Proceedings of ASME Turbo Expo 2012
GT2012
June 11-15, 2012, Copenhagen, Denmark
GT2012-6
FLAME LEADING EDGE AND FLOW DYNAMICS IN A SWIRLING, LIFTED FLAME
Michael Malanoski, Michael Aguilar, Jacqueline O’Connor
Dong-hyuk Shin, Bobby Noble, Tim Lieuwen
Georgia Institute of Technology
Atlanta, Georgia, USA
ABSTRACT
Flames in high swirl flow fields with vortex
breakdown often stabilize aerodynamically in front of interior
flow stagnation points. In contrast to shear layer stabilized
flames with a nearly fixed, well defined flame attachment point,
the leading edge of aerodynamically stabilized flames can move
around substantially, due to both the inherent dynamics of the
vortex breakdown region, as well as externally imposed
oscillations. Motion of this flame stabilization point relative to
the flow field has an important dynamical role during
combustion instabilities, as it creates flame front wrinkles and
heat release fluctuations. For example, a prior study has shown
that nonlinear dynamics of the flame response at high forcing
amplitudes were related to these leading edge dynamics. This
heat release mechanism exists alongside other flame wrinkling
processes, arising from such processes as shear layer rollup and
swirl fluctuations.
This paper describes an experimental investigation of
acoustic forcing effects on the dynamics of leading edge of a
swirl stabilized flame. Vortex breakdown bubble dynamics
were characterized using both high-speed particle image
velocimetry (PIV) and line-of-sight high-speed CH*
chemiluminescence. A wide array of forcing conditions was
achieved by varying forcing frequency, amplitude, and acoustic
field symmetry. These results show significant differences in
instantaneous and time averaged location of the flow stagnation
points. They also show motion of the flame leading edge that
are of the same order of magnitude as corresponding particle
displacement associated with the fluctuating velocity field.
This observation suggests that heat release fluctuations
associated with leading edge motion may be just as significant
in controlling the unsteady flame response as the flame wrinkles
excited by velocity fluctuations.
NOMENCLATURE
CH *
CH *
t
x
r
D

1
b
b, m
CH* Chemiluminescence
magnitude of CH* fluctuation at forcing
frequency
time variable
axial/longitudinal coordinate
radial/transverse coordinate
nozzle diameter
flame front location
fluctuating flame front location
fluctuating flame base location
u0
magnitude of particle displacement at the
forcing frequency
mean axial nozzle exit velocity
uru
reactant flow velocity along radial direction
u
x
reactant flow velocity along axial direction
u
d
local displacement velocity
u
u t ,0
mean tangential velocity along the flame
un ,1
fluctuating velocity normal to unperturbed
flame
local instantaneous transverse velocity
instantaneous transverse reference velocity
u
s
u
uT
uL ,1 F
uT ,1 F

S
Re
1
magnitude of fluctuating longitudinal
reference velocity at the forcing frequency
magnitude of fluctuating transverse reference
velocity at the forcing frequency
flame angle with respect to the axial
direction
geometric swirl number
Reynolds number
Copyright © 2012 by ASME
INTRODUCTION
This paper describes an investigation of acoustic forcing
effects on the dynamics of the leading edge of a swirl stabilized
flame. This work is motivated by the problem of combustion
instabilities in premixed flames, which is a major concern in the
development of modern low NOx combustors [1]. Recently,
significant progress has been made to understand and model the
physical processes controlling these instabilities. In addition,
recent developments in high repetition rate diagnostics have led
to substantial improvements in the ability to experimentally
characterize the spatio-temporal dynamics of the flame and flow
dynamics [2, 3]. This work focuses on the need to better
understand the dynamics of the leading edge of unattached,
lifted flames. To provide context for this issue, the rest of this
introduction first describes basic topological features of
swirling flow fields, and their implications on the steady and
unsteady flame characteristics. Then, it discusses flame
dynamics specifically, and shows the importance of the flame
leading edge on its space-time dynamics.
