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10.2514/6.2017-3675
AIAA AVIATION Forum
5-9 June 2017, Denver, Colorado
48th AIAA Plasmadynamics and Lasers Conference
Effect of Dielectric Barrier Discharge Body Forces
on Hydrogen Flames
Downloaded by UNIVERSITY OF ADELAIDE on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.2017-3675
L. Massa, ∗
J. E. Retter†
G. S. Elliott‡
J. B. Freund§
The Center for Exascale Simulation of Plasma-Coupled Combustion
Recent experiments show that a dielectric-barrier-discharge can fundamentally
change the character of a hydrogen diffusion flame, far more so than for a corresponding inert-fluid actuation. The stand burner flame surface deforms from
roughly conical to nearly flat, and light emissions increase. We develop a simulation
model to analyze the mechanisms that underlie these changes, and reproduce key
observations. The main mechanisms are body forces due to charge sheaths, with
radicals produced by plasma excitation playing a secondary role for the present
conditions. The non-actuated flame flickers at approximately 10 Hz, in good agreement with the experiments. As the DBD voltage is increased, the flame flattens
and oscillations decrease, eventually ceasing above a threshold value. In the fully
flattened case, the stoichiometric surface lies flat across the fuel orifice, and the
flame temperature exceeds the adiabatic flame value. When calibrated against an
independent air-only experiments, a linearized plasma sheath for model reproduces
the main features of the experiments and provides a good estimate for the threshold flattening potential. The model also anticipates faster flowing regimes in which
radical production by the plasma is anticipate to become more important.
I.
Introduction
We consider the ∼ 775 W stand-burner H2 flame, with water vapor emissions visualized
in figure 1 with a filter bandwidth of approximately 720 nm. When it is actuated by an
up to ∼ 8 W co-annual dielectric-barrier-discharge plasma actuator, it undergoes a series
of remarkable changes: becoming notably wider, then unsteady, and finally fully flattened
near the fuel orifice. The mechanism by which this occurs is not obvious, and the goal of
this study is to analyze this with physically grounded models, which are introduced in
detail in section III. In particular, the respective roles of force generation and radical
production are considered (forces dominate in this regime). The validation of these are
important for identifying effective models that can be used to design burners that can
harness available mechanisms to control combustion at large or small scales.
Our target is a low-Reynolds-number laminar jet flame at near unity Richardson
number. The DBD is operated in a glow discharge mode, so ion temperatures remain
close to the ambient gas temperature though electron energies are expected to be of
the order of few eVs. Ionization is driven by an 18 kHz AC signal at up to 9 kV in
our configuration. During each cycle the electron and ion currents transfer momentum
to the flow. It is because there no arcing and thus little current, the heating rate due
to the plasma is typically dwarfed the exothermic reactions, as is confirmed by direct
measurement in our configuration. It is understood, that different force distributions can
be realized with different electrode arrangements 9,19 , so that is a key consideration in
our model development.
∗ Aerospace
and Ocean Engineering, Va Tech, AIAA Senior Member
Engineering, University of Illinois, AIAA Student Member
‡ Aerospace Engineering, University of Illinois, AIAA Associate Fellow.
§ Mechanical Science & Engineering and Aerospace Engineering, University of Illinois. AIAA Associate Fellow.
† Aerospace
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Copyright © 2017 by The authors.
Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.
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Figure 1: DBD actuated flame regimes: ‘Baseline’ with V = 0, ‘Wide’ with ∆V = 5 kV, ‘Unsteady’
with ∆V = 7 kV, and ‘Flattened’ with ∆V = 8.8 kV. Visualizations show filtered emissions at 720 nm
(water vapor) with a 10 ms exposure.
This paper is organized as follows, the flame configuration and its actuation are
presented in §II and the experimental techniques are summarized in §A. Important
physical mechanisms and their corresponding representation in a viable simulations are
detailed in §III, with the resulting model predictions evaluated against the experimental
data in §IV and §V. The principal findings and conclusions are summarized in §VI.
II.
DBD–Burner Configuration
The configuration is shown in Fig. 2. Hydrogen exits into quiescent air from a
D = 3.81 mm orifice in a quartz dielectric (relative permittivity = 4.5, 23 ). The hydrogen
volumetric flow rate is 17.84 cm3 /s. Both air and hydrogen are assumed to be T = 297 K.
Both electrodes are brass. The electrodes are driven with a sinusoidal voltage difference
∆V = 0 to 9 kV at frequency f = 18 kHz. The plasma sheath generated by the discharge
is analyzed in more details in §2 & §2.
A.
1.
Diagnostics
Voltage and Current Measurements
Standard operating conditions for the AC DBD burner range from 0-9 kV at 18 kHz
supplied by a combined system of a Protek B8003FD Function Generator outputting to
a Crown XTi 4000 amplifier, which in turn output to a Custom HV transformer from
Corona Magnetics INC. For all measurements, the ring electrode was selected as the high
voltage electrode. The voltage and current were monitored by a Tektronix P6015A high
voltage probe and a Pearson Current Monitor Model 4100 respectively and collected onto
a Picoscope. Voltages presented in this paper represent the peak voltage per period (not
RMS), and typical standard deviations of the peak voltage at 9 kV are 0.25 kV.
