Proceedings of ASME Turbo Expo 2010: Power for Land, Sea and Air
GT2010
June 14-18, 2010, Glasgow, UK
GT2010-22133
Disturbance Field Characteristics of a Transversely Excited Annular Jet
Jacqueline O’Connor
Georgia Institute of Technology
Atlanta, GA, USA
Shweta Natarajan
Georgia Institute of Technology
Atlanta, GA, USA
Michael Malanoski
Georgia Institute of Technology
Atlanta, GA, USA
ABSTRACT
This paper describes an investigation of transverse acoustic
instabilities in premixed, swirl-stabilized flames. Additional
measurements, beyond the scope of the current work, are
described in O’Connor et al. [1]. Transverse excitation of
swirling flow involves complex interactions between acoustic
waves and fluid mechanic instabilities. The flame’s response to
transverse acoustic excitation is a superposition of both
acoustic and vortical disturbances that fluctuate in both the
longitudinal and transverse direction. In the nozzle near field
region, the disturbance field is a complex superposition of
convecting vortical disturbances, as well as longer wavelength
transverse and longitudinal acoustic disturbances. Farther
downstream, the disturbance field is dominated by the
transverse acoustic field.
The phasing between the
disturbances on the inside and outside of the burner annulus, as
well as the left and right sides of the burner annulus is a strong
function of the transverse disturbance field characteristics. For
cases where the burner centerline is an approximate pressure
node and velocity anti-node, the mass flow out of the left and
right sides of the burner actually oscillates out-of-phase with
respect to each other. In contrast, for cases where the
centerline is a pressure anti-node, the burner responds
symmetrically about the burner and annulus centerlines. These
results show that the burner response characteristics strongly
depend upon their location in the acoustic mode shape.
INTRODUCTION
The objective of this study is to improve understanding of
transverse combustion instabilities in premixed combustors.
Combustion dynamics is a problem that has plagued numerous
rocket and air-breathing engine development programs. The
coupling of resonant acoustics in the combustion chamber and
heat release fluctuations from the flame [2] can cause structural
Tim Lieuwen
Georgia Institute of Technology
Atlanta, GA, USA
damage, decrease operational flexibility and performance. In
particular, instabilities have caused major challenges in the
development of lean, premixed combustors used in low NOx
gas turbines [3].
Transverse instabilities have been discussed frequently in
the afterburner [4-7], solid rocket [8, 9], and liquid rocket
literature [10-15]. For low NOx gas turbines, most of the work
over the last two decades has focused on the longitudinal
instability problem [16-18]. Significantly less work has been
done on the analysis and characterization of transverse
instabilities for gas turbine type applications, characterized by a
swirling, premixed flame [19-24]. There are, however, two key
application areas where transverse acoustic oscillations are of
significant practical interest. The first occurs in annular
combustion systems, such as the instabilities in the Solar Mars
100, Alstom GT24, GE LM6000, Siemens V84.3A, and others
[20, 25-27]. Because of the larger length scales involved, these
instabilities often occur at similar frequencies (e.g., 100’s of
Hertz) as the longitudinal oscillations encountered in these
systems. As these modes cannot be simulated without the full
annulus, several of these companies report the results of
longitudinal instability tests obtained on single nozzle rigs
scaled to have similar longitudinal acoustic frequencies as the
observed transverse instabilities [25, 28, 29]. The second
application where transverse instabilities are of interest is the
higher frequency transverse oscillations encountered in can
combustion systems. These instabilities occur at relatively high
frequencies, in the 1-5 kHz range, and scale with the combustor
can diameter. While relatively little treatment of these high
frequency oscillations can be found in the technical literature,
there is significant discussion of them in the gas turbine
operator/user community; e.g., see Combined Cycle Journal
[30] or Sobieski and Sewell’s chapter in Combustion
Instabilities in Gas Turbine Engines [26].
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Copyright © 2010 by ASME
Transverse acoustic oscillations in combustors introduce a
variety of new coupling processes and disturbance field
phenomena relative to longitudinal modes. The focus of the
next two sections is to elucidate these differences. In essence,
the key problem of interest is the manner in which the flame
responds to oscillations in flow velocity. This is referred to as
the “velocity coupled” response mechanism [31-35], to be
distinguished from the also important “fuel/air ratio coupling”
[36, 37] mechanism, or the probably negligible “pressure
coupling” mechanism [38]. Flow oscillations lead to flame
wrinkling that, in turn, causes oscillations in flame surface area
and rate of heat release. In the discussion below, we break this
problem into two components (1) nature of the velocity field
that is exciting the flame, and (2) flame response to this flow
excitation.
