discharge and
concomitant reduction of radical production through the direct
ath. Conversely, Fig. 24 e and 24 f show that an increase in X O 2
i.e., a decrease in equivalence ratio) results first in an increase in
adical production through the indirect path and then a drop; the
adical contribution will obviously go to zero at X O 2 = 1 / 5 . Overall,
he indirect path contribution is small compared to the direct path,
ecoming stronger at larger reduced electric fields and weaker at
igher temperature. While excitation to the lowest repulsive state
2 ( b 3 �u
+) peaks at an energy comparable with the N
∗2 excitation
at about 20 eV [38] ) the Lyman- α emission peak is at 40 eV [35] ,
hus large fields, E / N > 300 Td, lead to a large ratio of direct to
ndirect radical production rates, ˙ ω H ,D / ̇ ω H ,I
.
In the simulations described in Section 8.2, we expect the ma-
ority of the radicals to be produced at high gas temperature and
arge E / N because the high temperature at the ignition kernel leads
o proportionally high reduced electric fields and selective concen-
ration of the power coupled at the hot spot. Similarly, large fuel
quivalence ratios support a stronger coupling (see discussion in
ection 8.4 and the experiments of Yin et al. [42] ) and stronger en-
rgy transfers [8,80] , so the majority of radicals will be produced at
r above the stoichiometric fuel-to-air ratio, where the direct path
s dominant over the indirect one. These considerations justify our
ocus on the direct path in the results presented in Section 8 .
In the present study (i.e., Table A.2 ), we have not included hy-
rogen dissociation by collisional quenching of N 2 (C
3 �u ), which
arrants additional discussion since in some regimes it can cer-
ainly be important. For example, Starikovskiy and Aleksandrov
81] mention that this channel is an important path of non-
quilibrium radical production in plasma-assisted combustion of
2 : O 2 : N 2 mixtures at high reduced fields. Still, the kinetic rates
nd branching ratios are not well known [81] , it is often neglected
14,48,80,82] , and we might anticipate that it has a subservient
ole at the current pressures. Starikovskaia et al. [48] assume that
he only products of the collisional quenching of N 2 (C
3 �u ) with
2 in the pressure range 1–8 Torr are molecular hydrogen and
round-state nitrogen. Higher pressures are expected to favor the
ound state stabilization over the dissociation to radical channel
83] , thus at the present atmospheric pressures the branching to-
ards the radical production channel will be small. In fact, a recent
igh-pressure study [82] also does not include this channel.
The sub-mechanism in question here can be written parametri-
ally as
N 2 ( C
3 �u
) + H 2 ⇒ N 2 + 2 γc H + ( 1 − γc ) H 2
A = 3 . 2 × 10
−10 cm
3
molecules −s , E = 0 , n = 0 ,
(A.97)
here γ c allows for parametric variation of the branching ratio of
he collisional quenching of N 2 (C
3 �u ) with hydrogen relative to
he overall conversion rate of Pancheshnyi et al. [84] . To make this
ssessment, we adjust γ c and examine H radical production for
O 2 = 0 . 15 .
We evaluate the fractional contributions of the most impor-
ant direct processes [ (14) with (2) –(5) ] and collisional quench-
ng ones (reactions A80, A84, A85, A86 and A97). Results for se-
ected processes are shown in Fig. 25 . For γc = 1 , we see that the
230 L. Massa, J.B. Freund / Combustion and Flame 184 (2017) 208–232
Table A.2
Reaction mechanism for triplet nitrogen quenching.