2.
Flame Visualization
The main flame visualization techniques revolved around schlieren and water vapor
emission measurements. Schlieren, recorded on a Photron APS RX camera at 500 fps,
revealed a steady, flickering flame at lower applied voltages with a more unsteady, nonflickering flat flame at 9 kV. Emission measurements of the flame focused on water vapor
to avoid the rest of the flame emission (OH and a Na impurity in the quartz) and the
plasma emission. Broadband emission of the flame-plasma system is given elsewhere 17 ,
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(a) Schematic
(b) Dimensions
Figure 2: Schematic of the flame with DBD actuator showing the actuator and its dimensions.
and demonstrates the main emission lines used for water vapor imaging (notch filter at
720 nm).
III.
A.
Flow Model
Screening Length Model
A weakly ionized gas induces a body force proportional to the electric field and the charge
with the other contribution negligible at low Mach number 4 ,
~
F~b ≡ q E.
(1)
The magnetic Reynolds number based on the inter-electrode distance ∆, a reference
conductivity σ, the vacuum permeability µ0 and the actuator frequency ω is Rem =
µ0 ∆2 σω ≈ 7 × 10−10 , small enough that magnetic fields are negligible and the electric
field is electrostatic
~ = −∇φ,
E
(2)
with potential
∇ · (∇φ) = −
q
.
ε0
(3)
Appropriate boundary conditions on the potential φ are discussed in §D. Because the
actuator time scale τact are much slower than the plasma time scales (τact τi τpe ), we
assume that the electrons are in a Boltzmann equilibrium with φ, so the electron density
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is ne = n0 exp (φ/Te ), where n0 is the (neutral) core plasma density Te is the electron
energy in eV. This leads to the Poisson-Boltzmann description of a plasma sheath 6 ,
∇ · (εr ∇φ) =
q
[n0 exp (φ/Te ) − ni (~x)] ,
ε0
(4)
where ni is the net density positive ion density, the difference between positive and
negative ion densities). If the ions are also assumed to be in thermal equilibrium, the
linearization yields the Debye–Hückel description
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∇ · (εr ∇φ) =
φ − φ0
.
λ2
(5)
Since the Debye length screening distance λ is now the only link between the plasma’s
properties and its forcing effect on the fluid, we call this
p a screening length model.
In the limit of fast actuation ω/ωpi 1 (ωpi ≡ n0 e2 /(mi ε0 ) is the ion plasma
~ there is negligible ion drift and the screening length depends only
frequency) or weak E,
q
0 Te
upon the electron properties λ = λ1 ≡ εen
, where −e is the electron charge; the ion
0
temperature is not a factor. If there is an appreciable ion current, a second length scale
is introduced λ2 = (Te µi )/us , where µi is the ion mobility and us the Bohm velocity 18
controlling the ion flux in the sheath. This models ion bombardment to the wall. When
the condition λ1 ≈ λ2 occurs, collisions are important in the sheath, and the effective
screening length is more complex, depending on both these scales. We estimate effective
λ by integrating the 1-D Child–Langmuir equations 13 to yield
p
32/3 3 ε0 µi ∆V02
(6)
λ=
√ q `i ,
2e2/3 n0 6 ελ1M̂
0
i
where `i is the ion mean free path, mi is ion molecular weight, and ∆V0 = Vcovered −Vexposed
is the time dependent potential difference across the sheath, which we assume to be the
applied voltage.
The instantaneous plasma potential φ0 in (5) is spatially uniform, thus it is a function
of the time only. Its value is related to the exposed and covered electrode potentials.
However, its value with respect to the electrode potentials is not a direct, symmetric
average as done by Orlov 16 , because of the asymmetry introduced by the particle flux at
the boundary on the charge. We propose
φ0 = Vexposed +
Vcovered − Vexposed
K
for K ∈ [1, ∞),
(7)
where the value K = 4 is calibrated by comparison with the experiments of Benard et al. 2 .
Essentially, the condition K > 2 expresses the fact that the majority of the force in a
DBD discharge is obtained in the negative-going half-cycle 1 , whereby the plasma is not
neutral because of the primary and secondary electrons emitted by the cathode. The large
duration of the DBD period with respect to the the electron-attachment characteristic
time, leads to the formation of negative ion sheath responsible for the majority of the
momentum transfers 12 .
1.
Model-0
Note that neither (4) nor (5) explicitly require one-dimensionality of the sheath, but the
assumption of a constant plasma density n0 together with the use of a one-dimensional
Child–Langmuir model for the sheath ion dynamics, requires that both the plasma density
in the neutral core and the potential φ0 are uniform. Models based on this have been
successfully applied to simulate planar DBD discharges 7 . However, the flame in the
present configuration presents the additional complication of large density gradients and
the possibility of significant vortical generation. Plasma contributions to the vorticity are
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determined by taking the curl of the specific momentum transfer F~b /ρ from (1), which
yields
~
ΩDBD ≡ ∇ × F~b /ρ = ∇(q/ρ) × E
(8)
This mechanism (i.e., interaction of electric field and density gradient) appears to be
too weak to produce vorticity commensurable with the experimental observation. In
particular, using the Debye–Hückel equation with screening length given by (6), we see in
Fig. 3 that the irrotational force density model does not reproduce the observed collapse
accompanied by significant rotation for ∆V0 & 9 kV.