Figure 1 illustrates a generic, annular swirling nozzle flow
with two span wise shear layers originating from the inner and
outer annulus edges. The convectively unstable nature of these
shear layers makes them particularly sensitive to acoustic
forcing [4-7]. Indeed, several recent publications have argued
that the flame wrinkling and heat release response of centerbody
stabilized flames to flow forcing is dominated by these flow
structures disturbing the flame [2, 4].
contrast, when the centerbody wake and vortex breakdown
bubble are merged, as in Figure 1b, no nearfield stagnation
point is present in the flow, and the flame stabilizes in the shear
layers. Several of our recent studies have focused upon this
latter configuration, where the flame is stabilized in the inner
shear layer [4]. In this case, the leading edge of the flame is
firmly attached near the flow separation point and exhibits
minimal response to forcing, except at very high forcing
amplitudes [14]. Flame wrinkle amplitudes grow downstream,
due to both the direct excitation of the flame by the acoustic
forcing, as well as the vortices in the separating shear layers.
This study focuses on a configuration where the VBB is not
attached to the centerbody. This introduces a significant
additional degree of freedom to the problem, as the whole
breakdown bubble and stagnation point oscillates axially and
transversely due to the inherent flow instabilities in the VBB
and in response to the forcing. If the leading edge of the flame
is stabilized by the stagnation point of the breakdown bubble,
this also implies that the flame leading edge oscillates
significantly in response to forcing. Indeed, prior investigations
on a similar geometry attributed some characteristics of the
unsteady heat release to the dynamics of the stagnation point
and bubble motion [10, 15]. For example, Figure 2 illustrates
the measured relationship between unsteady heat release of a
longitudinally forced swirl flame upon disturbance velocity
[16]. The response to the 410 Hz driving frequency shows a
flame heat release response that increases roughly linearly with
forcing amplitude before saturating at high forcing [16-20].
The response to the 170 Hz driving frequency shows a result
with a highly non-monotonic flame response-excitation
amplitude relationship. OH PLIF measurements indicated that
this behavior was directly correlated with the nonlinear
dynamics of the flame leading edge.
Figure 1. Possible flow and flame configurations for two
different vortex breakdown bubble structures where dashed
lines indicate edge of recirculation. (a) the bubble is lifted
and (b) the bubble is merged with the centerbody wake.
The centerbody of the nozzle introduces a wake flow. For
small centerbody diameters and/or weak swirl, the time-average
centerbody wake closes out upstream of the forward stagnation
point of the vortex breakdown region, and thus the two flow
structures (centerbody wake and VBB) are distinct, as shown in
Figure 1a. For larger centerbodies or high swirl flows, the wake
and vortex breakdown bubble merge into a single structure, as
shown in Figure 1b [8, 9]. When the vortex bubble is detached
as in Figure 1a, flame stabilization is possible in the stagnation
region preceding the VBB or in one or both of the low velocity
shear layers. In this way, several different flame configurations
(all of which have been experimentally observed [10-13]) are
possible as depicted in the sketches next to each figure. In
Figure 2. Flame chemiluminescence fluctuation response
as a function of longitudinal forcing amplitude at two
frequencies for a swirl-stabilized flame. Reproduced from
Bellows et al.[16].
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Copyright © 2012 by ASME
Forced high swirl flows exhibit an intrinsically nonlinear
response character, due to the global instability of the vortex
breakdown bubble. Globally unstable systems execute selfexcited, limit cycle motions, even in the absence of external
forcing [21]. For this reason, low amplitude forcing has minimal
impacts on the VBB [5, 22-24]. This behavior is to be
contrasted with that exhibited by the convectively unstable
shear layers [4, 5, 25-27]. Swirl flows often display narrowband
oscillations manifested by several types of flow structures, such
as the precession of the center of rotation of the flow, known as
the precessing vortex core (PVC) [15]. Several factors influence
the response of the PVC to acoustic forcing, including both
flow and geometric parameters. In some cases where the bubble
has intrinsic narrowband oscillations, external excitation at that
natural frequency of oscillation can cause further amplification
of this oscillation [28]. For example, LES studies by Iudiciani
and Duwig [23] show that low frequency forcing ( St  0.6 )
resulted in a decrease in the strength of the PVC fluctuation
amplitude, while higher frequency fluctuations resulted in
increases in PVC fluctuation amplitude.