Velocity Field Disturbing the Flame
While acoustic oscillations can directly excite the flame,
they also excite organized flow instabilities associated with
shear layers, wakes, or the vortex breakdown bubble [39-41].
Taken together, there are a number of potential sources of flow
disturbances that can lead to heat release oscillations. Two of
these sources are directly acoustic in origin - transverse
acoustic motions associated with the natural frequencies/mode
shapes of the combustion system, and longitudinal oscillations
in the nozzle due to the oscillating pressure difference across
the nozzle. An alternative way of thinking about the latter case
is that transversely traveling acoustic wave diffract around the
nozzle and enter the nozzle passages, leading to longitudinal
mass flow oscillations at the burner exit. Recent simulations by
Staffelbach [19] suggest that it is these longitudinal mass flow
oscillations that most significantly control the flame response to
the imposed transverse disturbance.
Recent studies suggest that it is vortical flow oscillations
that most significantly control the flame’s heat release response
[42-44]. In other words, acoustic oscillations excite flow
instabilities that, in turn, excite the flame. As such, the
receptivity of these flow instabilities to both transverse and
longitudinal acoustic oscillations must be considered. For
example, consider the convectively unstable shear layers,
which form tightly concentrated regions of vorticity through
the action of vortex rollup and pairing [45]. The transverse
acoustic oscillation will disturb them in both normal and
parallel directions, see Figure 1. Normally incident transverse
acoustic oscillations will push them from side to side in a
flapping manner, while parallel incidence will graze over them.
Transverse
acoustic
excitation
Grazing interaction
Normal interaction
Side View
Top View
Figure 1. Transverse excitation interacts both normal to
the flame and grazing the flame.
In contrast, longitudinal oscillations will lead to an axially
oscillating core flow velocity that will excite an oscillation in
shear layer strength [46, 47]. Other literature on the response
of wakes and swirling flows to longitudinal and transverse
excitation can be found in [40, 48, 49]. These potential sources
of excitation are summarized in the figure below.
Transverse Acoustic Excitation
Longitudinal
Acoustics
Flow Instabilities
Flow Instabilities
• Shear layer
• Wake
• Vortex breakdown
• Shear layer
• Wake
• Vortex breakdown
Flame Response
Figure 2. Disturbance pathway in transversely excited
flame.
These four disturbance modes are difficult to separate in
complicated geometries and all four play a roll in exciting the
flame. Although the initial disturbance is transverse, the
disturbance velocity field that is created in the region of the
flame is highly two or three-dimensional. The only known
literature to date that explores this topic shows very clearly the
two-dimensionality of the disturbance field [19, 20]. This is
significant in that the flame will experience a varying type of
disturbance along its length. For example, a point in the middle
of the flame may experience a strong transverse acoustic
excitation source locally, as well as the disturbance from a
vortex that was excited at the nozzle exit and has convected
downstream. Complex interactions like these are difficult to
separate, and it is one of the goals of this work to understand
these characteristics of the disturbance field.
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Copyright © 2010 by ASME
The significant impedance jump across the flame also
introduces important differences between the disturbance field
resulting from incident longitudinal and transverse
disturbances. In the longitudinal excitation case, a nominally
axisymmetric burner will see roughly the same amplitude/phase
of acoustic excitation at all azimuthal points; e.g., the source of
shear layer forcing will be uniform. In contrast, the flame will
partially reflect/refract a transversely propagating traveling
acoustic wave, resulting in different excitation fields on either
side of the flame. In other words, one side of the flame is
“shielded” by the impedance jump imposed by the other side.
Several studies [50-52] have shown that an acoustic
disturbance is considerably changed as it travels across a flame
as a result of dilatation. This point has been dramatically
illustrated in recent experiments of Ghosh and Yu for
transversely excited H2/O2 cryogenic flames, as seen in Figure
3 Note the significantly different degree of flame wrinkling of
the two flame branches.
Figure 3. OH* Chemiluminescence at various phases of
a flame forced at 1150 Hz showing the “shielding” effect
[50].