40
Computations
Experiments
500
30
y, mm
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~ However, the screening length description leads to the charge
for a locally uniform E.
q being a function of the potential q = F (φ − φ0 ), so the resulting force density F~b is
~
irrotational. Thus, vorticity is only created by misalignment of ∇ρ and E:
q
~
ΩDBD = − 2 ∇ρ × E.
(9)
ρ
20
0
10
−500
0
−40
−30
−20
−10
0
r, mm
10
20
30
40
Figure 3: Comparison of PIV with irrotational Model-0, motivating generalization of the force model.
Vertical velocity.
It is possible that charge might depend somewhat also on the local electric field,
q = F (φ, ∇φ), which would occur if the ion current length scale λ2 , which controls the
collision-limited ion drift, is λ2 λ1 =⇒ us µλi T1 e . In this case, a one-dimensional
approach to (4) with non-reactive, isothermal sheaths, leads to charge dependency
q ∝ exp φ̃ −
1
,
λ2 ∇φ̃
(10)
where φ̃ ≡ φ/Te . However, this would be strongest close to the electrode, not on the
dielectric surface where there is obvious rotation (§2 & §2). Therefore we do not consider
this in detail in the paper.
B.
Generalization of the Force Model
The lack of vorticity in the simulations with irrotational force density (Fig. 3) suggests us
the reconsideration of the force model to allow for a rotational force density. We work
with the Debye–Hückel , and consider two additional physical effects, built into Models-1
and -2 that are not included in the the basic (Model-0) formulation.
1.
Model-1
Based on the experiments of Benard et al. 2 , we assume the vertical force Fb,y to be much
smaller that the horizontal component at the top dielectric wall and include Fb,y only
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close to the exposed electrode. The proposed approach is similar to that of Opaits et al. 15 ,
who simulated vortex formation in planar nonreactive DBD under nanosecond activation.
Opaits et al. 15 link the horizontal force over the dielectric to the formation of horizontal
microjets. These jets are symptomatic of the micro charge induced by streaming ionization
waves. In the present AC driven DBD, this phenomenon is supported by the ionization
avalanches that transition into microstreamer waves during the negative-going period of
the voltage signal 4,11 . High speed schlieren images (not shown) of the collapsed flame
give credence to the microjet hypothesis. Because the geometry features a corner in
the dielectric and the normal force to the surface is always pointing into the dielectric,
we assume the following expression Fb,y = max (Fbi,y , 0), while the radial component is
unchanged Fb,r = Fbi,r , where Fbi is the irrotational force density.
Force measurements by Benard et al. 2 show that in planar DBD, the vertical force
is small compared to the horizontal analog and is concentrated only very close to the
electrode. A possible critique to those measurements is that the pressure gradient was not
included in the force calculations, which will lead to large error in the wall normal force
close to the wall. The theoretical justification for assuming the vertical component of
the electrical potential much smaller than the horizontal analog is that ionization during
the negative period (force producing) of the DBD is due to fast ionization waves that
propagate parallel to the dielectric surface 12 . The presence of this waves significantly
changes the electric field producing stronger push force along the surface than in the wall
normal direction.
It will be shown that Model-1 predicts that the sharp change of the combustion field
above the flattening potential is a result of a Hopf bifurcation to the flat state. This
theory also agrees with the experiments in the fact that a weak hysteresis is obtained:
the unflattening potential is slightly lower that the flattening counterpart. A nice feature
of this model is that no additional model hypothesis is necessary to predict flattening.
2.
Model-2
Another potential source of vorticity is the deviation from Boltzmann equilibrium, such
~ Where the E-field’s strength drops below
as occurs at a plasma edge 16 where ∇(q) ∦ E.
the breakdown voltage, there will be a sudden drop in the local q, which is not included
in the standard models discussed so far. As mentioned in the introduction, the existence
of a charge edge is rooted in the cylindrical symmetry of the present configuration, which
implies a drop in the electric field in the radial direction.
Images from the experiment (Fig. 4) suggest that indeed the plasma is independent,
glowing apparently only below the flattened flame and only appearing in this form in
this ∆V0 & 9 kV case. This supports the notion that the fundamental changes in the
plasma and the force are not directly tied to the flame. We also see in these images that
there indeed appears to be a sharp edge to the radial extend of the luminous region of
the plasma, suggesting that the plasma edge might also play a significant role.
