flame index measurements to assess partially-premixed ... · /acetone/air ﬂame in a canonical,...

Paper # 070LT-0203 Topic: Turbulent & Laminar Flames

8th US National Combustion MeetingOrganized by the Western States Section of the Combustion Institute

and hosted by the University of UtahMay 19–22, 2013.

Flame index measurements to assesspartially-premixed flame models

David A. Rosenberg Patton M. Allison James F. Driscoll

Department of Aerospace Engineering,University of Michigan, Ann Arbor, MI 48109, USA

A method has been developed to measure flame index and was applied to a fuel-lean and a fuel-richpropane/acetone/air flame in a canonical, well-defined partially-premixed burner—the Gas TurbineModel Combustor (GTMC). The flame index indicates the locations where premixed flames and wherenon-premixed flames exist. This information is needed to improve the modeling of gas turbine com-bustors. Acetone (CH3COCH3) was added to the propane (C3H8) fuel, and nitrogen dioxide (NO2) wasadded to the air. CHEMKIN computations and calibration experiments both showed that the acetonegradients faithfully track the fuel gradients (since both have nearly the same diffusivity) and NO2 gra-dients track the oxygen (O2) gradients. Planar laser-induced fluorescence (PLIF) images of the acetoneand NO2 clearly showed where the two gradients were aligned and where they were in opposite direc-tions. Statistics (mean, variance, probability mass functions) of the flame index are reported for thishighly-turbulent partially-premixed flame. Aspects of the new measurement technique are discussed,including: signal-to-noise, tracer gas seeding levels, and data analysis/gradient identification methods.The degree of partial-premixing was found to correlate with a strong combustion instability that wasmeasured in this burner.

1 Introduction

Many modern combustion applications involve conditions for which the fuel and oxidizer are notfully mixed prior to entering the flame. These partially-premixed flames contain some regions ofpremixed and some regions of non-premixed combustion. The Takeno flame index [1] is the dotproduct of the gradients of the fuel and oxidizer mass fractions:

GFO = ∇YF · ∇YO, (1)

where GFO is the flame index and YF and YO are the fuel and oxidizer mass fractions, respectively.

New computational approaches of Bray [2], Domingo et al. [3], and Knudsen and Pitsch [4,5] haveused a normalized flame index concept, ξ, defined as:

ξ =∇YF · ∇YO

|∇YF · ∇YO|, (2)

where ξ = +1 in premixed flamelets and ξ = −1 in non-premixed flamelets. Previously there hadbeen no measured values of flame index available to assess the modeling approaches.

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8th US Combustion Meeting – Paper # 070LT-0203 Topic: Turbulent & Laminar Flames

In computational models the flame index concept is useful in allowing the modeler to divide apartially-premixed flame into premixed and non-premixed reaction zones, where the appropriatecombustion model can be applied. There have been several studies that modeled the subgrid flameindex to be a function of the resolved scale gradients of fuel and oxygen concentrations [2–9],however no study has been performed to experimentally verify these models by measuring the fueland oxidizer gradient. Models of partially-premixed flames need to correctly predict the flameindex, so measurements are needed to assess the models.

A method was previously developed by the authors [10,11] to measure a new flame index—definedas:

ξLIF =∇Sacetone · ∇SNO2∣∣∇Sacetone · ∇SNO2

∣∣ , (3)

where ξLIF is the flame index based on the LIF signal, Sacetone is the acetone fluorescence signal,and SNO2

is the NO2 fluorescence signal—in turbulent partially-premixed flames. This methodwas previously [11] applied to a CH4/acetone/air flame in a canonical, well-defined partially-premixed burner—the Gas Turbine Model Combustor (GTMC) that was developed by Weigand etal. [12]. This paper discusses the application of the same method to propane/acetone/air flames inthe GTMC. Statistics (mean, variance, probability mass functions) of the flame index are reportedfor this highly-turbulent partially-premixed flame. Aspects of the new measurement technique arediscussed, including: signal-to-noise, tracer gas seeding levels, and data analysis/gradient identifi-cation methods. The degree of partial-premixing was found to correlate with a strong combustioninstability that was measured [12, 13] in this burner.