Flame response to Flow Excitation
In this section, we consider how transverse excitation
influences how flames respond to disturbances. Within the
flame sheet approximation, the response of the flame to flow
excitation is largely controlled by flame kinematics, i.e., the
propagation of the flame normal to itself into an oscillatory
flow field. This is mathematically described by the G-equation
[53]:
∂G
+ (u ⋅ n − S L ) | ∇G |= 0
∂t
(1)
In this equation, the flame position is described by the
parametric equation G ( x , t ) = 0 whose local normal vector is
given by n . Also, u = u ( x , t ) and SL denote the flow field just
upstream of the flame and laminar burning velocity,
respectively. In the unsteady case, the flame is being
continually wrinkled by the unsteady flow field, u . The key
thing to note from this equation is that the flame does not
distinguish between disturbance sources that are axial or
transverse in nature – rather, its response is controlled by the
scalar u ⋅ n - i.e., the component of the flow velocity in a
direction normal to the instantaneous flame front As such, the
response of a two-dimensional flame to a given perturbation
field is fundamentally the same, regardless of whether the
disturbance field is transverse or axial in nature
However, additional physics are present for axisymmetric
flames, because transverse disturbances will necessarily create
a non-axisymmetric disturbance field. In contrast, it can be
expected that longitudinal disturbances excite an essentially
axisymmetric acoustic and vortical disturbance field, leading to
axisymmetric flame wrinkling.
The non-axisymmetric
excitation of the flame introduces an additional degree of
freedom into the flame dynamics, as it leads to azimuthal
disturbance propagation along the flame sheet in a helical
fashion. Some initial work on this problem has been reported
by Acharya et al. [54].
Having discussed some basic features of the transverse
forcing problem, we conclude this section with an overview of
the rest of this paper. Characteristics of the two-dimensional
velocity disturbance field in a transversely forced, swirlstabilized flame are investigated using time-resolved particle
image velocimetry (PIV) [55]. First, the experimental setup is
explained and an overview of the diagnostic system is given.
Next, the disturbance field is characterized using several
metrics to capture the different types of disturbances found in
the region of the flame. Finally, several conclusions are drawn
as to the underlying physics of the disturbance field and the
effect of the velocity disturbance field on the flame behavior.
NOMENCLATURE
Â
Gain of Fourier transform
D
f
G
p
po
Outer diameter of nozzle
Frequency
Flame position
Pressure
Time averaged pressure
Spatially averaged instantaneous pressure
p
r
SL
t
u
ū
uo
û
vo
Radius from nozzle centerline
Laminar flame speed
Time
Axial velocity
Spatially averaged instantaneous axial velocity
Time averaged axial velocity
Harmonically reconstructed axial velocity
Total velocity vector
Transverse velocity
Spatially averaged instantaneous transverse velocity
Time averaged transverse velocity
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Copyright © 2010 by ASME
u
v
v
v̂
x
γ
φ
ω
ωo
ω̂
Harmonically reconstructed transverse velocity
Axial coordinate
Ratio of specific heats
Phase of Fourier transform
Vorticity
Time averaged vorticity
Harmonically reconstructed vorticity
EXPERIMENTAL FACILITY AND DATA ANALYSIS
The experimental facility used in this study is a single
nozzle rig that was designed to support purely transverse
acoustic modes in the combustion chamber. The inner chamber
dimensions are 1.14 m x 0.36 m x 0.08 m, with the 1.14 m
dimension is in the transverse direction. This configuration
mimics the shape of an azimuthal mode in an annular
combustor for the flame stabilized in at the nozzle in the center.
The transverse acoustic field is produced by two sets of drivers
on either side of the combustor. Each driver sits at the end of
an adjustable tube that allows for acoustic tuning. The drivers
on either side of the combustor can be controlled
independently. By changing the phase between the signals
driving each side of the combustor, different wave patterns,
both standing and traveling waves, can be created inside the
combustor. When the drivers are forced in-phase, a pressure
anti-node and velocity node are created at the center of the
experiment in the flame region. When the drivers are forced
out-of-phase, a pressure node and velocity anti-node are
created at the center. The resulting flame response from these
two forcing configurations can be significantly different. The
experiment is shown in Figure 4.
u’ – out of phase
p’ – in phase
p’ – out of phase
u’ – in phase
u’ – out of phase
p’ – in phase
+
+
p’ – out of phase
u’ – in phase
r2
+
-
r1
r1 = 1.09cm
r2 = 1.59cm
D = 3.18cm
Top view
D
Figure 5. Nozzle configuration and acoustic velocity and
pressure perturbations for in phase and out of phase
acoustic forcing, not shown to scale.
