[american institute of aeronautics and astronautics 45th aiaa/asme/sae/asee joint propulsion...

Optical Transfer Function Measurements for a Swirl

Burner at Atmospheric Pressure

D. Guyot∗ and Christian Oliver Paschereit†

Institute of Fluid Dynamics and Engineering Acoustics

Technische Universitat Berlin, 10623 Berlin, Germany

Thermoacoustic transfer functions of a generic swirl-stabilized gas turbine burner havebeen measured at atmospheric conditions. Loudspeakers were employed for the acousticexcitation of the combustion test rig. Arrays of condenser microphones have been usedto record the acoustic response of the system to this excitation. The flame’s OH∗, CH∗

and CO2∗ chemiluminescence response was measured by four photomultiplier tubes. ToIn addition, a light spectrometer recorded the light spectrum emitted by the flame and anICCD camera monitored the flame’s location in the combustion chamber.

The thermoacoustic transfer function has been obtained by three different techniques:A widely used purely acoustic technique has been employed to obtain the burner andflame transfer matrix. This technique makes use of the well-established multi-microphonemethod to determine the response of acoustic pressure and velocity in the combustion testrig to acoustic excitation. Based on the acoustic burner and flame transfer matrices theflame transfer function was obtained.

In addition, two combined acoustic-optical techniques have been used for the determi-nation of the flame transfer function. These techniques evaluate the response of the OH∗

(CW 308nm), CH∗ (CW 431nm) and CO2∗ (CW 408nm and 451nm) chemiluminescenceof the flame to the acoustic excitation in order to estimate the flame’s heat release fluc-tuations. Since fluctuations in the flame’s heat release have generally two contributions,e.g., fluctuations in mixture mass flow and equivalence ratio, at least two optical signals arerequired to obtain the flame’s heat release fluctuation. In the ’direct’ optical approach theflame’s heat release fluctuations are estimated based on the four measured photomultiplierintensities. In the ’CH/OH’ approach ratio of CH∗ and OH∗ chemiluminescence servesas one optical signal while also scaling with the equivalence ratio of the flame within theinvestigated operating range.

The transfer function results obtained by the purely acoustic and the two acoustic-optical techniques are presented and compared and the benefits and limitations of thethree method are discussed.

Nomenclature

A cross-sectional areaAf flame areaB burner transfer matrixC transfer matrix, relates chemiluminescence intensity to burner operating conditionsCW center wavelengthF flame transfer matrixF flame transfer functionH transfer function relating acoustic velocity across flameHf chemical enthalpyI chemiluminesence intensity

∗PhD student†Professor

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American Institute of Aeronautics and Astronautics

45th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit2 - 5 August 2009, Denver, Colorado

AIAA 2009-5413

Copyright © 2009 by the authors. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

Iλ spectral chemiluminesence intensityLred reduced lengthM Mach numberPFS premix fuel splitQ heat release rateR ideal gas constantSf flame speedT transfer matrixT temperatureTr transmissionc speed of soundclight speed of light in vacuum, clight = 299, 792, 458 m

sf, g Riemann invariantshp Planck constant, hP = 6.62607095 · 10−34 J skB Boltzmann constant, kB = 1.3806504 · 10−23 J

Kmair air mass flow ratemfuel fuel mass flow ratep pressureu velocityφ equivalence ratioζburner pressure loss coefficient across the burnerλ wavelengthω angular frequencyx steady component of xx′(t) unsteady component of x, x′(t) ≡ x(t)− xx(ω) Fourier coefficient of x′(t)

I. Introduction

Modern gas turbine technology relies on lean premixed combustion to satisfy stringent governmentalemission restrictions. Premixing the fuel with large quantities of air before injecting both into the combustorsignificantly reduces the peak temperatures in the combustion zone and thereby leads to lower NOx emissions.

However, combustion systems operating in the lean premixed mode are highly susceptible to the excitationof high amplitude pressure fluctuations called thermoacoustic instability (Poinsot et al. 1987,1 Candel 19922).These self-excited oscillations are a result of the interaction between unsteady heat release in the flame andthe combustion chambers acoustic field.

As described by Rayleighs Criterion (19453), these self-excited oscillations result from the interaction ofunsteady heat release in the flame with the combustion chambers acoustic field and usually lead to increasednoise, reduced system performance and reduced system durability.

Hence, the thermoacoustic analysis is an important part in the design process of new gas turbine com-bustion systems. A common approach in the gas turbine industry is to measure flame transfer functionsin single-burner combustion test facilities and then use the measured transfer function in thermoacousticnetwork models representing the full-scale engine to predict the stability behavior and the pulsation spectraof multi-burner combustion systems in full-scale.4,5 This combined experimental and numerical approach tothermoacoustic modeling is discussed in detail in Refs. 6 and 7. A crucial aspect of this modeling approachis to obtain a correct representation of the interaction between the heat release and the acoustic field.

Predicting the thermoacoustic behavior of a burner system in this way is state-of-the-art for methane andnatural gas combustion, since for these fuels the influence of pressure is negligible. The transfer functionscan be measured at atmospheric conditions and then be scaled to high pressure. In these cases the purelyacoustic technique using the multi microphone method is well-established.

In order to provide fuel flexibility to their costumer, gas turbine manufacturers are now also designingcombustion systems for fuels with high hydrocarbon and hydrogen content or liquid fuels. For these fuels, theinfluence of pressure on the transfer function is important and transfer function measurements at elevatedpressure are required in order to correctly predict the thermoacoustic behavior of combustion systems burning

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these fuels. Since industrial high-pressure combustion test facilities generally offer only limited possibilitiesfor sensor installation, the use of pulsation probe arrays for a multi microphone method approach might notbe feasible. Therefore, other techniques are required to determine transfer functions at elevated pressure.

This work is about the measurement of flame transfer functions of a generic swirl-stabilized gas turbineburner at atmospheric conditions. Loudspeakers were employed for the acoustic excitation of the combustiontest rig. Arrays of condenser microphones have been used to record the acoustic response of the system to thisexcitation. Based on the microphone data, the flame transfer function was determined in a purely acousticway using the multi microphone method. In addition, the flame’s OH∗, CH∗, and CO2∗ chemiluminescenceresponse was measured by a system of a fiber optic probe collecting the light of the flame in the combustionchamber and four photomultiplier tubes. The additional optical data was used in two combined acoustic-optical techniques to determine the flame transfer function. Since the implementation of one optical proberequires only one access point to the combustor compared to an array of pressure probes, the acoustic-opticalis expected to be more suitable for a high-pressure combustion facility. Also, an optical probe might offer ahigher robustness compared to microphones or other pressure sensors.

II. Experimental Set-Up

II.A. Combustion Facility

All combustion results presented in this paper were obtained using the combustion facility shown in Fig. 1.On the upstream side the combustion test facility features an air preheater through which the combustionair is fed into a duct. Inside this duct sits the burner lance, through which fuel (natural gas in this work) issupplied to the burner. The atmospheric combustor has a 300 mm long air-cooled quartz glass combustionchamber allowing for optical access to the flame. A water-cooled resonance tube of 1350 mm in length isattached to this combustion chamber. The resonance tube consisted of three parts mounted together byflanges. The upstream duct and the middle part of the resonance tube are equipped with arrays of water-cooled microphone holders. One speaker on the upstream end and two speakers on the downstream end ofthe test facility allow for acoustic excitation.

microphones

photo-multipliers

speakermodifiedEV-10 burner

microphones

speaker

preheater

OH* (308 nm)CO2* (407 nm)CH* (431 nm)

p

pressureprobe

light spectrometer (200 – 1000 nm)

ICCD camera

CO2* (451 nm)

thermocouple

Figure 1. Combustion test facility.