2 Modeling

Flamelet modeling—described previously [10], using CHEMKIN (v4.1.1)—of premixed and non-premixed methane (CH4) / acetone (CH3COCH3) / air flames was used to select acetone as a fueltracer, and nitrogen dioxide (NO2) as an oxygen (O2) tracer. Initially, formaldehyde (CH2O) andnitric oxide (NO) were studied as fuel and oxidizer tracers, both with and without seeding. It wasfound that the gradients of CH2O and NO did not follow those of CH4 and O2 in both premixedand non-premixed flames. Therefore CH2O and NO would not work as tracers because too muchof both species was naturally produced in the flame. A propane (C3H8) / air flame, with CH2Oand NO as the tracer species, was briefly considered. However, this flame and tracer combinationwas ruled out for the same reasons as the previously mentioned combination. Other tracers thatwere considered to track the fuel concentration were carbon monoxide (CO), octane (C8H18), andkerosene. All of these species fluoresce but CO was ruled out because large amounts of CO areformed within the flame so it does not track the fuel profile properly. Kerosene and octane fluorescebut their fluorescence yield is much less than that of acetone and they have a lower vapor pressure.OH was considered as a marker of the oxygen concentration profile, but since it is created in theflame the OH profile is an ambiguous indicator of the O2 profile. These models were all performedwith the GRI-Mech [14] reaction mechanism.

Finally a CH4/air flame with acetone and nitrogen dioxide as fuel tracers was modeled. The GRI-Mech reaction mechanism does not currently support acetone reactions, so a new mechanism hadto be found. In the end, the non-premixed, opposed flow flame model was run with a modified

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version of the National University of Ireland, Combustion Chemistry Centre’s acetone reactionmechanism [15], with University of California at San Diego, Combustion Research Group’s NOx

Formation Mechanism [16] added. The premixed, freely propagating flame model was run witha modified version of GRI-Mech, similar to the mechanism used by Chong et al. [17]. Aftermodeling several fuel and oxidizer tracers, it was decided that acetone, seeded at 20% by volume,would function as a good tracer for CH4. Likewise NO2, seeded at 5000 ppm by volume, wouldfunction as a good tracer for O2.

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(b) Mass fractions of a CH4/air premixed flamewith acetone and NO2 seeding, as modeled byCHEMKIN.

Figure 1: Fuel, oxidizer, and tracer mass fractions for (a) non-premixed and (b) premixed flames, asmodeled by CHEMKIN.

To show that acetone and NO2 would act as tracers for CH4 and O2, respectively, the results ofthe CHEMKIN models are shown in Fig. 1(a) for a non-premixed flame, and in Fig. 1(b) for apremixed flame. It can easily be seen in both Fig. 1(a) and 1(b) that the acetone tracks the CH4,and that the NO2 tracks the O2, meaning acetone and NO2 are good fuel and oxidizer tracers. Itis noted that it is not necessary that the profile of the tracer gas fall exactly on top of the fuel orthe O2 profile. The primary goal is to measure whether the flame index is a positive or a negativenumber, and not to measure the absolute value of the flame index with high accuracy. It is seenthat acetone pyrolyzes earlier than methane, and that NO2 also decomposes earlier than O2. Whatis encouraging is that the slopes of the tracer gases are monotonic and have the same signs as thefuel and O2 profiles.

While only CH4 flames have been modeled, it is expected that acetone will act as an even bettertracer for propane due to their more similar molecular weights.

