Combustion and Flame 145 (2006) 290–299www.elsevier.com/locate/combustflame

Transfer function characteristics of bluff-body stabilized,conical V-shaped premixed turbulent propane–air flames

Andres Chaparro, Eric Landry, Baki M. Cetegen ∗

Mechanical Engineering Department, University of Connecticut, 191 Auditorium Road, Storrs, CT 06269-3139, USA

Received 26 May 2005; received in revised form 10 October 2005; accepted 12 October 2005

Available online 7 December 2005

Abstract

The response of bluff-body stabilized conical V-shaped premixed flames to periodic upstream velocity oscil-lations was characterized as a function of oscillation frequency, mean flow velocity, and equivalence ratio. Theflame heat release response to the imposed velocity oscillations was determined from the CH∗ chemilumines-cence captured by two photomultiplier (PMT) detectors at a wavelength of 430 nm. One of the PMTs viewedflame radiation in a 10-mm horizontal slice, 50 mm above the bluff-body. The second PMT observed the overallflame radiation. The flame transfer function characteristics were determined from the spectral analysis of the ve-locity and PMT signals. It was found that the flame heat release amplitude response is confined to low-frequencyexcitation below a Strouhal number of 4. The phase relationship of the transfer function for these turbulent flameswas evaluated using the signal from the spatially masked PMT. The transfer function estimate based on these dataexhibits second-order characteristics with a phase lag between the velocity and heat release signals. The localizedheat-release response contains frequencies that are multiples of the excitation frequency, suggesting splitting andtilting of flame structures as well as some nonlinear effects. Increase of flame equivalence ratio from lean towardstoichiometric resulted in slight amplification of the high-frequency response. 2005 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Keywords: Combustion dynamics; Transfer function; Premixed flames; Turbulence; Bluff-body

1. Introduction

Interaction of premixed flames with flow distur-bances and the resulting coupling have been studiedextensively in the combustion literature. Candel [1]and Lieuwen [2] have provided excellent reviewson this subject. The premixed flame-flow interac-tions have attracted great interest in the combustionresearch community, particularly due to the prob-

* Corresponding author. Fax: +1 860 486 5088.E-mail address: cetegen@engr.uconn.edu

(B.M. Cetegen).

0010-2180/$ – see front matter 2005 The Combustion Institute.doi:10.1016/j.combustflame.2005.10.013

lems encountered in the operation of high-intensitycombustion systems such as gas turbine engine com-bustors, afterburners, ramjets, and rockets. In thesesystems, the flame heat release behavior couples in-timately with the oscillations that arise in the com-bustor flow field and the resulting coupled system dy-namics manifests itself as high-amplitude oscillationsof both heat release and flow field variables (pressure,temperature, velocity). This dynamic coupling, firstdescribed by Rayleigh [3], occurs under conditions offavorable phase coupling between the pressure oscil-lations and combustion heat release, which lead to thegrowth of combustion instabilities. Aside from reach-ing high levels of oscillation that lead to noise and

Published by Elsevier Inc. All rights reserved.

A. Chaparro et al. / Combustion and Flame 145 (2006) 290–299 291

eventually hardware failure, these oscillations causeunsteady flame liftoff, extinction, and eventuallyblowout [4]. In land-based gas turbine systems, thelean premixed operation of combustors accentuatesthese combustion instabilities and it is necessary tofind means of operating these systems at or near stableconditions. For such purposes, both active and pas-sive combustion control systems have been devised,as discussed by Candel [5] and McManus et al. [6].

Description of premixed flame interactions withflow disturbances has taken a number of differentforms depending on the configuration and phenom-enon of interest. In confined geometries where flameresides in a combustion chamber, the interactions takeplace as a result of acoustic, vortical, and/or entropycoupling [2]. Acoustic coupling involves the interac-tion of the flame with standing and/or traveling pres-sure waves, as studied both experimentally [7–11] andtheoretically [12–14]. Vortical interactions [15] occuras a result of flame response to upstream velocity per-turbations due either to fluid mechanical phenomenasuch as vortex shedding off a flame holder or interac-tion of the combustor with upstream or downstreamhardware (e.g., compressor or turbine-generated flowoscillations in the case of gas turbine combustors).The entropy interactions involve both density andtemperature oscillations. Among these, the first twohave been studied in greatest detail in the literature.