II.B. EV-10 Burner

The combustor incorporates a generic environmental burner (EV-10) designed by ABB with a cross-sectionalarea expansion ratio of 4 for flame stabilization. Figure 2 shows a detailed sketch of the burner. It is composedof two half cones shifted in such a way that the air is forced to enter the cone circumferentially through twoslots. The resulting swirling air flow generates a recirculation zone along the centerline at the burner outlet,thus stabilizing the flame in this region. In the standard configuration the main (premix) fuel is injectedthrough 62 boreholes, 0.7 mm in diameter each, which are distributed equidistantly along the burners two

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air slots and fed from one common fuel supply. Mixing of swirling air and main fuel results in a nearlypremixed combustion. To enable control of the fuel distribution profile and hence the flame location, anadditional premix fuel injector was installed in the burner slots. This injector was divided into two sections:an upstream section with 14 and a downstream section with 16 boreholes as illustrated in Fig. 2. The fuelsupply to the two upstream sections and the two downstream sections can be individually controlled by twomass flow controllers. This configuration allows to control the premix fuel split PFS, which is defined hereas

PFS =premix fuel mass flow through upstream injector section

total premix fuel mass flow (through upstream & downstream section). (1)

Figure 2. Modified ABB EV-10 burner.

Figure 3 shows images of the flame for different values of the PFS and otherwise identical operatingconditions (φ = 0.6,mair = 200kg/h, Tinlet = 150◦C). The effect of the PFS can clearly be observed: ForPFS = 1 all premix fuel is injected through the upstream injector sections. For this case the fuel mainly endsup in the inner recirculation zone and the flame reaches deep down into the burner cone. For PFS = 0 allpremix fuel is injected through the downstream sections. More fuel ends up in the outer recirculation zoneand the flame stabilizes downstream of the burner. At PFS = 0.3 (i.e., slightly more fuel flow through thedownstream injector sections) the flame stabilizes just downstream of the burner, is completely in the field ofview of the photomultipliers, and shows a very uniform flame chemiluminescence intensity distribution. Sincethese conditions are ideal for the optical approach to determine the flame transfer function all combustionresults presented in this work were obtained a this PFS. However, the influence of different PFS valuesis briefly discussed in the outlook. More information on the effect of fuel staging on the EV-10 burner’scombustion process is provided in Ref. 8.

PFS = 0 PFS = 0.3 PFS = 0.5 PFS = 1.0Figure 3. Effect of pilot fuel split on the flame location.

Aside from premix fuel injection, pilot fuel can be injected at the EV-10 cone apex using a pilot lance.However, only operating conditions without pilot fuel injection were investigated in this work. For a detaileddescription of the burner see Ref. 9.

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II.C. Sensors

Pressure oscillations in the combustion chamber were measured using 8 condenser microphones placed intothe microphone holders of the test facility. The light emitted by the flame was captured by a fiber opticprobe through the quartz glass combustion chamber (see Figs. 1 and 2). This arrangement allowed theoptical probe to collect the light of the complete flame.

At the optical probes end looking at the flame, the probe features one single 1.8 mm thick fiber. Thelight collected by this thick fiber was passed on to 210 very small fibers forming a bundle of also 1.8 mmthickness via an optical splitter. The 210 small fibers are bundled together in groups of 30 to form 7 fiberbundles to which photomultiplier tubes or other optical sensors can be connected. This rather complicatedset-up of the optical probe ensures that each of the 7 fiber bundles at the end receives the same light fromthe flame. However, for this work only 5 of these 7 bundles were used.

The flames chemiluminescence response to acoustic excitation was measured using four photomultipliertubes, which were connected to the optical probe and equipped with narrow band-pass filters centered at308, 407, 431, and 451 nm. At these wavelengths, the photomultipliers captured light from OH∗, the CO2∗

background, CH∗ (including the CO2∗ background), and again only the CO2∗ background chemilumines-cence. The transmission of the individual filters is shown in Fig. 4. The microphone and photomultipliersignals were amplified and low-pass filtered at 2 kHz to avoid aliasing. In addition to the photomultipliers, ahigh-sensitivity light spectrometer was used to measure the light spectrum of the flame. To record the spatialheat release distribution of the flame, an ICCD camera equipped with a narrow band-pass filter centered at308 nm was employed.

300 400 500 600 7000

20

40

60

80

100

wavelength λ in nm

filt

er tr

ansm

issi

on T

r in

%

CW 308 nm (OH*)CW 407 nm (CO2*)CW 431 nm (CH*)CW 451 nm (CO2*)

Figure 4. Transmission of the optical band-pass filters.

III. The Flame Chemiluminescence Spectrum

III.A. Measured Light Spectrum

For each burner operating condition the light emission of the flame was measured using an Ocean OpticsQE65000 high-sensitivity light spectrometer. The spectrometer incorporates a Hamamatsu back-thinneddetector that is responsive from 200-1100 nm, features low readout noise, and can be cooled with an onboardthermoelectric cooler to reduce dark noise. As an example, Fig.,5 shows the measured light spectrum obtainedfor the operating conditions, which will later be used as the reference conditions (blue line). Note that thespectrometer sensitivity and the transmission of the optical probe have been accounted for in the presentedspectrum. The distinct peaks corresponding to OH∗ and CH∗ chemiluminescence are clearly visible, as isthe more distributed CO2∗ chemiluminescence.

III.B. Black Body Correction

Additionally, a steep intensity increase is present above 600 nm. This increase is due to heat radiationof the burner plate, which was within the field of view of the optical probe. To obtain only the flame

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300 400 500 600 7000

50

100

wavelength λ in nm

spec

tral

inte

nsit

y I λ (

norm

.)

Figure 5. Flame chemiluminescence spectrum: spectrum obtained from the light spectrometer (black), fitted blackbody spectrum (red), and corrected flame spectrum (blue). The black dotted lines indicate the CW of the employedoptical filter. Operating conditions: φ = 0.65, mair = 200 kg/h, Tinlet = 150C.

chemiluminescence spectrum, a black body radiation spectrum was fitted to the measured spectrum above670 nm. For this fit the radiation intensity of a black body was assumed to follow Planck’s Law:

Iλ,BB(λ, TBB) = A2hP c2light

λ5

(ehP clightλkBTBB − 1

)−1

, (2)

where Iλ,BB is the spectral black body radiation, TBB the black body temperature, A a scaling constantclight the speed of light, hP the Planck constant, and kB the Boltzmann constant. The flame spectrum(Fig. 5, blue line) was then obtained by subtracting the approximated radiation spectrum (Fig. 5, red line)from the measured spectrum.

In the fitting routine the two unknowns, the scaling constant A and the black body temperature TBB ,were fitted to the flame spectrum. While the scaling constant A was very similar for different operatingconditions, the approximated black body temperature TBB increased (as to be expected) with the heatrelease in the flame (i.e., with increasing fuel mass flow), indicating a hotter burner plate. For the flamespectrum presented in Fig. 5 TBB was approximated to be 1050 K, which is in the order of the expectedsurface temperature of the burner plate, thus giving confidence into the correction approach.

