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Flame Spectra of a Turbulent Liquid-Fueled Swirl-Stabilized LDI Combustor

Tongxun Yi1 and Domenic A. Santavicca2 Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, University Park, PA

16802

Flame spectra within the UV-VIS range are measured for a turbulent, liquid-fueled, swirl-stabilized, LDI combustor, using both a spectrometer and PMTs. The flame spectra are quite similar to those of lean premixed gaseous combustion, which can be attributed to the small droplet size and fast fuel/air mixing. Within a rather broad range of working conditions, background emissions around 430 nm, which mainly consist of CO2

*

chemiluminescence, are found to be self-similar with wavelength, at both stable and unstable conditions. Chemiluminescence from OH*, CH*, and CO2

* is found to be nonlinear functions of the air flow rate, the equivalence ratio, preheat temperature, and pressure. Procedures for determination of the instantaneous heat release rate and the instantaneous equivalence ratio along the flame front are developed. For both combustion instability and forced flame responses, the errors between measurements and estimation are within 2.0% for the mean heat release rate, the mean air consumption rate, and the mean equivalence ratio. The assumption that chemiluminescence is proportional to the instantaneous heat releaser rate is generally invalid. Probably the proportionality is valid only in the weakly turbulent or wrinkled flamelet region in the absence of equivalence ratio variations and strong acoustic oscillations. For forced flame responses under fuel modulations, the gain difference between the heat release rate and CH* chemiluminescence can be more than 20%, and the phase difference can be more than 90o above 400 Hz. For self-excited combustion instability, the phase difference can be more than 10o, while the gain difference can be up to 20%.

Nomenclature )(tI = the instantaneous chemiluminescence intensity, A.U.

fL = the curvilineal flame front

)(tma& = the instantaneous air consumption rate, g/s

)(~ tma& = the instantaneous air consumption rate normalized by 100 g/s

)(' tpa = acoustic pressure nearby the heat release zone, Pa

)(~ tp = the instantaneous combustor pressure normalized by the atmospheric pressure

)(tp f = the instantaneous fuel pressure 0.29 m upstream of the fuel nozzle, Pa

)(tQR& = the instantaneous heat release rate, kW

s = symbol of the Laplace Transform

LS = the laminar burning velocity, m/s

iT = the preheat temperature, K

)(' tTa = acoustic temperature nearby the heat release zone, K

T = the mean temperature in the heat release zone, K

1 PostDoctoral Fellow, Department of Mechanical and Nuclear Engineering, AIAA member, tzy1@psu.edu. 2 Professor, Department of Mechanical and Nuclear Engineering, AIAA member, das8@psu.edu.

47th AIAA Aerospace Sciences Meeting Including The New Horizons Forum and Aerospace Exposition5 - 8 January 2009, Orlando, Florida

AIAA 2009-985

Copyright © 2009 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

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L! = thickness of the laminar flame, m " = thermal diffusivity, m2/s # = the fuel/air equivalence ratio

$ = wave length normalized by 431 nm $ = wavelength, nm

a% = the air density, kg/m3

u% = the reactant density, kg/m3

c& = the chemical reaction time, s

RH' = the lower heating value of fuel, J/kg )(sX = the Laplace Transform of )(tx

)(sW( = the phase angle of the transfer function )(sW , Deg

)(sW = the gain of the transfer function )(sW ICCD = intensified charge-coupled device IR = infrared light LBO = lean blowout LDI = lean direct fuel injection NA = numerical aperture PMT = photomultiplier tube SMD = Saunter Mean Diameter, m VIS = visible light UV = ultra-violet light Upper bar = the mean quantity

I. IntroductionHe instantaneous heat release rate and the instantaneous equivalence ratio are key parameters for combustion instability analysis and control. HCO is believed to be a good indicator of the instantaneous heat release rate,

even in the presence of large strain rates1. However, HCO* chemiluminescence, which appears as several tiny peaks between 310 nm and 390 nm, is barely above the broadband background emissions. HCO PLIF also suffers from low signal-to-noise ratios, because of the short fluorescence lifetime, low quantum yield, and low HCO concentration. A viable approach for heat release measurements is to use the PLIF product of OH and CH2O, as demonstrated by Paul et al.2 and Ayoola et al.3. This method requires rather complicated optical setup, including lasers, cameras, lenses, and optical filters. On the contrary, chemiluminescence-based heat release measurements may just need an optical access, an interference bandpass filter, and a detector like a PMT. Chemiluminescence is the spontaneous emission of photons from electronically excited species when they return to the background state. The formation of radial species, such as OH*, CH*, and C2

*, are directly associated with the chemical reactions. The equivalence ratio can be measured from the PLIF signal, line-of-sight infrared absorption, and the

chemiluminescence ratio of radial species. With excitation at 266 nm, kerosene vapor PLIF within 270-420 nm could be used to determine the fuel vapor concentration4. The PLIF signal is mainly associated with one-ring and two-ring aromatics. The stretching C-H band, which is strongly absorbing around 3.39 µm, is prevalent in almost all hydrocarbon fuels. Thus absorption measurements of equivalence ratios are usually performed using a 3.39-!m Helium–Neon laser5,6. This method can be extended to measure fuel vapor concentration for two-phase liquid/vapor mixtures. This is based on the difference in optical extinction between two wavelengths, usually with one laser beam in the VIS range and the other in the IR range7. Both PLIF and absorption measurements require rather complicated optical setup, which is different from chemiluminescence-based methods. Chemiluminescence-based equivalence ratio determination has been studied for premixed laminar, turbulent, and even spray flames8-10. Besides line-of-sight measurements, chemiluminescence can also be measured locally using Cassegrain receiving optics, as demonstrated by Hardalupas et al.11.

For unstretched, premixed, laminar flames, the reaction zone structure, the flame speed, and the relationship between chemiluminescence and heat release are intrinsic properties of the fuel/air mixture. However, the situation would be quite different for turbulent flames. In modern combustion theory, turbulent flames are conceived as a

T

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series of cascaded laminar flamelets, which drift with the local velocity and propagate normally towards the reactants. The location and orientation of these laminar flamelets are solved using the G-Equation12, where the local flame speed is determined from a “flamelet library” based on the local temperature, the local equivalence ratio, and the local stretch rate. In the wrinkled flamelet region, the flame is only slightly distorted by vortices or the velocity gradients, and the reactant conditions upstream of the flame front can be assumed the same. Thus linearity between chemiluminescence and the heat release rate holds. In corrugated and broken flamelet regions, the flame structure and the flame speed are considerably affected by the local stretch rate and upstream inhomogeneities, thus nonlinearity between chemiluminescence and heat release cannot be ignored. It is worthwhile to notice that, for premixed flames, Samaniego et al.13 report that the unsteady effects of strain rates on CO2

* chemiluminescence can be neglected. This is very different from diffusion flames, where nonlinearity in flames’ responses to upstream velocity perturbations prevails14. Several researchers report that the global chemiluminescence intensity is not sensitive to the strain rate. For example, Hardalupas et al.11 find that, for premixed, laminar, counterflowing, methane/air flames, the ratio of background-emission-corrected chemiluminescence OH*/CH*, is not sensitive to the strain rate within 80~400 s-1. Lee et al.15 report that CH* chemilumienscence is not sensitive to the air flow rate in a turbulent premixed dump combustor fueled with methane. This is probably because in their combustor, very large strain rates associated with flame/vortex interactions or the velocity gradients only occur locally, and major portion of the flame still lies in the wrinkled flamelet region.