In addition to these, fundamental studies of pre-mixed flame-flow interactions have been carried outin simple geometries to gain a better understandingof the coupling phenomena. These analytical [16–18],computational [19,20], and experimental [17] studieshave focused on primarily laminar premixed flameinteractions. Axisymmetric laminar conical and in-verted conical or V flames have been subjected toperiodic upstream velocity oscillations and the flameresponse has been characterized in terms of a flametransfer function as a function of excitation ampli-tude and frequency, laminar burning speed, and flameangle. The flame transfer function is a convenientway of describing the amplitude and phase responsecharacteristics of a flame in the linear limit. In theexperiments, the flame response has typically beenmeasured by detecting the overall flame CH∗ chemi-luminescence, as it has been shown that this is a goodindicator of flame heat release fluctuations. In the-oretical analyses, the flame surface area variation isdetermined based on the so-called G-scalar transportequation and the computed flame area variation is in-terpreted as that of the heat release, assuming thatthe burning rate per unit area remains constant. Inlaminar conical and V-shaped flames, the amplitudeand phase characteristics of the transfer function, de-termined from experiments and computations, havebeen found to compare favorably [19,20]. While these

studies establish the foundational basis of improvedunderstanding of flame-flow interactions, the study ofturbulent flames in a similar context remains mostlyunexplored [2]. Dynamic response of turbulent flamesposes a number of differences from their laminarcounterparts, including the effects of turbulence on lo-cal burning rates, localized extinction, flame quench-ing, and reignition events, as well as the influence ofturbulence on the phase characteristics of the transferfunction. Motivated by these and the fact that mostof the practical combustion devices operate in the tur-bulent flow regime, we embarked on an experimentalcharacterization of turbulent inverted conical flamesof propane and air.

In this study, experiments were conducted in anunconfined axisymmetric flow configuration with theinverted conical flame being anchored by a disk-shaped bluff body. Flow velocity upstream of theflame was modulated in a sinusoidal manner at differ-ent frequencies at low amplitude and flame responsewas determined from CH∗ chemiluminescence. Theresults are presented here in terms of flame transferfunction as a function of upstream flow velocity, ex-citation frequency, and mixture equivalence ratio. Inthe remainder of this article, the description of ex-perimental systems is followed by the presentationand discussion of the experimental data. The articleis concluded by a summary of findings and conclu-sions.

2. Experimental

The experimental setup is schematically shown inFig. 1. The flow nozzle was made out of brass witha 3.2:1 nozzle diameter contraction with exit diame-ter 40 mm. A stainless steel rim of 2.5 cm height andof the same diameter as the nozzle was attached tothe nozzle exit to prevent damage to the brass nozzlein the case of flame attachment to the brass burnerrim. The fuel–air mixture was fed into the nozzlethrough eight equally spaced 9.5-mm-diameter radialports on the side wall before the contraction sec-tion. A stainless steel circular rod with a diameter of6.4 mm, centered in the nozzle, held the disk-shapedflame holder with a diameter of 10 mm. Upstream ofthe contraction, the nozzle contained a 12.5-cm-thickhoneycomb with a cell size of 4.0 mm and a stain-less steel mesh screen above it to reduce the inlet flownonuniformities. Attached at the bottom of the noz-zle was a loudspeaker cavity containing a 15.2-cm-diameter subwoofer (Kenwood Model KFC-1656) tomodulate the flow. The loudspeaker cavity was de-signed to allow free movement of the loudspeaker di-aphragm while preventing leakage of the combustiblemixture through the speaker diaphragm. The loud-

292 A. Chaparro et al. / Combustion and Flame 145 (2006) 290–299

Fig. 1. Experimental setup utilized in the transfer function experiments.

speaker was driven by a sine wave input generatedby the data acquisition computer using LabView soft-ware. The speaker excitation signal was first amplifiedby an audio amplifier before being fed into the loud-speaker. Speaker performance was first characterizedas a function of the excitation parameters (frequencyand amplitude) by measuring the velocity oscillationat the nozzle exit. A calibrated hot film probe wasplaced 19 mm below the bluff body tip halfway be-tween the bluff-body stem and the nozzle inner wallto measure the axial velocity.