~
The change in plasma emissions can be anticipated based upon the E−field
solution
of the Debye–Hückel equation (5). For screening length (6), this is visualized in Fig. 5
both below (∆V = 5kV) and above (∆V = 8kV) the flattening potential. At the low
potential value, ∆V = 5kV, only the feeding tube supports a field it above the breakdown
value of H2 (Es = 1.6kV/mm, 5 ) while the electric field in the outside air is below the
corresponding strength (Es = 2.9kV/mm, 5 ). In contrast, at ∆V = 8kV the potential
field outside the tube equals the dielectric strength of air, precipitating a probable change
in both the plasma and force field. This hypothesis is consistent with an experimental
observation that the flattening potential is reduced by an increase in dielectric temperature:
the dielectric potential of gases decreases sharply with the temperature 8 , so it is more
easy in this hotter gas case to drive flattening by this mechanism.
~ q changes suddenly and will not be in
Just beyond the breakdown threshold of E,
~ This is not included in the equilibrium model we have developed
equilibrium with E.
to this point. We include this effect phenomenologically by mollifying Fb,i , which at the
same time makes it rotation. A somewhat similar limiting for the force was proposed
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by Orlov 16 to restrict the electrohydrodynamic force (EHD) to the observed extent of
the plasma emissions by scaling forces with their intensity, thought the explicit role of
vorticity generation was not considered.
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(a) Voltage below the flattening threshold
(b) Voltage above the flattening threshold
Figure 4: Images of the plasma and the flame from an experiment with varying potential.
(a) ∆V = 5kV
(b) ∆V = 8kV
Figure 5: Electric field in kV/mm.
The link between the plasma edge and vorticity production is further demonstrated
by the experimental observation of the position of the vortex ring induced by the plasma
(cf. Fig. 2(a)). The radial position of the vortex is plotted against the applied potential
in Fig. 6. The potential for the flame collapse (8 kV) also corresponds to a sudden radial
shift of the vortex ring position. This is a consequence of the plasma breakdown outside
the tube, which causes the edge to move in the radial direction.
Finally, we note in Fig. 5 that the electric field is very small close to the convex edge
of the dielectric (i.e., located at rc = 2.45 and yc = 0 in Fig. 5). Therefore, we also reduce
the force density close to such a corner.
The shape of the modified force for Model-2 is thus
r − r1
R − Rd
R + Rd
F~b = F~bi exp − max
,0
1 − tanh
+ tanh
/2
(11)
1 mm
Rd
Rd
q
2
2
with R ≡ (r − rc ) + (y − yc ) , rc , yc the coordinates of the top convex corner of the
dielectric, Rd = 0.2 mm and r1 = rc if ∆V < 8kV, while r1 = 10 mm if ∆V ≥ 8kV. Here
the value r1 = 10 mm corresponds with the location of the maximum magnitude of the
electric field versus r in Fig. 5(b). The second term in the right hand side of (11) is an
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25
PIV Average
Particle Accumulation
rV , mm
20
Flattening Potential
15
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10
5
5.5
6
6.5
7
7.5
8
8.5
9
9.5
10
10.5
11
∆V , kV
Figure 6: Measured vortex position (rV ) as a function of the applied Voltage.
exponent similar to that used by Orlov 16 . The third term acts to reduce the force in
~
the neighborhood of the dielectric corner, consistent with the insufficiency of the E-field
strength there for breakdown, which also creates an inner edge.
C.
Numerical Method and Discretization
The Navier-Stokes equations are solved using an SBP-8/4 (eighth-order in the interior
and fourth-order on the boundary) discretization 21 , combined with the simultaneous
approximation term (SAT) approach at the domain boundaries 3 . The solution is advanced
in time with a fourth-order Runge–Kutta algorithm. The Poisson equation (e.g. (5)) for
the electric field is solved with a sixth-order seven-point central difference scheme with
fifth-order one-sided stencils for the jump conditions at the material boundaries.
The flow is assumed axisymmetric, and the simulation domain extends 60 mm radially
and 205 mm axially. A 750 × 750 mesh was used for all the reported results. It was
compressed near the orifice, with minimum ∆r = 0.03 mm and ∆x = 0.08 mm.
D.
Boundary Conditions
On solid boundaries, we specify a no-slip condition for the velocity, zero flux conditions
for H2 , O2 and N2 , and an absorbing conditions (YH ) for the radical H. The electrode
walls are isothermal 297 K, while the temperature at the relatively insulating quartz walls
is assumed to be governed by
∇T · ~n =
T − Twall
,
δw
(12)
which models a thermal conduction into the solid. Here δw is 1 mm and Twall = 475 K
is the mean wall temperature measured in the experiments described in §A. The Robin
boundary condition is numerically more stable than the Dirichlet counterpart, which
can be obtained from (12) with δw → 0, and allow the solid gas temperature to relax
to the ambient level away from the flame, thus mimicking the thermal feedback from
the flame to the solid. Far-field (large r and y) and injection (H2 inflow) boundary
conditions are all implemented using the “far-field” formulation of Svärd et al. 24 . An
axisymmetric Poiseuille flow evaluated based on the experimental volumetric flow rate
is assumed at the hydrogen injection boundary, which is located 40 mm below the top
corner of the exposed electrode. The Reynolds number in the inflow is 45.4 and the tube
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11.5
12
is long enough to support a well developed laminar flow, so this should afford an excellent
approximation of the actual inflow velocity profile. The inflow temperature is T = 297 K
per the experimental conditions.