Having discussed the fluid mechanic features of swirling
flows of relevance to this paper, we next discuss the flame
dynamics specifically. In order to motivate the significance of
the leading edge flame dynamics on the overall response of all
points of the flame, as well as the unsteady heat release, it is
useful to consider the simplified situation of an axisymmetric
flame front whose location is a single valued function,  , of
the coordinate x , as shown in Figure 3.
u
1

 u ut ,0 cos  1  n,1
t
x
cos 
where
(2)
u ut ,0 represents the mean tangential velocity along the
flame and
un ,1 denotes the fluctuating velocity component in
the direction normal to the unperturbed flame front. The left
hand side of Equation (2) is simply a convection operator and
describes the propagation of wrinkles along the flame with a
velocity projected in the
x -direction given by
uut ,0 cos  uutx ,0 .
The right hand side describes excitation
of flame disturbances. Significant progress has been made in the
last decade in predicting the response of flames to these
velocity fluctuations associated with acoustic disturbances,
vortical disturbances, and swirl fluctuations [6, 29-33]
Our focus in this paper is on the additional effects of flame
leading edge motion, which manifests itself through a
fluctuating flame boundary condition in this formulation. The
simplest example to demonstrate the effect of leading edge
flame motion is to consider a case without flow forcing, i.e.,
where un,1  0 and that the forward edge of the flame is
oscillating as
1  b  t  .
These leading edge oscillations
lead to propagation of flame wrinkles, and heat release
fluctuations at all other points of the flame as shown by the
following solution of Equation (2):

1  x, t   b  t 


x

u ut ,0 cos  
(3)
Indeed, prior experiments have demonstrated the
downstream propagation of waves explicitly by oscillating the
flame holder position. For example, results from Petersen [34]
showing this effect can be seen in Figure 4.
Figure 3. Schematic of model problem of an axisymmetric
flame whose position is a single valued function of the
coordinate, x .
The dynamics of the flame position [29], obtained from the full
G-equation are given by:


  
 uru  uxu
 sdu 1   
t
x
 x 
2
(1)
Linearizing this equation and assuming a constant flame
speed leads to:
Figure 4. Photograph of flame with oscillating flame
holder, indicated by arrow direction, showing downstream
propagation of flame wrinkles. Reproduced from Petersen
[34].
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Copyright © 2012 by ASME
Similar flame wrinkles are excited by velocity
oscillations near the flame attachment point if the flame holder
is stationary. More generally, it can be shown that flame
holder and flow motion relative to each other leads to flame
wrinkling. The main point here, then, is that flame wrinkles and
heat release fluctuations are excited by not only velocity
disturbances, but also leading edge flame motion relative to the
flow. Thus, the relative values of db / dt and un ,1 play an
important role in determining whether flame leading edge
motion or flow velocity fluctuations dominate the flame
wrinkling processes or, alternatively, whether they cancel each
other out. The rest of this paper describes an experimental
study performed to experimentally characterize both the flame
and flow field to obtain further insight into these questions.
EXPERIMENTAL SETUP
The following section describes the experimental facility,
the acoustic excitation, and the diagnostic techniques utilized
for this study. The experimental facility shown in Figure 5 was
designed to simulate acoustic motions in annular combustion
chambers, and replicates the geometry of an unwrapped sector
of the annular combustor. A CAD model depiction of the
experiment viewed from the backside with the main windows
removed is shown in the lower right corner. The design is
similar to that discussed in O’Connor et al. [9] but with
modifications for improved diagnostic access to the combustor.
The internal dimensions of the combustor are 1.14 m x 0.10 m x
0.34 m where the longest dimension is the direction of forced
transverse acoustic excitation. The exhaust plane of the
combustor enables optical access through a rectangular quartz
window 0.2 x 0.09 m, while allowing exhaust gases to pass
through 0.08 m diameter ports on either side of the optical
window. The two large quartz windows, referred to as the main
windows, allow access to the flow field through a 0.27 m x 0.27
m viewing area. The last remaining quartz window is located in
the lower right corner on the backside of the combustor as seen
in the model and allows additional access for laser diagnostics.