Two photomultiplier tubes (PMT) with a narrowbandpass filter at λc = 430 nm ± 10 nm were usedto monitor the flame CH∗ chemiluminescence. Oneof these (PMT1) viewed a horizontal section of theflame between 50 and 60 mm above the bluff body.The second one observed the overall flame emission.The main reason for employing two photomultiplierdetectors was to be able to resolve the phase rela-tionship of the transfer function, which becomes dif-ficult with the signal from the PMT viewing the over-all turbulent flame. Both the hot film probe and thePMT outputs were first filtered by first-order ana-log filters and they were digitally sampled at 100times the excitation frequency with a simultaneoussample-hold data acquisition system (National Instru-ments, Model PCI-MIO-16E1 board with SC-2040sample/hold module). The filter frequency was ad-justed to prevent aliasing. In the reported experiments,the speaker excitation amplitude was maintained at arelatively low constant-flow-velocity modulation am-plitude of uRMS/Um = 0.08 at all of the studiedmodulation frequencies and mean flow speeds. Theair flow was supplied by a 0.1 kg/s capacity com-pressor (Gardner-Denver, Model Electra-ECHQHE).The compressor air discharge was first dried by arefrigeration-type dryer (Hankinson Model 80200)and metered by a bank of critical flow orifices to ob-

tain the desired air-mass flow rate or nozzle exit ve-locity. Fuel (instrument grade propane, 99.5% purity,from CT Airgas) was metered using a set of mass flowcontrollers (Porter Instruments Model 202). Fuel andair were premixed in a mixing chamber containing aseries of perforated plates and baffles to intimatelymix the fuel and air streams before the mixture en-tered the nozzle through eight radial ports, as shownin Fig. 1.

3. Results and discussion

In these experiments, the response of turbulentconical V-shaped flames was characterized as a func-tion of excitation frequency, mean flow speed, andmixture equivalence ratio. Experiments were con-ducted at three different flow velocities, Um of 5,10, and 15 m/s with an excitation amplitude ofuRMS/Um = 0.08. The cold-flow Reynolds numbersbased on the bluff body diameter were 3190, 6380,and 9570. These values would be reduced by a fac-tor of 25 if the Reynolds numbers were evaluatedat the temperature of the wake at around 2000 K.The modulation of the upstream flow was character-ized by a calibrated hot-film probe 8 mm upstreamof the bluff-body flame holder. Fig. 2 shows long-exposure photographs of these bluff-body stabilizedflames under four excitation conditions. It was ob-served that the flame response was most vigorousaround 100 Hz, with the overall flame shape changingand the upper part of the flame widening consider-ably. Effect of the imposed oscillations diminished athigher frequencies, with the flame taking on a nar-rower conical shape at 400 Hz. It is also worth notingthat the wake region immediately behind the flameholder became more luminous at the high excitationfrequency.

A. Chaparro et al. / Combustion and Flame 145 (2006) 290–299 293

Fig. 2. Gray-scale time-averaged photographs of propane air flames taken at Um = 10 m/s and φ = 0.9: (a) no excitation,(b) 100, (c) 200, and (d) 400 Hz. uRMS/Um = 0.08.

Fig. 3. Variation of flame height normalized with bluff-bodydiameter (d = 10 mm) as a function of excitation frequency.

