Flame Leading Edge and Flow Dynamics in a …effects on the dynamics of the leading edge of a swirl stabilized flame. This work is motivated by the problem of combustion instabilities

1 Copyright © 2012 by ASME

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* Chemiluminescence

*CH magnitude of CH* fluctuation at forcing

frequency t time variable x axial/longitudinal coordinate

r radial/transverse coordinate

D nozzle diameter

flame front location

1 fluctuating flame front location

b fluctuating flame base location

,b m magnitude of particle displacement at the

forcing frequency

0u mean axial nozzle exit velocity

u

ru reactant flow velocity along radial direction

u

xu reactant flow velocity along axial direction

u

ds local displacement velocity

,0

uu t mean tangential velocity along the flame

,1nu fluctuating velocity normal to unperturbed

flame u local instantaneous transverse velocity

Tu instantaneous transverse reference velocity

,1L Fu magnitude of fluctuating longitudinal

reference velocity at the forcing frequency

,1T Fu magnitude of fluctuating transverse reference

velocity at the forcing frequency

flame angle with respect to the axial

direction

S geometric swirl number

Re Reynolds number

Proceedings of ASME Turbo Expo 2012 GT2012

June 11-15, 2012, Copenhagen, Denmark

GT2012-68256


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].

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

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 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].


Forced high swirl flows exhibit an intrinsically nonlinear

response character, due to the global instability of the vortex

breakdown bubble. Globally unstable systems execute self-

excited, 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 ( 0.6St )

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.

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:

2

1u u u

r x du u st x x

( 1 )

Linearizing this equation and assuming a constant flame

speed leads to:

,0

,11 1coscos

u nuu

t x

t

( 2 )

where ,0

uu t represents the mean tangential velocity along the

flame and ,1nu 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

,0 ,0cosu uu u t tx . 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 ,1 0nu

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

,0

,cos

b u

xx t t

u

t

( 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 4. Photograph of flame with oscillating flame

holder, indicated by arrow direction, showing downstream

propagation of flame wrinkles. Reproduced from Petersen

[34].


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 /bd dt and ,1nu

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

Radial Response

Symbols

Axial Response

Symbols

400 Hz IP

400 Hz OP 1500 Hz IP 1500 Hz OP


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. 2

1( ) ( , 0, )

D

T

D

u t u x r t dxD

( 4 )

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.

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 10f 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

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 line-

of-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 7. Time average axial velocity contour (left) and

time average azimuthal vorticity contour(right) for

unforced reacting test case.


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.

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.

a)

b)

c)


d)

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 10. Unforced axial velocity spectrum at (r,x) = (0,

0.8D). Strouhal number defined as fD/uo.

Figure 11. Forced axial velocity spectrum along centerline

for 400Hz in-phase at ,1 0T Fu u 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


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 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.

Figure 13. Time sequence of instantaneous flame leading

edge forced at 400 Hz in-phase with ,1 0T Fu u = 7%.

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 in-

phase 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.


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.

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.

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:

,

,1 |

2

| F

b m

n

f

u

(5)

where ,1n Fu is a reference velocity normal to the unperturbed

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%.

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


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.

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Documents

Flame Leading Edge and Flow Dynamics in a …effects on the dynamics of the leading edge of a swirl stabilized flame. This work is motivated by the problem of combustion instabilities