Chemiluminescence measurements of OH*, CH*, and C2* are common in combustion instability experiments.

Combustion instability refers to the self-excited, positively-coupled, large-amplitude, limit-cycle oscillations of combustor pressure and heat release. The instantaneous heat release rate is a key parameter for determining the onset and limiting amplitude of combustion instability. In combustion instability analysis, it is typically assumed that chemiluminescence is proportional to the instantaneous heat release rate. This assumption in fact, suffers from several major deficiencies. Firstly, the relationship between chemiluminescence and the heat release rate is not necessarily linear, since the elementary reactions for the production and removal of radical species may involve more than one radical atom. In addition, chemical reactions may follow different paths. Secondly, even the relationship between chemiluminescence and heat release were linear, the proportionality depends on the physicochemical conditions, such as the equivalence ratio, the flame temperature, and pressure. At lower pressure, the chance of collisions between a radical atom and other species is reduced, thus a radical atom has a larger opportunity to release the photon than at higher pressure. For laminar, premixed, methane/air flames, a power index of -0.86 and -0.64 of pressure is reported by Higgins et al.16,17 for OH* and CH* chemiluminescence, respectively. The chemiluminescence yield is proportional to a positive power of the flame temperature or the equivalence ratio. For premixed ethane/CO/air combustion, chemiluminescence from C2

* and CH* is found to be a fourth power of ethane concentration18. For laminar, premixed, methane/air flames, a power index of 5.23 and 2.72 of the equivalence ratio is reported for OH* and CH* chemiluminescence, respectively16,17. Thirdly, during combustion instability a portion of chemiluminescence oscillations are caused by acoustic pressure and temperature, which in fact have nothing to do with heat release. Thus acoustics-induced chemiluminescence oscillations should be discounted for quantitative determination of the heat release rate. Fourthly, PMT-based chemiluminescence measurements using interference filters, say around 307 nm for OH* chemiluminescence and around 430 nm for CH* chemiluminescence, are inevitably contaminated by broadband background emissions. The background emissions include chemiluminescence from CO2

* and HCO*, and possibly a small amount of gray-body radiations from soot. Chemiluminescence from CO2

* and HCO* can be used for heat release measurements, but gray-body radiations from soot are not necessarily associated with the chemical reaction rate. Fortunately for LDI combustion, the fuel-rich pockets are significantly reduced because of the very low equivalence ratio and good fuel/air mixing.

The present paper is organized as follows. Firstly, a liquid-fueled, swirl-stabilized, LDI combustion rig and the optical setup are described; Secondly, flame spectra at both stable and unstable conditions are presented and analyzed; Thirdly, PMT-based chemiluminescence measurements are presented and analyzed; Fourthly, methods for quantitative determination of the instantaneous heat release rate and the instantaneous equivalence ratio are developed, which account for acoustics-induced chemiluminescence oscillations and nonlinearity among chemiluminescence, the equivalence ratio, and the heat release rate.

II. Experiment Setup Figure 1 shows the liquid-fueled, swirl-stabilized, LDI combustion rig and the optical setup. Preheated air enters

a quartz combustion chamber, which is 0.10 m in diameter and 0.30 m in length, through a 30o radial-entry swirler. The exit diameter of the swirler is 3.56 cm. Pressure drop across the air swirler varies with the air flow rate and the preheat temperature, but it is within 5% for all results reported here. Jet-A is injected into swirling air flow 0.02 m

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upstream of the dump plane, using a 2.5GPH single-point macrolaminated fuel nozzle from Parker Hannifin. With a pressure drop of 689 kPa across the fuel nozzle, the droplet SMD is less than 10 !m for water (Engineers from Parker Hannifin Corp., private communication). The air flow rate is measured using a Vortex flowmeter from Omega, with a measurement uncertainty of 5%. Stable combustion is achieved by inserting three baffle plates downstream of the quartz tube. Without explicit denotation, all data reported in this paper are obtained at stable conditions.

Global emissions are sampled using a UV-VIS optical fiber with a viewing angle of 25o (NA=0.22). The optical fiber is oriented perpendicular to and 0.41 m away from the quartz tube. The beam forming devices include three spherical lenses. The beam is converged to a waist diameter less than 1mm, and enters an Oriel MS125™ spectrograph through a 100-!m-wide slit. The spectrometer is featured with a ruled grating (Model No. 77416) with 400 lines/mm, 350 nm blaze, and works for 200~800 nm. An ICCD camera with 576x384 pixels from Princeton Instruments is used for spectral line imaging. An Oriel Hg(Ar) lamp (Model No.6035) is used for spectral line calibration. At the exit of the spectrometer, light from the Hg(Ar) lamp exhibits several bright narrow spectral bands in an ICCD image, corresponding to 435.84 nm, 404.66 nm, 365.02 nm, 313 nm, and 284.8 nm, respectively. A linear curve-fitting polynomial relating wavelength and the horizontal pixel index of the ICCD image is obtained as xnm 38507.041.261)( )*$ . Here x refers to the horizontal pixel number in an ICCD image. Detector noises due to dark current are accounted for by subtracting the background image which is taken without exposure to light at the same exposure duration and the same intensifier gain. Chemiluminescence from OH*, CH*, and CO2

* is also measured using a PMT housing. The PMT housing is placed 2.3 m away and perpendicular to the quartz chamber. Light emissions from the quartz chamber are split into three streams using UV plate beam splitters. Each light stream is focused using spherical lenses into a rectangular image 2mm x 6mm, which lies exactly in the central region of the PMT effective area. This enables global chemiluminescence measurements and linear responses between light intensity and the output voltage. Optimal focusing is achieved by adjusting the location of the PMT housing until a smallest and brightest image is obtained. Three bandpass filters with FWHM of 10 nm are placed in front of the PMTs to select chemiluminescence from specific radical species, i.e. around 307 nm for OH*, around 365 nm for CO2

*, and around 430 nm for CH*. Light absorption across air is believed to be negligibly small within the UV-VIS range. Since spectral measurements involve emissions within the VIS range, combustion experiments are performed in a dark room.