III.C. Subtraction of the CO2∗ Contribution in the Flame Spectrum

One of the optical methods used in this work to obtain the flame transfer function estimates the equivalenceratio of the flame based on the ratio of OH∗ to CH∗ chemiluminescence intensity. Since in the flame spectrumthe CH∗ chemiluminescence peak is superimposed with the broadband CO2∗ emission, the CO2∗ contributionhas to be subtracted to obtain only the CH∗ emission. To do so, the CO2∗ emission spectrum is obtained ina second fitting routine. The CO2∗ intensity is assumed to follow an ‘extreme’ fit function as proposed bySeipel et al.:10

Iλ,CO2 = A · exp[−exp

(−(λ− λC)w

)− (λ− λC)

w+ 1], (3)

where Iλ,CO2 is the normalized spectral CO2∗ chemiluminescence intensity, A a scaling constant, λ thewavelength, λC the wavelength of maximum intensity, and w scaling constant (in nm) for the width of theextremum. Hence, the shape of the intensity distribution over the wavelength is only dependent on the twovariables λC and w.

The fit was performed in the wavelength ranges around the CH∗ peak, where only CO2∗ emission ispresent in the spectrum. Figure 6 presents the flame spectrum together with the fitted CO2∗ contributionand the flame spectrum without the CO2∗ contribution for the reference operating point. The fit agrees verywell with the background found in the flame spectrum.

By subtracting the approximated CO2∗ contribution from the flame spectrum the CH∗ peak at approxi-mately 431 nm is isolated. By integrating the spectral CH∗ intensity over the wavelength the absolute CH∗

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300 400 500 600 7000

50

100

wavelength λ in nm

spec

tral

inte

nsit

y I λ (

norm

.)

Figure 6. Flame chemiluminescence spectrum with extreme fit for the CO2∗ emission: flame spectrum (blue),CO2∗ fit (green), and flame spectrum without CO2∗ contribution (magenta). Operating conditions: φ = 0.65,mair = 200 kg/h, Tinlet = 150C.

intensity can be computed:

ICH =∫ λCH

Iλ,CH dλ =∫ λCH

(Iλ,flame − Iλ,CO2) dλ, (4)

where λCH indicates the wavelength range in which the CH∗ occurs.In the same way the absolute OH∗ intensity can be obtained by integrating the spectral CH∗ intensity.

Note, however, that since the CO2∗ is approximately zero within the wavelength range of OH∗ chemilumi-nescence, no correction for CO2∗ emission is required.

IOH =∫ λOH

Iλ,OH dλ. (5)

Figures 7 and 8 present the change of chemiluminescence intensity with air mass flow and equivalenceratio.

250 300 350 400 450 500 550180

200

220

0

50

100

wavelength in nmm

air in kg/h

spec

tral

inte

nsit

y I λ (

norm

.)

Figure 7. Spectral intensity vs. air mass flow (φ=0.65, Tinlet=150◦).

With the outlined approach the computation of the OH∗ and CH∗ chemiluminescence intensity from thelight spectrometer data is straightforward for a steady flame spectrum. In case of heat release oscillations(forced or self-induced), however, the flame spectrum will not be steady. Since an accurate measurement ofthe flame spectrum with only low noise is essential to achieve meaningful intensity data that can be used

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300 4005000.6

0.7

0.80

50

100

150

200

wavelength in nmequivalence ratio φ

spec

tral

inte

nsit

y I λ (

norm

.)

Figure 8. Spectral intensity vs. air mass flow (mair=200, Tinlet=150◦).

to compute the flame transfer function, fluctuations in the OH∗ and CH∗ intensities have to be adequatelyresolved. For the frequency range of interest for the present work (i.e., 30 to 500 Hz) this is generally notpossible with commercial light spectrometers. The high-sensitivity light spectrometer used in this work,for example, has a minimal shutter speed of 8 ms, which would allow to resolve frequencies of maximal to62.5 Hz not accounting for readout time. Furthermore, the recording times needed to achieve a good signalto noise ratio are commonly much longer, especially since premix flames feature only low light emissioncompared to, for example, diffusion flames. For most light spectra presented in this work the recording timewas 10 s to max out the buffer limits of the light detector, although good results were also obtained withrecording times of 1 s. If the recording time is to be reduced even further, averaging of multiple recordings isa possible way to maintain a good signal to noise ratio. To still resolve fluctuations using averaging a phase-logged triggering of the spectrometer would have been required, which would have dramatically increasedthe necessary measurement time.

Therefore, the CH∗ chemiluminescence intensity had to be obtained using photomultiplier tubes, whichoffer a high gain, low noise and high frequency response.

III.D. Subtraction of the CO2∗ Contribution in the PMT Signals

The output voltage UPMT obtained from a photomultiplier can be expressed as

UPMT = GPMT

∫ ∞0

((Iλ,flame + Iλ,BB) Trλ,probe Trλ,BP Seλ,PMT ) dλ+ UPMT,dark, (6)

where Trλ,probe and Trλ,BP denote the spectral transmission of the fiber optic probe and the optical bandpassfilter, respectively, and Seλ,PMT the spectral sensitivity of the PMT. GPMT represents the PMT gain, whichwas hold constant for throughout the whole test campaign. The dark signal UPMT,dark of all PMTs wasadjusted to zero before the first measurement by applying an offset voltage.

Since the probe transmission and the PMT sensitivity are approximately constant within the narrowwavelength range of the employed optical band pass filters, they can be included into the gain. Also, theblack body radiation is approximately zero within the range of the band pass filters.

Upmt = Gpmt

∫ λBP

(Iλ,flame Trλ,BP ) dλ, (7)

where λBP denotes the band pass filters wavelength range of transmission, i.e., approximately 299 to 318 nmin case of the CW 308 nm band pass filter.

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As a measure for the OH∗ chemiluminescence intensity the output voltage of the PMT equipped withthe CW 308 nm band pass filter was used. As pointed out before, the signal does not have to be correctedfor CO2∗, since no CO2∗ emission is present in the wavelength range of the optical filter.

To obtained a signal that represents only the CH∗ intensity, however, a combination of light spectrometerand PMT measurements with a steady flame are required to account for the CO2∗ emission captured by theCW 431 nm filter.

According to Eq. 7 the output voltage of the PMTBP,431nm can be expressed as

UBP,431nm = GBP,431nm

∫ λBP,431nm

(Iλ,CH + Iλ,CO2) Trλ,BP,431nm dλ. (8)

Since the (normalized) spectral intensities, the filter transmission and the output voltage are known, thegain factor GBP,431nm can be determined. Once this gain factor is known the output voltage UBP,431nm canbe separated into its CH∗ and CO2∗ contribution.

UBP,431nm,CH = GBP,431nm

∫ λBP,431nm

Iλ,CH Trλ,BP,431nm dλ (9)

UBP,431nm,CO2 = GBP,431nm

∫ λBP,431nm

Iλ,CO2 Trλ,BP,431nm dλ (10)

Since the CO2∗ intensities at 407, 431 and 451 nm are proportional, UBP,431nm,CO2 can be related to theoutput voltages acquired at the other two wavelength ranges:

UBP,431nm,CO2 = A407nm→431nmUBP,407nm (11)

UBP,431nm,CO2 = A451nm→431nmUBP,451nm (12)

Once the proportionality factors A407nm→431nm and A451nm→431nm have been determined, UBP,431nm,CO2

can be obtained from either the UBP,407nm or the UBP,451nm PMT signal. This now also holds for an unsteadyflame with chemiluminescence intensity fluctuations and allows to subtract the CO2 contribution from theunsteady UBP,431nm signal to finally obtain UBP,431nm,CH . Note that for the transfer function measurementsthe CH signal was determined using the average of the CO2 contributions at 431 nm obtained from Eqs. 11and 12.