In Fig. 3, the time-averaged flame heights areshown as a function of excitation frequency. It can beseen that there is a minimal effect of excitation fre-quency on the overall flame height, with a possibleexception at around 100 Hz for Um = 10 and 15 m/s.The flame height increased with increasing flow ve-locity for all excitation frequencies. It was found thatthe mixture equivalence ratio did not have a measur-able effect on the average flame heights. Fig. 4 showsthe time traces of velocity and the two photomulti-plier signals, as well as the coherence between the

velocity and photomultiplier signals for an excitationfrequency of 100 Hz. As expected, the masked pho-tomultiplier (PMT1) exhibits a response that clearlyshows the periodic variation of CH∗ emission in thatregion of the flame, whereas the unmasked photo-multiplier (PMT2) shows a very small amplitude ofoscillation as its signal is spatially integrated over thewhole flame. This difference can also be seen in thecoherence plot in Fig. 4b, where the coherence is kepthigh for the masked PMT at all frequencies but dimin-ishes to low values at higher excitation frequencies forthe PMT viewing the overall flame radiation.

To get a better insight into flame response char-acteristics, instantaneous images of the flames wereobtained as shown in Fig. 5 for several flow veloci-ties and different excitation frequencies. Also markedin these figures is the region observed by the maskedphotomultiplier. These images were acquired duringPIV measurements reported elsewhere [4]. This figureshows the negative images of the seed density as il-luminated by the 10-ns duration of the Nd-YAG laserpulse. Since the seed density is low in the products re-gion due to thermal expansion, the image contrast wasinverted to better visualize the flame. Also indicatedby arrows next to the top row of images is the convec-tive length scale given by l = Um/fex. The vertical

294 A. Chaparro et al. / Combustion and Flame 145 (2006) 290–299

Fig. 4. Time variation of velocity and photomultiplier voltages at 100 Hz (a); coherence between velocity and photomultipliersignals (b). PMT1: masked at 500 mm height above the flame holder; PMT2: unmasked viewing the whole flame.

Fig. 5. Flame images obtained by reversing the Mie scattering images obtained during the PIV experiments for the 10-mm-dia-meter disk-shaped bluff-body flame holder (arrows show the length scale, l = Um/f ).

separation of vortical flame structures and the lengthscale of flame undulations are similar to the convec-tive length scales shown in the first row of images inFig. 5. It is also worth noting that the outer-shear-layerstructures have half the spacing since they move at

Um/2. It is interesting to observe that the flame inter-actions are present at all excitation frequencies whenviewed with this technique and flame surface mod-ulations are very significant for the low level of theflow excitation amplitude (uRMS/Um = 0.08). The

A. Chaparro et al. / Combustion and Flame 145 (2006) 290–299 295

high coherence obtained for the masked PMT overthe whole range of excitation frequencies is due to itsability to resolve these oscillations. Since the viewingregion of this PMT was 10 mm, the highest frequencyof detection is limited to 100Um, which would be 500,1000, and 1500 Hz for 5, 10, and 15 m/s.

The transfer function was determined from thedigitally acquired data streams of velocity measuredat the burner exit and one of the photomultiplier sig-nals utilizing the discrete Fourier transform method.In its implementation in the MATLAB platform, thedata were subdivided into M segments of N sampleseach, where xj (n) is the nth sample of the j th seg-ment. The discrete Fourier transform of each segmentwas then calculated as

(1)Xj (k) =N−1∑

n=0

xj (n)e−2iπkn/N .

Then the power spectral density could be estimatedby averaging over the M segments, leading to an esti-mate of the power spectral and cross spectral densitiesas

Sxx(fk) = �t

MN

M∑

j=1

∣∣Xj (k)∣∣2

and

(2)Sxy(fk) = �t

MN

M∑

j=1

Xj (k)Y ∗j (k),

where Y ∗j(k) is the complex conjugate of Yj (k), fk =

k�f , and �f = 1/N�t .Transfer function was determined from

(3)H(fk) = Sxy(fk)

Sxx(fk),

where H(fk) is a complex quantity whose magnitude,A(f ), and phase, Φ(f ), correspond to those of thetransfer function. Additionally, the coherence of thetwo signals is determined from

(4)γxy(fk) = |Sxy(fk)|2Sxx(fk)Syy(fk)

.