Figure 1. The combustion rig and the optical setup

To Exhaust

Dynamic and Static Pressure

ICCD Camera

1.25 m

Choking Plate Temperature

Radial S i l

Fuel Injector

Choking Pl t

Dynamic Pressure

0.13

Preheated Air

Liquid Fuel

Rotary Fuel Actuator

P

Fuel Pressure Measurement

ICCD Camera

Spectrometer

UV-Grade Long Optical Fiber

Spherical Lenses

Quartz Tube

0.56 m

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III. Flame Spectra

A. Broadband Background Emissions Figure 2 shows the flame spectra for Jet-A-fueled combustion at stable conditions. The narrow-band peaks

around 310 nm, 430 nm, and 470 nm are associated with chemiluminescence from OH* ( +,-) 22 XA ), CH* ( +,' 22 XA ), and C2

*, respectively. Each narrow-band peak extends over a finite wavelength range, which can be attributed to natural broadening due to energy-time uncertainty principles, thermal Doppler broadening due to atomic velocities, and pressure broadening. The flame spectra are quite similar to those of lean premixed combustion. The smaller peak around 310 nm does not necessarily imply that OH* chemiluminescence is weaker than CH* chemiluminescence. This can be caused by differences in the transmission efficiency of the optical system and the quantum efficiency of detectors. The overall efficiency of a detection system, as a function of wavelength, can be measured using a calibrated tungsten lamp.

(a) (b)

Figure 2. Flame spectrum and ICCD imaging of OH* chemilumienscence for Jet-A-fueled LDI combustion. (a) The flame spectra; (b) ICCD imaging. The air flow rate is 44.5g/s, and the preheat temperature is 423 K.

Also shown in Fig.2 is the ICCD imaging of OH* chemiluminescence at 33.0*# and the preheat temperature of 423 K. The axial center of heat release lies at 2.5 cm downstream of the dump plane. If the average axial velocity along the swirling shear layer is assumed to be 40% of the swirler exit velocity, i.e. 21 m/s, then the convective time delay will be about 1 ms. If we assume a representative droplet size of 18 µm and the representative temperature of 900 K, and neglect velocity slip, droplets interactions, droplets/vortex interactions, initial transients, and radiative heat transfer, then the evaporation time is found to be 1.0 ms. Here the boiling point of Jet-A is taken as 503 K, density as 800 kg/m3, thermal conductivity of fuel vapor as 0.063 W/m-K, the constant-pressure specific heat as 3138.3 J/kg-K, and the latent heat of vaporization as 260 kJ/kg. Following the procedures in Ref. 19, the evaporation constant is determined as 3.2092e-7m2/s. From the time scales of convection and evaporation, one can see that before fuel is transported to the major heat release zone, droplets may have fully evaporated. If we assume a laminar flame speed of 0.5 m/s, then the time scale of chemical kinetics can be estimated as

msS

KS LL

Lc 14.1)900(@2

2 *.*"!

& . The time scales of evaporation and chemical kinetics increase

substantially with decreases in the flame temperature. From Fig.1 one can see that, high-speed air enters the diverging swirler through eight radial-entry slots, mixes with the fine droplets, recombines into one stream, and then suddenly expands at the dump plane. Expectedly droplets entrainment and fuel/air mixing are extremely fast, resulting in a rather homogeneous mixture of fuel vapor and air upstream of the flame front. This may explain why the flame spectra shown in Fig.3 are very similar to those of lean premixed gaseous combustion.

The broadband spectra extending from 280 nm to 490 nm mainly consist of CO2* chemiluminescence, HCO*

chemiluminescence, and possibly a small amount of gray-body soot radiations. Some small peaks between 320 nm and 410 nm are associated with HCO* chemiluminescence. Chemiluminescence from CO2

* and HCO* can be used as heat release rate indicators. In this sense, the terms of “background emissions” may be a misnomer. In the present paper, the term of “background emissions” is simply used to distinguish the broadband spectra from the narrowband peaks associated with OH*, CH*, and C2

*. Background emissions around 307 nm (within a wavelength range of 16

!=0.33

0.10 m

2.5 cm

fuel and air

0123456789

1011

260 290 320 350 380 410 440 470Wavelength(nm)

Inte

nsity

(A.U

.) Phi=0.54 Phi=0.51Phi=0.48 Phi=0.45Phi=0.42 Phi=0.39Phi=0.36 Phi=0.33

OH* ~306 nm

CH* ~431 nm

CH* ~390 nm C2

* ~474 nm

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nm) is approximated using a linear curve-fitting polynomial which is determined from the UV spectra within 281~295 nm and 338~377 nm. Background emissions around 430 nm (within a wavelength range of 15 nm) is approximated using a quadratic curve-fitting polynomial which is determined from the VIS spectra within 396~419 nm and 442~462 nm. Figure 3 shows the ratio of background emissions among the gross intensity within 300~316 nm and 422~438 nm, respectively. The data are acquired from experiments repeated multiple times within a month with the air flow rate at 27.8 g/s, 33.4 g/s, 38.9 g/s, 44.5 g/s, or 55.6 g/s, and the preheat temperature at 373 K, 381 K, 398 K, 423 K, 448 K, or 473 K. In these tests, the combustor exit is not restricted so that the combustor pressure is almost the same as the atmospheric pressure, with variations less than 2%. Thus pressure effects on the flame spectra can be neglected. At the same equivalence ratio, the ratio of background emissions varies with the air flow rate and the preheat temperature. The variations are within 5% around 307 nm and within 10% around 430 nm. In addition, the difference in the ratio of background emissions around 430 nm increases with decreasing equivalence ratios, but that around 307 nm does not. With decreasing equivalence ratios from 0.54 to 0.33, the ratio of background emissions around 430 nm increases more than 30%, while that around 307 nm increases less than 4%. This is probably because CH* chemiluminescence is more affected by the hydrocarbon concentration, i.e. the equivalence ratio, than OH* chemiluminescence. In other words, CH* chemiluminescence is a higher-order nonlinear function of the equivalence ratio than OH* chemiluminescence. This can be seen from the empirical correlation functions to be presented later in this paper.

0.52

0.52

0.53

0.53

0.54

0.54

0.55

0.55

0.56

0.56

0.57

0 30 0.35 0.40 0.45 0 50 0.55Equivalence Ratio

OH

*(bk

g)/O

H*(

gros

s)

0.30

0.32

0.34

0.36

0.38

0.40

0.42

0.44

0.46

0.48

0 30 0 35 0.40 0.45 0.50 0.55Equivalence Ratio

CH

*(bk

g)/C

H*(

gros

s)

Figure 3. Ratio of background emissions at the approach of LBO. There are large variations in the equivalence ratio, the air flow rate, and the preheat temperature among the experiments.

B. Self-Similarity of Broadband Spectra around 430 nm The broadband spectra around 430 nm (within a wavelength range of 15 nm) are approximated using a second-

order curve-fitting polynomial, 2

210)( $$$ aaaI ))* . (1)

Here 431$$ * . $ is the wavelength, nm. Expectedly, the polynomial coefficients will vary with the working conditions, such as the air flow rate, the preheat temperature, the equivalence ratio, and pressure. The above model is of second order in wavelength. Expectedly it is applicable only within a short wavelength range. Table 1 shows the normalized polynomial coefficients with decreasing equivalence ratios from 0.51 to 0.33. The curve-fitting coefficients are normalized by those at 39.0*# . In one experiment, the air flow rate is 55.6 g/s and the preheat temperature is 473 K. In the second experiment, the air flow rate is 27.8 g/s and the preheat temperature is 398 K. One can see from Table 1 that at the same air flow rate and preheat temperature, the three normalized coefficients vary with the equivalence ratio at almost the same rate, with the differences less than 3.0%. The ratio of the baseline polynomial coefficients is also almost the same, i.e. [1.3239 1.3247 1.3211]. The differences are within 0.3%. The self-similarity between chemiluminescence intensity and wavelength implies that, if the broadband emissions nearby 430 nm, say within 396~406 nm or 450~460 nm, are measured using a PMT, then background emissions around 430 nm can be determined using Eq. 1. Note that self-similarity between the spectral intensity and wavelength does not exist around 307 nm or around 365 nm.