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3 Experiment

3.1 Combustor and flame conditions

The experimental methods described previously [10, 11] have been applied to a gas turbine modelcombustor (GTMC), pictured in Fig. 2 [12, 13]. The injector consisted of a central air nozzle,an annular fuel nozzle, and a co-annular air nozzle. Both air nozzles supplied swirling air atatmospheric pressure and temperature from a common plenum. The inner air nozzle had an outerdiameter of 15 mm. The annular nozzle had an inner diameter of 17 mm and an outer diameterof 25 mm. The measured swirl number was approximately 0.55. Non-swirling fuel was providedthrough three exterior ports fed through the annular nozzle, which was subdivided into 72 channelswith a 0.5 mm × 0.5 mm cross section. The exit plane of the central air nozzle and fuel nozzle lay4.5 mm below the exit plane of the outer air annulus. The exit plane of the outer air annulus willbe referred to as the injector face. The combustion chamber had a square cross section of 85 mmin width and 110 mm in height. The exit of the combustion chamber was an exhaust tube with adiameter of 40 mm and a height of 50 mm. In the present investigation, the burner was operatedwith four fused silica windows, with a thickness of 1.5 mm, for flame visualization.

Figure 2: Cross-sectional view of gas turbine model combustor designed by Meier et al. [12] Thedashed box shows the field of view used in the experiment.

The air was seeded with NO2, while the propane was seeded with acetone. The NO2 seeding wasachieved by using a premixed gas cylinder. The acetone seeding in the propane was achievedby bubbling the propane through an acetone bath. The bath had a bypass line, through whichthe flow of propane could be controlled. Heat tape, connected to a PID temperature controller,kept the acetone in the bath at a constant temperature ±2 ◦C to more precisely control the acetoneconcentration.

Using the GTMC the flame index was measured in two propane/acetone/air flames, one that wasfuel-lean (P-1) and one that was fuel-rich (P-2). The conditions are described in Table 1.

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Table 1: Flame conditions. The mass flow rate of species i is mi, and φglobal is the equivalence ratiofor the overall mixture.

Case ma, g/min* mf, g/min† φglobalNO2 Volume

Fraction‡AcetoneVolume

Fraction‡

P-1 281 16 0.79 5000 ppm 24.0%P-2 285 25 1.21 5000 ppm 21.1%

* Includes air and NO2.† Includes propane and acetone.‡ Volume fractions are for the pure fuel or pure air stream.

3.2 Planar laser-induced fluorescence system

As suggested by prior studies [18–20] and the previous flame modeling study [10], acetone makesan excellent fuel tracer, which fluoresces from 400 nm to 500 nm when excited by a 266 nm laser.While NO2 is not traditionally considered to be an oxygen tracer, the models showed that NO2 willfunction as such. Agarwal et al. [21] showed that NO2 will fluoresce from 540 nm to 675 nm whenexcited by a 488 nm argon-ion laser, while Donnelly et al. [22] showed that NO2 will fluoresce from550 nm to wavelengths longer than 800 nm when excited by a 532 nm Nd:YAG laser. Cattolica [23,24] has shown that applying NO2 planar laser-induced fluorescence (PLIF) to combustion studiesis possible.

A diagram of the layout of the lasers, cameras, and burner for the simultaneous acetone and NO2PLIF system can be seen in Fig. 3. The NO2 PLIF was achieved with a frequency doubled Nd:YAGlaser (Spectra Physics LAB-150, Laser #1) operated at a wavelength of 532 nm. The acetonePLIF was achieved with a frequency quadrupled Nd:YAG laser (Spectra Physics GCR-130, Laser#2) operated at a wavelength of 266 nm. Both lasers had a linewidth of approximately 1.0 cm−1.The 266 nm laser had a pulse width of about 6 ns, while the 532 nm laser had a pulse width ofapproximately 8 ns. The 266 nm laser had an energy of 30 mJ/pulse, and the 532 nm laser wasoperated at 110 mJ/pulse. At the burner the 266 nm laser energy had been reduced to 10 mJ. Thenormalized spectral irradiance was 40 MW/cm2/cm−1. The 532 nm laser energy had been reducedto 45 mJ, and the normalized spectral irradiance was 290 MW/cm2/cm−1. Both lasers were pulsedat a rate of 10 Hz. Over time the power and shape of the 266 nm laser beam tended to degrade, soit was decided to correct for the non-uniformities in the laser sheet on a shot-to-shot basis using adye cell.

