Proceedings

Proceedings of the Combustion Institute 31 (2007) 2693–2700

www.elsevier.com/locate/proci

of the

CombustionInstitute

Studies of radiation absorption on flame speedand flammability limit of CO2 diluted methane flames

at elevated pressures

Zheng Chen a,*, Xiao Qin a, Bo Xu a, Yiguang Ju a, Fengshan Liu b

a Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USAb Combustion Research Group, National Research Council Canada, 1200 Montreal Road, Building M-9, Ottawa,

Ont., Canada K1A 0R6

Abstract

The effects of spectral radiation absorption on the flame speed at normal and elevated pressures wereexperimentally and numerically investigated using the CO2 diluted outwardly propagating CH4–O2–Heflames. Experimentally, the laminar burning velocities of CH4–O2–He–CO2 mixtures at both normaland elevated pressures (up to 5 atm) were measured by using a pressure-release type spherical bomb.The results showed that radiation absorption with CO2 addition increases the flame speed and extendsthe flammability limit. In addition, it was also shown that the increase of pressure augments the effectof radiation absorption. Computationally, a fitted statistical narrow-band correlated-k (FSNB-CK) modelwas developed and validated for accurate radiation prediction in spherical geometry. This new radiationscheme was integrated to the compressible flow solver developed to simulate outwardly propagating spher-ical flames. The comparison between experiment and computation showed a very good agreement. Theresults showed that the flame geometry have a significant impact on radiation absorption and that theone-dimensional planar radiation model was not valid for the computation of the flame speed of a sphericalflame. An effective Boltzmann number is extracted from numerical simulation. Furthermore, the FSNB-CK model was compared with the grey band SNB model. It was shown that the grey band SNB modelover-predicts the radiation absorption. It is concluded that quantitative prediction of flame speed and flam-mability limit of CO2 diluted flame requires accurate spectral dependent radiation model.� 2006 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Keywords: Spectral dependent radiation; Burning velocity; Flammability limit; CO2 addition

1. Introduction

Thermal radiation receives a renewed interestbecause it is a dominant transport mechanism inspace, urban fires, and ultra lean high pressure

1540-7489/$ - see front matter � 2006 The Combustion Institdoi:10.1016/j.proci.2006.07.202

* Corresponding author. Fax: +1 609 258 6233.E-mail address: zhengc@princeton.edu (Z. Chen).

combustion. The strong spectral radiationabsorption of CO2 and the appearance of largeamount of CO2 in the exhausted gas recircula-tion and CO2 fire suppressant raise the follow-ing question: what is the role of CO2 radiationin flame speed and flammability limit? This con-cern becomes more serious when the ambientpressure increases. Recently, it has become clearthat spectral radiation is the dominant loss

ute. Published by Elsevier Inc. All rights reserved.

2694 Z. Chen et al. / Proceedings of the Combustion Institute 31 (2007) 2693–2700

mechanism for flammability limit [1–5] and itleads to radiation extinction [6–9], flamebifurcations [10–12] and radiation inducedinstability [13]. Therefore, the effect of radiationheat loss on near limit flames has beenextensively studied [1–5,14–17]. However, CO2

is not only a radiation emitter but also anabsorber.

The effect of radiation absorption on flamespeed was first analyzed by Joulin and Deshaies[18] using a gray gas model. It was shown thatthere is no flammability limit when radiationabsorption is considered. The gray model wasalso used to study flame ball dynamics [19].However, CO2 radiation is not gray. Rather, itis spectral dependent and has temperature andpressure broadening. Ju and his coworkers[20,21] first used the non-gray statistical narrowband (SNB) model in studying the CO2 dilutedpropagating flames and showed that a ‘‘funda-mental’’ flammability limit exists because ofthe emission-absorption spectra differencebetween the reactants and products and bandbroadening. This model was later used in flameballs [22] and high pressure planar flames [23].However, even the prediction was better thanthat of optically thin model [8,9], it still couldnot reproduce the experimental data [7]. More-over, because of the limitation of computationtime, radiation modeling [20] still used the grayassumption on each spectral line and was limit-ed to one-dimensional (1D) planar flame geom-etry although many experimental data arefrom spherical flames. More importantly, exper-imental data of radiation absorption was notavailable to validate the modeling. AlthoughAbbud-Madrid and Roney [24] tried to measurethe radiation absorption effect using a particleladen flame, the radiation effect is not yet con-firmed because of the large heat capacity of par-ticles. Therefore, it is particularly important to:(1) obtain experimental data of CO2 spectralradiation absorption to validate radiation mod-eling; (2) develop accurate and efficient radiationmodel; and (3) understand the dependence ofradiation absorption on pressure, flame scale,and flame geometry.