The combustor is fabricated from stainless steel and insulated
with ceramic inserts from ZIRCAR Refractory Composites, Inc.
refractory sheet type RSLE-57.
The experiment air supply is metered using an orifice plate
in conjunction with a differential pressure transducer. Preheated
air at 400 K enters the combustor through an insulated settling
and conditioning chamber. The air enters the combustion
chamber through a single dual-annular counter-rotating swirler
(DACRS) premixer [35-37] with a swirl number of
approximately S=0.62, a methane equivalence ratio of 0.95, 1
atm pressure, and a nominal exit velocity of 25 m/s
(corresponding to a Re=30,600 based on the outer diameter of
the premixer).
Figure 5. Photograph and solid model (bottom right) of
transverse forcing test facility.
The combustor has three 100 W Galls speakers on each
side that can be independently driven. The speakers are
connected to the end of adjustable tubes, seen on the side of the
facility in Figure 5, to allow tuning for optimizing control
authority. By changing the phase between the two driver
signals, the transverse acoustic field can exhibit wave patterns
ranging from standing to traveling waves. Ideally, when the
speakers are driven at the same phase, referred to as in-phase,
an acoustic pressure anti-node and velocity node exist at the
nozzle. Similarly, when the speakers are driven out-of-phase
with a 180 degree offset, the nozzle region experiences an
acoustic pressure node and an acoustic velocity anti-node. In
non-reacting, non-flowing experiments, pressure distribution
measurements showed that a standing wave pattern was created
in this geometry that had the expected profiles described above.
In the reacting, flowing experiments, there are additional
velocity fluctuations associated with hydrodynamic flow
instabilities. In addition, inherent asymmetries in time averaged
flame shape lead to asymmetries in the velocity field
fluctuations. As shown later, the result of this is that in-phase
velocity fluctuations are smaller than out-of-phase, but not
negligible. The forcing conditions and corresponding symbols
are summarized in Table 1 below, where IP denotes the in-phase
case, and OP denotes the out-of-phase case. The symbols
indicate the representation of each particular test case in
subsequent figures.
Table 1. Nomenclature to indicate axial and radial velocity
and flame position response to transverse acoustic forcing.
Transverse Forcing
Frequency
400 Hz IP
400 Hz OP
1500 Hz IP
1500 Hz OP
4
Radial Response
Symbols
Axial Response
Symbols
Copyright © 2012 by ASME
Spatial averages of the transverse flow velocities were
calculated in order to determine representative values of the
amplitude of acoustic forcing at each acoustic condition. An
instantaneous transverse reference velocity, defined in Equation
(4), was obtained from averaging local instantaneous velocities
along the centerline of the flow over one jet diameter
downstream.
uT (t ) 
1
D
2D
 u( x, r  0, t )dx
(4)
D
The Fourier transform of the fluctuating transverse reference
velocity was calculated, and the amplitude of velocity
fluctuation at the forcing frequency was extracted. The
magnitude of the transverse reference velocity fluctuation at the
forcing frequency as a function of driver voltage, calculated
from equation (4), is shown in Figure 6. The transverse
response increases with driver input voltage, and as expected,
the out-of-phase excitation produced a larger response in the
magnitude of fluctuation. The velocity fluctuations at the
forcing frequency in the shear layer were typically 5 times
larger than uT, showing that the dominant velocity source of
flame wrinkling is vortical, and not acoustic.
Star SA1.1 camera at 10,000 frames per second, with 640x448
pixel resolution. 2000 PIV image pairs were acquired with a
separation time of 18 microseconds. The high sample rate and
quantity of images provided a spectral frequency resolution of 5
Hz. The calculations for the velocity field were performed in
DaVis 7.2 software provided by LaVision.
The leading edge flame dynamics were captured from lineof-sight integrated flame chemiluminescence with the Photron
High Speed Star SA3 camera coupled to the LaVision
Intensified Rely Optic(IRO). The full flame chemiluminescence
data set was recorded at 5kHz, and the optimized flame edge
tests were recorded at 10 kHz. Each test case consisted of 1000
images. The delay and gate of the IRO were set at 0.2
microseconds and 90 microseconds, respectively, at a 65% gain
setting. An optical filter with a bandpass of 430 nm +/-5 nm
restricted the imaged luminescence to the wavelengths emitted
by the excited CH radical. Additionally, select data sets were
acquired without a filter to image the entire luminosity range of
the flame.