The laser beams were formed into sheets using two cylindrical lenses and were passed betweenknife edges, set 10 mm apart, to chop the top and bottom of the laser sheets. They next passedthrough 10% pick-off mirrors to a dye cell with an optically thick Rhodamine 6G solution tocorrect for the non-uniformity of the laser sheet. The distances were set up such that the lasersheets would be focused inside the dye cell. The remaining 90% of the laser sheets were thencombined using a dichroic beam splitter (CVI Melles Griot BSR-25-2025) and passed through theburner. At the test section the 266 nm laser sheet had a height of 10 mm and a 1/e thickness of250 µm at its focal point. At the same location the 532 nm laser sheet had a height of 10 mm and

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Nd:YAG Laser #1

Nd:YAG Laser #2

ICCD #1

ICCD #2

CL

M

MCL CL

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PM

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Cell

BS BD

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MM

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CCD #1 ND

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Test Section

266 nm 532 nm 266 nm + 532 nm

CL

CL CL

K

K

Figure 3: Diagram of laser and camera setup for simultaneous PLIF. BD - beam dump, BS - beamsplitter, CL - cylindrical lens, K - knife edge, M - mirror, ND - neutral density filter, PM - partial mirror.

a 1/e thickness of 200 µm. The knife edge was used to create a sharp edge in the observed PLIFsignals and the fluorescence observed in the dye cell, so that the two images could later be aligned,as suggested by Clemens [25].

NO2 fluorescence was observed by a red-sensitive intensified CCD (ICCD) camera (Andor iStarDH334T-18U-A3, ICCD #1) with an interference filter (CVI Melles Griot LPF-600) and two 3 mmthick color filters (Schott OG-550) to allow light with wavelengths 600 nm and longer to passthrough. Observing the NO2 fluorescence using a red-sensitive ICCD, with a third generationintensifier, was necessary to achieve the maximum possible signal-to-noise ratio. The acetonefluorescence also was observed by an ICCD camera (Andor iStar DH734-25F-03, ICCD #2) withan interference filter (Omega Optical 500ASP) to allow light at wavelengths of 400 nm to 500 nmto pass. Each camera was fitted with a 105 mm f/2.8D Micro-Nikkor lens. A CCD camera (SonyXCD-X710, CCD #1) was fitted with a 50 mm f/2.8 Nikkor lens. It imaged the dye cell for shot-to-shot corrections to the non-uniformity of the laser sheets. A neutral density (ND) filter, with anoptical density of 2, was placed to cover only the half of the dye cell that the 532 nm laser sheethit. A second ND filter, with an optical density of 1, was placed to cover the entire dye cell image.The dye cell camera had an exposure time of 3 ms, and it captured the fluorescence from both ofthe laser sheets in that time.

To ensure that the NO2 camera’s gate was fully open, the intensifier gated to turn on 50 ns beforethe arrival of the 532 nm laser pulse. The intensifier gain on the NO2 camera was turned up to themaximum possible level. The acetone camera’s intensifier was gated to turn on 50 ns before thearrival of the 266 nm laser pulse. Both cameras operated with a 100 ns intensifier gate width. Atotal of 450 images were taken by each camera.

There is some overlap between the fluorescence spectra of acetone and NO2 that the optical filterson the cameras did not filter out. If nothing had been done, some of the acetone fluorescence wouldhave been seen on the NO2 camera. As a result, the lasers were timed such that the 266 nm laserpulse reached the burner 500 ns before the 532 nm laser pulse.

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The cameras each had an array of 1024 × 1024 pixels. The resolution was 21.8± 3.3 µm/pixel forthe NO2 camera, and 21.7± 3.3 µm/pixel for the acetone camera.

On a daily basis several calibration steps had to be taken. The laser sheets were checked to besure they overlapped and passed through the center of the burner. The camera timing was tuned tobe sure that both the NO2 and acetone PLIF camera gates opened 50 ns before the arrival of theirrespective laser pulses. Finally, the cameras were both focused on a targeting grid, which had beenaligned with the laser sheets, and field-of-view images of the target were taken with each cameraso that the images could later be registered.