IV. Transfer Matrix Measurement

The thermo-acoustic behavior of the combustion test facility can be described by a network model assketched in Fig. 9. In this model, the behavior of the systems individual elements (e.g. the burner and theflame) are expressed by their acoustic transfer matrix. The acoustic transfer matrix T of an acoustic elementgives the dynamic relation between the acoustic field on both sides of the element and is defined here as:[

pd

ud

]=

[T11 T12

T21 T22

][pu

uu

]. (13)

The subscripts d and u refer to locations upstream and downstream of the element. The symbols p andu represent the Fourier coefficients of the acoustic pressure and velocity. These quantities correspond to theunsteady, irrotational part of the pressure and velocity field. Note that the matrix is a function of frequencyand that the Fourier coefficients of the pressure are normalized by ρc, thus p has units of meters per second.

The four frequency dependent elements of the transfer matrix T are obtained by forcing the system withloudspeakers and measuring the response with microphones. A detailed description of this technique is givenin Ref. 11. The most important aspects are summarized here. Because Eq. (13) provides two equations infour unknowns, at least two independent test states are required to extract the four elements of T: excitationfrom the upstream side (denoted with superscript A) and excitation from the downstream side (denoted withsubscript B). Thus, the transfer matrix T can be obtained as:[

T11 T12

T21 T22

]=

[pAd pBduBd uBd

][pAu pBuuBu uBu

]−1

. (14)

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Burner Flame

Orifice

Plenum

CombustionChamber

Resonance

Tube

Speaker Speaker

Duct

pu1 ... pu4

pd1 ... pd4

Duct

Figure 9. Acoustic network model of the combustion test facility.

The Multi Microphone Method (MMM) is used in order to obtain the acoustic velocity and pressure atthe reference position from data of acoustic pressure at multiple microphone locations. It makes use of thesolution of the one dimensional wave equation in presence of mean flow:

p(ω, x) = f(ω)e−iωc

x1+M + g(ω)ei

ωc

x1−M ,

in which the Riemann invariants f(ω) and g(ω) are integration constants whose values depend on theboundary conditions. The acoustic pressure measured by N microphones in a straight duct at positions xncan thus be expressed as:

p1

...pN

=

e−i

ωc

x11+M ei

ωc

x11−M

......

e−iωc

xN1+M ei

ωc

xN1−M

[f

g

]= Z

[f

g

]. (15)

The Riemann invariants can be calculated from the measured microphone signals by solving Eq. (15), pro-vided that at least two microphones have been used. The solution in the least squares sense is given by:

[f

g

]= Z†

p1

...pN

, (16)

where the superscript † denotes the pseudo-inverse. The acoustic velocity at the reference position is thengiven by u(x = 0) = f − g. Using matrix notation, this can conveniently be expressed as:

[pAd pBduBd uBd

]=

[1 11 −1

]Z†

pA1 pB1...

...pAN pBN

. (17)

Applying the operation of Eq. (17) to both the microphones upstream and downstream of the element yieldsthe desired matrices with acoustic pressures and velocities required to solve Eq. (14) for T.

IV.A. Flame Transfer Matrix

In order to measure a transfer matrix, arrays of microphones have to be placed at both sides of the element.Since a flame is always stabilized by some kind of flame holder (the “burner”), it is not possible to measurea flame transfer matrix directly. However, the transfer matrix of the combined burner and flame element Tcan be measured, along with the transfer matrix of the burner B only (in absence of combustion but withflow). The desired flame transfer matrix F can then easily be obtained from:

F = TB−1. (18)

The underlying assumption is that the transfer matrix (B) does not change due to the combustion process.

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IV.B. Flame Transfer Function

Often the measurement of the complete transfer matrix is not feasible due to limited access to the combustionsystem and hence limited possibilities to install the required sensors (e.g. microphone arrays). In these cases,some of the matrix elements can be represented by analytical solutions.

If the burner is assumed to behave like an area discontinuity with mean flow, the burner transfer matrixB (without combustion) can be expressed as

B =

1 M

(1− ζburner −

(AuAd

)2)− iωc Lred

0 AuAd

, (19)

with the mean flow Mach number M , the reduced length Lred, the pressure loss coefficient ζburner, and thecross-sectional areas upstream (Au) and downstream (Ad) of the burner.6

The flame transfer matrix F can also be simplified by considering only low Mach number flows and hencepd ≈ pu (i.e., F11 ≈ (ρc)d

(ρc)u, F12 ≈ 0), as well as a negligible effect of pressure fluctuations onto the fuel

injection (i.e., F21 ≈ 0):

F =

[(ρc)d(ρc)u

0

0 H(ω)

]. (20)

By making use of the Rankine-Hugoniot relations for low Mach number flows, the transfer function H(ω)can be linked to the heat release fluctuation in the flame:

H(ω) =uduu

= 1 +(TdTu− 1)Q

Q

u

u= 1 +

(TdTu− 1)F (ω), with F (ω) =

Q

Q

u

u, (21)

where F (ω) is the flame transfer function.

V. Transfer Function Measurement Using Optical Signals

Three combined acoustic-optical methods are used in this work to determine the flame transfer function:

• the optical one-signal method,

• the optical direct multi-signal method, and

• the optical OH-OH/CH multi-signal method.

As indicated by their names, the first method is based on only one flame chemiluminescence signal, while theother two methods are based on multiple flame chemiluminescence signals. Furthermore, for the one-signaland the direct multi-signal method, the flame chemiluminescence intensities are used as measured by thePMTs (i.e. directly). No distinction is required regarding the chemical species involved in the chemilumi-nescence emission at a certain optical wave length (e.g., the contribution of CO2∗ chemiluminescence to theCH∗ chemiluminescence signal is not an issue). In contrast, the OH-OH/CH multi-signal method uses theratio of OH∗ and CH∗ chemiluminescence intensity, which is shown be proportional to the equivalence ratioin the combustion zone. Therefore, the CH∗ chemiluminescence signal acquired through the CW 431nmoptical filter has to be corrected for the contribution of the CO2∗ chemiluminescence. In the following thedifferent contributions to heat release fluctuations in the flame are discussed and the three methods outlinedin detail.

V.A. Heat Release Fluctuations in the Flame

The heat release rate of the flame is given by the following expression:

Q = mfuelHfuel = mairφ

(mfuel

mair

)stoich

Hfuel, (22)

where mfuel and mair are the instantaneous values of the mass flows of fuel and air entering the reactionzone, φ the equivalence ratio and Hfuel the chemical enthalpy of the fuel.

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The mass flow of the mixture through the flame front fulfills the following equality: mfuel + mair =∫ρSdA = ρSflameAflame. The definition of the flame surface and flame velocity is somewhat arbitrary.

However, the definition of both quantities should be such that the product of flame speed and flame areaconserves mass across the flame front. Please note that in the following, all relevant quantities are consid-ered as averages of the quantity over the flame surface (hence assuming homogeneity of the time-averagedquantities and linearity of the perturbations).

For the determination of the flame transfer function F (ω), the relative heat release fluctuations arerequired. By linearizing Eq. (22) they can be expressed as:

Q′

Q=m′air

mair+φ′

φ. (23)

Hence, the relative heat release fluctuations have two contributions: air mass flow fluctuations and equiva-lence ratio fluctuations, which can generally not be measured directly.

V.B. The Optical One-Signal Method

If only one of the two contributions is present (i.e., φ′ = 0 or m′air = 0), the heat release fluctuations canbe linked to the intensity of one chemiluminescence signal. The OH∗ signal, for example, has frequentlybeen reported in the literature as being proportional to the heat release of premixed flames.12 In this caseEq. (21) can by simplified to

F (ω) =Q

u1

u1

Q=InIn

u1

u1, (24)

where In denotes one of the recorded chemiluminescence signals.Theoretically, the one-signal method would also work, if the dependence of the used intensity signal on

the two contributions to heat release fluctuations is identical and linear. However, this is usually not thecase.