RESULTS AND DISCUSSIONS
This section presents typical results illustrating the flow
field dynamics and flame leading edge motion.
Velocity Field Characteristics
Figure 7 illustrates the time average flow field for the
unforced test, showing the strong axial jet at the nozzle outlet
which divides into an annular jet around the VBB. The image
is colorized, with the left half indicating velocity and the right
half depicting the azimuthal vorticity field. The white line
designates the points of zero axial velocity in the VBB region,
while below it the gray scale region with black vectors
represents positive axial flow. The time averaged stagnation
point of the VBB lies about 1.4 diameters downstream of the
dump plane, indicated here by the two white concentric circles.
Figure 6. Magnitude of fluctuating transverse reference
velocity at the forcing frequency to driver voltage.
Measurements of the velocity field were recorded through
the main front window. Seeded image pairs were obtained with
a 10 kHz PIV system, using a Litron Lasers Ltd. LDY303He
Nd:YLF laser with a wavelength of 527nm and 5 mJ/pulse
pulse energy. Aluminum oxide particles, 1 – 2 microns in
diameter, were introduced to the preheated air flow upstream of
the settling chamber to ensure uniform particle mixing. A
LaVision divergent sheet optic, with a f  10 mm
cylindrical lens, created a 1 mm thick laser sheet. The sheet
entered the experiment through the window port in the lower
right corner on the backside of the combustor and diverted to
pass through the flame parallel to the main window plane. The
illuminated particles were imaged with a Photron HighSpeed
Figure 7. Time average axial velocity contour (left) and
time average azimuthal vorticity contour(right) for
unforced reacting test case.
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Copyright © 2012 by ASME
The vorticity depicted on the right side Figure 7 represents the
inner and outer shear layers associated with the two sides of the
annular jet. The darker contours indicate vorticity in the
counter-clockwise direction (out of the plane) and the light
contours indicate vorticity in the clockwise direction (into the
plane). The dashed lines in the vorticity contour indicate linear
fits to maxima in absolute value of the vorticity.
Figure 8 plots the measured axial location of the time
average centerline stagnation point as a function of disturbance
amplitude. For reference, the unforced location is indicated by
the dashed line. Note how the time average stagnation point
location exhibits a weak amplitude dependence over this
|uT,1|/uo~0-16% velocity range, with slightly different
sensitivities at the different forcing frequencies.
a)
b)
Figure 8. Dependence of the time averaged axial location of
centerline velocity stagnation point upon centerline acoustic
forcing amplitude.
The instantaneous flow field exhibits substantially more
structure than the time average, as shown by the sequence of
images in Figure 9. The colored contours depict the magnitude
of the axial velocity where the lighter contours indicate higher
velocity. The black vectors indicate forward instantaneous axial
flow and the white vectors indicate reversed instantaneous axial
flow. For reference, the location of the time averaged centerline
stagnation point is indicated in the figure, as well as the
instantaneous locus of points of zero velocity by the solid white
dots. These images show that the negative axial flow region
sways from the left side to the right side of the flow centerline,
and also moves a substantial amount in the axial direction.
c)
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Copyright © 2012 by ASME
d)
Figure 10. Unforced axial velocity spectrum at (r,x) = (0,
0.8D). Strouhal number defined as fD/uo.
e)
Figure 9.
Sequence of reacting, unforced instantaneous
velocity field.
These and other images show that the reverse flow region
consists of a helical region that precesses around the flow
centerline. The leading stagnation point appears to precess in
and out of the laser plane in the image sequence shown. The
fact that the reverse flow region advances to the nozzle exit also
shows that the time averaged stagnation point is not a useful
indicator of the instantaneous axial velocity stagnation point.