After each day of runs a series of background images was taken. One series of images recorded theflame seeded with NO2 and acetone but with the lasers turned off. Additional images recorded theflame without the tracer gas a given camera looks for but with the other tracer gas present (e.g., aflame without NO2 seeding but with acetone seeding, imaged by the NO2 camera), with the laserson. A final set of images recorded the same flame without the lasers. Typically, each camera wouldcapture 20 images for each of the background conditions. The theory behind the image correctionsthat require the background and dye cell images was described previously, in Ref. [11].

4 Results

The method used to process the PLIF images from raw data to ξLIF values has been described ingreater detail in Ref. [11], but will be summarized here. The raw PLIF images are corrected forthe non-uniformity in the laser sheets and a non-zero background. The images taken by the NO2camera are then registered to the images taken by the acetone camera. The images are then binned4 × 4 and filtered using non-linear anisotropic diffusion filter (NADF) [26]. (The NADF smoothsthe images within a given region, but resists smoothing the image across large gradients.) Nextthe spatial gradients of Sacetone and SNO2

are determined, a Canny edge detector [27] is used toprocess the images, and only at locations where an edge is detected is the gradient saved. Usingthe gradients, a method of searching for corresponding acetone and NO2 locations is employed todetermine, on a pixel-by-pixel basis, whether a flamelet was present and whether that flamelet waspremixed or non-premixed. The edge detection and ξLIF search method are needed because, ascan be seen in Fig. 1, the locations of maximum gradient in Sacetone and SNO2

do not necessarilyoverlap in the premixed and non-premixed cases. So a method needed to be developed to detectthe locations of maximum gradient, to determine which locations of maximum gradient in Sacetone

correspond to which (if any) locations of maximum gradient in SNO2, and to determine ξLIF .

The signal-to-noise (SNR) ratios of the acetone and NO2 PLIF images before any processing andafter the NADF is applied are shown in Table 2. In flame P-1, the acetone SNR improved by a

Table 2: Signal-to-noise ratios (SNR) in the raw and processed acetone and NO2 PLIF images.

Flame P-1 Flame P-2

Processing Level Acetone NO2 Acetone NO2

Raw Image 13.7 5.2 12.2 4.6Filtered Image 24.3 11.8 16.2 10.6

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factor of 1.8, while the NO2 SNR improved by a factor of 2.3. For flame P-2, the acetone SNRimproved by a factor of 1.3, while the NO2 SNR improved by a factor of 2.3.

Sample ξLIF images are shown in Fig. 4 for flame P-1 and in Fig. 5 for flame P-2. A schematic

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(b) Time when predominantly non-premixed flamelets occurred near the injector face fromr = 10 mm to 16 mm, predominantly premixed flamelets occurred at r > 16 mm near theinjector face, and predominantly premixed flamelets occurred away from the injector face,in flame P-1.

Figure 4: Two instantaneous images of flame index, ξLIF , from flame P-1. A value of −1 marks anon-premixed flamelet in blue, and +1 marks a premixed flamelet in red.

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of the GTMC has been overlaid on both image sets. The fuel injector, inner air swirler, and outerair swirler locations are shown in the diagrams, as well as the fuel and air paths. At the locationof r = 8 mm is the fuel injector. The location 0 mm on the r-axis corresponds to the centerline ofthe burner, and the location 0 mm on the y-axis corresponds to the top of the injector face. The topof the fuel injector is located at −4.5 mm on the y-axis. The distance between the injector face andthe bottom of the region in which ξLIF is determined—defined by the overlap region of the 532 nmand 266 nm laser sheets—was approximately 770 µm for flame P-1 and 1.06 mm for flame P-2.

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Figure 5: Two instantaneous images of flame index, ξLIF , from flame P-2. A value of −1 marks anon-premixed flamelet in blue, and +1 marks a premixed flamelet in red.

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−1 −0.5 0 0.5 10

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Figure 6: Probability mass function of ξLIF for a single super-pixel. A is the probability that ξLIF =+1 (premixed flamelet), B is the probability that ξLIF = 0 (no flamelet), and C is the probability thatξLIF = −1 (non-premixed flamelet).