The effect of in and out-of-phase forcing on the spatially
averaged transverse velocity (defined in Equation 3) is
illustrated in Figure 6, showing how it changes from large to
small values. The non-zero value of the transverse velocity
observed for the in phase case is likely due to slight imbalances
in excitation amplitudes of the left and right speakers.
0.6
In Phase
Out of Phase
0.4
v`/uo
0.2
0
-0.2
-0.4
0
2
4
6
t*f
8
10
o
Figure 4. Tunable transverse forcing combustion facility.
Figure 6. Spatially averaged transverse velocity
fluctuations along the nozzle centerline for 400 Hz
acoustic forcing at 10 m/s non-reacting flow.
Although up to three nozzles can be supported, the current
configuration has a single nozzle. The nozzle consists of a
swirler with 12 non-aerodynamic blades with a 45º pitch and
5.1 cm centerbody. The outer diameter of the swirler is 3.18
cm and the inner diameter is 2.21 cm.
The nozzle
configuration, including the theoretical mode shapes around the
nozzle for different acoustic forcing conditions, is shown in
Figure 5.
Particle Image Velocimetry (PIV) is used to measure the
velocity field and the flame edge. The window at the front of
the combustor is a 22.9 cm x 22.9 cm quartz window
originating 0.635 cm downstream of the dump plane. The PIV
system is a LaVision Flowmaster Planar Time Resolved system
that allows for two-dimensional, high-speed velocity
measurements. The laser is a Litron Lasers Ltd. LDY303He
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Copyright © 2010 by ASME
uˆ ( x , t ) = Re ⎡⎣ Aˆ ( x )e− i (ωt +ϕ ( x )) ⎤⎦
(2)
Second, spatially averaged instantaneous velocities were
calculated in both the axial and transverse direction at the
nozzle in order to compare the magnitude of the fluctuations in
different directions. The calculation of spatially averaged
transverse velocity is calculated along the centerline of the
flow, across a length of one nozzle diameter. These formulas
are shown in Equation 3. These signals are filtered using a 2nd
order Butterworth bandpass filter at ±200 Hz around the
forcing frequency.
r2
u (t ) =
2π ∫ u ( x = 0, r , t )rdr
r1
2π (r2 2 − r12 )
,
D
1
v (t ) = ∫ v( x, r = 0, t )dx
D0
(3)
Finally, the local unsteady pressure was estimated using a
linearized energy equation as seen in Equation 4.
1 ∂p( x , t )
+ ∇iu ( x , t ) = 0
γ po ∂t
(4)
p (r , t ) =
1 2D
∫ p( x, r , t )dx
2D 0
(5)
All results are non-dimensionalized. The velocities are
(where ρ
normalized by the bulk approach flow velocity, m
ρA
and A denote approach flow density and annulus area), the
spatial coordinates by the nozzle diameter, D, time by the
inverse of the forcing frequency, 1/fo, and the vorticity by the
bulk velocity divided by the annular gap width, Uo/(r2-r1).
RESULTS AND DISCUSSION
This section is organized by first discussing the time
averaged flow features, then the qualitative features of the
unsteady flow, and finally the quantitative characteristics of the
unsteady flow. The time averaged axial velocity and mean
vorticity fields for a non-reacting flow are shown in Figure 7.
1
1
0.5
0.5
r/D
velocity, Â (x) and φ(x), were calculated at each spatial point
and used to harmonically reconstruct the time varying flow
field at the forcing frequency using the relation:
The dilatation field is estimated from the two-dimensional
velocity field. While not much dilatation is expected in the
out-of-plane direction, this estimate does present a source of
error in the pressure calculation. Because of the large length
scale of the dilatation field (e.g., the acoustic wavelength is
0.85 meters at 400 Hz), this calculation is extremely sensitive
to noise. As such, indicated pressures are averaged axially
across the entire viewing window (2 diameters) using the
formula:
r/D
Nd:YLF laser with a wavelength of 527nm and a 5 mJ/pulse
pulse energy at a 10 kHz repetition rate. The laser is capable of
repetition rates up to 10 kHz in each head. The Photron
HighSpeed Star 6 camera has a 640x448 pixel resolution with
20x20 micron pixels on the sensor at a frame rate of 10 kHz.