Boundary conditions for the electric potential are homogeneous Neumann at the
computational box boundary, Dirichlet at the electrodes per the applied potential, and
continuity of the normal electric field is enforced on the dielectric wall.
IV.
Observed Flickering
Diffusion flames supported by low speed jets feature limit cycle fluctuations, which are the
results of an instability supported by the coupled action of buoyancy and convection 22 .
Combustion provides the heat release and resulting buoyancy. Therefore, the chemistry
time scales do not directly couple with this phenomenon, so it can be described by just three
non-dimensional parameters, the Reynolds number ReJ = ρJ UJ DJ /µJ , the Richardson
J ρair,0 −ρb
number Ri = gD
, and the density ratio ρAir,0 /ρJ . Here g is the gravitational
ρb
UJ2
acceleration, D is the diameter, subscript Air, 0 indicates the cold quiescent ambient
air, J indicates fuel inflow conditions, and b indicates the stoichiometric adiabatic burnt
mixture. In the present conditions ReJ = 45.4, Ri = 0.389, and ρair,0 /ρJ = 14.5. The
experimentally measured fundamental frequency of the flickering oscillation is fexp = 10 Hz.
This value is consistent with previous experimental observations by Grant and Jones 10 ,
and corresponds to a Strouhal number St ≡ f DJ /UJ = 0.048. The spectral content of the
flickering based on the observed water vapor emissions is shown in Fig. 7(b). The mean
position of the flame as inferred from the water emissions at 720 nm with 10 msexposure
is shown in Fig. 7(b).
Amplitude
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A.
Baseline Flame
40
20
0
0
10
20
30
40
f , Hz
(a) Mean
(b) Spectrum
Figure 7: Mean and spectrum of the flame flickering motion from a Fourier decomposition of the
sequence of the water emission images.
B.
Model Predictions
To quantify flame structure and behavior, we use a dynamic mode decomposition (DMD) 20 ,
which we summarize in Fig. 8. We rank the global modes according to the coherency of
their fluctuation energy 14 . The DMD analysis identifies the fluctuation frequencies as
the eigenvalues of a reduced order system. The most energetic frequencies are shown in
Fig. 8(a). The most amplified numerical mode has a frequency fpred = 10.15 Hz, that
closely match the experiments. Figure 8(b) shows the mean temperature field. The flame
height and width are consistent with the measurements previously shown in Fig. 7(a).
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The Fig. 8 (c) and (d) show the fundamental and the first harmonic of the flickering
flame. The dark flame-shaped band in Fig. 8(c), is where the temperature fluctuation is
small, thus it corresponds to the mean position of the hot gas in the fundamental mode.
This provides an estimate for the visual height of the flame, which matches the observed
40 mm. The corresponding dark line in the first harmonic mode (Fig. 8(d)) is shifted
towards the top. Therefore, these plots suggest that the dynamics modes are standing
waves and that, in the fundamental mode, the node (minimal fluctuation) is on the inside
of the antinode (maximal fluctuation), while the opposite is true for the first harmonic
oscillation.
(a) Coherency
(b) Mean
(c) Fundamental Mode
(d) First Harmonic
Figure 8: Dynamic mode decomposition of the standing burner flame with no DBD actuation.
V.
DBD Actuated Flames
For evaluating the importance of the different mechanisms built into the models of §B,
we focus on three principal experimental observations:
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1. The deformation to the flame, as inferred from the water emission, increases with
∆V0 , such that the flame aspect ratio (height over width) is reduced with increasing
∆V0 ;
2. For larger ∆V0 , a ring vortex forms above the dielectric surface; it intensifies and
moves away from the axis as ∆V0 is increased; and
3. The flickering fluctuations are reduced in amplitude when the voltage is increased,
while their frequency is essentially unaffected.
In making these comparisons, we appeal to three flame regimes: wide flames, unsteady
flames and flat-flames.
A.
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1.
Wide Flames
Thermal field
The period average thermal fields for ∆V = 5 kV for the three models are presented in
Fig. 9 and should be compared with the ‘Wide’ flame in Fig. 1. Model-0 is insufficient to
decrease the flame aspect ratio. The alteration of the body force in Models-1 and -2 do a
better job in reproducing the flame shape, with Model-1 causing the larger deformation.
Model-2’s shape might be closer to the observation, though there is insufficient quantitative
data for this shape comparison to be conclusive at this stage.
2.
Velocity field
Velocity predictions are evaluated in Figs. 10-12, with Fig. 10, Fig. 11 and Fig. 12 referring
in order to Model-0, Model-1 and Model-2. In all panels, the experiments are shown in
the right while the computations are on the left. Experimental data are missing in the
flame region, thus the blanked regions in correspondence of the flame represent region
of no-data. We see that the flame deformation is associated with a vortex ring centered
at r ≈ 10 mm, just inside the flame surface. The irrotational Model-0 force density
model reproduces this experimental poorly, leading to a qualitatively incorrect behavior
and supporting the necessity of inclusion of a rotational component of the force. Both
Model-1 and Model-2 predict the location of the vortex satisfactorily well, though Model-1
significantly over-predicts the velocity magnitude, more so than Model-2.
