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A STUDY OF THE ROLE OF EQUIVALENCE RATIO FLUCTUATIONS DURINGUNSTABLE COMBUSTION IN A LEAN PREMIXED COMBUSTOR

Jong Guen Lee1, Kwanwoo Kim2 and Domenic A. Santavicca3

Department of Mechanical and Nuclear EngineeringThe Pennsylvania State University

University Park, PA 16802

1 Research Associate, Department of Mechanical and Nuclear Engineering2 Ph. D. Student, Department of Mechanical and Nuclear Engineering, currently at GE Power Systems3 Professor, Department of Mechanical and Nuclear Engineering, AIAA Senior Member

AbstractThe instability occurring in a single-injector leanpremixed combustor equipped with an in-scaleindustrial injector (Solar Turbines' Centaur 50) wascharacterized from the measurements of pressure in thecombustor, heat release from the flame andequivalence ratio in the premixing region. Resultsclearly show that equivalence ratio fluctuations play animportant role in the process of sustaining combustioninstabilities by providing the feedback betweenpressure and heat release fluctuations. Characteristictimes associated with the feedback process weredetermined from the measurements and a detailedtime-lag analysis was carried out. The role ofequivalence ratio fluctuation in the observed instabilityseemed to be properly captured by the time-lag model,but the prediction of the occurrence of unstablecombustion by the model produced contradictoryresults in tests employing a slightly modified injector.A passive control approach with the modification ofacoustic characteristics in the fuel line resulted in ashift of the instability range towards higherequivalence ratios.

IntroductionLean premixed (LPM) combustion has been

widely accepted as the most promising strategy formeeting current NOx emission regulations and asstandard technology in industrial gas turbineapplications. Unfortunately, lean premixed combustionsystems are very susceptible to dynamic instabilities. Anumber of experimental and theoretical studies1-14 havebeen conducted to investigate the mechanism and todevelop strategies to prevent the occurrence or suppress

the strength of instabilities. To date, however, there areno tools available which can be used to predict thestrength and/or onset of instabilities in practicalcombustors. This means that the stabilitycharacteristics of a new combustor are known onlyafter the prototype is tested, resulting in a time-consuming and costly development effort.

Experiments carried out in a variety ofconfigurations indicate that combustion instabilities aresustained by feedback between the combustion processand the acoustic fields within the combustor as firstexplained by Rayleigh15. Though the so-calledRayleigh criterion provides a necessary condition forsuch instabilities to occur, it does not provide anyinformation as to which mechanism(s) plays a role ininitiating and sustaining the unstable combustion. It isalso possible that several mechanisms coexist and thatthe dominant mechanism may change with differentoperating conditions. Additionally, a mechanism thatis responsible for the initiation and growth ofoscillations might cause the onset of anothermechanism that will eventually sustain the instability.To date, most studies have focused on understandingthe limit-cycle behavior where the initial cause of theinstability is not of concern.

One instability mechanism which has receivedconsiderable attention recently is what is referred to asfeed system coupling.8-14 Feed system coupling occurswhen acoustic oscillations (p’) induced by periodic heatrelease (q’) are transmitted to the inlet supply pipesand result in oscillations of the air and/or fuel velocityat the fuel-injection location. This results influctuations in equivalence ratio which are convectedinto the combustor producing heat release fluctuations(q’). The total time lag (τ) is defined as the summation

38th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit7-10 July 2002, Indianapolis, Indiana

AIAA 2002-4015

Copyright © 2002 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

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of the convective time lag (τconv), i.e., the time takenfor the equivalence ratio fluctuations to convect fromthe injector to the flame region, and a chemical timelag (τchem), i.e., the time taken for the fuel to react inthe reaction zone. Following Rayleigh’s criterion, thereshould exist a band of specific ratios of τ to the periodof oscillation (T) over which the instability is likely tooccur for a given combustor configuration.

An understanding mechanism of unstablecombustion can provide measure(s) to prevent it.Pressure oscillations associated with Solar Turbines'low emission, natural gas fired Centaur family of gasturbine engines were eliminated by a modification tothe annular premixing chamber.16 The rationale forthis modification was to change the residence time ofthe fuel and air mixture inside the injector by changingthe cross sectional area of the inlet duct and thereforeto decouple the heat release with the combustoracoustics. Similar results were reported by Steele etal.13 and Straub and Richards9 where instabilities weresuppressed by relocating the axial location of fuelinjection. Even though these minor design changeswere sufficient to ensure stable operation, theunderlying causes of instabilities were not completelyunderstood.