The spectrum of the fluctuating axial velocity at the
centerline is shown in Figure 10 for the unforced case,
illustrating that it consists of a complex superposition of
narrowband peaks and broadband motion, with the majority of
the fluctuation energy occurring below 300 Hz. The low
frequency narrowband fluctuations are associated with the
natural dynamics of the vortex breakdown region. In the
presence of forcing, these features remain evident in the spectra,
in addition to a strong tonal component at the forcing frequency,
as shown in Figure 11 for a 400 Hz forcing case. The
fluctuation energy appears to peak between 0.5D - 1.5D
downstream of the dump plane.
Figure 11.
Forced axial velocity spectrum along centerline
for 400Hz in-phase at uT ,1 F u0 7%.
Flame Leading Edge Dynamics
This section presents flame data illustrating the dynamics
of the leading edge. The velocity data in the prior section from
planar measurements show that inferences about the axial flow
stagnation points, and therefore the flame leading edge, are
problematic because of the helical character of the recirculation
zone. In addition, visual observations from high speed movies
provide similar indications - namely, that the forward part of the
flame exhibits a helical pattern that appears to intermittently
attach and detach from the nozzle exit.
For these reasons, we focused on line of sight flame
imaging for these characterizations. One issue with line of
sight imaging is that the camera's dynamic range is controlled
by heat release regions farther downstream. This occurs because
the flame expands radially and so its surface area, heat release
rate, and luminosity grow with downstream distance. Thus,
we found that it was difficult to infer information about the faint
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Copyright © 2012 by ASME
leading edge from images designed to visualize the whole
flame.
For these reasons, we obtained line of sight images using
two camera range settings: one to image the entire flame and the
other optimized to visualize the much fainter leading edge.
Figure 12 illustrates a time average image of the entire flame.
Similar to the time average stagnation point, the time average
flame base in Figure 12 is lifted. The optimized camera range
captured the region from the dump plane of the combustor to
approximately 0.7 diameters downstream.
Figure 13. Time sequence of instantaneous flame leading
edge forced at 400 Hz in-phase with uT ,1 F u0 = 7%.
Figure 12. Time average line-of-sight intensified image of
CH* Chemiluminescence.
Figure 13 illustrates a number of extracted instantaneous
forward flame leading edges. The flame edges were extracted
by threshold filtering the data, using a saturated intensity
threshold value, and then spatially averaging 12-by-12 blocks of
pixels within the image. The image was then binarized and the
edge of the flame was tracked using a boundary tracking
algorithm. The dark region indicates the nozzle outlet region
acquired from the unfiltered luminosity images. The image
sequence progresses in time through the left column and
continues at the top of the right column. The camera was
aligned with a 3 degree offset, introducing a 5% and 1%
uncertainty in the vertical and horizontal leading edge position,
respectively. The strong axial and transverse motion of the
flame is evident from these images. The images indicate that the
flame leading edge propagates all the way to the nozzle exit in
some images and clearly downstream in others. Additionally,
the images indicate that the leading point of the flame appears
to rotate around the nozzle. Image 4 shows the leading edge of
the flame on the left of the nozzle, while it is located on the
right in image 8.
The axial and transverse location of the flame leading
point, defined as the farthest forward axial position of the flame
edge, was extracted from these images. The flame does move
completely out of the viewing window, typically about 30% of
the recorded images, so the number of analysis points is less
than the number of available images. Moreover, only a
continuous range of images where the flame was in the viewing
window for the entire portion of the record was used for the
analyses, limiting the data to about 50% of the recorded images.
There is no correlation between these percentages and forcing
amplitude, implying that the movement out of the viewing area
is a result of the natural flame motion and negligibly influenced
by forcing. This suggests that our estimates of natural flame
motions are biased low, but that estimates of flame motions at
the forcing frequency are not biased.
The forced leading point motion from excitation is
extracted using spectral analysis on the tracked leading point.
The spectrum of the resulting time series for the axial flame
leading point location is shown in Figure 14 for 400 Hz inphase forcing. Note the presence of the narrowband response at
the 400 Hz forcing frequency, but also the significant levels of
broadband fluctuation. The magnitude of the peak at the forcing
frequency indicates the leading point response to excitation.
The normalized magnitude of the fluctuations in the radial
direction and for other forcing conditions is similar in
magnitude as the value in Figure 14. The importance of the
forced motion of the leading point is discussed next in
comparison to natural leading point motion and particle
displacement.