For all 450 images in each of the two flame cases, some statistical data was determined. TheξLIF images were binned 16 × 9 (horizontal × vertical). For each super-pixel, a probability massfunction (PMF) of ξLIF was determined for the three possible values −1, 0, and +1. An examplePMF for a single super-pixel is shown in Fig. 6, where A is the probability that ξLIF = −1 (non-premixed flamelet):

A = Pr (ξLIF = −1) , (4)

B is the probability that ξLIF = 0 (no flamelet):

B = Pr (ξLIF = 0) , (5)

and C is the probability that ξLIF = +1 (premixed flamelet):

C = Pr (ξLIF = −1) . (6)

While the lines in the figure appear to have some thickness, in reality they are delta functions soprobabilities A, B, and C are located only at −1, 0, and +1, respectively, and are thus infinitelythin. The sum of the areas under all three curves, A + B + C = 1. Contours of the PMF for thefull data set are shown in Fig. 7 for flame P-1 and in Fig. 8 for flame P-2.

Using the PMF, the average value of the flame index for each super-pixel is:

〈ξLIF 〉 =(−1)A+ (0)B + (1)C

A+B + C, (7)

where 〈ξLIF 〉 is the average flame index for that super-pixel. Because B is centered at ξLIF = 0and A+B + C = 1, Eq. (7) can be simplified to be:

〈ξLIF 〉 = C − A. (8)

This ensemble average flame index, while useful, is not the best indicator of where premixed andnon-premixed flamelets occur. A better indicator is the following conditioned average:

〈ξLIF | ξLIF 6= 0〉 = (−1)A+ (1)C

A+ C, (9)

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Figure 7: The probability mass function for ξLIF in flame P-1.

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Figure 8: The probability mass function for ξLIF in flame P-2.

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(b) Conditionally averaged flame index, ignoring locations with no flamelets,〈ξLIF | ξLIF 6= 0〉, in flame P-1.

Figure 9: For flame P-1, the average of ξLIF , (a) 〈ξLIF 〉, and the conditional average, (b)〈ξLIF | ξLIF 6= 0〉, where all locations without flamelets are ignored.

where 〈ξLIF | ξLIF 6= 0〉 is the average of ξLIF , conditioned on the condition that ξLIF is nonzero,meaning that a flamelet was present. Equation (9) can be simplified to be:

〈ξLIF | ξLIF 6= 0〉 = C − AA+ C

. (10)

Both the average flame index and the conditionally averaged flame index are shown in Fig. 9 forflame P-1 and in Fig. 10 for flame P-2.

In addition to the average flame indices, the standard deviation of the flame index, σξLIF , for a givensuper-pixel was calculated to be:

σξLIF =

√A [(−1)− 〈ξLIF 〉]2 +B [(0)− 〈ξLIF 〉]2 + C [(+1)− 〈ξLIF 〉]2. (11)

Values of the standard deviation can be seen in Fig. 11 for flame P-1 and in Fig. 12 for flame P-2.

It now becomes useful to quantify how premixed or non-premixed the flame is. For each super-pixel we define the probability that flamelet is premixed (ξLIF = +1), if a flamelet is present, βp,

13


0.01

0.015 0.015

0.01

5

0.0150.015

0.02

0.02

0.01

0.01

0.01

0.025

0.005 0.00

5

0.005

0

0

0.02

0.02

−0.005

0.03

0.020.02

−0.010.01

0.03

0.025

−0.015

0.015

r [mm]

y [m

m]

5 10 15 20 25

2

3

4

5

6

7

8

−0.01

0

0.01

0.02

0.03

(a) Averaged flame index, 〈ξLIF 〉 in flame P-2.

0.3

0.3

0.3

0.4

0.4

0.2

0.2

0.2

0.2

0.5

0.5

0.6

0.6

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0.1

0.1

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0.4

0

0

0.7

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−0.1

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0.30.40.8

0.50.6 0.9

r [mm]

y [m

m]

5 10 15 20 25

2

3

4

5

6

7

8

0

0.2

0.4

0.6

0.8

(b) Conditionally averaged flame index, ignoring locations with no flamelets,〈ξLIF | ξLIF 6= 0〉, in flame P-2.