The objectives of the present work are toexplore the validity of the time-lag theory and to devisespecific control strategies for a combustor equippedwith an in-scale industrial injector (Solar Turbines'Centaur 50) under lean premixed combustionconditions. Characteristic times associated with thefeedback process between the heat release and thepressure in the combustor will be determinedexperimentally, eliminating ambiguities ofapproximating or modeling these parameters. Withthese results, a detailed time-lag analysis will becarried out to determine if time-lag theory can explainthe causes of instabilities in this combustor. Accordingto the results obtained, an effective control strategy willbe suggested and evaluated.

Experimental Setup and Procedure

ApparatusThe apparatus used in this study is a single-

injector rig which is shown schematically in Fig. 1.The rig is a modular design that can be arranged to testdifferent injector configurations. Compressed air ismetered, electrically-preheated to the requiredtemperature and introduced into the diffuser sectionthrough a choke-plate. Natural gas (nominally 96.3CH4, 2.4 % C2H6, 0.3 % C3H8, and 1.0 % N2) is used

as a fuel. The combustor is a coaxial dump combustorwith a rearward-facing step and consists of a fused-silica section (diameter = 15 cm) followed by astainless steel section. The total combustor length (84cm) was adjusted to match its instability frequency tothe one around 450 Hz observed during the engine testof Centaur 50 fuel injector. The combustor exit can bechoked or partially restricted to change the exitboundary conditions.

The details of the combustor are shown in Fig.2. The dump plane is flush with the end face of anannular premixing section of the fuel injector, formedby the outer wall and a center bluff-body. The outerdiameter of the mixing section is 7.0 cm, and the innerdiameter is 4.0 cm. The cross sectional area of themixing section can be changed by a removable barrelinsert (thickness=0.32 cm), which reduces the outerdiameter to 6.36 cm. Sixteen swirl vanes are located4.2 cm upstream of the dump plane and the fuel isinjected co-axially via injection spokes extendingradially towards the center bluff-body and locateddownstream of the swirl vanes and 3.8 cm upstream ofthe dump plane. To prevent overheating of the fused-silica section of combustor, cooling air is provided by acooling ring through 40 holes directed at its surface.

Test ConditionsThe operating conditions are summarized in

Table 1. The inlet air temperature is fixed at 385 oC.The mass flow rate of air is varied from 60–110 g/s,resulting in mean combustor velocity (Ucomb) in the

Figure 1. Schematic drawing of the apparatus

Fused silica section

Stainless steel section

Cooling ring

Center bluff-body

Insert

Mixing section

Figure 2. Detail view of combustor

Diffuser

Fused-silica Section

Choke PlateInjector

Preheatedair inlet

Stainless SteelSection

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range of 6- 11 m/s. These correspond to 41-75 m/s and55-100 m/s in the annular premixing region (Uavg) inthe injector without and with insert, respectively. Allexperiments were done at atmospheric pressure,although partial restriction of the combustor exitslightly increased the mean pressure in the combustor.

Table 1. Operating conditions

Combustor inlet temperature 385 oCMean velocity in the combustor 6.1, 8.5, 10.8 m/secMean combustor pressure 1.0 - 3.75 psigEquivalence ratio L.B.O. - 0.8

MeasurementsIn order to characterize the instability

occurring during unstable combustion, pressure, heatrelease and inlet equivalence ratio are measuredsimultaneously. High frequency piezo-electric pressuretransducers are used to measure the fluctuatingpressure. Pressure oscillations in the combustor (Pc) aremeasured at the dump plane, the fuel line pressure (Pf)is measured 37 cm upstream of fuel injection locationand the pressure in the diffuser (Pd) is measured 17 cmupstream of dump plane. Global heat release from theflame (q) is measured using a photomultiplier tube(PMT). A collection lens is used to collectchemiluminescence from the whole flame. Thechemiluminescence from various flame radicals, suchas OH*, C2*, CH*, and CO2*, has been used as anindicator of global and local heat release in leanpremixed flames of hydrocarbon fuels 17-19. In thisstudy, a broad band-pass filter (BG-40) is used with aPMT to collect chemiluminescence from CO2* (350-550 nm). The equivalence ratio (φ) fluctuation duringunstable combustion is measured using the absorptionof infrared light at 3.39 µm wavelength by methane.14