Table 1. Normalized curve-fitting coefficients for background emissions around 430 nm

# Air 27.8 g and 398 K Air 55.6 g/s and 473 K

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0a 1a 2a 0a 1a 2a 0.51 2.3263 2.3580 2.3692 2.1259 2.1588 2.1755 0.48 1.7885 1.8164 1.8208 1.8014 1.8304 1.8581 0.45 1.6792 1.6904 1.7097 1.5516 1.5709 1.5908 0.42 1.3932 1.4064 1.4276 1.2988 1.3065 1.3185 0.39 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.36 0.7716 0.7697 0.7676 0.7519 0.7455 0.7423 0.33 0.5846 0.5823 0.5785 0.6040 0.5990 0.5926

0a 1a 2a 0a 1a 2a 0.39 -116.23 223.73 -101.97 -153.88 296.37 -134.71

C. Flame Spectra during Combustion Instability Figure 4 shows the phase-locked flame spectra during self-excited combustion instability, at three phases from

acoustic pressure at the dump plane, i.e. at 10o, 100o, and 190o, respectively. The unstable frequency is around 550 Hz, corresponding to half-wave mode of the combustion chamber which is 0.56-m-long for this experiment. The air flow rate is 44.5 g/s, the equivalence ratio is 0.35, and the preheat temperature is 398 K. The three flame spectra roughly correspond to the maximum, medium, and minimum heat release within a pressure cycle, respectively. The second-order curve-fitting polynomial coefficients for broadband emission spectra around 430 nm are determined as [-1.8047e+001 3.3991e+001 -8.6690e+000], [-1.3353e+001 2.4492e+001 -6.3188e+000], and [9.7051e+000 1.7969e+001 -4.5892e+000], respectively. Again the broadband background emission spectra around 430 nm are found to be self similar with wavelength.

Figure 4. Flame spectra at three phases from pressure at the dump plane, i.e. at 10o, 100o, and 190o,respectively. The ICCD exposure time duration is 200 µs, the intensifier gain is 9, and the accumulation is 500.

IV. PMT-based Chemiluminescence Measurements Correlation functions relating chemiluminescence intensity with the air flow rate, the equivalence ratio, the

preheat temperature, acoustic pressure, and acoustic temperature are developed from PMT-based chemiluminescence measurements. The development of correlation functions is based on several assumptions, including complete combustion, a fixed percentage of heat loss, and a fixed constant-pressure specific heat. Complete combustion implies that the global heat release rate is proportional to the fuel flow rate. The assumptions of a fixed percentage of heat loss and a fixed constant-pressure specific heat imply that, the flame temperature rise is proportional to the equivalence ratio. For LDI flames, the fuel/air equivalence ratio may somewhat vary along the flame front, thus a representative equivalence ratio is assumed. Note that for premixed flames, the equivalence ratio is the same everywhere upstream of the flame front. The air flow rate affects the strain rate or the velocity gradients upstream of the flame front. At the same air flow rate, the swirler exit velocity is proportional to the preheat temperature. Both the air flow rate and the preheat temperature affect droplets distribution, evaporation, and fuel/air mixing. For unstretched laminar premixed flames, the chemiluminescence intensity is a unique function of the equivalence ratio, combustor pressure, and the preheat temperature. But for liquid-fueled, turbulent, LDI combustion, the situation is further complicated by the strain rate, droplets distribution, evaporation, and fuel/air

05

1015202530354045

260 285 310 335 360 385 410 435 460 485Wavelength(nm)

Inte

nsity

(A.U

.)

10 Deg

190 Deg

100 Deg

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mixing. Expectedly the correlation functions for liquid-fueled, turbulent, LDI flames would differ from those for unstretched, laminar, premixed flames.

To incorporate pressure effects into the correlation functions, a perforated plate with different blocking ratios is installed at the combustor exit. Thus combustor pressure can vary up to 40% of the atmospheric pressure. The combustor static pressure is measured using a Sensotec pressure transducer (sensitivity 172 kPa/Volt and uncertainty 0.25%), which is installed 1.5 m away from the combustion chamber using an extension tube. The dynamic pressure nearby the heat release zone is measured using a high-sensitivity PCB pressure sensor (112A05/422E51) installed at the dump plane. Chemiluminescence from OH*, CH*, and CO2

* are measured within a broad range of working conditions, with the air flow rate ranging from 27.8 g/s to 66.7 g/s with an incremental increment of 5.56 g/s, the equivalence ratio ranging from 0.30 to 0.50 with an incremental increment of 0.02, and the preheat temperature at 373 K, 423 K, and 473 K. Experiments are repeated eight times within one month, and about 1100 data sets are obtained. Although bandpass filters with FWHM of 10 nm are used to select narrowband emissions, chemiluminescence measurements still contain a considerable amount of background emissions as shown in Fig.4. Since background emissions mainly consist of CO2

* chemilumnescene, which itself can be used as an indicator of the heat release rate, no background corrections are made. Correlation functions are developed as follows,

4522010601

1369275581307

~2000

~61.94 ,/01

234 )* pTmI i

anm ##& (2)

2183082170

2280236371365

~2000

~85.115 ,/01

234 )* p

TmI i

anm ##& (3)

4045043521

0735366271430

~2000

~05.212 ,/01

234 )* p

TmI i

anm ##& (4)

am~& refers to the normalized air flow rate, i.e. the air flow rate normalized by 100 g/s. p~ refers to the normalized pressure, i.e. the combustor pressure normalized by one atmospheric pressure. The above correlation functions have explicit physical meaning. For unsteady combustion, i.e. self-excited combustion instability and forced flame responses under fuel modulations, )(tma& should be interpreted as the instantaneous air consumption rate along the flame front, i.e.

