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Stability limits and non-linear characteristics of a self-excited combustion instability

Conference Paper

Stability limits and non-linear characteristics of a self-excited combustion instability

Abstract and Figures

Self-excited combustion instabilities of a bluff-body-stabilized premixed flame are investigated. The burner is situated in a duct of rectangular cross-section with closed/open acoustic boundary conditions, representing a quarter-wave acoustic resonator. Fuel gas (methane) is injected through small holes a short distance upstream of the flame, such that it burns in partially premixed mode. Operating points (i.e. thermal power and equivalence ratio) where instability occurs are identified. Variation of amplitude and frequency while operating conditions are changed are discussed for the dominant mode of oscillation, as well as its second and third harmonic. For certain operating points, the harmonics of the first mode seem to couple with higher independent modes. Pressure oscillations during limit cycle operation for one constant operating point are measured along the combustor length. The shape and amplitude of several independent thermo-acoustic modes, as well as the most significant higher harmonics, are reconstructed, identified and interpreted in relation to the combustor geometry. The phase shift between pressure variation at the flame and heat release (Rayleigh index) is discussed for the independent modes, as well as the higher harmonics.
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STABILITY LIMITS AND NON-LINEAR CHARACTERIST-
ICS OF A SELF-EXCITED COMBUSTION INSTABILITY
Roel A. J. Müller, Jakob Hermann
IfTA Ingenieurbüro für Thermoakustik GmbH, 82194 Gröbenzell, Germany, www.ifta.com
Wolfgang Polifke
Lehrstuhl für Thermodynamik, Technische Universität München, 85747 Garching, Germany
Self-excited combustion instabilities of a bluff-body-stabilized premixed flame are investigated.
The burner is situated in a duct of rectangular cross-section with closed/open acoustic boundary
conditions, representing a quarter-wave acoustic resonator. Fuel gas (methane) is injected
through small holes a short distance upstream of the flame, such that it burns in partially
premixed mode. Operating points (i.e. thermal power and equivalence ratio) where instability
occurs are identified. Variation of amplitude and frequency while operating conditions are
changed are discussed for the dominant mode of oscillation, as well as its second and third
harmonic. For certain operating points, the harmonics of the first mode seem to couple with
higher independent modes.
Pressure oscillations during limit cycle operation for one constant operating point are measured
along the combustor length. The shape and amplitude of several independent thermo-acoustic
modes, as well as the most significant higher harmonics, are reconstructed, identified and
interpreted in relation to the combustor geometry. The phase shift between pressure variation at
the flame and heat release (Rayleigh index) is discussed for the independent modes, as well as
the higher harmonics.
1. Introduction
The EU-funded Marie Curie research project LIMOUSINE (
Lim
it cycles of thermo-ac
ous
tic
oscillations in gas turb
ine
combustors) aims to strengthen the fundamental scientific work in the field
of thermo-acoustic instabilities in combustion systems. A bluff-body-stabilised, partially premixed test
combustor was built to provide experimental data for validation of numerical and analytical results.
This paper presents the combustion instabilities as they occur in this test combustor.
Operating points (thermal power
P
th
and equivalence ratio
Φ
) where instability occurs are
identified and discussed. During limit cycle operation, the pressure amplitude of the dominant
oscillation, as well as its higher harmonics, are recorded. For a reference operation point (
P
th
= 40kW
and
Φ = 0.7
), the pressure signal was measured along the length of the combustor. Pressure profiles
were reconstructed from these measurements. The following mode shapes are identified: the first
thermo-acoustic mode, which is the dominant oscillation (
I,1
), its second and third harmonic (
I,2
and
I,3
)
and the next two independent modes (
II,1
and
III,1
). These mode shapes are discussed, as well as their
phase shift compared to the heat release represented by the OH* chemiluminescence signal from the
flame.
ICSV19, Vilnius, Lithuania, July 8–12, 2012 1
19
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International Congress on Sound and Vibration, Vilnius, Lithuania, July 8–12, 2012
2. Set-up
2.1 Combustor
Fig. 1 gives an overview of the LIMOUSINE combustor as installed at IfTA GmbH. The burner
is situated in a duct of rectangular cross-section with closed/open acoustic boundary conditions,
approximating a quarter-wave acoustic resonator. The rectangular cross section with relatively large
aspect ratio leads to an approximately 2-D flow in the x,y plane.