V.C. The Optical Direct Multi-Signal Method

Obtaining the flame transfer function based on multiple chemiluminescence signals was first was first proposedand investigated in Schuermans et al.13,14 Nevertheless, the approach is outlined in detail in the following,partly with slight variations.

Generally, air mass flow fluctuations and equivalence ratio fluctuations will be present in a flame. Inthese cases one optical signal is not sufficient to correctly estimate the relative heat release fluctuations andhence the flame transfer function. The two contributions can generally not be measured directly. However,by linking them to at least two optical signals of the flame’s chemiluminescence, they can be determined viaa matrix inversion. Note that due to the linearization this expression is valid for small perturbations only.

In the literature the, flame’s chemiluminescence intensity I of a chemical species (e.g. OH∗ or CH∗) isoften assumed to follow a power law dependence with air mass flow mair, equivalence ratio φ and staticpressure p:15

I = km,φ,pmαairφ

βpγ , (25)

where km,φ,p, α, β and γ are constants for one species.Since the experiments for the present work were all performed at atmospheric conditions, the pressure

influence can be included into the factor k = km,φ,ppγ . Furthermore, the exponent α has been shown to be

unity by Higgins et al.:15

I = kmairφβ . (26)

The dependence of the chemiluminescence intensity of two species, for example OH∗ and CH∗, on theequivalence ratio and the air mass flow can hence be written as

IOH = kOHmairφβOH and ICH = kCHmairφ

βCH (27)

or in matrix form [log(IOH)log(ICH)

]= C

[log(mair)

log(φ)

]+

[log(kOH)log(kCH)

], where C =

[1 βOH

1 βCH

]. (28)

12 of 21


The equivalence ratio and mass flow time traces can be determined from the intensity signals of OH∗ andCH∗, after the matrix C and the factors kOH and kCH have been determined in a calibration experiment:[

log(mair)log(φ)

]= C−1

([log(IOH)log(ICH)

]−[

log(kOH)log(kCH)

])= C−1

log(IOHkOH

)log(ICHkCH

) , (29)

provided that βi 6= βj . Hence, the direct optical multi-signal method provides also the amplitude of the twodriving mechanisms of heat release fluctuations considered here. This is important for when adapting thecombustor design to further reduce these driving mechanisms.

From Eq. (29), the absolute values for mair and φ can be obtained. To determine the flame transferfunction F , however, the relative air mass flow and equivalence ratio fluctuations are sufficient. Afterlinerization their dependence on the relative intensity fluctuations can be expressed as[

I′OHIOHI′CHICH

]= C

[m′airmairφ′

φ

]. (30)

The relative equivalence ratio and mass flow fluctuations can be determined from:[m′airmairφ′

φ

]= C−1

[I′OHIOHI′CHICH

]. (31)

Note that even though the chemiluminescence signals of two species are sufficient to use this method, theaccuracy can be increased by using additional chemiluminescence signals, for example the CO2∗ background.For N chemiluminescence signals, Eq. (31) becomes

[m′airmairφ′

φ

]= C†N

I′1I1...I′NIN

, with CN

1 β1

......

1 βN

. (32)

As the system in Eq. (32) is over-determined it can be solved in a least-square sense. After solving Eq. (32),the relative heat release fluctuation can be determined according to Eq. (23) and finally the flame transferfunction F (ω) is obtained from Eq. (21).

V.D. The OH-OH/CH Multi-Signal Method

The general approach of the OH-OH/CH multi-signal method is identical to direct multi-signal method inthat sense, that the air mass flow and equivalence ratio fluctuations are determined based on two opticalsignals, as expressed in Eq. (31). Instead of using only PMT output voltages, the ratio of OH* to CH*chemiluminescence intensity (OH/CH ratio) is determined as outlined in Sec. III. The OH* signal is used asthe second optical signal.

Since the OH/CH ratio is proportional to the equivalence ratio (IOH/ICH = AOH/CH φ), the relativeequivalence ratio fluctuations can be computed directly from the OH/CH ratio:

(IOH/ICH)′

(IOH/ICH)=φ′

φ(33)

To compute the equivalence ratio itself, however, the proportionality factor AOH/CH would first have to bedetermined from the calibration measurements.

Knowing φ′

φthe relative air mass flow fluctuations can easily be obtained from:[

I′OHIOH

(IOH/ICH)′

(IOH/ICH)

]=

[1 βOH

0 AOH/CH

][m′airmairφ′

φ.

](34)

Note that the OH-OH/CH multi-signal method avoids the inversion of calibration matrix with a possiblybad condition. However, it required a more detailed analysis of the flame chemiluminescence to correctlydetermine the OH/CH ratio.

13 of 21


VI. Acoustic Transfer Matrix Results

The transfer matrix of the EV-10 burner was measured for an air mass flows of 200 kg/h and an equivalenceratio of 0.65 in a frequency range of 40 to 500 Hz with steps of 5 Hz. The burner inlet temperature was heldconstant at 150◦C.

VI.A. Acoustic Transfer Matrix Results

At first, the burner transfer matrix B was determined in tests without combustion. The loudspeakers wereoperated using a chirp signal, which covered the frequency range of interest within 500 s.

0 100 200 300 400

0

f in Hz

∠ T

11

-π

π

0 100 200 300 400

0

f in Hz∠

T12

-π

π

0 100 200 300 400

0

f in Hz

∠ T

21

-π

π

0 100 200 300 400

0

f in Hz

∠ T

22

-π

π

0

1

2

|T11

|

0

1

2

|T12

|

0

1

2

|T21

|

0

1

2

|T22

|

Lζ−modelmeasured

Figure 10. Measured burner transfer matrix B (mair=200 kg/h, Tinlet and fitted L-ζ-model.

Figure 10 presents the absolute values and the phase of the measured burner transfer matrix as a functionof the excitation frequency. The results show a very good agreement between the measured value and theL-ζ-model. The thermoacoustic behavior of the burner is similar to that of an area discontinuity accordingto Eq. (19): The B11 element relates the pressures across the burner. | B11 | is approximately 1, whilethe phase is zero throughout the whole frequency range investigated. B12 relates the velocity upstream tothe pressure downstream of the burner. B12 shows a linearly increasing slope in its absolute value and aphase of approximately −π/2 (for higher frequencies), which is a typical behavior for a confinement in theacoustic field.6 The B21 element relates the pressure upstream to the velocity downstream of the burner. Itis relatively small in absolute value and hence of little importance. The B22 element relates the velocities up-and downstream to each other. For an area discontinuity its absolute value represents the area ratio, whichis 0.27 in case of the EV-10 burner. Indeed, | B22 | is very close to 0.27, while the phase is approximatelyzero.

VI.B. Flame Transfer Matrix

After the burner transfer matrix had been measured, the combustor was ignited and the transfer matrix ofburner and flame was measured (mair=200 kg/h, φ=0.65, Tinlet). The forcing amplitude is of importancein this case, since too low forcing amplitudes result in poor signal to noise ratios, while too large amplitudes

14 of 21


can cause a non-linear response of the flame, for which the transfer matrix approach used here is not validanymore.

Experience has shown that a good signal to noise ratio without non-linear flame response can be achieved,if the generated velocity fluctuation amplitude upstream of the flame equals approximately 10% of the meanflow velocity. Since the acoustic reponse of the test facility is different at different frequencies, this velocityfluctuation can generally not be achieved with a speaker command of constant amplitude for all frequencies.