5*fL

Laa dlfslm0

)()(%& (5)

LS and a% refer to the laminar flame speed and the air density along the flame front, respectively. Note that the instantaneous air consumption rate along the flame front may differ considerably from the instantaneous air flow rate at the combustor inlet in both amplitude and phases. For Jet-A combustion, the air density a% differs from the

reactant density u% by 2~3% with the equivalence ratio from 0.30 to 0.50. Based on the assumptions of a fixed

percentage of heat loss and a fixed constant-pressure specific heat, /01

234 )

2000iT# is proportional to the flame

temperature. Here we assume an increase of 2000 K in the adiabatic flame temperature. Equations (2-4) show that the chemiluminescence intensity is a nonlinear function of the air flow rate, the

equivalence ratio, the flame temperature, and pressure. The equivalence ratio plays a dominant role in the chemiluminescence yield. In other words, chemiluminescence is most sensitive to equivalence ratio variations. Figure 5 compares the measured chemiluminescence Vs. the curve-fitting results. The average error between measurements and curve-fitting is 2.37% for OH*, 1.96% for CO2

*, and 3.8% for CH*. The relatively large error in CH* correlation probably can be attributed to the different emission characteristics between CO2

* chemiluminescence and CH* chemiluminescence. However, an error of 3.8% may be acceptable for many applications. The fact that rather accurate curve-fitting models are obtainable within a large range of working conditions can be attributed to the small variations in the flame structure at different working conditions [20]. The flame structure refers to the spatial distribution of the reaction zone. It is also found that, even during self-excited combustion instability, there are mainly temporal variations in the chemiluminescence intensity rather than spatial variations in the flame structure20.

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0

2

4

6

8

10

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0 100 200 300 400 500 600 700 800 900 1000 1100Experiment Index

OH

* Che

milu

min

esce

nce(

A.U

.)

Measurement Curve-Fitting

0

2

4

6

8

10

12

0 100 200 300 400 500 600 700 800 900 1000 1100Experiment Index

CO

2* C

hem

ilum

ines

cenc

e (A

.U.) Measurement Curve-Fitting

0123456789

1011

0 100 200 300 400 500 600 700 800 900 1000 1100Experiment Index

CH

* C

hem

ilum

ines

cenc

e(A.

U.) Measurement Curve-Fitting

Figure 5. Chemiluminescence measurements Vs. curve-fitting. Data are obtained within a large range of air flow rates, equivalence ratios, and preheat temperature. More than 30% of the data are obtained at unstable conditions.

V. Determination of the Instantaneous Heat Release Rate and Equivalence Ratios The instantaneous heat release rate and the instantaneous equivalence ratio are key parameters for combustion

instability analysis and control. For self-excited combustion instability, equivalence ratio variations are caused by the differential acoustic impedance between the fuel line and the air line. The unsteady heat release can be caused by several mechanisms, including variations in the flame surface area, the reaction heat, and the laminar burning speed due to equivalence ratio perturbations, combustor inlet velocity oscillations, and acoustic effects. For liquid-fueled combustion instability, strong acoustic oscillations may considerably enhance droplet evaporation and modify the reacting flow field. Thus whether the correlation functions developed from steady conditions can be applied to unsteady combustion requires further exploration. In the present combustor, the droplet SMD is small, below 20 !m, so the droplets will follow the surrounding air velocity with almost no velocity slip, and evaporation is extremely fast. Consequently evaporation enhancement by acoustic velocity oscillations or acoustic streaming, if any, may be neglected. We have also observed that there are almost no variations in the mean flame structure between steady and unsteady combustion within a large range of working conditions20. At the same inlet air flow rate, the same inlet equivalence ratio, and the same preheat temperature, the differences in the mean chemiluminescence intensity between steady and unsteady combustion are negligibly small, within 2.0%. Even during unsteady combustion, i.e.

American Institute of Aeronautics and Astronautics

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self-excited combustion instability and forced flame responses under fuel modulation, there are mainly variations in the chemiluminescence intensity rather than in the flame structure20. Thus for the present combustor, the correlation functions can be used to estimate the instantaneous heat release rate and the instantaneous equivalence ratio for unsteady combustion.

The role of large vortex shedding synchronized with pressure cycles has been frequently emphasized by researchers for combustion instability in bluff-body-stabilized combustors and dump combustors21. However, the situation would be somewhat different for swirling combustion stabilized by vortex breakdown. In swirling flows, the shear layer growth and decay rates are significantly enhanced22,23, thus there are fewer opportunities for the Kelvin-Helmholtz shear layer mode to continuously grow and for the wake-like absolutely unstable mode to form. Several researchers have observed almost no variations in the flame structure in swirling combustion during both self-excited combustion instability and inlet air modulations24,25. Even for sharp-edged non-swirling combustors, large vortex shedding does not occur unless air forcing is applied around the preferential frequencies of the shear layer and the forcing amplitude exceeds certain thresholds26. Even in the presence of large-scale vortex shedding, major portion of the flame rides over the large vortices, and the flame curvature is much larger than the flame thickness, thus the empirical correlation functions developed for steady conditions may still be applied to unsteady conditions.

In the following, it is assumed that the preheat temperature and the combustor pressure nearby the heat release zone can be measured. The instantaneous air consumption rate, the instantaneous equivalence ratio, and the instantaneous heat release rate are determined as follows,

6 7 6 7 6 7 6 76 7 6 7 6 7 6 7

6 7 6 7 6 7 6 7 6 7 6 7 6 7 )(~7.281~00674.0~1.0

)(~)()()(1392.0)(

)(~)()()(1571.0)(~

2021014370430

49421365

29661307

1974055401430

72940365

47471307

kWttmttmHmm

ttmHtQ

tptItItIt

tptItItItm

R

trystoichiomea

fRR

nmnmnm

nmnmnm

###

#

&&&

&&&

&

*'*//0

1223

4'*

*

*,,

,

(6)

Equation (6) is obtained from Eqs. (2~4) by eliminating /01

234 )

2000iT

# . In the case of combustion instability, the

normalized flame temperature becomes //0

1223

4 ))

2000

'ai TT

# . Here )11()('

'

pp

TtT aa 8

8 ,)* and 33.1*8 . )(' tpa

is the acoustic pressure nearby the heat release zone. The lower heating value of Jet-A is taken as 41.8 MJ/kg. The chemical formula of Jet-A is taken as C11H23, thus the stoichiometric fuel/air ratio is 0.0674. The mean heat release rate is determined as,

)(8173.20674.0 kWmmHmm

mHQ R

trystoichiomea

fRR ### &&

&

&&& *'*/

/0

1223

4'* (7)

Here m& and # refer to the mean air consumption rate and the mean equivalence ratio, respectively.

A. Parameter Estimation for Self-Excited Combustion Instability Figure 6 shows the estimated mean heat release rate and the estimated mean equivalence ratio in a series of

experiments. Here the air flow rate is 66.7g/s, the preheat temperature is 373 K, and the equivalence ratio is decreased from 0.41 to 0.31. Strong combustion instability (corresponding to half-wave mode of the combustion chamber) occurs when the equivalence ratio is decreased below 0.34. The estimation error is within 1.4% in the mean equivalence ratio, within 1.9% in the mean air consumption rate, and within 1.0% in the mean heat release rate.

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0.20

0.25

0.30

0.35

0.40

1 3 5 7 9 11 13 15 17Experiment Index

Equ

ival

ence

Rat

io

MeasurementPrediction

30

40

50

60

70

1 3 5 7 9 11 13 15 17Experiment Index

Air

Flow

Rat

e (g

/s)

MeasurementPrediction

Figure 6. The estimated mean air consumption rate and the mean equivalence ratio. The air flow rate is 66.7g/s, the preheat temperature is 373 K, and the equivalence ratio is decreased from 0.41 to 0.31.