The PIV calculation was done using DaVis 7.2 software from
LaVision. In the current study, PIV images were taken at a
frame rate of 10 kHz with a time between laser shots of 30
microseconds at a bulk approach velocity of 10 m/s and 15
microseconds at a bulk approach velocity of 40 m/s. 500
velocity fields were calculated at each test condition.
Several methods were used to process the data. DaVis 7.2
was used to calculate velocity fields, vorticity fields, and
divergence fields from the particle images. Since the highspeed PIV system produces time-resolved velocity fields,
spectral analysis was used in much of this study. Three main
data processing methods were used.
First, spectra were calculated for each point in space in the
velocity fields, the vorticity fields, and the divergence fields.
The amplitude and phase of the Fourier transform of the
0
0
0
-0.5
-0.5
-1
-1
0
0.5
0.5
1
x/D
1.5
0
-0.5
0.5
1
x/D
1.5
Figure 7. Time average axial velocity and mean vorticity
in non-reacting flow. Bulk velocity is Uo=40 m/s, jet and
shear layer centers are marked in black.
The black lines indicate the jet and shear layer centers.
These were calculated by finding the location of maximum
velocity and vorticity, respectively, at each axial location. Later
in the paper we will plot the evolution of different unsteady
quantities along these trajectories.
The response of the swirling flow to transverse acoustic
excitation results in a highly multi-dimensional disturbance
field. Figure 2 shows four different pathways by which the
flame can be disturbed. In general, the disturbances are of two
types, acoustic and vortical.
The acoustic disturbances
propagate at the speed of sound and, in this case, set up a
dominantly transverse standing wave with relatively weak
transverse phase variations. In addition, vortical disturbances
triggered by the acoustic motion at the nozzle exit convect
downstream at the local flow velocity.
These vortical
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Copyright © 2010 by ASME
disturbances induce fluctuations in both the axial and the
transverse velocity.
This results in transverse velocity
fluctuations that are a superposition of both the acoustic and the
vortical motion.
These two types of disturbances, acoustic and convecting
disturbances, can be visualized best when considering the
coherent disturbances, or the magnitude of the disturbance at
the forcing frequency. Spectral analysis shows that both the
acoustic and the convecting motions respond very clearly at the
forcing frequency with broadband noise background at other
frequencies. In the following visualizations (Figures 8-11),
only the harmonically reconstructed motion at the forcing
frequency is shown. Figure 8 illustrates an overlay of the
instantaneous velocity vectors (consisting of both acoustic and
vortical disturbances) and isocontours of the vorticity
fluctuations. While similar trends were seen for all the flow
velocities measured in this study (10 m/s, 20 m/s, 40 m/s), the
highest velocity case is shown here as the inner and outer shear
layers are most clearly distinguished from each other.
120deg
1
r/D
0.5
0
-0.5
-1
0
0.5
1
x/D
180deg
1.5
0.5
1
x/D
240deg
1.5
0.5
1
x/D
1.5
1
0.5
r/D
0deg
0
1
-0.5
0.5
r/D
-1
0
0
-0.5
-1
1
0.5
1
x/D
60deg
1.5
0.5
r/D
0
0
1
-0.5
0.5
r/D
-1
0
0
-0.5
-1
0
0.5
1
x/D
1.5
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Copyright © 2010 by ASME
300deg
1
r/D
0.5
0
-0.5
-1
0
0.5
1
x/D
1.5
Figure 8. Harmonically reconstructed velocity and
vorticity field for fo=400 Hz out-of-phase acoustic forcing,
non-reacting flow at Uo=40 m/s bulk velocity. The solid
vorticity isocontours is at Uo/(r2-r1)=-0.1 and the dotted
vorticity isocontours is at 0.1.
Several physical processes are evident over the six phases
pictured here. First, transverse fluctuation of the flow is
dominant from approximately one diameter downstream to the
end of the frame. Second, transverse flapping of the jet region
is evident. Finally, the unsteady formation and downstream
convection of vorticity is present. The unsteady vorticity is
generated in the two annular shear layers and rolls up into
larger structures in the separating wakes associated with the
inner and outer recirculation zones. While two counter-rotating
structures are clearly evident at the annular slot exit, see Figure
8 at 0 degrees, they subsequently merge farther downstream to
form a single structure that is located in the jet core, see Figure
8 at 120 degrees. Note that this merging process occurs
between staggered vorticity whose vorticity direction is the
same.