Therefore, the appropriate forcing amplitude was determined in two steps. First, the test facility wasexcited using a chirp signal and the generated velocity fluctuations were determined using the multi micro-phone method. A linear interpolation between speaker forcing amplitude and achieved velocity fluctuationamplitude was then used to determine the appropriate speaker forcing. In a second measurement, the trans-fer matrix was measured using the optimized forcing amplitude and pure tone excitation. For each frequencystep, a 10 s recording was performed. The achieved velocity fluctuation amplitude upstream of the flame wasin the range of 8 to 12% of the mean flow velocity as desired.

The flame transfer matrix F was then determined by solving Eq. (18). The obtained flame transfermatrix is shown in Fig. 11. F shows good agreement with the simplified form given in Eq. (20): | F11 |approximately equals (ρc)d

(ρc)u≈ 1.8 with ∠F11 ≈ 0, while | F12 | and | F21 | are close to zero. The dynamic

behavior of the flame is primarily captured in the F22 element. The slope of ∠F22 features the typicaldecreasing trend.

which is also expected, since the relative difference in air mass flow is only small. The results also showthat, especially at low frequencies, the thermoacoustic behavior of the burner is similar to that of an areadiscontinuity according to Eq. 7: The B11 element relates the pressures across the burner. abs(B11) is 1 forlow frequencies, but increases slightly with frequency, while the phase is zero throughout the whole frequencyrange investigated. B12 relates the velocity upstream to the pressure downstream of the burner. abs(B12)shows a linearly increasing slope and a phase of approximately −π/2 (for higher frequencies) which is atypical behavior for a confinement in the acoustic field.6 The B21 element relates the pressure upstream tothe velocity downstream of the burner. It is relatively small in absolute value and hence of little importance.The B22 element relates the velocities up- and downstream to each other. For an area discontinuity itsabsolute value represents the area ratio, which is 0.27 in case of the EV-10 burner. Indeed, abs(B22) is veryclose to 0.27 especially for low frequencies, while the phase is approximately zero.

B. Flame Transfer Matrix

After the burner transfer matrix had been measured, the combustor was ignited and the transfer matrix ofburner and flame were measured at different air mass flows and equivalence ratios. The forcing amplitudeis of importance in this case, since too low forcing amplitudes result in poor signal to noise ratios, while toolarge amplitudes can cause a non-linear response of the flame, for which the transfer matrix approach usedhere is not valid anymore.

Experience has shown that a good signal to noise ratio without non-linear flame response can be achieved,if the generated velocity fluctuation amplitude upstream of the flame equals approximately 10% of the meanflow velocity. Since the acoustic reponse of the test facility is different at different frequencies, this velocityfluctuation can generally not be achieved with a speaker command of constant amplitude for all frequencies.

Therefore, the appropriate forcing amplitude was determined in two steps. First, the test facility wasexcited using a chirp signal and the generated velocity fluctuations were determined using the multi micro-phone method. A linear interpolation between speaker forcing amplitude and achieved velocity fluctuationamplitude was then used to determine the appropriate speaker forcing. In a second measurement, the trans-fer matrix was measured using the optimized forcing amplitude and pure tone excitation. For each frequencystep, a 10 s recording was performed. The achieved velocity fluctuation amplitude upstream of the flame wasin the range of 8 to 12% of the mean flow velocity as desired.

The flame transfer matrix F was then determined by solving Eq. 6. For φ = 0.75 and air mass flow ratesof 180, 200 and 220 kg/h, the obtained flame transfer matrices are shown in Fig. 5. For all air mass flows, Fshows good agreement with the simplified form given in Eq. 8: abs(F11) approximately equals (ρc)d

(ρc)u≈ 1.8

with phs(F11) ≈ 0, while abs(F12) and abs(F21) are close to zero. The dynamic behavior of the flame isprimarily captured in the F22 element. The slope of phs(F22) features the typical decreasing trend andis steeper for lower air mass flows, since the time-lag between the combustion air exiting the burner andreaching the flame front decreases due to the higher flow velocity.

0 100 200 300 400 5000

1

2

3

4

frequency (Hz)

abs(F

11)

0 100 200 300 400 5000

1

2

3

4

frequency (Hz)

abs(F

12)

0 100 200 300 400 5000

1

2

3

4

frequency (Hz)

abs(F

21)

0 100 200 300 400 5000

1

2

3

4

frequency (Hz)

abs(F

22)

air = 180 kg/h

air = 200 kg/h

air = 220 kg/h

0 100 200 300 400 500

-pi

-pi/2

0

pi/2

pi

frequency (Hz)

phs(F

11)

0 100 200 300 400 500

-pi

-pi/2

0

pi/2

pi

frequency (Hz)

phs(F

12)

0 100 200 300 400 500

-pi

-pi/2

0

pi/2

pi

frequency (Hz)

phs(F

21)

0 100 200 300 400 500

-pi

-pi/2

0

pi/2

pi

frequency (Hz)

phs(F

22)

air = 180 kg/h

air = 200 kg/h

air = 220 kg/h

Figure 5. Absolute values (left) and phase (right) of the flame transfer matrix F for air mass flows of 180, 200and 220 kg/h.

8 of 16


Figure 11. Absolute values (left) and phase (right) of the flame transfer matrix F for air mass flows of 180, 200 and220 kg/h

VI.C. Acoustic Flame Transfer Function

The flame transfer function F (ω) can also be obtained from purely acoustic data by rearranging Eq. (21) to

F (ω) =(u2

u1− 1)(

T2

T1− 1)−1

, (35)

where the subscripts 1 and 2 indicate a property upstream and downstream of the flame, respectively, asindicated in Fig. 12. u2 was already determined (obtained from MMM in the downstream duct), while u1 canbe computed from p0 and u0 (obtained from MMM in the upstream duct) and the burner transfer matrixB:

u1 = B21p0 +B22u0. (36)

VII. Optical Chemiluminescence Intensity Signals

VII.A. Calibration of the Photomultiplier Signals

To obtain the calibration matrix C containing the coefficients βOH , βCH , and βCO2, the EV-10 burner wasoperated at different combustion air mass flow rates (170 to 230 kg/h) and equivalence ratios (0.55 to 0.80),

15 of 21


Burner Flame0 1 2

B F

T

Figure 12. Thermo-acoustic network model of burner and flame with the locations 0 (upstream of burner), 1 (betweenburner and flame), and 2 (downstream of flame).

0

0.5

1

1.5

2

0 100 200 300 400 500

frequency (Hz)

ab

s(F

( ωω ωω) ) acoustic method

-3.2

-1.6

0

1.6

3.2

0 100 200 300 400 500

frequency (Hz)

ph

s(F

( ωω ωω) )

Figure 13. Flame transfer function F (ω) determined from acoustic data for an air mass flow of 200 kg/h and anequivalence ratio of 0.75.

16 of 21


while the burner inlet temperature was held constant at 150◦C. At 24 operating points within this parameterrange, the time traces of the flame’s chemiluminescence were recorded by the photomultipliers. Additionally,images of the flame were taken a standard photo camera.

Figures 14 shows the recorded images for selected combinations of air mass flow and equivalence ratios.In these images, the mean flow direction is from bottom to top. The burner plate appears on the bottomas a red glowing disc with the burner exit in the center. The bright yellow glowing pole sticking out of theburner plate in the center of the images is the ignition electrode, which also shows up in two reflections inthe quartz glass of the combustion chamber. The flame is stabilized downstream of the burner exit, whereits light emission is completely captured by the optical probe.