Strong combustion instability appears at the equivalence ratio of 0.33. Figure 7 (a) shows the time traces of chemiluminescence and acoustic pressure nearby the dump plane. The phase difference between CH* chemiluminescence and pressure is 33.7o. The in-phase oscillations of acoustic pressure and heat release provide energy to maintain acoustic oscillations. Figure 7(b) shows the estimated instantaneous air consumption rate, the estimated instantaneous equivalence ratio, and the estimated instantaneous heat release rate. All these parameters oscillate in phase. The amplitude of the air consumption rate is about 35% of the mean, and the amplitude of equivalence ratio oscillations is about 17% of the mean.

Self-excited combustion instability becomes stronger when the equivalence ratio is decreased from 0.34 to 0.33. In Table 2, the equivalence ratio is expressed as a 3-dignit number. This does not necessarily mean that the accuracy in the equivalence ratio can be as high as 0.001. This is simply to denote the discernible differences in the equivalence ratio. With decreasing equivalence ratios from 0.34 to 0.33, the phase lag between the heat release rate and CH* chemiluminescence increases from 10.2o to 0.74o, while the gain increases by about 20%. This example shows that during combustion instability, chemiluminescence is not proportionally to the instantaneous heat release rate. The same conclusion will be drawn for forced flame responses under fuel modulations, as will be shown in the next section.

0

1

2

3

4

5

6

7

8

0 0.005 0.01 0 015 0.02 0.025Time(s)

CO2*(A.U.) CH*(A.U.)OH*(A.U.) Combustor Pressure(x0.1, kPa)

0

1

2

3

4

5

6

7

0 0.005 0.01 0.015 0.02 0.025Time(s)

CH*(A.U.) Combustor Pressure(x0.1, kPa)Estimated Air Consumptiion Rate(x0.05,g/s) Estimated Equivalence Ratio(x10)Estimated Heat Release(x0.05, kW)

Figure 7. (a) Time traces of chemiluminescence and combustor pressure; (b) The estimated instantaneous air consumption rate, the estimated instantaneous equivalence ratio, and the estimated instantaneous heat release rate.

Table 2. Estimated parameters for self-excited combustion instability

# Prms (kPa) pCH ~/*( pQR~/&( */ CHQR

&( */ CHQR&

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12

0.341 4.4751 50.5380 40.2940 -10.2440 22.7920 0.336 8.5880 41.4840 36.0660 -5.4176 23.6650 0.330 9.9346 33.6610 32.9170 -0.7439 27.1310

B. Parameter Estimation for Forced Flame Responses under Fuel Modulations The instantaneous heat release rate and the instantaneous equivalence ratio are determined for forced flame

responses under fuel modulations. Fuel modulations are achieved using a motor-driven, high-frequency, rotary fuel valve specially designed for this experiment. Detailed description of the rotary valve and the fuel setup is described in Ref. 27. The rotary valve (Fig.8) is located 0.46 m upstream of the fuel nozzle. A 0.8-litre accumulator is located 0.2 m upstream of the rotary valve. A Sensotec pressure transducer (sensitivity 172 kPa/Volt and uncertainty 0.25%) capable of working up to 2 kHz are installed 0.29 m upstream of the fuel nozzle. A bypass flow passage is installed parallel to the rotary fuel valve, and fuel modulation amplitude is controlled by varying fuel split between the rotary fuel valve and the bypass passage. The fuel modulation frequency is determined by the number of rotor teeth and the motor rotating speed. The valve is featured with 16 equally spaced teeth, capable of fuel modulations up to 1 kHz.

Figure 8. The rotary fuel valve

Figure 9 shows the estimated mean parameters with fuel modulations up to 1 kHz. These parameters are the mean air consumption rate, the mean equivalence ratio, and the mean heat release rate. The errors in the estimated mean parameters are within 2.0%. Figure 10 shows the flame transfer functions which are defined in multiple forms. In Figs.10 (a~c), the gain of the transfer functions consistently increases up to 700 Hz and then declines. Note that the fuel pressure 0.29 m upstream of the fuel nozzle may differ considerably from that immediately upstream of the fuel nozzle in both gain and phases, which is particularly true at high frequency [27]. Small abnormalities in the flame transfer functions, between 300 Hz and 400 Hz and between 620 Hz and 700 Hz, can be attributed to the relatively strong forcing-induced acoustic oscillations. In this experiment, the combustion chamber is 1.05-m-long. Although the rig has been modified to enhance acoustic damping by reducing the blockage ratio at the chamber exit and installing three baffle plates, fuel modulations around the acoustic resonant frequencies, i.e. around 330 Hz (half-wave mode) and around 660 Hz (one-wave mode), still result in considerable acoustic oscillations up to 1.5 kPa above the background noise. As pointed out before, acoustic oscillations not only directly affect the chemiluminescence yield, but also may modify the flame kinetics. In Fig 10 (a~c), the phases of the transfer function decrease with the frequency but at different rates, with the fastest decrease in phases with )()( sPsQ fR

&

and the slowest decrease in phases with )(/)(* sPsCH f .

Fuel Outlet Fuel Inlet

Motor Shaft

Rotor (16 teeth equally spaced)

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0

10

20

30

40

50

0 200 400 600 800 1000Frequency(Hz)

Estimated Mean Heat Release Rate (kW)Estimated Mean Air Flow Rate (g/s)Estimated Mean Equivalence Ratio

0.00

0.04

0.08

0.12

0.16

0.20

0 200 400 600 800 1000Frequency(Hz)

Fuel

Mod

ulat

ion

Rat

io

(a) (b)

Figure 9. (a) The estimated mean equivalence ratio (multiplied by 100), the estimated mean air consumption rate, and the estimated mean heat release rate. (b) The fuel modulation ratio, which is defined as the RMS to the mean fuel pressure 0.29 m upstream of the fuel nozzle. At most frequencies, the fuel modulation ratio is above 10%.