To illustrate these points further, each of these fluctuating
components, the vorticity, the axial velocity, and the transverse
velocity, are plotted separately. Figure 9, Figure 10, and Figure
11 show the harmonically reconstructed vorticity, axial
velocity, and transverse velocity disturbances across several
phases of the acoustic cycle.
In the first vorticity image, a positive vorticity fluctuation
is evident at the nozzle exit. The fluctuation location can be
seen by the black arrows in the 0 degrees figure. Prior
disturbances that were created at the nozzle base and convected
downstream are still noticeable at a downstream location of 1
diameter.
In the third image, 120 degrees, these disturbances have
convected downstream a distance of approximately 0.5
diameters. The inner and outer vorticity disturbances merge in
the jet core and then continue to travel downstream with the jet.
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Copyright © 2010 by ASME
disturbance in one shear layer is out of phase with that of the
adjoining shear layer. These disturbances, induced by the
coalesced vorticity disturbances in the jet core seen above, also
convect downstream.
Figure 9. Harmonically reconstructed vorticity fluctuations
for fo=400 Hz out-of-phase acoustic forcing, non-reacting
flow at Uo=40 m/s bulk velocity.
The arrows in Figure 10 point to the coherent axial
velocity fluctuations in the shear layers. Note that the axial
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Copyright © 2010 by ASME
direction manifests itself in the jets, as seen by the black
arrows. These also travel downstream with the vortex. This
fluctuation is superposed on the bulk fluctuation due to the
transverse acoustic excitation.
Figure 10. Harmonically reconstructed axial velocity
fluctuations for fo=400 Hz out-of-phase acoustic forcing,
non-reacting flow at Uo=40 m/s bulk velocity.
Finally, the coherent transverse velocity disturbances are
shown. The vorticity induced disturbance in the transverse
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Copyright © 2010 by ASME
and induce a dominantly axial motion in the shear layer and a
dominantly transverse motion in the jet core. Also evident
from these plots is that the motions in adjacent shear layers
oscillate out-of-phase with each other. As the axial velocity
disturbance in the inner left shear layer rises at 0 degrees, it
falls in the inner right shear layer. Furthermore, the motions on
the left side of the annulus are out-of-phase with those on the
right side. As will be explained in the context of Figure 5, this
is apparently due to the 180 degree phase change of the
pressure (note that the centerline is a pressure node for the out
of phase acoustic forcing), a feature that will be discussed later.
The vortex also induces a transverse motion along the jet
core, which is superposed with the periodic transverse acoustic
motion that can be seen as the rise, fall, and downstream
convection of the transverse surface throughout the series of
plots. These effects can be seen quantitatively in Figure 12,
Figure 13, and Figure 14, where the magnitude of the
harmonically reconstructed vorticity, axial velocity, and
transverse velocity fluctuations from the surfaces above are
plotted along the jet and shear layer centerlines.
Figure 12 shows the fluctuation of coherent vorticity along
the jet centers. The top subplot shows the left jet, and the
bottom subplot shows the right jet. Although vorticity
originates in the shear layers, it subsequently rolls up into
larger structures in the separating wake zones that, in turn,
merge farther downstream. This merged structure appears to be
located in the jet core.
The top subplot of Figure 13 shows the motion of the
coherent axial velocity at several different phases of the cycle
in the outer left shear layer, indicated by the leftmost arrow in
Figure 10. For example, at 0 degrees in Figure 13 (solid blue
line), the maximum disturbance amplitude is at a downstream
distance of 0.2. After 115 degrees of the cycle (solid red line)
this disturbance has convected and is now at a downstream
distance of 0.6.
The bottom portion of this figure compares the shape and
amplitude of the disturbance at 0 degrees in all four shear
layers. It is evident, again from Figure 13, that the outer left
shear layer and the outer right shear layer have similar
disturbance amplitudes, but are out-of-phase, as was shown in
Figure 10.
Figure 11. Harmonically reconstructed transverse
velocity fluctuations for fo=400 Hz out-of-phase acoustic
forcing, non-reacting flow at Uo=40 m/s bulk velocity.
The two types of disturbances are clearly seen in these
surface plots. Vortical disturbances originate at the nozzle exit,
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Copyright © 2010 by ASME
Figure 12. Harmonically reconstructed vorticity
fluctuations along the left jet across several phases (top),
and right jet across several phases (bottom) for fo=400 Hz
out-of-phase acoustic forcing, non-reacting flow at Uo=40
m/s bulk velocity.