The line-of-sight measurement involves measuring thetotal absorption of the light along a chord located 7mm upstream of the dump plane. The opticalarrangement and the equipment used for theequivalence ratio measurements are illustrated inFigure 3. Light from an infrared HeNe laser passesthrough the injector and the transmitted light ismeasured by an InAs detector. In order to allow for thepassage of light, holes are drilled on both sides of theinjector and adapters with a sapphire window on oneend are mounted in the holes.

An intensified CCD camera is used to recordchemiluminescence images of the flame zone. Themeasurements are phase-synchronized with thepressure in the combustor during unstable combustion,providing a sequence of images which show thetemporal and spatial evolution of the heat releaseduring one period of pressure oscillation. The exposuretime of the ICCD camera is set to 25 µsec whichcorresponds to 1 % of the instability period. The two-dimensional heat release structure is extracted from theline-of-sight integrated image by using a tomographicdeconvolution procedure.20

Results and Discussions

Stability CharacteristicsThe instability characteristics of the

combustor with the insert over the range of testconditions listed in Table 1 are presented in Figure 4 inthe form of a so-called stability map. Figure 4a is a plotof the RMS pressure fluctuation in the combustor at thedominant frequency versus equivalence ratio. Also,shown in Fig. 4b is the dominant frequency at whichthe peak pressure fluctuation is observed. Results arepresented for the three inlet velocity conditions listedin the Table 1. As the combustor inlet velocityincreases, the instability starts at a lower equivalenceratio, the maximum pressure fluctuation increases and

Figure 3. Schematic drawing of set up for equivalence ratio measurements using IR absorption of methane (a) front view and (b) side view

Data acquisitionsystem

InAs Detector

HeNe Laser(3.39 µµm)

InAs Detector

Dataacquisition

system

Center bluff-body Fuel injectionlocation

Preheatedair in

7 mmDiffuser Measurement

Location

Swirl vanes

Adapters

(a) (b)

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the range of equivalence ratios over which theinstability occurs becomes broader. For the meancombustor inlet velocity of 6.1 m/sec case, the

combustion would generally be considered to be stableover the range of equivalence ratios tested, althoughinspection of the frequency spectra of the pressure

Frame number1 2 3 4 5 6 7 8 9 10 11 12

Pc(

psi

)

-1

0

1

#1 #2 #3 #4

#9 #10 #11 #12

#5

#7 #8

#6

HighLow

Figure 5. Evolution of heat release structure during one period of unstable combustion at Ucomb = 10.8 m/sec and φφ=0.65

0.50 0.55 0.60 0.65 0.70 0.75 0.80

RM

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f (H

z) a

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6.1 m/sec (stable)6.1 m/sec (unstable)8.5 m/sec (stable)8.5 m/sec (unstable)10.8 m/sec (stable)10.8 m/sec (unstable)

Ucomb

(a) (b)

Figure 4. Stability maps (a) RMS of Pc vs. φφ and (b) Frequency at the maximum RMS fluctuation of Pc vs. φφ

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fluctuations in fact does show clear evidence of adominant frequency near 450 Hz at certain equivalenceratios. When the combustor inlet velocity is increasedto 8.5 m/s, unstable combustion is more evident, wherethe relative RMS pressure fluctuation (Prms/Pavg) has amaximum value of 0.6 % at an equivalence ratioaround 0.65. Again, the frequency spectra of thepressure fluctuations at this condition show a dominantfrequency near 465 Hz, which closely matches thefundamental half-wave longitudinal mode of thecombustor. When the combustor inlet velocity isincreased to 10.8 m/s, very strong instabilities areobserved. In this case the strongest instability has arelative RMS pressure fluctuation greater than 3 %.The dominant frequencies for all of the conditionstested are summarized in Fig. 4(b), where only thosecases with relative pressure fluctuations greater than0.2 % are considered to be unstable. A general trend ofincreasing frequency with increasing equivalence ratiois observed in these results, which can be attributed toan increase in the speed of sound due to increasedtemperatures at higher equivalence ratios. Similarly,increased heat release at higher velocities results inhigher average combustor temperatures and thereforehigher frequencies. Also, it can be noted that the mostof unstable combustion occurs within a band offrequencies, i.e. 445-470 Hz.