B.
Flat Flames
The Flat Flame regimes (Fig. 1) reflect more fundamental changes to the flame and are
more challenging for the models to reproduce. We consider these here.
1.
Thermal field
The flat flame thermal field for ∆V = 9 kV are shown in Fig. 13. Model-1, with is zero
vertical force, predict flame quenching (not shown) when the dielectric temperature is set
to the usual Twall = 475 K in (12). A unphysically lower Twall = 300 K, does lead to a
self-sustaining flame Fig. 13 (c), though obviously different from that observed Fig. 13 (a).
The quenching occurs because the air ventilation is cut off, as we shall see subsequently
when considering the velocity fields.
The Model-2 prediction, however, is unaffected by this problem and the high-temperature
region Fig. 13 (d) is similar to the experimental observations. In Model-2 the breakdown
potential is an assigned parameter, thus this observation cannot be used to test the
consistency between model and experiments. Nonetheless, simulations not shown reveal
that an increase in wall temperature reduces the height of the flattened flame predicted
by Model-2, because it leads to a larger entrainment of air in the vortex rings as a
consequence of the increase in viscosity and diffusivity with the gas temperature. Both
he flame height and width are well predicted by Model-2.
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(a) No Actuation
(b) Model-0
(c) Model-1
(d) Model-2
Figure 9: Gas Temperature in K and stoichiometric surface (white line) at ∆V = 5 kV (except
top-left panel, where ∆V = 0 kV).
As anticipated, Model-0 does not flatten the flame at all Fig. 13 (b). Since it is
obviously not a viable model for this configuration, we omit it from subsequent discussion
in this section.
Comparison with CARS measurements
We have recently performed a set of hybrid CARS measurements in collaboration
with Sandia National Labs. Although these measurements have not been cleared for
release yet, they reveal the nature of the collapsed flame and that the model matches
well both the gas temperature and the molar fractions of oxygen and hydrogen. These
comparison will be presented at the oral presentation. They reveal that the biggest error
of the computations is the evaluation of the temperature close to the surface, where the
simplified boundary condition in (12) is not accurate at the location where the flame
impinges on the dielectric. Nonetheless, the flame width, height and thickness is well
reproduced by the rotational force model.
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(a)Magnitude & Streamlines
V, mm/s
500
0
10
−500
0
−25 −20 −15 −10 −5
0
5
10
15
20
(b)Radial Component
25
V, mm/s
500
y, mm
20
0
10
−500
0
−25 −20 −15 −10 −5
0
5
10
15
20
(c)Vertical Component
25
V, mm/s
500
20
y, mm
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y, mm
20
0
10
−500
0
−25 −20 −15 −10 −5
0
5
r, mm
10
15
20
25
Figure 10: Comparison of velocity field from Model-0 against measurements at ∆V = 5 kV. Left
computations, right PIV measurements. On the left panel the white line is the stoichiometric surface.
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(a)Magnitude & Streamlines
V, mm/s
500
0
10
−500
0
−25 −20 −15 −10 −5
0
5
10
15
20
(b)Radial Component
25
V, mm/s
500
y, mm
20
0
10
−500
0
−25 −20 −15 −10 −5
0
5
10
15
20
(c)Vertical Component
25
V, mm/s
500
20
y, mm
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y, mm
20
0
10
−500
0
−25 −20 −15 −10 −5
0
5
r, mm
10
15
20
25
Figure 11: Comparison of velocity field from Model-1 against measurements at ∆V = 5 kV. Left
computations, right PIV measurements. On the left panel the white line is the stoichiometric surface.
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(a)Magnitude & Streamlines
V, mm/s
500
0
10
−500
0
−25 −20 −15 −10 −5
0
5
10
15
20
(b)Radial Component
25
V, mm/s
500
y, mm
20
0
10
−500
0
−25 −20 −15 −10 −5
0
5
10
15
20
(c)Vertical Component
25
V, mm/s
500
20
y, mm
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y, mm
20
0
10
−500
0
−25 −20 −15 −10 −5
0
5
r, mm
10
15
20
25
Figure 12: Comparison of velocity field from Model-2 against measurements at ∆V = 5 kV. Left
computations, right PIV measurements. On the left panel the white line is the stoichiometric surface.
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(b)Model-0
(a)Measured water vapor emission
30
30
20
20
10
10
0
0
y, mm
1,500
1,000
500
−10
0
−10
10
(c)Model-1
0
10
(d)Model-2
2,000
30
30
20
20
10
10
0
0
1,500
y, mm
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2,000
1,000
500
−10
0
r, mm
−10
10
0
r, mm
10
Figure 13: Gas Temperature in K and stoichiometric surface (white line) at ∆V = 9 kV. The
bottom-left panel was evaluated with Twall = 300K.
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2.