Figure 10: For flame P-2, the average of ξLIF , (a) 〈ξLIF 〉, and the conditional average, (b)〈ξLIF | ξLIF 6= 0〉, where all locations without flamelets are ignored.

0.10.12

0.14

0.16

0.18

0.180.18

0.2

0.2

0.2

0.2

0.22

0.22

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0.24

0.240.24

0.260.26

0.28

r [mm]

y [m

m]

6 8 10 12 14 16 18 20 22 241

2

3

4

5

6

7

0.1

0.15

0.2

0.25

Figure 11: Standard deviation of ξLIF , σξLIF , in flame P-1.

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0.1

0.15

0.20.2

0.25

0.25

0.3

r [mm]

y [m

m]

5 10 15 20 25

2

3

4

5

6

7

8

0.1

0.15

0.2

0.25

0.3

Figure 12: Standard deviation of ξLIF , σξLIF , in flame P-2.

as:βp = Pr (ξLIF = +1 | ξLIF 6= 0) =

C

A+ C. (12)

We can then define βp to be equal to the spatial average of βp for the entire flame. This quantity,βp, can have any value from 1 to 0. The notable values of βp are explained as:

βp =

1 if all flamelets are premixed0.5 if all flamelets are fully partially-premixed0 if all flamelets are non-premixed

. (13)

We can now quantify the degree of partial-premixing in the flame, εpp , defined as:

εpp =βp(1− βp

)0.25

. (14)

As with βp, εpp can have any value from 1 to 0. It is obvious from We can explain the notablevalues of εpp as:

εpp =

{1 if all flamelets are fully partially-premixed0 if all flamelets are either premixed or non-premixed

. (15)

The values for βp and εpp for cases P-1 and P-2 are shown in Table 3.

Table 3: Probability of a premixed flamelet and degree of partial-premixing.

Case βp εpp

P-1 66.3% 0.894P-2 69.6% 0.847

15


5 Discussion

In Figs. 9 and 10 there is an enclosed (dark) region where a non-premixed flamelet is more likelyto occur. For flame P-1, this region sits between a height of 1 mm and 3.5 mm, and between radiallocations of 8.5 mm and 16 mm. For flame P-1, this region sits between a height of 2 mm and4.5 mm, and between radial locations of 9.5 mm and 17 mm. Below these bubbles, in both cases, apremixed flamelet is more likely to occur.

A previous study [13] of the GTMC with propane fuel has shown that a combustion instabilityoccurs with resonations taking place at 320 Hz. Coupled with this acoustic noise are large-scalefluctuations in flame shape and liftoff height. The liftoff height can vary such that the base of theflame lies below or up to 8 mm above the injector face. As the liftoff height oscillates, the fuel-airresidence time between the injector nozzle and flame-base also varies. This fluctuation in residencetime may result in various degrees of premixedness. In addition to changes in flame location,velocity fluctuations near the injector nozzle can alter the mixing mechanics of the combustor suchthat the flame index can drastically shift in time around this region. Fluctuations in pressure weremonitored when the data in this paper was taken so that the variations in premixedness can bebetter studied. However, the pressure data has not yet been analyzed.

From Table 3, we see that the degree of partial-premixing is slightly higher for the fuel-lean case,P-1, and lower for the fuel-right case, P-2.

6 Conclusion

The flame index measurement method has been applied to fuel-lean and fuel-rich propane flameconditions in a Gas Turbine Model Combustor. Variations in premixedness of the flame appear tocorrelate to a combustion instability that occurs with resonations taking place at 320 Hz.

The degree of partial-premixing in fuel-lean propane flames in the GTMC appears to be slightlyhigher than that of fuel-rich flames.

Acknowledgments

Funding for this research was provided by the National Science Foundation award CBET 0852910,which was monitored by Dr. Arvind Atreya and Dr. Ruey Hung Chen.

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