Figure 5 shows a typical sequence of phase-averaged two-dimensional CO2* chemiluminescenceimages during one period of unstable combustion(Ucomb=10.8 m/sec and φ=0.65). In each image, onlythe upper half of flame is displayed and the flowdirection is from left to right. Shown in the inset is the

pressure at which each image is taken. The flameappears to be attached to the outer edge of the centerbluff-body at all times and the downstream part offlame displays an evidence of flame-vortex interaction.

Figure 6 shows the mean and RMS fluctuationof heat release as a function of equivalence ratio at themean combustor inlet velocity of 10.8 m/sec. Unstablecombustion observed in this study is accompanied byvery large heat release fluctuations; at an equivalenceratio around 0.65, the RMS fluctuation in heat releaseis as large as 25 % of the mean. Also, shown in thisfigure is a curve fit of mean heat release from stableflames. Note that at a given equivalence ratio the meanheat release from unstable flames is greater than that ofthe flames which would have been stable.

During unstable combustion, the pressure atthe dump plane (Pc), in the fuel line (Pf) and before thenozzle in the diffuser (Pd), the total chemiluminescenceintensity (q) and the transmittance (I/IO) of the IR-laserbeam across a part of the fuel/air mixture weremeasured simultaneously. Transmittance of the IR-laser beam was converted into the correspondingequivalence ratio (φ) using the relationship shown inthe Figure 7. This relationship is obtained from thecurve fit of the transmittance (I/IO) vs. φ data takenfrom a separate experiment in the same combustor andat the same operating conditions as specified in Table 1but without combustion. It is assumed that theequivalence ratio distribution across the absorptionpath does not change during unstable combustion eventhough the instantaneous overall equivalence ratio andthe total flow rate do. It can be noted that the samerelationship between I/IO and φ holds for different

Figure 6. Mean and RMS chemiluminescence intensity vs. φφ for Ucomb=10.8 m/sec

Equivalence ratio

0.50 0.55 0.60 0.65 0.70 0.75Ch

emilu

min

esce

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inte

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(a.

u.)

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QMean for stable flame

QMean for unstable flame

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0.40

0.45

0.50

0.55Ucomb=6.1 m/secUcomb=8.5 m/secUcomb=10.8 m/sec

I/Io=e-1.688*φφ

Figure 7. Normalized transmitted intensity (I/Io) as a function of equivalence ratio

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mean mixture velocities in the premixer, suggestingthat the fuel distribution across the laser beam passagedoes not change when the mean mixture velocitychanges.

Figure 8 shows time traces of Pc, Pf, Pd, q andφ during unstable combustion at a combustor inlet

velocity of 10.8 m/sec and an overall equivalenceratio of 0.65, i.e., where the strongest instability isfound. The pressure in the combustor oscillatespredominantly at the instability frequency but isaccompanied by smaller oscillations at higherharmonic frequencies. Measurements show that theamplitude of pressure fluctuations in the fuel line (Fig.8b) is comparable to that in the combustor while theamplitude of pressure fluctuations in the diffuser (Fig.8c) is about an order of magnitude less. This suggeststhat the resonance modes of pressure fluctuation in thefuel line and diffuser at the instability frequency aredifferent and/or the acoustic impedances of fuel lineand diffuser section are different. Similar to thecombustor pressure, both the fuel line and diffuserpressure exhibit oscillations at higher frequencycomponents. The fuel line and diffuser pressurefluctuations result in the equivalence ratio fluctuationsshown in Fig. 8d where the RMS fluctuation ofequivalence ratio is about 5 % of the mean equivalenceratio and higher harmonic fluctuations are evident. Theheat release fluctuations, which are produced by theseequivalence ratio fluctuations and perhaps otherfactors, are shown in Fig. 8e. It is interesting to note,however, that the heat release fluctuations do notexhibit higher harmonic frequency components,indicating that the flame acts as a low pass filter tosmooth out the higher frequency fluctuations. This isnot unexpected given the fact that the flame is spreadover a finite axial distance, hence fuel arrives atdifferent locations along the flame front at differenttimes.