Velocity field
Velocity fields for Model-1 and Model-2 are shown in Figs. 14 and 15, respectively. A
notable difference is that Model-1 predicts that the vortices are fixed in position as the
voltage is increased, whereas for Model-2, Fig. 15(a) and Fig. 12(a), show that Model-2
predicts a significant shift of the vortex ring to larger radius, facilitating entrainment and
avoiding the quenching seen for Model-1. Both models do over-predict the velocity, but
Model-2 is much more accurate in this regard. Model-1 under-predicts the vertical and
radial displacement of the vortices from the orifice mouth, while Model-2 is in quantitative
agreement with the experiments; see also Fig. 6 for a plot of the experimental measurement
of the vortex ring position.
(a)Magnitude & Streamlines
V, mm/s
400
y, mm
200
0
20
−200
−400
0
−40 −30 −20 −10
0
10
20
30
40
V, mm/s
(b)Radial Component
400
40
y, mm
200
0
20
−200
−400
0
−40 −30 −20 −10
0
10
20
30
40
(c)Vertical Component
V, mm/s
400
40
200
y, mm
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40
0
20
−200
−400
0
−40 −30 −20 −10
0
10
r, mm
20
30
40
Figure 14: Comparison of velocity field from Model-1 against measurements at ∆V = 9 kV. Left
computations, right PIV measurements. On the left panel the white line is the stoichiometric surface.
An analysis of the streamlines in Fig. 15 shows that the main ventilation to the flame
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is from the air entrained from large r. It also shows that that for large ∆V , it becomes a
counterflow flame, with the air being advected downward from the top, which explains
the sharpness of the flame thermal emissions in Fig. 13(a) (and Fig. 1), and the lack of
usual plume shape. Water formed is ejected sideways rather than upward.
The changes in the vertical velocity, relative to the corresponding experiments are
quantified more directly in Fig. 16. Model-2 predictions are obviously closer to the
observations, whereas the other two models show qualitative differences. Model-2 consistently predicts a decrease in outflow velocity with an increase in applied voltage, while
Model-1 predicts the opposite. The agreement between predictions and experiments is
quantitatively good at 0 kV and 5 kV (Model-2), while is quantitatively unsatisfactory at
9kV.
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C.
Unsteady Flames
The transition between wide flames and flat flames is characterized by a regime in which
the flame periodically approaches the surface, where emissions increase before it again
lifts back up. This unsteadiness is, of course, just a modification of the basic flame
flickering due to the actuation. Still, the interplay of it with the DBD body force afford
another test of the model description. Since the breakdown voltage is not reached atop
the quartz Model-2 degenerates to Model-1 in this case, so we refer to them collectively
as Model-1/2.
As the potential is increased towards the flattening value ∆V ≈ 8 kV, the vortex at
r ≈ 10mm in Fig. 11(a) intensifies leading to a stronger vertical component of the velocity.
When the induced velocity matches the local flame speed, the flame detaches and its edge
travels along the stoichiometric surface from outside to inside the vortex. This process is
illustrated for a potential of ∆V = 7kV in Fig. 17.
Once a flame is established in the inner region of the vortex ring, i.e., where the
flow is directed downward, the instability becomes more energetic and the flame slams
periodically into the actuator wall while remaining confined within the vortex ring. The
flame height, the maximum temperature and the mean thermal field are shown in Fig. 18.
The flame height reported in this section is evaluated always on the axis of the feeding
tube to avoid any discontinuity due to the change in the radial location of the maximum
distance; i.e., the height is measured at the intersection between the stoichiometric line
and the feeding tube axis. Figure 18(a) shows that, when the system reaches its limit
cycle, a minimum in flame height corresponds to a maximum in peak temperature and
vice-versa. Such a phase shift between the curves explains the existence of bright spots
periodically occurring near the orifice in the unsteady regime. They are caused by the
localized increase in temperature caused by the downward movement of the flame. These
hot spots dominate the period-averaged thermal field shown in Fig. 18(b).
As the the voltage is increased the amplitude of the instability increases until the
flame remains flattens as shown in Fig. 13 at approximately ∆V = 8 kV. The flattening
corresponds with the stoichiometric surface transitioning from being located above the
vortices in Fig. 18(b) to underneath them in Fig. 13(c). Such a new condition is more stable
than that in Fig. 18(b), leading to hysteresis. The hysteresis makes it difficult to pinpoint
the exact value of the flattening potential in either the experimental measurements and
the computations.
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V, mm/s
(a)Magnitude & Streamlines
400
40
0
20
−200
−400
0
−40 −30 −20 −10
0
10
20
30
40
V, mm/s
(b)Radial Component
400
40
y, mm
200
0
20
−200
−400
0
−40 −30 −20 −10
0
10
20
30
40
(c)Vertical Component
V, mm/s
400
40
200
y, mm
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y, mm
200
0
20
−200
−400
0
−40 −30 −20 −10
0
10
r, mm
20
30
40
Figure 15: Comparison of velocity field from Model-2 against measurements at ∆V = 9 kV. Left
computations, right PIV measurements. On the left panel the white line is the stoichiometric surface.