50
40
25
x = 0
-272
-227
+780
-50
-100
-200
50
100
200
250
750
133
B
C
-150
Flow direction
300
350
700
400
450
500
550
600
650
(a) Cross section of the combus-
tor: inner dimensions (in mm)
on the left, locations of holes for
sensor access on the right
Detail C
8
2
4×11×
1
3
Detail B
1
14
2
× 31×
7
19
Flame
holder
Combustion
chamber
Plenum
3
x
y z
(b) Details of flame holder (above) and air inlet
(below)
(c) The combustor as in-
stalled in the laboratory at
IfTA
Figure 1. Overview of the combustor with coordinate axes. The origin of x is the top of the flame holder. The
inner width of the duct in z direction is 150mm.
Air enters the bottom of the combustor at the front and at the back through choked orifices, which
guarantees an acoustically hard boundary condition, after which perforated tubes distribute the air
along the span (
z
direction) of the combustor. The prismatic flame holder, triangular in cross section,
rests at about one quarter of the height of the combustor. The fuel gas (methane) is also passed through
orifice plates and injected through 62 holes along the flame holder. A partially premixed flame forms,
stabilised at the top of the flame holder, where quartz glass windows on three sides provide optical
access to the flame. The window in the front wall is replaced by a steel plate to allow mounting of
acoustic sensors here as well.
There are holes along the length of the front combustor wall for sensor access, which are usually
closed. The holes are placed at
50mm
intervals where space allows. In the vicinity of the flame holder
the holes deviate from this pattern for constructional reasons. A Photo Multiplier Tube (PMT) views
the flame along z direction from the back.
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19
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International Congress on Sound and Vibration, Vilnius, Lithuania, July 8–12, 2012
2.2 Measurement equipment
2.2.1 Pressure sensors
Two sensors, PCB Model 106B50, have been used during this measurement. Throughout the
experiments, water-cooled sensor adaptors were used to protect the sensors against the high combustor
wall temperature. Before the measurement on the combustor, the difference in frequency response
between the sensors was determined in phase and amplitude. For
f < 500 Hz
the sensor signals differ
less than one per cent. The data presented for the mode shapes are compensated for this difference in
sensor response.
2.2.2 Photo Multiplier Tube (PMT)
A PMT measured the overall OH* chemiluminescence of the flame from the back of the
combustor. The phase shift between this signal and the local pressure is used as a qualitative measure
of the modal Rayleigh index
Ri( f ) = R
ˆp( f ) ˆq ( f )
. If
Ri( f ) > 0
, the flame acts as an acoustic
source at frequency
f
. The heat release rate in the frequency domain
ˆq( f )
is represented by the PMT
signal. ˆq( f )
denotes its complex conjugate.
1,2
2.2.3 Frequency domain and correlation analysis
IfTAs Argus Oscillation Monitoring and Diagnostics System (OMDS) recorded the various
signals with a sampling frequency of
5120Hz
. The signals of the sensors are cut in segments of
0.2s
with an overlap of
50%
. After application of a Blackman window, the signal is transformed into
the frequency domain using a Fast Fourier Transform (FFT). Here, the sign of the phase is defined
such that a positive phase shift corresponds to a shift ahead in time. Auto- and cross power spectral
density are computed and averaged over 200 of these cycles according to Welchs method.
3
One such
measurement takes
20s
, and delivers a spectrum for
f [0, 2000]Hz
. Based on the Auto Spectral
Density (
ASD R
) and Cross Spectral Density (
CSD C
) of two arbitrary signals
X
and
Y
, Argus
OMDS delivers amongst others:
An over-prediction of the transfer function
4
from X to Y : TF
+
X,Y
=
ASD
Y
CSD
X,Y
An under-prediction of the transfer function from X to Y : TF
X,Y
=
CSD
X,Y
ASD
X
The coherence between both signals: Coh
X,Y
=
|
CSD
X,Y
|
2
ASD
X
ASD
Y
=
TF
X,Y
TF
+
X,Y
Amplitude and frequency of the dominant oscillation within set frequency bands, both of which
are compensated to overcome the usual frequency resolution restriction (“picket fence effect”)
of the FFT.
3. Stability depending on operating conditions
3.1 Method
For these measurements, a sensor was located at
x = 100 mm
. Measurement at this position
does not require a cooling adapter, which makes comparative measurements on other burners easier.
For three (fixed) fuel flow rates, the equivalence ratio
Φ
was varied
(0.5 < Φ < 1)
by increasing and
subsequently decreasing the air flow rate. The combustor had been running before the start of the
experiment, and the operating conditions were changed slowly (around
2min
between
Φ = 1
and
Φ = 0.5) to reduce the effects of transient cooling and heating of the structure.