Evaluation of the validity of the time-lag theoryMeasurement results shown in Fig. 8 seem to

suggest the mechanism of the instability at theparticular operating condition is adequately explainedby the time-lag theory. In Fig. 8a and 8d, it is shownthat the fluctuation of equivalence ratio at themeasurement location lags that of combustor pressureby about 200 degrees. The convection time delaybetween location where the equivalence ratio ismeasured to the location where the mixture isconsumed (τφq) results in a phase delay between thecombustor pressure and the heat release within 90degrees which ensures positive feedback between thetwo.

Based on the time-lag model suggested byStraub and Richards9 and Lieuwen et al.11, the totaltime-lag can be estimated. The exact time-lag betweenthe combustor pressure and the flow velocities of fueland air at the fuel injector exit is determined by the

Figure 8. Time traces of (a) combustor pressure, Pc ; (b) fuel line pressure, Pf ; (c) diffuser pressure, Pd; (d) equivalence ratio φφ; (e) heat release, q

0.0 0.2 0.4 0.6 0.8 1.0

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q

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(a)

(b)

(c)

(e)

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actual acoustic impedance of fuel line and diffuser atthe instability frequency. Since the fuel injector is notchoked in the present setup, it is assumed that the fuelflow rate at the injector exit is out of phase with thecombustor pressure. With this assumption, the time lagbetween the combustor pressure fluctuation and theequivalence ratio fluctuation at its measurementlocation (τpcφ) can be estimated as Li-φ/Uavg where Li-φ isthe distance between the fuel injection location and theequivalence ratio measurement location (=3.1 cm) andUavg is the mean mixture velocity in the annularpremixing region. The convection time delay duringwhich the locally rich and lean mixture pockets movefrom the measurement location of equivalence ratio tothe flame front where the mixture is consumed (τφq)canbe estimated by (Li-d+Lflame)/Uavg by assuming that themixture burns instantaneously as it reaches the flamefront. Li-d is the distance between the dump plane andthe equivalence ratio measurement location (=0.7 cm)and Lflame the distance from the latter to the flamesurface. The location of flame surface is estimated asthe distance from the center of the annular premixingsection at the dump plane to the location where themaximum heat release occurs when the total heatrelease from the flame is maximum during heat releaseoscillation. The chemiluminescence images shown inthe Fig. 5 were used and from the frame #1 imageLflame is found to be 5.67 cm. The estimated time-lagsare compared with the measured ones from the crossspectrum of Pc and φ and φ and q. The result is shownin Table 2.

Table 2. Comparison between measured and estimated time-lags for the unstable flame at Ucomb=10.8 m/sec and φφ=0.65

τpcφa (msec) τφq

b (msec) τ/Τc

Estimated 1.428 0.640 0.962Measured 1.176 1.193 1.102

a Time-lag between the combustor pressure fluctuation and the equivalence ratio fluctuation at the measurement locationb Time-lag between the equivalence ratio fluctuation at the measurement location and the heat release fluctuationc τ: Τotal time lag (τpcφ+τφq) T: Period of the instability (2.15 msec)

Estimated time-lag τpcφ is overestimated by 11% of the instability period compared with the measured

value. This discrepancy may be attributed to the factthat the actual acoustic impedance of the fuel line anddiffuser section at the fuel injection location are notexactly such that the fuel flow is out of phase with thecombustor pressure at the injector exit. Also,comparison in Table 2 shows that τφq is underestimatedby 25 % of the instability period. Since fuel arrives atdifferent locations along the flame surface at differenttimes, it is expected that a single value of Lflame or Uavg

can not describe a proper time delay. In addition, if theflame surface moves back and force during the unstablecondition, the unburned mixture is accelerated anddecelerated and it is more difficult to estimate the time-lag.