Figure 14. Harmonically reconstructed transverse
velocity fluctuations along the left jet (top), and right jet
(bottom) across several phases for fo=400 Hz out-ofphase acoustic forcing, non-reacting flow at Uo=40 m/s
bulk velocity.
Several important physical mechanisms can be deduced
from these series of plots. First, there is a bulk transverse
motion, which is associated with the acoustic field. Second, the
downstream convection of the vortical motion is evident.
Third, the movement in the adjacent shear layers is out-ofphase in the out of phase forcing case. For example, the inner
left shear layer and the inner right shear layer disturbances are
out-of-phase for the axial velocity fluctuations, particularly in
the region of 0 to 10 mm downstream. The opposite, in-phase,
behavior is also present for the in phase forcing cases, as seen
in Figure 15 and Figure 16. In this case, the coherent vorticity
disturbances convecting in the jet cores have different signs,
inducing opposite phase relations between the axial velocities
in the adjacent shear layers, as well as the transverse velocities
in the jet cores, which are not shown here.
Figure 13. Harmonically reconstructed axial velocity
fluctuations along the outer left shear layer across several
phases (top), and across all four shear layers at 0
degrees (bottom) for fo=400 Hz out-of-phase acoustic
forcing, non-reacting flow at Uo=40 m/s bulk velocity.
Figure 14 shows the coherent transverse velocity. The top
subplot shows the left jet, and the bottom subplot shows the
right jet.
Again, disturbances can be seen convecting
downstream, as in Figure 11 above. For example, the 0 degree
line (solid blue) has a minimum value at a downstream value of
0.4, and this disturbance can be seen again at 115 degrees (solid
red) at a location of 0.8.
Figure 15. Harmonically reconstructed vorticity
fluctuations along the left jet across several phases (top),
and right jet across several phases (bottom) for fo=400 Hz
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in-phase acoustic forcing, non-reacting flow at Uo=10 m/s
bulk velocity.
Figure 16. Harmonically reconstructed axial velocity
fluctuations along the outer left shear layer across several
phases (top), and across all four shear layers at 0
degrees (bottom) for fo=400 Hz in-phase acoustic forcing,
non-reacting flow at Uo=10 m/s bulk velocity.
centerline of the annulus. The out-of-phase acoustic forcing
creates a velocity anti-node at the centerline of the combustor
and a pressure node, causing the pressure on either side of the
centerline to oscillate out-of-phase, see Figure 5. Conversely,
in-phase forcing creates a pressure anti-node and a velocity
node, as also shown in Figure 5. The oscillating pressure field
over the nozzle exit creates fluctuations in mass flow through
the nozzle, which is manifested in fluctuations in the strength
of the shear layer. The mass flow fluctuations on either side of
the nozzle are approximately out-of-phase when the acoustic
forcing is out-of-phase. Conversely, the mass flow on either
side of the nozzle is in-phase when the acoustic forcing is inphase. These mass flux conditions correlate with the phase of
the pressure on either side of the nozzle. Mass flow
fluctuations lead to vorticity fluctuations at the corner of the
nozzles, as seen at the very first upstream locations. The
vorticity, initially out-of-phase and located at the nozzle edges,
convects downstream and merges in the jet. This merged
structure induces the out-of-phase axial velocity fluctuations in
the shear layer and the convecting transverse velocity
fluctuations in the jet cores. The process described here is
summarized in Figure 18 for the out-of-phase forcing case.
These results do not change significantly with a flame
present. To illustrate this point, the phase resolved motion of
the vorticity disturbances is shown in Figure 17. The key
difference appears to be a much longer lasting vortical
disturbance, particularly in the left jet.
v’
vˆ '
uˆ '
p’
ωˆ '
m'
Figure 17. Harmonically reconstructed vorticity
fluctuations along the outer left shear layer across several
phases (top), and across all four shear layers at 0
degrees (bottom) for fo=400 Hz out-of-phase acoustic
forcing, reacting flow at Uo=10 m/s bulk velocity.
The comparison of axial velocity between the four shear
layers for the in phase forcing shows that this forcing
configuration causes in-phase fluctuations between adjacent
shear layers. This difference in shear layer response is
apparently due to the different acoustic conditions at the
Figure 18. Instantaneous snapshot of fluctuations in out
of phase acoustic forcing case, with an acoustic velocity
maximum, acoustic pressure node, asymmetric mass
flow fluctuations, asymmetric vorticity fluctuations,
asymmetric axial velocity fluctuations, and unidirectional
transverse velocity fluctuations.