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Copyright © 2012 by ASME
For a record of 1000 images sampled at10 kHz, each of the 25
phase realizations shown represents the average of 40 separate
instances of the flame leading point. Note how the leading point
motion is dominantly transverse in the out-of-phase forcing
case. The presence of the velocity anti-node near the nozzle
center line for out-of-phase forcing accounts for the increased
motion in the radial direction. In both cases, axial fluctuations
are induced in the nozzle, leading to the axial flame motions.
The points in the figure are normalized by the amplitude of
particle displacement calculated at the given forcing frequency
and corresponding velocity fluctuation amplitude using the
relation:
b , m 
Figure 14. Response magnitude of fluctuating axial flame
leading point to 400Hz in-phase forcing at |uT,1|F/u0 = 7%.
The corresponding root mean square(RMS) value of the
total (over all frequencies) flame leading edge motion is plotted
as a function of disturbance amplitude in Figure 15, where the
radial response is depicted in blue and the axial response is
shown in red. The overall RMS of the total motion is about 5-10
times greater than the forced motions; i.e., flame leading point
motion is dominated by its natural motion, presumably tracking
with the natural precession of the flow stagnation point.
Because of this, the overall RMS displacement exhibits
negligible sensitivity to disturbance amplitude. The radial RMS
displacement exhibits a higher response as a result of the
precession around the nozzle.
| un,1 |F
2 f
(5)
where un ,1 is a reference velocity normal to the unperturbed
F
flame, calculated by spatial averaging the velocity fluctuation
0.5 D along the shear layer near the nominal flame position.
Figure 16. Phase ensemble averaged axial and radial
location of flame leading point. 400Hz in-phase (diamond)
with |uT,1|F/u0 = 7%, 400Hz out-of-phase (square) with
|uT,1|F/u0 = 16%.
Figure 15. Overall flame leading point RMS for axial (red)
and transverse (blue) flame base movement.
Positions of the phase ensemble averaged fluctuating flame
leading point for a 400 Hz disturbance frequency are shown in
Figure 16 at the maximum excitation amplitude for each
acoustic test case. With the 10 kHz sample frequency, 25 phase
realizations are possible for a 400 Hz disturbance frequency.
Thus, fluctuations of the leading point position that are small or
large relative to ξb,m imply that the leading point displacement is
small or large relative to oscillatory particle displacement,
respectively. As discussed in the introduction, this signifies
whether the flame wrinkles are dominated by velocity
disturbances or leading point motion, respectively. In all cases,
we found that this ratio is O(1), implying that leading point
motion has comparable contributions to the overall flame
wrinkling as the vortical velocity disturbances. The comparable
contribution to overall flame wrinkling requires accounting for
an additional degree of freedom associated with modeling the
heat release response characteristics of lifted flames, as velocity
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Copyright © 2012 by ASME
fluctuations induce wrinkles both directly on the flame and
indirectly by exciting motions of the flame base.
CONCLUDING REMARKS
The dynamic response of aerodynamically stabilized flames
has an additional degree of freedom relative to attached flames,
because of motion of the flame base. These motions are an
additional mechanism for heat release fluctuations. The motions
of the flame leading edge are controlled by the complex fluid
mechanic instabilities in the vortex breakdown region, as well
as the flow forcing. The most important conclusion from this
study is that the forced motions in response to the excitation are
small relative to the natural motions, but similar in magnitude to
the particle displacement of the oscillating flow. This implies
that flame leading edge motions are equally important as
previously studied velocity fluctuations as a contributor for
flame wrinkles.
ACKNOWLEDGMENTS
This work has been partially supported by the US
Department of Energy under contracts DEFG26-07NT43069
and DE-NT0005054, contract monitor Mark Freeman, as well
as the National Science Foundation through a Graduate
Research Fellowship to M. Aguilar.
REFERENCES
1.
Lieuwen, T. and V. Yang, Combustion Instabilities in
Gas Turbine Engines. Progress in Astronautics and
Aeronautics, ed. F.K. Lu. Vol. 210. 2005, Washington
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