Though the total time-lag is estimated asabout the same as the measured one, satisfying thetime-lag theory in that 0.75 < τ/T < 1.25, thecomparison shown in Table 2 indicates that the correctestimation of the total time-lag requires additionalinformation such as the actual acoustic impedance ofthe fuel and air lines, the proper length and velocityscales, etc. Even if these are available, the time-lagtheory can not provide an explanation to the instabilitycharacteristics observed in the present study where at agiven mixture velocity (and hence a fixed convectiontime delay) both stable and unstable conditions exist asthe equivalence ratio changes. Torres et al.10 explainedthis by stating that time lag theory predicts conditionsthat are necessary but not sufficient for an instability tooccur. If a specific condition satisfy the τ/T predictedby the time lag theory, it can be stable or unstable,

Figure 9. Comparison between the estimated and measured total time-lag normalized by the instability period (ττ/T)

ττ/T

0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5

PR

MS (

psi

)

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0.6

EstimatedMeasured

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depending on whether or not the gain is sufficient toovercome the damping at that condition. The otherpossible explanation is that for some condition (such asnear the lean blow out) the chemical time delay maycontribute significantly to the total time-lag and be adetermining factor.

τpcφ and τφq are measured for all unstablecombustion over the test conditions listed in Table 1and the total time-lags (τ) are compared to theestimated ones. Constant value of Lflame of 5.67 cm isassumed for the estimation. The result is shown in theFig. 9. Most estimated and measured values lay in aband of the instability region predicted by the time-lagtheory (i.e. 0.75 < τ/T < 1.25), seemingly suggestingthat the physics of the instability is properly capturedby the time-lag theory. However, it should be notedthat at a given mixture velocity the stable flameconditions at different φ’s will lay in the same band,suggesting the time-lag theory does not completelyexplain the observed instabilities.

Passive control approachesIf the time-lag theory can accurately predict

the occurrence of unstable combustion, the unstablecombustion could be avoided by modifying time-lags sothat the pressure oscillation in the combustor may bedecoupled from the heat release fluctuation. One wayto achieve this is by changing the convective time-lagas suggested by Straub and Richards9 and Steele etal.13. where they demonstrated that by changing fuelinjector location, unstable combustion can beeliminated. They attributed the positive effect of simplemodification of fuel injector configuration to themodified time-lag. Based on the same idea, thecombustor was run at the conditions listed in Table 1without insert in the annular premixing region. For agiven mass flow rate of fuel/air mixture, thismodification leads to 35 % increase of cross-sectionalarea and hence residence time in the premixing region.Following the analysis in the previous section, the totaltime-lag can be estimated. This is shown in Table 3.

Table 3. Estimated total time-lag without insert in the premixing region

Ucomb (m/sec) τ/Τ6.1 1.6048.5 1.29310.8 1.124

The time-lag theory predicts that if thecombustor is run without the insert, the combustion

will be unstable for Ucomb=10.8 m/sec and stable forUcomb=6.1m/sec and 8.5 m/sec. However, test resultsshow that the combustion is unstable only forUcomb=6.1 m/sec case. The contradictory test resultssuggest that although the time-lag theory is a usefultool to interpret the observed instability, it is difficult topredict the occurrence of unstable combustion usingthis theory. This is especially true in situations wherethe total time lag is altered by modifying the injectorgeometry or injection location, since suchmodifications might also change the mixingcharacteristics in the combustor inlet, which in itselfcan change the stability characteristics.

A different approach is adopted to control thecombustion dynamics. As mentioned previously, theacoustic impedance of the fuel line (the diffuser)determines the time-lag between the combustorpressure and fuel (air) flow velocity fluctuations at thefuel injection location. And the relative phase angledifference between the fuel and air flow fluctuationsdetermines the magnitude of equivalence ratiofluctuation. Since the acoustic impedance of anelement at a frequency depends on its dimension andacoustic boundary conditions, the time-lag between thecombustor pressure and the fuel/air velocities can be

0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80

(Pc) R

MS

(p

si)

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Far upstream54 cm upstream

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Fuel flow-choke location Ucomb=6.1 m/sec

Ucomb=8.5 m/sec

Ucomb=10.8 m/sec

Figure 10. Comparison of stability maps between cases where fuel-choke location is located far upstream and 54 cm upstream of injector exit