Reaction A (cm-molecules-sec-K) n E (K)
A1. N 2 ( A 3 �u +) + O 2 ⇒ N 2 + O + O 2.54e–12 0 0
A2. N 2 ( A 3 �u +) + O 2 ⇒ N 2 O + O 8.68e–16 0.55 0
A3. N 2 ( A 3 �u +) +O ⇒ NO + N ( 2 D ) 7e–12 0 0
A4. N 2 ( A 3 �u +) + N 2 O ⇒ N 2 + N + NO 1e–11 0 0
A5. N 2 ( A 3 �u +) + N 2 ( A
3 �u +) ⇒ N 2 ( B 3 �g ) + N 2 7.7e–11 0 0
A6. N 2 ( A 3 �u +) + N 2 ( A
3 �u +) ⇒ N 2 ( C 3 �u ) + N 2 5.54e–4 –2.64 0
A7. N 2 ( A 3 �u +) + N 2 ⇒ N 2 + N 2 3e–18 0 0
A8. N 2 ( A 3 �u +) + O 2 ⇒ N 2 + O 2 ( a
1 �g ) 8.68e–15 0.55 0
A9. N 2 ( A 3 �u +) + O 2 ⇒ N 2 + O 2 ( b
1 �+
g ) 8.68e–15 0.55 0
A10. N 2 ( A 3 �u +) +N ⇒ N 2 + N ( 2 P ) 1.79e–19 –0.67 0
A11. N 2 ( A 3 �u +) +O ⇒ N 2 + O ( 1 S ) 2.1e–11 0 0
A12. N 2 ( A 3 �u +) +NO ⇒ N 2 + NO 7e–11 0 0
A13. N 2 (B 3 �g )+ N 2 ⇒ N 2 ( A
3 �u +) + N 2 5e–11 0 0
A14. N 2 (B 3 �g ) ⇒ N 2 ( A
3 �u +) 1.5e5 0 0
A15. N 2 (B 3 �g )+NO ⇒ N 2 ( A
3 �u +) +NO 2.4e–10 0 0
A16. N 2 (B 3 �g )+ O 2 ⇒ N 2 + O + O 3e–10 0 0
A17. N 2 (W
3 �u )+ O 2 ⇒ N 2 + O + O 3e–10 0 0
A18. N 2 ( B ′ 3 �−
u ) + O 2 ⇒ N 2 + O + O 3e–10 0 0
A19. N 2 ( a ′ 1 �−
u ) + N 2 ⇒ N 2 + N 2 2.2e–11 0 0
A20. N 2 ( a ′ 1 �−
u ) + O 2 ⇒ N 2 + O + O 3e–10 0 0
A21. N 2 (a 1 �g )+ O 2 ⇒ N 2 + O + O 3e–10 0 0
A22. N 2 (w
1 �u )+ O 2 ⇒ N 2 + O + O 3e–10 0 0
A23. N 2 ( a ′′ 1 �+
g ) + O 2 ⇒ N 2 + O + O 3e–10 0 0
A24. N 2 (B 3 �g )+O ⇒ NO + N ( 2 D ) 3e–10 0 0
A25. N 2 (W
3 �u )+O ⇒ NO + N ( 2 D ) 3e–10 0 0
A26. N 2 ( B ′ 3 �−
u ) +O ⇒ NO + N ( 2 D ) 3e–10 0 0
A27. N 2 (C 3 �u )+O ⇒ NO + N ( 2 D ) 3e–10 0 0
A28. N 2 ( E 3 �+
g ) +O ⇒ NO + N ( 2 D ) 3e–10 0 0
A29. N 2 ( a ′ 1 �−
u ) +O ⇒ NO + N ( 2 D ) 3e–10 0 0
A30. N 2 (a 1 �g )+O ⇒ NO + N ( 2 D ) 3e–10 0 0
A31. N 2 (w
1 �u )+O ⇒ NO + N ( 2 D ) 3e–10 0 0
A32. N 2 ( a ′′ 1 �+
g ) +O ⇒ NO + N ( 2 D ) 3e–10 0 0
A33. N 2 (a 1 �g )+ N 2 ⇒ N 2 ( B
3 �g ) + N 2 2e–13 0 0
A34. N 2 (a 1 �g )+NO ⇒ N 2 + N + O 3.6e–10 0 0
A35. N 2 (C 3 �u ) ⇒ N 2 (B
3 �g ) 3e7 0 0
A36. N 2 (C 3 �u )+ N 2 ⇒ N 2 ( a
1 �g ) + N 2 1e–11 0 0
A37. N 2 (C 3 �u )+ O 2 ⇒ N 2 + O + O ( 1 S ) 3e–10 0 0
A38. N 2 ( E 3 �+
g ) + O 2 ⇒ N 2 + O + O ( 1 S ) 3e–10 0 0
A39. O 2 (a 1 �g )+ O 3 ⇒ O 2 + O 2 + O 9.7e–13 0 1564
A40. O 2 (a 1 �g )+N ⇒ NO + O 2e–14 0 600
A41. O 2 (a 1 �g )+ N 2 ⇒ O 2 + N 2 3e–21 0 0
A42. O 2 (a 1 �g )+ O 2 ⇒ O 2 + O 2 2.3e–20 0.8 0