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19
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International Congress on Sound and Vibration, Vilnius, Lithuania, July 8–12, 2012
3.2 Results
Fig. 2 gives an overview of the amplitude and frequency of the fundamental pressure oscillation in
the combustor for three discrete values of the thermal power
P
th
, while the equivalence ratio decreases
and subsequently increases. The edge colour of the markers indicate the thermal power, the marker
orientation and filling differentiate between increasing or decreasing equivalence ratio. Generally, for
a given equivalence ratio, higher power will lead to a higher amplitude and higher frequency. There is
a difference in amplitude and frequency between the oscillation during decreasing and increasing
Φ
.
Possible causes are path dependence (hysteresis) of the flame stability state, but also transient heating
of the combustor.
5,6
The heat capacity of the combustor causes the temperature to react slowly to the
operating conditions, which Subsection 4 will discuss as well.
Φ []
|
ˆp
I,1
|
[Hz]
I: incr. Φ, C: decr. Φ
20, 30, 40 kW
Φ []
f
I,1
[Hz]
I: incr. Φ, C: decr. Φ
20, 30, 40 kW
Figure 2. Amplitude
|
ˆp
I,1
|
(left) and frequency f
I,1
(right) of the dominant mode for various thermal powers,
plotted against equivalence ratio. Sensor location: x = 100 mm.
The combustion is stable at lower equivalence ratios. For all but the lowest thermal powers,
the transition from stable to unstable combustion, or vice versa, takes place very abruptly
( 0.1 s)
between
Φ = 0.5
and
0.6
. As a result, the left side of Fig. 2 shows just a few points between 1000
and
2000Pa
. Between
Φ = 0.6
and 0.7 the amplitude remains approximately constant. For higher
equivalence ratios there is again a trend to higher amplitudes. In the case of
P
th
= 40kW
more than
5000Pa
are reached. For
P
th
= 20 kW
, the transition between stable and unstable combustion or vice
versa, is much smoother. There is no trend to higher amplitudes near Φ = 1.
The dominant frequency
f
I,1
depends on thermal power, where higher power leads to higher
frequency due to a higher temperature of combustion products. The dependence on
Φ
is not monotonic,
with a maximum around
Φ = 0.8
. For lower values of
Φ
, the excess air reduces the adiabatic flame
temperature, leading to a lower speed of sound. For
Φ > 0.8
slow mixing could cause a lower
temperature in the flame region.
3.2.1 Increasing versus decreasing equivalence ratio Φ
Fig. 3 shows two intensity plots, showing the influence of the equivalence ratio
Φ
on the spectrum
of the pressure signal at
x = 100 mm
for
P
th
= 40kW
. The transition between stable oscillation and
limit cycle is seen as a sharp line near the bottom of both plots, at
Φ 0.56
and
Φ 0.60
respectively.
Again, path dependence (hysteresis) of the flame stability state as well as transient heating of the
combustor could cause this difference. Both effects were observed on the LIMOUSINE combustor.
Besides the
Φ
-dependent curves, there are two straight vertical lines in Fig. 3, around
570Hz
and
680Hz
respectively. Their apparent temperature-independence suggests these modes are structural, or
originate in cold sections of the set-up. Subsection 4 corresponds to a mode at
672Hz
whose pressure
profile describes half a wave in the (cold) plenum, which likely causes this peak. Altunlu et al.
7
mention a structural mode at 673Hz as well, but none near 570Hz.
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19
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International Congress on Sound and Vibration, Vilnius, Lithuania, July 8–12, 2012
f [Hz]
Φ []
|
ˆp
|
[Pa]
f [Hz]
Φ []
|
ˆp
|
[Pa]
Figure 3. Spectral intensity for changing equivalence ratio, at P
th
= 40kW. Decreasing Φ on the left,
increasing Φ on the right. Sensor location: x = 100 mm.
3.2.2 Relative amplitudes of the higher harmonics
Besides the fundamental frequency, the higher harmonics of the dominant oscillation mode
are clearly visible as an equidistant array of peaks. Looking at the raw time signal of the pressure
fluctuation, these higher harmonics are (for most operating points) phase-locked to the fundamental
oscillation, leading to a relatively constant wave form over time.
The amplitudes of the first two harmonics, relative to the fundamental amplitude,
|
ˆp
I,2
|
|
ˆp
I,1
|
and
|
ˆp
I,3
|
|
ˆp
I,1
|
respectively, are shown in Fig. 4. As these plots show, the first harmonic is rather
small in amplitude, while the second harmonic can reach significant amplitudes. It tends to be stronger
at higher equivalence ratios, but depending on thermal power, the exact location of the peak varies
without obvious trend.