The goal of this study was to experimentallymeasure the effect of radiation absorption onflame speed at elevated pressures using theCO2 diluted outwardly propagating CH4–O2–He flames and to develop a more accurate andefficient spectral radiation model for sphericalflame modeling. First, the flame speed and flam-mability limit of the CO2 diluted flames weremeasured. A new radiation model was thendeveloped and validated using the measureddata. Finally, the dependence of radiationabsorption on pressure and flame scale wasexamined and the Boltzmann number forradiation absorption was computed.

2. Experimental method

The experimental measurements of flame speedwere conducted in a dual-chambered, pressure-re-lease type high pressure combustion facility atnormal gravity [25]. Due to the effect of buoyancy,the maximum test pressure was limited to 5 atm.The combustible mixture was spark-ignited atthe center of the inner chamber with minimumignition energy so as to minimize ignition distur-bances. The flame propagation sequence wasimaged with Schlieren photography and a high-speed digital video camera (Photron FastcamAPX) with 4 ls shutter speed and a frame rateof 8000 fps was used. 1024 pixels were used for5 cm width domain in horizontal direction. Datareduction was performed only for flame radiibetween 1.0 and 2.5 cm. The pressure increase isnegligible because the volume of the chamber isapproximately 100 times larger than the flame sizeat which flame speed was measured.

The stretched flame speed was first obtainedfrom the flame history and then was linearlyextrapolated to zero stretch rate to obtain theunstretched flame speed [25]. The estimated mea-surement uncertainty is �5%. The reactant mix-tures were prepared using the partial pressuremethod. Helium was introduced to adjust the mix-ture Lewis number (Le) to suppress the flameinstability. Mixtures of CH4 � {0.3O2 + 0.2He+ 0.5CO2}, with Le = 1.15–1.20, were examinedand all runs were performed in a quiescent envi-ronment at an initial temperature of 298 ± 3 Kand initial pressures ranging from 1 to 5 atm.The results presented at each point were the aver-age of three tests.

3. Fitted SNB-CK radiation model and numericalalgorithm

For combustion gas radiation properties, anumber of databases have been compiled basedon line-by-line (LBL) [26,27], and narrow band[28,29] model, and global full-spectrum model[30,31]. The LBL is accurate at low temperatures,but requires excessive CPU time and is not suit-able for high temperature combustion gasesbecause the high temperature vibration-rotationabsorption bands are not included. For globalmodels, the weighted-sum-of-grey-gases (WSGG)model [30] and the full-spectrum correlated-kmethods [31] were developed. These models haveexcellent computation efficiency but are less accu-rate than the band models and have difficultiestreating non-gray boundaries. The statistical nar-row-band (SNB) models [28] are favored. RecentCO2 absorption experiment [32] showed thatEM2C SNB model has an excellent accuracy upto 1300 K. In the SNB model for non-homoge-neous mixtures, the ray tracing method [33] and

Z. Chen et al. / Proceedings of the Combustion Institute 31 (2007) 2693–2700 2695

the Curtis–Godson approximation were widelyused [33,34]. However, the ray tracing method iscomputationally inefficient, and the Curtis–God-son approximation is accurate only in the optical-ly thick and thin limits.

Lacis et al. [35] developed a new category ofthe SNB based correlated-k method (SNBCK).By reordering the absorption coefficients inLBL into a monotonic k-distribution in a nar-row spectral range, the model can produce exactresults at a small computation cost [36]. Forinhomogeneous media, it was shown that CKmodel gives much better results than the stan-dard Curtis–Godson correlation. Furthermore,it allows the implementation of conventionaldiscrete ordinate method (DOM) [37]. However,the inversion of CK model requires numericaliterations and sometimes convergence is notguaranteed. In addition, the SNB-CK modelhas not been considered in radiation modelingfor spherical flames.

In this study, to resolve the convergence diffi-culty of SNB-CK in multi-component mixturesand to increase the computation efficiency, wedeveloped a fitted SNB-CK model and extendedit for radiation calculation of spherical flames.Hereafter, we call this model FSNB-CK.