A43. O 2 (a 1 �g )+O ⇒ O 2 + O 7e–16 0 0
A44. O 2 (a 1 �g )+NO ⇒ O 2 + NO 2.5e–11 0 0
A45. O 2 ( b 1 �+
g ) + O 3 ⇒ O 2 + O 2 +O 1.8e–11 0 0
A46. O 2 ( b 1 �+
g ) + N 2 ⇒ O 2 ( a 1 �g ) + N 2 4.9e–15 0 253
A47. O 2 ( b 1 �+
g ) + O 2 ⇒ O 2 ( a 1 �g ) + O 2 4.3e–22 2.4 241
A48. O 2 ( b 1 �+
g ) +O ⇒ O 2 ( a 1 �g ) + O 8e–14 0 0
A49. O 2 ( b 1 �+
g ) + O ⇒ O 2 + O ( 1 D ) 6e–11 –0.1 4201
A50. O 2 ( b 1 �+
g ) +NO ⇒ O 2 ( a 1 �g ) + NO 4e–14 0 0
A51. N( 2 D)+ O 2 ⇒ NO + O 8.66e–14 0.5 0
A52. N( 2 D)+ O 2 ⇒ NO + O ( 1 D ) 3.46e–13 0.5 0
A53. N( 2 D)+NO ⇒ N 2 O 6e–11 0 0
A54. N( 2 D)+ N 2 O ⇒ NO + N 2 3e–12 0 0
A55. N( 2 D)+ N 2 ⇒ N + N 2 2e–14 0 0
A56. N( 2 P)+ O 2 ⇒ NO + O 2.6e–12 0 0
A57. N( 2 P)+NO ⇒ N 2 ( A 3 �u +) +O 3.4e–11 0 0
A58. N( 2 P)+ N 2 ⇒ N ( 2 D ) + N 2 2e–18 0 0
A59. N( 2 P)+N ⇒ N ( 2 D ) + N 1.8e–12 0 0
A60. O( 1 D)+ N 2 ⇒ O + N 2 1.8e–11 0 –107
A61. O( 1 D)+ O 2 ⇒ O + O 2 ( b 1 �+
g ) 2.56e–11 0 –67
A62. O( 1 D)+ O 2 ⇒ O + O 2 6.4e–12 0 –67
A63. O( 1 D)+ O 3 ⇒ O + O + O 2 2.3e–10 0 0
A64. O( 1 D)+O 3 ⇒ O 2 +O 2 1.2e–10 0 0
A65. O( 1 D)+NO ⇒ N + O 2 1.7e–10 0 0
A66. O( 1 D)+ N 2 O ⇒ NO + NO 7.2e–11 0 0
A67. O( 1 D)+ N 2 O ⇒ N 2 + O 2 4.4e–11 0 0
A68. O( 1 S)+ N 2 ⇒ N + NO 5e–17 0 0
A69. O( 1 S)+ O 2 ⇒ O ( 1 D ) + O 2 1.333e–12 0 850
A70. O( 1 S)+ O 3 ⇒ O ( 1 D ) + O + O 2 2.9e–10 0 0
A71. O( 1 S)+ O 3 ⇒ O 2 + O 2 2.9e–10 0 0
A72. O( 1 S)+ NO ⇒ O + NO 2.9e–10 0 0
( continued on next page )
L. Massa, J.B. Freund / Combustion and Flame 184 (2017) 208–232 231
Table A.2 ( continued )
Reaction A (cm-molecules-sec-K) n E (K)
A73. O( 1 S)+NO ⇒ O ( 1 D ) + NO 5.1e–10 0 0
A74. O( 1 S)+ N 2 O ⇒ O + N 2 O 6.3e–12 0 0
A75. O( 1 S)+ N 2 O ⇒ O ( 1 D ) + N 2 O 3.1e–12 0 0
A76. O( 1 S)+ O 2 ( a 1 �g ) ⇒ O ( 1 D ) + O 2 ( b
1 �+
g ) 3.6e–11 0 0
A77. O( 1 S)+ O 2 ( a 1 �g ) ⇒ O + O + O 3.4e–11 0 0
A78. O( 1 S)+ O 2 ( a 1 �g ) ⇒ O + O 2 ( a
1 �g ) 1.3e–10 0 0
A79. O( 1 S)+O ⇒ O ( 1 D ) + O 5e–11 0 301
A80. N 2 ( A 3 �u +) + H 2 ⇒ N 2 + H + H 4.4e–10 0 3500
A81. N 2 (B 3 �g )+ H 2 ⇒ N 2 ( A
3 �u +) + H 2 5.e–11 0 0
A82. N 2 (W
3 �u )+ H 2 ⇒ N 2 ( A 3 �u +) + H 2 2.5e–11 0 0
A83. N 2 ( B ′ 3 �−
u ) + H 2 ⇒ N 2 ( A 3 �u +) + H 2 2.5e–11 0 0
A84. N 2 ( a ′ 1 �−
u ) + H 2 ⇒ N 2 + H + H 2.6e–11 0 0
A85. N 2 (a 1 �g )+ H 2 ⇒ N 2 + H + H 2.6e–11 0 0
A86. N 2 (w