Fig. 6 shows the normalized amplitude charac-teristics of the transfer function based on the CH∗chemiluminescence as detected by the unmasked(Fig. 6a) and masked (Fig. 6b) photomultipliers. Theabscissa of these plots were normalized with the flamelength, Lf, and approach velocity, Um, to form aStrouhal number St = f Lf/Um. The CH∗ ampli-tude response, which is proportional to the flame heatrelease rate, has a peak between St = 1.0 and 2.0and diminishes with increasing Strouhal number, asshown in Fig. 6a. The flame appears to be practicallyunresponsive to excitation for St � 4. The use of a

Fig. 6. Transfer function amplitude as a function of Strouhalnumber based on flame length scale and based on (a) overallflame emission, (b) the masked PMT signal for a mixtureequivalence ratio of φ = 0.95.

Fig. 7. Comparison of the second-order transfer functionmodel amplitude (thick line) and experimental amplitude(a); model phase variation (b) with excitation frequency.

Strouhal number based on flame length and approachvelocity results in a relatively similar response char-acteristics. When the masked PMT signal is utilizedfor the transfer function determination, the localizedflame response becomes more pronounced over awider range of frequencies, since the localized flameemission is much more coherent (see Figs. 4b and 5)at these frequencies. The particularly broad frequencyresponse at the approach velocity of 15 m/s is con-nected with the higher degree of modulation and morelateral spread of the flame structures, as observed inFig. 5 for Um = 15 m/s. The Strouhal number cor-

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Fig. 8. Comparison of experimental (thin lines) and modeled (thick lines) response at 50, 125, and 200 Hz excitation frequency.

Fig. 9. Velocity power spectral density at excitation frequencies of 50, 100, 150, and 200 Hz.

A. Chaparro et al. / Combustion and Flame 145 (2006) 290–299 297

Fig. 10. Unmasked PMT power spectral density at excitation frequencies of 50, 100, 150, and 200 Hz.

responding to the peak amplitude appears to shift toslightly higher values.

One of the main reasons for employing two pho-tomultipliers in measuring flame CH∗ chemilumines-cence was the difficulty in obtaining the phase rela-tionship between the input (velocity) and output (CH∗chemiluminescence) signals when the overall flameemission was monitored only. This is due to the tur-bulent nature of the flame and the effect of turbulenceblurring or masking the phase relationship. For thisreason, the CH∗ signal from the masked photomulti-plier (PMT1) was utilized. The approach taken herewas to fit the experimental data to a transfer functionestimate. Utilizing the MATLAB transfer functionestimation tool, the best estimate for Um = 10 m/sdata was found to be a second-order transfer function,given by

(5)G(s) = 9.26s + 4.04 × 105

s2 + 234.7s + 6.94 × 105,

where s = σ + iω, with σ and ω representing thereal and imaginary parts and i = √−1. In Fig. 7, this

transfer function is plotted in the frequency domainalong with the amplitude relationship obtained fromthe experiments. While the comparison between themeasured and estimated amplitudes does not appearto be very good, the ability of the model transfer func-tion to track the experimental data was found to bequite good, as shown in Fig. 8. At 50 and 125 Hz, theexperimental time traces exhibit additional harmonicsthat will be discussed further later on.

The second-order character of the turbulent flametransfer function has been also reported in the litera-ture by Goldschmidt et al. [21]. However, the laminarflame response has been found to follow a first-ordermodel, as discussed by Fleifil et al. [16] and Ducruixet al. [17]. There is, however, qualitative similarity be-tween the transfer function gain characteristics shownin Fig. 7a and those of the predicted transfer functionsfor narrow V flames by Schuller et al. [19], with apeak in the gain for narrow flame angles such as thosestudied here. The phase relationship obtained fromthe model is that of a time-delayed response, wherephase angle between the velocity and CH∗ chemilu-

298 A. Chaparro et al. / Combustion and Flame 145 (2006) 290–299

Fig. 11. Masked PMT power spectral density at excitation frequencies of 50, 100, 150, and 200 Hz.

minescence increases up to about 200 Hz and remainsrelatively constant thereafter. The phase relationshipfor the turbulent flame does not appear to follow thatof a continuously increasing phase with frequency ob-tained from laminar flame computations [19]. It is notreasonable to expect agreement of the turbulent flamephase variation with phase relationship of laminarflames as the turbulence modifies the flame in a num-ber of important ways, such as modification of flameburning speed and local structure and introduction ofspectrum of turbulence length scales, in addition tothe imposed disturbance among others.