φ = 0.60 φ = 0.65 φ = 0.75

mai

r=

180

kg/h

mai

r=

200

kg/h

mai

r=

220

kg/h

Figure 14. Photo images of the flame at different air mass flows and equivalence ratios (Tinlet=150◦).

After the calibration measurements had been performed, the matrix C was determined by fitting theconstants k and β in Eq. (26) to the average chemiluminescence intensities of OH∗, CH∗ and CO2∗.

Figure 15 shows the recorded chemiluminescence intensity together with the intensity fit for the threephotomultipliers. The recorded data points are indicated by circles. The fit is presented as a surface plot.The color of the data point circles indicates the deviation between fit and measurement normalized by theintensity range of the measurement points. Black indicates an error of less than 5%, magenta an errorbetween 5 to 10%.

As evident from Fig. 15, the trends found in the measured chemiluminescence intensity are well capturedby the fit with mainly relative errors below 5% between fit and measurement. The obtained coefficients k andβ are given in Tab. 1. Note that the relative heat release fluctuations can only be correctly determined frommultiple chemiluminescence signals, if the coefficients β are different for different chemical species, which isthe case. Note also that the coefficients k, which depend on the sensitivity and gain of the photomulipliersand the transmission of the optical set-up, are not needed to obtain the relative heat release fluctuations.The result βOH = 4.93 is in the order of the results reported by Higgins15 who found βOH to be 5.23. Anexact match is not expected, since the operating conditions used in this work differ from the ones of Higgins’investigation.

To illustrate the quality of the OH∗ intensity fit in more detail, Fig. 16 presents the measured OH∗

17 of 21


0.50.6

0.70.8

0.9

160

180

200

220

2400

1

2

3

4

5

φ (-)

OH* (CW 308 nm)

mair

(kg/h)

PM

T in

ten

sity (

V)

0.50.6

0.70.8

0.9

160

180

200

220

2400

2

4

6

8

φ (-)

CH* (CW 431 nm)

mair

(kg/h)

PM

T in

ten

sity (

V)

0.50.6

0.70.8

0.9

160

180

200

220

2400

1

2

3

4

φ (-)

CO2* (CW 407 nm)

mair

(kg/h)

PM

T in

ten

sity (

V)

Figure 10. Recorded intensity of OH*, CH* and C2* chemiluminescence and corresponding surface fit as afunction of air mass flow and equivalence ratio.

0

1

2

3

4

5

160 180 200 220 240

m air (kg/h)

OH

* in

ten

sit

y (

V)

measurementphi = 0.55phi = 0.65phi = 0.75phi = 0.80

0

1

2

3

4

5

0.5 0.6 0.7 0.8

equivalence ratio (-)

OH

* in

ten

sit

y (

V)

measurementair = 180 kg/hair = 200 kg/hair = 220 kg/h

Figure 11. Recorded intensity of OH* chemiluminescence and lines of constant equivalence ratio (left) and airmass flow (right).

to Eq. 20 as well as the result obtained from the multi optical signal approach according to Eq. 9 and 11(labeled optical (multi signal)). For comparison, also the result obtained from purely acoustic data (alreadypresented in Fig. 6) is shown (labeled acoustic).

The phases of the three optical flame transfer functions obtained from a single chemiluminescence signal

13 of 16


Figure 15. Recorded intensity of OH∗, CH∗ and CO2∗ chemiluminescence and corresponding surface fit as a functionof air mass flow and equivalence ratio

Table 1. Coefficients k and β obtained from the calibration measurements

Tinlet

= 120°C

φφφφ = 0.55 φφφφ = 0.65 φφφφ = 0.75

mair

= 2

20

kg

/hm

air

= 2

00

kg

/hm

air

= 1

80

kg

/h

Figure 9. Spatial distribution of OH* chemiluminescence of the flame recorded with the ICCD camera atdifferent air mass flows and equivalence ratios.

and the transmission of the optical set-up, are not needed to obtain the relative heat release fluctuations.The result βOH∗ = 4.93 is in the order of the results reported by Higgins,10 who found βOH∗ to be 5.23. Anexact match is not expected, since the operating conditions used in this work differ from the ones of Higgins’investigation.

OH* CH* C2*k 0.062 0.171 0.080β 4.93 7.20 7.45

Table 1. Coefficients k and β obtained from the calibration measurements.

To illustrate the quality of the of the OH* intensity fit in more detail, Fig. 11 presents the measured OH*intensity as a function of the air mass flow (left) and equivalence ratio (right) together with lines of constantair mass flow and equivalence ratio according to the fit. The fit captures the measured trends very well. Theresults confirm the linear dependence of the OH* intensity on air mass flow and the exponential dependenceon equivalence ratio. Similar good agreements were found for the CH* and C2* intensities.

The coefficients βCH∗ and βC2∗ are very similar, while βOH∗ is somewhat different. This is also reflectedin the time traces of the photomultiplier signals. As an example, Fig. 12 shows the phase-averaged timetraces of the photomultiplier signals for upstream excitation at 80 Hz. Note that the amplitudes of all timetraces have been scaled to one for easier comparison of their trends. The combustor was operated at φ = 0.75and mair = 200 kg/h. Indeed, the CH* and C2* signals are almost identical, while the OH* signal exhibitssome small differences. Since all three signals depend in the same way (i.e. linearly) on the air mass flow, butdifferently on equivalence ratio (due to their different exponents β, the difference between OH* and the othertwo signals indicates the presence of equivalence ratio fluctuations. However, all chemiluminescence timetraces feature an approximately sinusoidal shape, i.e., the chemiluminescence intensity changes approximatelylinearly with the excitation amplitude, suggesting that air mass flow fluctuations are the main cause of thechemiluminescence intensity fluctuations.

VII. OPTICAL TRANSFER FUNCTION RESULTS

The chemiluminescence time traces were used to obtain the flame transfer function F (ω) for an air massflow rate of 200 kg/h and an equivalence ratio of 0.75. Figure 13 shows the flame transfer function F (ω)obtained from individual chemiluminescence signals (labeled with the species used, e.g. OH*) according

12 of 16


18 of 21


intensity as a function of the air mass flow (left) and equivalence ratio (right) together with lines of constantair mass flow and equivalence ratio according to the fit. The fit captures the measured trends very well. Theresults confirm the linear dependence of the OH∗ intensity on air mass flow and the exponential dependenceon equivalence ratio. Similar good agreements were found for the CH∗ and CO2∗ intensities.

0.50.6

0.70.8

0.9

160

180

200

220

2400

1

2

3

4

5

φ (-)

OH* (CW 308 nm)

mair

(kg/h)

PM

T inte

nsity (

V)

0.50.6

0.70.8

0.9

160

180

200

220

2400

2

4

6

8

φ (-)

CH* (CW 431 nm)

mair

(kg/h)

PM

T inte

nsity (

V)

0.50.6

0.70.8

0.9

160

180

200

220

2400

1

2

3

4

φ (-)

C2* (CW 515 nm)

mair

(kg/h)

PM

T inte

nsity (

V)

Figure 10. Recorded intensity of OH*, CH* and C2* chemiluminescence and corresponding surface fit as afunction of air mass flow and equivalence ratio.