These trends are further illustrated in Figure 19 and Figure
20, where the average axial velocity in the left half of the
annulus, right half of the annulus, and overall average is
compared with the pressure fluctuations on either side of the
nozzle.
12
Copyright © 2010 by ASME
Left
Right
Total
u`/u o
1
0
-1
0
2
4
6
8
10
p`/p o
t*fo
0.04
0.02
0
-0.02
-0.04
0
Left
Right
2
4
6
8
10
t*fo
Figure 19. Spatially averaged axial velocity and pressure
fluctuations at the nozzle exit for fo=400 Hz out-of-phase
acoustic forcing at Uo=10 m/s non-reacting flow.
Left
Right
Total
u`/u o
1
0
-1
0
2
4
6
8
10
p`/p o
t*fo
0.04
0.02
0
-0.02
-0.04
0
Left
Right
2
4
6
8
10
t*fo
Figure 20. Spatially averaged axial velocity and pressure
fluctuations at the nozzle exit for fo=400 Hz in-phase
acoustic forcing at Uo=10 m/s non-reacting flow.
The phase between the axial velocities and pressures
shown in Figure 19 and Figure 20 was calculated from their
Fourier transform at f = fo. The estimated uncertainty in these
values is 15 degrees. The phase between the pressure on either
side of the nozzle for out-of-phase acoustic forcing is 120
degrees, and for in-phase forcing is -65 degrees. The phase
between the spatially averaged axial velocity on either side of
the nozzle for out-of-phase forcing is 220 degrees, and for inphase forcing is -5 degrees. These phases show that the
acoustic forcing has a significant impact on the characteristics
of the disturbance field. If the left and right sides of the burner
annulus were acoustically isolated from each other, we would
expect these phases to be 0 and 180 degrees. However,
because the left and right sides of the annulus are in acoustic
communication with each other, which presumably would tend
to equalize the pressure, these values differ from the “ideal”
values of 0 and 180 degrees. The phase of the pressure field in
the downstream half of the viewing window, away from the
nozzle, is -175 degrees in the out-of-phase acoustic forcing
case, and -1 degrees in the in-phase acoustic forcing case.
The magnitudes of the average axial velocities between inphase and out-of-phase forcing are very similar, despite being
out-of-phase. The acoustic forcing amplitudes in both cases is
relatively constant and as such, the fluctuation amplitudes are
similar. This is not the case, however, in the average transverse
velocity. The out-of-phase forcing situation creates a highamplitude sinusoidal velocity signal, while the average
transverse velocity in the in-phase forcing case is much weaker,
as shown in Figure 6.
The flame is susceptible to this multi-dimensional
disturbance field because of the stabilization of the flame in
shear layers.
The base of the flame experiences the
longitudinal velocity fluctuations that are dominant in the shear
layer as well as the vortex rollup and convection also present in
the jet. Downstream, though, the flame is subject to the high
amplitude transverse motion that dominates in the far field.
CONCLUDING REMARKS
In this work, we have analyzed the multi-dimensional
disturbance field caused by transverse acoustic excitation of a
premixed, swirl-stabilized flame. Both non-reacting and
reacting experiments were used to gain insight into the
complicated disturbance field. The following conclusions can
be drawn from this work.
1.
Transversely excited flames are excited by a
superposition of acoustic and vortical disturbances,
including direct transverse acoustic excitation,
longitudinal acoustic excitation, as well as
excitation of fluid mechanic instabilities sensitive
to both longitudinal and transverse flow
perturbations.
2.
Different disturbance mechanisms manifest
themselves in different portions of the flow. Axial
velocity fluctuations are dominant in the shear
layers, while vorticity fluctuations and transverse
velocity fluctuations are dominant in the jet core.
3.
Transverse acoustic excitation leads to a multidimensional velocity disturbance field.
The
velocity fluctuations near the base of the flame are
multi-directional, while the velocity fluctuations
near the tip of the flame are almost completely
transverse.
Future work will include tracking of the flame edge and
vortex motion with simultaneous chemiluminescence
measurements. These measurements will allow for correlation
between vortex motion, flame disturbance, and heat release
fluctuations.
ACKNOWLEDGMENTS
This work has been partially supported by the US
Department of Energy under contracts DEFG26-07NT43069
13
Copyright © 2010 by ASME
and DE-NT0005054, contract monitors Mark Freeman and
Richard Wenglarz, respectively.
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