Φ []
|
ˆp
I,2
|
|
ˆp
I,1
|
I: incr. Φ, C: decr. Φ
20, 30, 40 kW
Φ []
|
ˆp
I,3
|
|
ˆp
I,1
|
I: incr. Φ, C: decr. Φ
20, 30, 40 kW
Figure 4. Relative amplitude of the second (I,2 left) and third (I,3 right) harmonic of the first mode for various
powers plotted against equivalence ratio. Sensor location: x = 100mm.
Plotting the relative amplitudes of the harmonics against their respective frequencies on the
other hand, does show a clear trend. Irrespective of thermal power, the higher harmonics are stronger
when their frequency is either close to
570Hz
or
680Hz
. These are the same frequencies as noted in
Subsection 3.2.1 and do not depend on the operating point.
Since proximity to these two frequencies has such a strong influence on the amplitudes of the
higher harmonics, it is hard to identify other influences, such as those of thermal power or equivalence
ratio.
4. Pressure profiles
4.1 Method
The measurements described in this section were conducted at the operating point of
P
th
= 40kW
and
Φ = 0.74
. Before the measurements started, the combustor had been running at constant operating
conditions for
10min
to reduce the effect of transient heating. One pressure sensor was positioned
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19
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International Congress on Sound and Vibration, Vilnius, Lithuania, July 8–12, 2012
f
I,2
[Hz]
|
ˆp
I,2
|
|
ˆp
I,1
|
I: incr. Φ, C: decr. Φ
20, 30, 40 kW
f
I,3
[Hz]
|
ˆp
I,3
|
|
ˆp
I,1
|
[]
I: incr. Φ, C: decr. Φ
20, 30, 40 kW
Figure 5. Relative amplitude of the second (I,2 left) and third (I,3 right) harmonic of the first mode for various
powers plotted against frequency. Sensor location: x = 100 mm.
at the most upstream hole (
x
ref
= 200 mm
) while the other one traversed along the length of the
combustor (going downstream along the combustion chamber first, followed by the plenum). To
construct the pressure profiles in the LIMOUSINE combustor, the correlation quantities as described in
Subsection 2.2.3 were calculated in real time by the Argus OMDS, following the method of Hermann
8
.
4.2 Results
Fig. 6 gives an overview of the pressure fluctuation against position and frequency
p( f ,x)
. The
plotted intensity shows the square root of the ASD of the pressure signal per sensor access hole, which
is the
L
2
norm (averaged over the analysis segments) of the absolute value of the Fourier transformed
pressure signal. The signal is clipped between
1
and
100Pa
to adequately show the weaker resonances.
f [Hz]
x [mm]
p
ASD
p
|
ˆp
|
[Pa]
I,1 II,1 I,2 III,1 I,3 I,4 I,5 I,6
I,7
Figure 6.
p
ASD
p
( f ,x), which is the L
2
norm of the Fourier transformed pressure signal, per frequency bin,
averaged over 200 cycles.
4
The plot gives an overview of the amplitude of the pressure fluctuation as a function
of frequency and position at the operating conditions P
th
= 40kW and Φ = 0.74.
The plot shows two phenomena clearly. Firstly, vertical bright lines show the resonant frequencies.
Drift in temperature during the experiments deforms these lines, especially at higher frequencies.
Secondly, there is a pressure node at the outlet, and at integer half wavelengths upstream of the inlet.
These are seen as hyperbolic blue bands. There should be a pressure anti-node at the inlet, though
there are not enough measurement points to show this clearly. At a quarter wave length (plus an integer
of half wave lengths) downstream of the inlet there are pressure nodes as well.
Fig. 7 shows
p
ASD
p
( f )
measured at the reference sensor at
x = 200mm
, both at start and end
of the experiment. The dominant peaks are harmonics of the first mode. Contrary to the behaviour at
x = 100 mm
, discussed in Section 3, at the current position the amplitude of the second harmonic
ˆp
I,2
is higher than the third,
ˆp
I,3
. The frequency of the second mode of oscillation
II,1
is hard to pin-point,
since it is so close to
f
I,1
. The third mode of oscillation
III,1
is seen as a separate peak between the first
and second harmonic (I,2 and I,3) of the dominant mode.
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19
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International Congress on Sound and Vibration, Vilnius, Lithuania, July 8–12, 2012
4.2.1 Pressure profiles
f [Hz]
|
ˆp
|
[Hz]
x [mm]
|
ˆp
I,1
|
[Pa]arg ˆp
I,1
[]
Figure 7. Left: Pressure spectrum
p
ASD( f ) at the first and last analysis run of the experiment (around 10
respectively 30 minutes after ignition of the combustor). Peaks corresponding to the mode shapes plotted in the
following figures are indicated. Sensor location:
x = 200mm
. Right: Pressure profile of the dominant mode of
oscillation, I,1 of the LIMOUSINE combustor at P
th
= 40kW and Φ = 0.74.