0

1

2

3

4

5

160 180 200 220 240

m air (kg/h)

OH

* in

ten

sit

y (

V)

measurement

phi = 0.55

phi = 0.65

phi = 0.75

phi = 0.80

0

1

2

3

4

5

0.5 0.6 0.7 0.8

equivalence ratio (-)

OH

* in

ten

sit

y (

V)

measurement

air = 180 kg/h

air = 200 kg/h

air = 220 kg/h

Figure 11. Recorded intensity of OH* chemiluminescence and lines of constant equivalence ratio (left) and airmass flow (right).

to Eq. 20 as well as the result obtained from the multi optical signal approach according to Eq. 9 and 11(labeled optical (multi signal)). For comparison, also the result obtained from purely acoustic data (alreadypresented in Fig. 6) is shown (labeled acoustic).

The phases of the three optical flame transfer functions obtained from a single chemiluminescence signal

13 of 16


Figure 16. Recorded intensity of OH∗ chemiluminescence and lines of constant equivalence ratio (left) and air massflow (right)

VIII. Optical Transfer Function Results

The chemiluminescence time traces were used to obtain the flame transfer function F (ω) for an air massflow rate of 200 kg/h and an equivalence ratio of 0.75. Figure 17 shows the flame transfer function F (ω)obtained from individual chemiluminescence signals (labeled with the species used, e.g. OH∗) according toEq. (34) as well as the result obtained from the multi optical signal approach according to Eq. (21) and(23) (labeled acoustic-optical (multi)). For comparison, also the result obtained from purely acoustic data(already presented in Fig. 13) is shown (labeled acoustic method).

-3.2

-1.6

0

1.6

3.2

0 100 200 300 400 500frequency (Hz)

ph

s(F

( ωω ωω) )

0

1

2

3

4

5

6

0 100 200 300 400 500

frequency (Hz)

ab

s(F

( ωω ωω) )

only OH* signal

only CH* signal

only C2* signal

acoustic method

acoustic-optical (multi)

Figure 17. Flame transfer function F (ω) obtained from the purely acoustic method and the two acoustic-optical methods(individual / multiple chemiluminescence signals.

19 of 21


The phases of the three optical flame transfer functions obtained from a single chemiluminescence signalare almost identical. The amplitude of the absolute values also show the same trends with similar amplitudes.For the OH∗ signal, however, the amplitudes are somewhat lower compared to the CH∗ and CO2∗ signals.Since the chemiluminescence intensity of all three optical signals depends in the same way (i.e. linearly) onthe air mass flow, but differently (i.e. exponential with different exponents) on equivalence ratio fluctuations,this deviation in amplitude indicates heat release fluctuations due to fluctuations of the equivalence ratio.

In comparison with the acoustic results, the phase trends of the flame transfer function obtained fromindividual flame optical signals show good agreement (except for some frequency ranges above 300 Hz, wherethe amplitude of the absolute values is low), this is not the case for the absolute values. Especially forfrequencies below 230 Hz, abs(F (ω)) obtained by the optical method shows an increase in amplitude withdecreasing frequency, while the purely acoustic method features decrease in amplitude towards zero forf → 0 Hz, as expected for a stiff fuel injection system.16 The acoustic results are believed to capture theflame transfer function correctly (as this method is already well-established and the obtained trends agreewell with the simplified analytical solution). Hence, the deviation of the two methods clearly indicates thatthe heat release fluctuations cannot be determined accurately from just one chemiluminescence signal.

The multi signal optical method shows a significantly better agreement with the acoustic results. Whilethe obtained phase of the flame transfer function is very similar to the single signal optical approach (whichwas already good), the trends in absolute value are good between 70 and 280 Hz and still reasonable abovethis frequency range.

IX. Conclusions

Thermoacoustic transfer functions of a generic swirl-stabilized gas turbine burner have been measuredat atmospheric conditions. Loudspeakers were employed for the acoustic excitation of the combustion testrig. Arrays of condenser microphones have been used to record the acoustic response of the system to thisexcitation. The flame’s OH∗, CH∗ and CO2∗ chemiluminescence response was measured by four photomul-tiplier tubes. To In addition, a light spectrometer recorded the light spectrum emitted by the flame and anICCD camera monitored the flame’s location in the combustion chamber.

The thermoacoustic transfer function has been obtained by three different techniques: A widely usedpurely acoustic technique has been employed to obtain the burner and flame transfer matrix. This techniquemakes use of the well-established multi-microphone method to determine the response of acoustic pressureand velocity in the combustion test rig to acoustic excitation. Based on the acoustic burner and flametransfer matrices the flame transfer function was obtained.

In addition, two combined acoustic-optical techniques have been used for the determination of the flametransfer function. These techniques evaluate the response of the OH∗ (CW 308nm), CH∗ (CW 431nm)and CO2∗ (CW 408nm and 451nm) chemiluminescence of the flame to the acoustic excitation in order toestimate the flame’s heat release fluctuations. Since fluctuations in the flame’s heat release have generallytwo contributions, e.g., fluctuations in mixture mass flow and equivalence ratio, at least two optical signalsare required to obtain the flame’s heat release fluctuation. In the ’direct’ optical approach the flame’s heatrelease fluctuations are estimated based on the four measured photomultiplier intensities. In the ’CH/OH’approach ratio of CH∗ and OH∗ chemiluminescence serves as one optical signal, while also scaling with theequivalence ratio of the flame within the investigated operating range.

The transfer functions obtained from acoustic-optical data are in good agreement with the transfer func-tions obtained from purely acoustic data. From the acoustic-optical method equivalence ratio fluctuationshave been identified as the dominant driving mechanism for heat release fluctuations in the low frequencyregime. For high frequencies the effect of equivalence ratio fluctuations were found to be less pronouncedcompared to the effect of air mass flow fluctuations.

Since the described acoustic-optical methods do not necessarily rely on arrays of multiple microphoneslike the standard purely acoustic method, but only require a mean to measure the velocity fluctuations atthe burner exit (e.g., by monitoring the pressure drop across the burner), it has the potential to be moresuitable for transfer function measurements in high pressure combustion test facilities, where the access tothe combustor is generally very limited.

Being able to measure transfer functions at high pressure conditions on full scale burners opens up thepossibility to predict thermoacoustic behavior of gas turbines using fuels whose combustion properties dependon pressure such as natural gases with higher hydrocarbon content, syngases and liquid fuels.

20 of 21


References

1Poinsot, T. J., Trouve, A. C., Veynante, D. P., Candel, S. M., and Esposito, E. J., “Vortex-driven acoustically coupledcombustion instabilities,” Journal of Fluid Mechanics, Vol. 177, 1987, pp. 265–292.

2Candel, S. M., “Combustion instabilities coupled by pressure waves and their active control,” 24th Symposium (Interna-tional) on Combustion, The Combustion Institute, 1992, pp. 1277–1296.

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Pulsations in a Premixed Combustor Using Fuel Staging,” 2009, ASME paper GT2009-59300.9Dobbeling, K., Knopfel, H. P., Polifke, W., Winkler, D., Steinbach, C., and Sattelmayer, T., “Low NOx Premixed

Combustion of MBtu Fuels Using the ABB Double Cone Burner (EV Burner),” 1994, ASME Paper 94-GT-394.10Seipel, A., Brockhinke, A., and Kohse-Hoinghaus, K., “TP3: Spectroscopic Characterization and Simulation of Chemi-

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Chemiluminescent Light Emission and Heat Release Rate under Non-adiabatic Conditions,” 2000, ASME Paper 2000-GT-0121.13Schuermans, B., Guethe, F., and Mohr, W., “Transfer Function Measurements for Technically Premixed Flames Using a

Novel Optical Method,” ASME GT2008-51500, Proc. ASME Turbo Expo 2008, Berlin, June 9-13 , 2008.14Schuermans, B., Guethe, F., Pennell, D., Guyot, D., and Paschereit, C. O., “Thermoacoustic Modeling of a Gas Turbine

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