The most interesting yet somewhat puzzling is the transfer function )()( * sCHsQR& . Except the small

abnormalities around the acoustic resonant frequencies, the phase consistently decreases with the frequency above 50 Hz, and saturates at -96o above 400 Hz. Above 100 Hz, the gain varies with the frequency, but the variations are within 20%. Remember that for self-excited combustion instability shown in Table 2, the phase differences between

)(sQR& and )(* sCH can be up to 10o, and the gain variations can be up to 20%. Thus the assumption of

proportionality between chemiluminescence and the heat release rate is generally invalid for unsteady combustion, including self-excited combustion instability and forced flame responses under fuel modulations. Probably the proportionality is valid only for the weakly turbulent or wrinkled flamelet region in the absence of equivalence ratio variations along the flame front and strong acoustic oscillations. Take steady combustion as an example. In one experiment with an air flow rate of 27.8 g/s and an equivalence ratio of 0.44, the mean CH* chemluminescence is 3.23 (A.U.) and the mean heat release rate is 34.5 kW. In another experiment with an air flow rate of 44.8 g/s and an equivalence ratio of 0.38, the mean CH* chemilumienscence is 2.33 (A.U.) and the mean heat release rate is 48.0 kW. That is, while CH* chemiluminescence yield of the first experiment is 38.6% larger than the second experiment, its mean heat release rate is 39% less. Note that for steady combustion, the flame temperature is uniquely determined by the equivalence ratio and the preheat temperature. The instantaneous chemiluminescence intensity is an integral of the specific chemiluminescence yield per unit air consumption rate along the flame front, and the instantaneous heat release rate is proportional to the integral of the instantaneous air consumption rate along the flame front. Both the instantaneous chemiluminescence and the instantaneous heat release rate are directly affected by the time-varying flame surface area. With fuel modulations off the acoustic resonant frequencies, variations in the air flow rate across the air swirler are usually negligibly small, because of the small forcing-induced acoustic oscillations, typically below 200 Pa. Thus flame surface area variations are mainly caused by equivalence ratio perturbations along the flame front. The location of a laminar flamelet is determined by the history of the upstream reactant velocity and the laminar burning velocity. The laminar burning velocity is a highly nonlinear function of the equivalence ratio. Equivalence ratio perturbations along the flame front caused by fuel modulations are always accompanied by large variations in the laminar burning velocity and consequently the flame surface area, which is particularly true for lean combustion. Although variations of the flame surface area are the same for both the chemiluminescence yield and the heat release rate, the sensitivity of the laminar flame speed and the chemiluminescence yield to the equivalence ratio is different. This may explain the phase differences between the instantaneous chemiluminescence intensity and the instantaneous heat release rate.

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0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

0 200 400 600 800 1000Frequency(Hz)

Gai

n(A

.U.)

-200

-150

-100

-50

0

50

100

150

200

Pha

se(D

eg)

Gain(A.U )Phase(Deg)

0.0000

0.0005

0.0010

0.0015

0.0020

0.0025

0.0030

0.0035

0 200 400 600 800 1000Frequency(Hz)

Gai

n(A

.U.)

-200

-150

-100

-50

0

50

100

150

200

Pha

se(D

eg)

Gain(A.U.)Phase(Deg)

(a) )(/)(* sPsCH f (b) )(/)( sPs f#

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0 200 400 600 800 1000Frequency(Hz)

Gai

n(A

.U.)

-200

-150

-100

-50

0

50

100

150

200

Pha

se(D

eg)Gain(A.U.)

Phase(Deg)

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

0 200 400 600 800 1000Frequency(Hz)

Gai

n(A

.U.)

-120

-100

-80

-60

-40

-20

0

20

40

Pha

se(D

eg)

Gain(A.U.) Phase(Deg)

(c) )()( sPsQ fR

& (d) )()( * sCHsQR&

Fig.10 Flame transfer functions. (a) CH* chemiluminescence (A.U.) to the fuel pressure (kPa); (b) The estimated equivalence ratio to the fuel pressure (kPa); (c) The estimated heat release rate (kW) to the fuel pressure (kPa); (d) The estimated heat release rate (kW) to CH* chemiluminesence (A.U.).

Figure 11 shows the time traces of several parameters with fuel modulations at 297 Hz and 874 Hz, respectively. These parameters are CH* chemilumienscence, the estimated instantaneous air consumption rate, the estimated instantaneous equivalence ratio, the estimated instantaneous heat release rate, and the fuel pressure 0.29 m upstream of the fuel nozzle. All parameters are normalized by their mean quantity. All data are filtered using a 4th order Butterworth filter with bandwith 200 Hz around the fuel modulation frequency. The amplitude of the normalized CH* chemiluminescence is about five times higher than that of the heat release rate. In both cases, substantial phase differences exist between CH* chemiluminescence and other parameters. With fuel modulations at 297 Hz and 874 Hz, the instantaneous heat release rate lags chemiluminescence in phases more than 80o, which is very different from self-excited combustion instability shown in Fig.7. However, with fuel modulations at 297 Hz and 874 Hz the phase differences among the equivalence ratio, the air consumption rate, and the heat release rate are rather small, which is the same as that of self-excited combustion instability. From Fig.11, one can see that variations in the normalized air consumption rate along the flame front have almost the same magnitude as those of the normalized equivalence ratio. This implies that fuel modulations result in large variations in the flame surface area. For lean fuel/air mixtures, the laminar flame speed is exponentially sensitive to the equivalence ratio or the flame temperature. A simple linear analysis of an inverted laminar V-flame shows that, for unsteady combustion involving small-amplitude equivalence ratio perturbations, dynamics of the flame surface area can be modeled as a first-order system with a negative high-frequency gain. That is, the phases lag between the flame surface area and the equivalence ratio moves towards 270o with increasing frequency. Figs.11 (a, b) show that the instantaneous chemiluminescence lags the equivalence ratio in phases about 270o. This implies, although the chemiluminescence yield per unit air consumption rate does increase with the equivalence ratio, the overall chemiluminescence intensity decreases because of larger reductions in the flame surface area.

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-0.32

-0.24

-0.16

-0.08

0.00

0.08

0.16

0.24

0.32

0.40

0 0.005 0 01 0.015 0.02

Time(s)

Normalized CH* Chemiluminescence Normalized Air Consumption RateNormalized Equivalence Ratio Normalized Heat Release RateNormalized Fuel Pressure

-0.50

-0.40

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0 0.001 0.002 0.003 0.004 0.005 0 006

Time(s)

Normalized CH* Chemiluminescence Normalized Air Consumption RateNormalized Equivalence Ratio Normalized Heat Release RateNormalized Fuel Pressure

(a) (b)

Fig.11 Time traces of CH* chemilumienscence, the estimated air consumption rate, the estimated representative equivalence ratio, the estimated heat release rate, and the fuel pressure. (a) Fuel modulations at 296 Hz; (b) Fuel modulations at 874 Hz. All parameters are normalized by their mean quantity.

VI. Discussion For unsteady combustion, including self-excited combustion instability and forced flame responses under fuel

modulations, the estimated instantaneous air consumption rate and the estimated instantaneous equivalence ratio along the flame front should not be considered the same as those at the combustor inlet. Because of the complicated physicochemical processes in between, substantial differences in both amplitude and phases may exist between the parameters along the flame front and those at the combustor inlet.

Quasi-steady relationship among the heat release rate, the air consumption rate, the equivalence ratio, and the preheat temperature are assumed for unsteady combustion. This is valid for the present combustor, which exhibits very small variations in the flame structure during unsteady combustion. The quasi-steady relationship is expected to be applicable to combustion instability in the presence of acoustically synchronized large vortex shedding. This is because in such cases, the flame curvature is typically much larger than the flame thickness.

Pressure effects on chemiluminescence yield are taken into account in the determination of the instantaneous heat release rate and the instantaneous equivalence ratio. Quasi-steady responses among combustor pressure, chemical kinetics, and chemiluminscence production are assumed. This assumption has been widely used in combustion community and is valid at least at low frequency. The life time of radical species or the time scale of photo release is at least three-order-of-magnitude higher than the acoustic cycle [18], thus the chemiluminescence yield can be assumed instantaneous with the chemical reaction rate.