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2,500
∆V = 0
Exp 20 mm
Exp 30 mm
Comp 20 mm
Comp 30 mm
2,000
V, mm/s
1,500
1,000
500
0
2
4
6
8
10
12
14
16
r, mm
18
20
22
24
26
28
30
2,500
∆V = 5kV
Exp 20 mm
Exp 30 mm
Model-0 20 mm
Model-0 30 mm
Model-1 20 mm
Model-1 30 mm
Model-2 20 mm
Model-2 30 mm
2,000
V, mm/s
1,500
1,000
500
0
0
2
4
6
8
10
12
14
16
r, mm
18
20
22
24
26
28
30
2,500
∆V = 9kV
Exp 20 mm
Exp 30 mm
Model-0 20 mm
Model-0 30 mm
Model-1 20 mm
Model-1 30 mm
Model-2 20 mm
Model-2 30 mm
2,000
1,500
V, mm/s
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0
1,000
500
0
0
2
4
6
8
10
12
14
16
r, mm
18
20
22
Figure 16: Axial velocity at 20 mm and 30 mm from the top wall.
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24
26
28
30
0 ms
1.85 ms
Edge
y, mm
20
Edge
20
10
10
2,000
10
1,000
0
−10
0
0
−10
10
0
5.5 ms
500
−10
10
7.4 ms
Edge
20
y, mm
Edge
20
1,500
0
0
10
9.25 ms
Edge
20
Edge
20
2,000
1,500
10
10
10
1,000
0
0
−10
0
r, mm
0
−10
10
0
r, mm
500
−10
10
0
r, mm
10
Figure 17: Time sequence of the flame detachment and transition of the flame from the outside to
the inside of the vortex. The thick cyan lines are the streamlines departing from the hydrogen inlet.
(a)Flame Height & Max. Temperature
(b)Period-averaged Temperature
2,400
Height
Temp.
2,000
20
2,000
Tmax , K
y, mm
2,200
10
h, mm
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3.7 ms
1,500
10
1,000
5
1,800
0
500
0
0
50
100
150 200
t, ms
250
300
350
−10
0
r, mm
10
Figure 18: Development of the instability supported by the flame inside the DBD vortices at
∆V = 7kV. In the left panel the horizontal axis is the time.
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VI.
Conclusions
Experiments show that low Reynolds number hydrogen jet-flames with DBD-plasma
actuation can be collapsed by increasing the applied potential. The flame collapse
(flattening) is a sudden event with a sharp change in the combustion field that, in its
flat state, features a much reduced flame surface and lower unsteadiness. We explore the
possibility that flame collapse can be explained by body forces associated with plasma
sheaths close to the dielectric surface. A Poisson-Boltzmann description of the sheath
leads to an irrotational force density, whereby the only contribution by the plasma to the
vorticity equation is due to the misalignment of electric field and density gradient. Using
a linearized model we determine that such an irrotational force field is not sufficient to
explain the large deformation induced by the plasma on the flame at a potential near or
above the collapsing value.
We assume that rotationality of the force density is introduced because of a) the spatial
development of ionization waves that support a streamwise component of the electric
field much larger than the wall normal component; or b) a two dimensional plasma edge
that leads to a localized misalignment of the charge density and the electric field. We
test these two hypotheses by comparing the gas temperature and velocity fields against
water emissions and PIV measurements. We observe that the second hypothesis leads
to a better matching of flame height, PIV data and frequencies of the flame flickering
frequencies. Therefore, the main contribution of the present study is the determination
that the flattening of this so-called “Retter-flame” is due to the gas breakdown outside
the feeding tube and the consequent sudden movement of the plasma edge in the radial
direction. The sharp movement of the vortex ring at the collapse potential is indicative
of the fact that vorticity generation is mainly due to the cross product of the charge
gradient and the electric field at the plasma edges. The combined action of the radial
movement of the vortex ring and its strengthening allows for enough air to be entrained
towards the feeding tube and burn the hydrogen flow.
Other points we would like to highlight are that the plasma-edge vorticity hypothesis leads to predictions that agree with the observed reduction of unsteadiness of the
combustion field and the ability of an increase in dielectric temperature to lower the
collapsing (flattening) potential. The combustion field after the collapse is substantially
different from that characteristic of the standing flame. The air ventilation is forced onto
the smaller flat flame by the side ring-vortices induced by the plasma. The flame is a
counterflow flame with the hot combustion gases being recirculated into the cold hydrogen
stream. Because of the recirculation, the major energy transfer in the collapsed case is to
the walls through heat conduction, thus the efflux temperature is much smaller than in
the non-activated case. Both model and experiments agree in obtaining a reduction of the
speed of the burnt-gas leaving the burner that becomes more significant as the applied
voltage is increased. Finally, although an irrotational force density does not predict flame
deformations consistent with the experiments, it leads to a strong reduction of flame
flickering in agreement with the measurements.
Acknowledgment
This material is based in part upon work supported by the Department of Energy, National
Nuclear Security Administration, under Award Number DE-NA0002374.
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