The power spectral densities of excitation signal(velocity) and the two photomultiplier signals areshown in Figs. 9–11. The velocity excitation signalsall have a single peak at the excitation frequency withlow-amplitude distribution of small frequencies dueto turbulent flow, as shown in Fig. 9. The unmaskedPMT signal shows a frequency content where thehighest peak occurs at the excitation frequency. Thepower spectral density is at a maximum near 100 Hz

and diminishes sharply at higher frequencies. It be-comes of the same order of magnitude as the turbulentbackground fluctuations beyond 200 Hz. On the otherhand, the masked PMT shows a strong response atthe excitation frequency, as depicted in Fig. 11. Whilethis is expected, since the response is associated withthe convective modulation of flame structure, as seenin Fig. 5, there appear several superharmonics of theexcitation frequency. This can also be seen in Fig. 8 atthe two lower frequencies. Based on the flame imagesshown in Fig. 5, this is likely caused by splitting andtilting of flame structures and the associated nonlineareffects.

Finally, the effect of overall mixture equivalenceratio on the transfer function amplitude is shown inFig. 12 for Um = 10 m/s. Based on the overall CH∗emission, the trend of normalized amplitude is similarto that shown earlier in Fig. 6a, but the peak ampli-tude shifts slightly to higher frequencies for φ = 1.0,indicating that the stoichiometric flame has a strongerheat release response than fuel-lean flames at higher

A. Chaparro et al. / Combustion and Flame 145 (2006) 290–299 299

Fig. 12. Transfer function amplitude as a function of Strou-hal number based on flame length scale and based on(a) overall flame emission, (b) the masked PMT signal atdifferent mixture equivalence ratios at um = 10 m/s.

frequencies. Nevertheless, the differences are not verysubstantial. When flame response is determined basedon localized flame emission, better collapse of ampli-tude data is found in the vicinity of peak response. Athigher frequencies where flame response is reduced,a trend of increasing response is seen from lean to-ward stoichiometric. This can be explained by the factthat the heat release modulation of premixed flamesbecomes stronger as stoichiometric conditions are ap-proached. In our study, the lower equivalence ratioscould not be studied, as flame detachment and liftofffrom the bluff-body became an issue.

4. Concluding remarks

An experimental study of the response of turbu-lent premixed V-shaped flames to upstream flow ve-locity oscillations is presented. Bluff-body stabilizedconical flames were subjected to upstream flow oscil-lations by a loudspeaker and the flame response wasmeasured by two photomultiplier detectors. Analy-sis of the time series data of flow velocity and CH∗chemiluminescence was performed in the frequencydomain to determine the flame transfer function char-acteristics. It was found that the flame responds toimposed oscillations, with the peak response occur-ring between St = 1 and 2. Flame response dimin-

ishes with increasing frequency with flame becomingessentially unresponsive beyond St ≈ 4. Due to thedifficulty of obtaining the phase relationship from theoverall flame emission data for turbulent flames, thetransfer function was estimated based on the localizedflame emission characteristics. This yielded a second-order transfer function which exhibited a phase lagincreasing with increasing frequency. The instanta-neous images of the perturbed flames suggest thatsignificant flame modulations result from relativelylow excitation amplitude of flow velocity. Tilting andsplitting of flame structures are also observed in theseimages, as well as having an indication of these inthe time traces and power spectral density of the localflame chemiluminescence. This suggests that nonlin-ear effects may become important even at these lowamplitude excitation levels.

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