VII. Conclusion9 Flame spectra of the present turbulent, liquid-fueled, swirl-stabilized, LDI combustor are quite similar to those of

lean premixed gaseous combustion. This can be attributed to the small droplet size and fast fuel/air mixing. Background emissions around 430 nm, which mainly consists of CO2

* chemiluminescence, are found to be self-similar with wavelength within a rather broad range of working conditions. This implies that background emissions around 430 nm can be determined from emission measurements nearby 430 nm.

9 Accurate correlation functions relating chemiluminescence, the air flow rate, the equivalence ratio, and the preheat temperature, are developed for combustion within a large range of working conditions. The average error between measurements and correlation is within 2.37% for OH*, within 1.96% for CO2

*, and within 3.8% for CH*.

9 Methods for determination of the instantaneous air consumption rate and the instantaneous equivalence ratio along the flame front are developed. For both self-excited combustion instability and forced flame responses under fuel modulations, the errors in the estimated mean heat release rate, the estimated mean air consumption rate, and the estimated mean equivalence ratio are below 2.0%.

9 The assumption that chemiluminescence is proportional to the instantaneous heat releaser rate is generally invalid. This is mainly because of the differences in sensitivity to equivalence ratio among the chemiluminescence yield, the heat release rate, and the flame surface area. Both the instantaneous chemiluminescence and the instantaneous heat release rate are directly affected by the time-varying flame

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surface area. Equivalence ratio perturbations along the flame front are always accompanied with variations in the laminar flame speed and consequently in the flame surface area.

9 Acoustic motions are isentropic, but both acoustic pressure and acoustic temperature affect the chemiluminescence yield. Acoustics-induced chemiluminescence oscillations are taken into account for the determination of the instantaneous heat release rate and the instantaneous equivalence ratio.

Acknowledgments Support from NASA Glen under grant NNX07C98A, “Active Combustion Control for Low-Emission

Combustors,” is gratefully acknowledged. Dr. Clarence Chang is the project manager. This project is also supported by Air Force under grant FA9550-07-1-0451, “Advanced Thermally Stable Coal-based Jet Fuels”. The authors would like to thank Mr. P. Stephen and Dr. B. Quay for sharing the PMT housing, and would like to thank Prof. R. Santoro for sharing the spectrometer.

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Gaseous Hydrocarbons at 3.39 !m,” Measurement Science and Technology, Vol.17, 2006, pp.1950-1957. 7Drallmeier, J. A., “Hydrocarbon-Vapor Measurements in Pulsed Fuel Sprays,” Applied Optics, Vol.33, No.33, 1994,

pp.7781-7788. 8Kojima, J., Ikeda, Y., and Nakajima, T., “Basic Aspects of OH(A), CH(A), and C2(d) Chemiluminescence in the Reaction

Zone of Laminar Methane–Air Premixed Flames,” Combustion and Flame, Vol.140, 2005, pp.34-45. 9Muruganandam, T. M., Kim, B. H., Morrell, M. R., Nori, V., Patel, M., Romig, B. W., and Seitzman, J. M., “Optical

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using Chemiluminescent Emission from a Flame,” Combustion and Flame, Vol.139, 2004, pp.188-207. 12Markstein, G. H., Nonsteady Flame Propagation, The MacMillan Company, 1964, pp. 5-13. 13Samaniego, J. M., Egolfopoulos, F. N., and Bowman, C. T., “CO2* Chemiluminescence in Premixed Flames,” Combustion

Science and Technology, Vol.109, 1995, pp.183-203. 14Egolfopoulos, F. N. and Campbell, C. S., “Unsteady Counterflowing Strained Diffusion Flames: Diffusion-Limited

Frequency Response,” Journal of Fluid Mechanics, Vol.318, 1996, pp.1-29. 15Lee, J. G., Gonzalez, E., and Santavicca, D. A., “On the Application of Chemiluminescence to the Estimation of Unsteady

Heat Release during Unstable Combustion in Lean Premixed Combustor,” 41st AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, Tucson, Arizona, 2005, AIAA paper 2005-3575.

16Higgins, B., McQuay, M. Q., Lacas, F., Rolon, J. C., Darabiha, N., and Candel, S., “Systematic Measurements of OH Chemiluminescence for Fuel-Lean, High-Pressure, Premixed, Laminar Flames,” Fuel, Vol.80, 2001, pp.67-74.

17Higgins, B., McQuay, M. Q., Lacas, F., and Candel, S., “An Experimental Study on the Effect of Pressure and Strain Rate on CH Chemiluminescence in Premixed Fuel-Lean Methane/Air Flame,” Fuel, Vol.80, 2001, pp.1583-1591.

18Gordan, A. G., Spectroscopy of Flames, Chapman and Hall, 1974, pp. 13, 164, and 166. 19Turns, S. R., An Introduction to Combustion: Concepts and Applications, 2nd Edition, McGraw-Hill, 2000, pp.362-378 and

pp.461. 20Yi, T. and Santavicca, D. A., “Combustion Instability in a Turbulent Liquid-Fueled Swirl-Stabilized LDI Combustor: I.

Experiments,” to be presented at the 45th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, Denver, Colorado, Aug. 2-5, 2009.

21Culick, F. E. C., “Combustion Instabilities in Liquid-Fueled Propulsion Systems, - an Overview,” AGARD/NATO, 1989, AGARD CP-450.

22Syred, N., and Beer, J. M., “Combustion in Swirling Flows: a Review,” Combustion and Flame, Vol. 23, No.2, 1974, pp. 143-201.

23Lilly, D. G., “Swirling Flow in Combustion: a Review,” AIAA Journal, Vol. 15, No. 89, 1977, pp. 1063-1078.

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24Anderson, T., and Morford, S., “Dynamic Flame Structure in a Low NOx Premixed Combustor,” Proceedings of the ASME Turbo Expo 1998, Stockholm, Swede, June, 1998, ASME paper GT98-568.

25Eckstein, J., Freitag, E., Hirsch, C., Sattelmayer, T., Von Der Bank, R., and Schilling, T., “Forced Low-Frequency Spray Characteristics of a Generic Airblast Swirl Diffusion Burner,” ASME Journal of Engineering for Gas Turbine and Power, Vol.127, 2005, pp.301-306.

26Balachandran, R., Ayoola, B. O., Kaminski, C. F., Dowling, A. P., Mastorakos, E., “Experimental Investigation of the Nonlinear Response of Turbulent Premixed Flames to Imposed Inlet Velocity Oscillations,” Combustion and Flame, Vol.143, 2005, pp.37–55.

27Yi, T. and Santavicca, D. A., “Flame Transfer Functions and their Applications to Combustion Analysis and Control,” Proceedings of the ASME Turbo Expo 2009, Orlando, Florida, June, 2009, ASME paper GT2009-60181.