The pressure profiles are presented in the form of amplitude and phase plots, based on the
correlation data as discussed in Subsection 2.2.3. The amplitude at
x
ref
= 200 mm
is based on
the average between the peaks of the two spectra in Fig. 7. At the other positions the amplitude is
determined via the transfer functions calculated by the Argus OMDS. Red dots indicate the estimated
transfer function
TF
=
TF
TF
+
, while the range between
TF
and
TF
+
is shaded. The phase
plots show the pressure signal as red dots, relative to OH* chemiluminescence indicated by a plus.
The
1
/4
wave pressure profile of the dominant mode of oscillation is shown on the right in Fig. 7.
The discontinuity in cross section at the flame holder and the acoustic effect of the flame cause a
cusp in the profile. The OH* signal has a small phase shift compared to pressure, indicating the
thermo-acoustic interaction of the flame with the dominant mode generates fluctuation energy, in
agreement with the Rayleigh index (
Ri
I,1
> 0
). Fig. 8 shows the profiles associated with the second and
third harmonic of the dominant mode. Both profiles show standing waves obeying the zero pressure
fluctuation boundary condition around
x = 800 mm
, i.e. near 0.3 times the hydraulic diameter behind
the outlet.
9
The profile shape in the upstream section and the behaviour at the flame holder, are harder
to interpret. The phase between OH* signal and pressure is more than
π
/2
, which indicates that these
harmonics, although forced by higher-order, harmonic components of the non-linear flame response,
dissipate fluctuation energy due to their negative modal Rayleigh indices Ri
I,2
< 0 and Ri
I,3
< 0.
x [mm]
|
ˆp
I,2
|
[Pa]arg ˆp
I,2
[]
x [mm]
|
ˆp
I,3
|
[Pa]arg ˆp
I,3
[]
Figure 8.
Pressure profile of the second and third harmonic of the first mode (
I,2
on the left and
I,3
on the right)
of the LIMOUSINE combustor at P
th
= 40kW and Φ = 0.74.
The geometry of the combustor suggests the existence of
3
/4
wave,
5
/4
wave and higher modes
as well. A profile reminiscent of
3
/4
wave is found around
f
II,1
380Hz
. At
x = 200 mm
its peak
is hidden by spectral leakage of the dominant oscillation, but at locations further downstream it is
seen more clearly. This mode is shown on the left in Fig. 9. For this mode, there is a pressure node
7
19
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International Congress on Sound and Vibration, Vilnius, Lithuania, July 8–12, 2012
close to the location of the flame, which might explain why this mode has such a low amplitude. Also,
the pressure node at the flame holder means a velocity anti-node. The energy of this mode is likely
dissipated efficiently by aerodynamic resistance of the bluff body flame holder.
x [mm]
|
ˆp
II,1
|
[Pa]
arg ˆp
II,1
[]
x [mm]
|
ˆp
III,1
|
[Pa]arg ˆp
III,1
[]
Figure 9. Pressure profiles of the second and third fundamental mode. II,1:
3
/4 wave on the left and III,1:
5
/4
wave on the right. P
th
= 40kW and Φ = 0.74.
The
5
/4
wave mode
f
III,1
, discussed by Tufano et al.
10
, has its peak around
670Hz
. The profile,
on the right in Fig. 9, shows a pressure anti-node, and therefore a velocity node at the flame holder.
Following the reasoning before, the relatively high amplitude of this mode seems reasonable. For II,1
and especially
III,3
, the phase shift between the OH* and pressure signals is small again, indicating a
positive Rayleigh index for these frequencies; Ri
II,1
> 0 and Ri
III,1
> 0.
5. Conclusion
Self-excited combustion instabilities of the LIMOUSINE combustor were investigated. The
pressure profiles associated with the dominant oscillation, its second and third harmonic, and of
two higher independent modes are measured, identified and discussed. The relative strength of the
individual modes can be explained by the geometry of the combustor. The higher harmonics of the
first mode are far stronger than those of the following modes. The strength of the third harmonic of the
first mode is assumed to be influenced by coupling with the
5
/4 wave mode.
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... The mode shapes found in this way, are presented in Figs. 3 and 4 in comparison to the mode shapes found in experiment 15 . Phase is defined to be zero at the peak in the heat release, or experimentally at the peak in the OH* chemiluminescence signal. ...
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