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varied by changing the dimension and/or acousticboundary condition of fuel/air lines. For example,changing the distance from the fuel injector to theupstream flow-choke location can change the acousticimpedance at the injector exit and hence affect thetime-lag. The fuel line is modified so that the chokelocation is moved from far upstream to 54 cm upstreamof injection location. The new flow-choke location ischosen so that at the injector exit the impedancebecomes zero at the instability frequency of 465 Hz.With this modification, the combustor was run at theconditions listed in Table 1. Test results are shown andcompared with those of the far upstream choke locationcase in Fig. 10. Although the maximum intensity ofpressure oscillation is not reduced by the modificationof fuel line, at all velocity the instability ranges areshifted towards the higher equivalence ratio region.Without measuring acoustic impedance at the rightdownstream of fuel injection location, it is difficult toevaluate the acoustic effect of changing flow-chokelocation in the fuel line. However, the pressure

measured in the fuel line (Pf) and the diffuser (Pd)shows that as the flow-choke location in the fuel linechanges, the phase angle difference between fuel andair flows at the fuel injection location would bechanged. Since the magnitude of equivalence ratiofluctuation changes with respect to the phase differencebetween the two, this would affect the magnitude ofequivalence ratio fluctuation, too. Figure 11 shows thephase angle measurement results made at Ucomb=10.8m/sec for the two flow-choke location cases. Note thatthe measurements were made at unstable conditionsand each phase angle is measured with respect to thecombustor pressure. As the equivalence ratio changes,the phase angle of fuel line pressure changes overwider ranges compared with that of diffuser pressure.At a given equivalence ratio, the phase angle ofdiffuser pressure doesn’t seem to be affected that muchby the change of flow-choke location but the phaseangle of fuel-line pressure changes by a relatively largeamount, reflecting the effect of modification of fuel-line on acoustics.

Summary and ConclusionsThe instability characteristics of a single

injector combustor were determined from themeasurement of pressure in the combustor, heat releaseand equivalence ratio. Unstable combustion wasaccompanied by large equivalence ratio fluctuations (asmuch as 5 % of the mean) and heat release fluctuations(as much as 25 % of the mean). A detailed time-laganalysis based on the measurements showed that theconvection time delay in the premixing region wasoverestimated and that in the combustor isunderestimated by the time-lag model but the estimatedtotal time-lag is about the same as the measured one. Apassive control approach based on the time-lag modelwas implemented by changing the flow area in the fuelinjector. However, at the condition where the time-lagmodel predicts unstable (stable) combustion the flamewas stable (unstable). Another passive controlapproach employing the modification of the fuel linewas tested. The location where the flow is choked inthe fuel supply line was changed. The rationale wasthat by changing the acoustics of the fuel line, thetime-lag between combustor pressure and fuel velocityfluctuations and hence the equivalence ratio fluctuationat the fuel injection location would be modified.Although the maximum intensity of pressureoscillation is not reduced, the modification leads to ashift of the instability range towards higherequivalence ratios. These results clearly indicate thatthe information on the acoustic characteristics of fuelinjector and more careful estimation of the time-lag in

φφ0.55 0.60 0.65 0.70 0.75

Ph

ase

ang

le o

f P

f an

d P

d w

ith

res

pec

t

to t

he

com

bu

sto

r p

ress

ure

-400

-350

-300

-250

-200

-150

-100

-50

Pf

Pd

φφ0.55 0.60 0.65 0.70 0.75

Ph

ase

ang

le o

f P

f an

d P

d w

ith

res

pec

t

to t

he

com

bu

sto

r p

ress

ure

-400

-350

-300

-250

-200

-150

-100

-50

(a)

(b)

Pf

Pd

Figure 11. Phase angles of Pf and Pd with respect to the combustor pressure (a) when the fuel line is choked far upstream of fuel injection location and (b) when the fuel line is choked at 54 cm upstream of fuel injection location

American Institute of Aeronautics and Astronautics10

the combustor are needed for the time-lag model to beused as a predictive tool for the occurrence ofinstabilities.

AcknowledgmentsThe authors would like to thank Solar Turbines

for supporting this research, and in particular KenSmith and Leonel Arellano from Solar Turbines fortheir support and encouragement. We would also liketo acknowledge the contributions of Ramu Bandaruand Sanem Berksoy in making the test facilityoperational.

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