1 �u )+ H 2 ⇒ N 2 + H + H 2.6e–11 0 0
A87. O 2 (a 1 �g )+ H 2 ⇒ OH + OH 2.8e–09 0 17,906
A88. O 2 (a 1 �g )+ H 2 ⇒ O 2 + H 2 2.6e–19 0.5 0
A89. O 2 (a 1 �g )+ H ⇒ O + OH 1.3e–11 0 2530
A90. O 2 (a 1 �g )+ H ⇒ O 2 + H 5.2e–11 0 2530
A91. O 2 (a 1 �g )+ HO 2 ⇒ O 2 + HO 2 2.0e–11 0 0
A92. O 2 ( b 1 �+
g ) + H 2 ⇒ O 2 + H 2 1.0e–12 0 0
A93. N( 2 D)+ H 2 ⇒ NH + H 4.6e–11 0 880
A94. N( 2 P)+ H 2 ⇒ N + H 2 2.0e–15 0 0
A95. O( 1 D)+ H 2 ⇒ H + OH 1.1e–10 0 0
A96. O( 1 S)+ H 2 ⇒ O + H 2 2.6e–16 0 0
c
c
3
C
i
F
d
t
d
b
f
a
o
f
r
s
b
q
t
A
i
t
p
[
o
o
R
[
[
[
[
[
ontribution of collisional quenching of N 2 (C
3 �u ) does indeed be-
ome comparable with the production via the direct path for E / N ≈00 Td at low gas temperatures with equal composition mixtures.
onversely, when γ c ≈ 0, the contribution of collisional quench-
ng is mainly via de-excitation of N 2 ( A
3 �u
+) and negligible (see
ig. 25 c).
However, for the purposes of the present study, the total pro-
uction maps in Fig. 26 a–e show insensitivity. When the reac-
ion in Eq. is included alongside those in Table A.2 , radical pro-
uction through the collisional quenching channel is influenced
y γ c . Even though the addition of A97 significantly changes the
ractional contributions to H, the collisional quenching production
t X O 2 = 0 . 15 is two orders of magnitude smaller than the direct
ne evaluated in fuel-rich mixtures (see Fig. 24 a and b). There-
ore, H 2 :air jet flames will support a selective energy coupling in
egions of high fuel concentration typical of non-premixed atmo-
pheric flames [7] , where the majority of radical production will
e through dissociation by electron impact. Thus, the collisional
uenching contribution can be neglected for the present condi-
ions.
Finally, we compare Table A.2 against other reported models.
prediction with the model of Shcherbanev et al. [82] is shown
n Fig. 26 f. A comparison between Figs. 26 f and 24 f show that the
wo models predict a similar radical production over the range of
arameters analyzed. Moreover, the model of Shcherbanev et al.
82] predicts a lower radical production via collisional quenching
f N
∗2 than that proposed in the present work over the entire range
f conditions of interest.
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