In the SNB model, the gas transmissivity, sm, atwave number m over a light path L is given as [38]

sm ¼ exp �pbffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ 4SL=pb

p� 1

� �=2

h ið1Þ

where b ¼ 2�bm=p, S ¼ �kmXp, and �bm ¼ 2p�cm=�dm arethe SNB model parameters [28] for CO, CO2

and H2O. The bandwidth is 25 cm�1 for wavenumbers between 150 and 9300 cm�1. By per-forming an inverse Laplace transformation, thedistribution function of the absorption coefficientat each narrow band can be obtained as [35]

f ðkÞ ¼ 0:5k�3=2ðbSÞ1=2

� exp 0:25pbð2� S=k � k=SÞ½ � ð2Þ

and the cumulative function of k-distribution

gðkÞ ¼Z k

0

f ðk0Þdk0 ð3Þ

can be given as

gðkÞ ¼ 1

21� erf

ffiffiffiffiffiffiffiffipbS4k

r�

ffiffiffiffiffiffiffiffipbk4S

r !" #

þ 1

21� erf

ffiffiffiffiffiffiffiffipbS4k

rþ

ffiffiffiffiffiffiffiffipbk4S

r !" #expðpbÞ

ð4ÞUsing the cumulative distribution function, the

average radiation intensity at each narrow bandcan be calculated using a Gauss type quadrature[36]

Im ¼XN

i¼1

xiIm½kiðgiÞ� ð5Þ

where N is the number of Gaussian quadraturepoints, xi the weight function, and gi the Gaussianpoint. The estimation of ki(gi) from Eq. (4) needsiterations and sometimes diverges for multi-com-ponent mixtures [35]. In order to resolve thisproblem, we rewrote Eq. (4) as

kii=SðbÞ ¼ F iðbÞ; i ¼ 1; N ð6Þ

Here, Fi(b) is a fitted function at all Gaussianpoints for CO, CO2 and H2O using the SNB data[28], respectively. Therefore, Eq. (4) is replaced byEq. (6) using 3 · N fitted functions. Since a four-point Gaussian quadrature is accurate enoughfor Eq. (5), we only need 12 fitting functions.These fittings are straight forward and the maxi-mum error between B = 10�4 and 104 for ki/S isless than 0.5%. For b < 10�4 and b > 104, the opti-cally thin and thick limits can be applied. The useof Eq. (6) and high accuracy of fitting completelyremove the need of iteration for ki(gi) from Eq. (4)and thus this technique avoids the problem ofdivergence.

For radiating gas mixtures, the approximatetreatment of overlapping bands from opticallythin and thick limits [35,36] is employed

S ¼ SCO þ SCO2þ SH2O; S2=b

¼ S2CO=bCO þ S2

CO2=bCO2

þ S2H2O=bH2O ð7Þ

The contribution from soot radiation at eachnarrow band can be added to the gas phase radi-ation. The spectral radiative transfer equation inspherical coordinates at each band in m directionis given as

lmoImm

orþ 2lmImm

rþ 1

ro

olm½ð1� l2

mÞImm�

¼ �kmImm � kmIbm ð8Þ

where lm = cos (hm), and m is the index from 1 toM of polar angle h, and Ib the blackbody radia-tion intensity.

By using the following angular derivative,

oolm½ð1� l2

mÞImm� ¼amþ1=2Imþ1=2�am�1=2Im�1=2

xm

amþ1=2 � am�1=2 ¼ �2xmlm; a1=2 ¼ aMþ1=2 ¼ 0

ð9Þand the central difference scheme for spatial andangular discretizations,

2ICiþ1=2;m ¼ I i;m þ I iþ1;m

¼ ICiþ1=2;mþ1=2 þ IC

iþ1=2;m�1=2 ð10Þ

the final discretized radiation transfer equationfor lm < 0 becomes

2696 Z. Chen et al. / Proceedings of the Combustion Institute 31 (2007) 2693–2700

2jlmjICm;iþ1=2;m � Im;iþ1;m

riþ1 � ri

þðamþ1=2 þ am�1=2ÞðIC

m;iþ1=2;mþ1=2 � ICm;iþ1=2;mÞ

riþ1=2xm

¼ kmð�Im;iþ1=2;m þ Ibm;iþ1=2Þð11Þ

The boundary conditions at r = 0 and r = r2 aregiven as

Im ¼ IMþ1�m at r ¼ 0; Im

¼ ewIbwðT wÞ þ ð1� ewÞXlm>0

Imwmlm=p at r ¼ R

ð12Þ

The total volumetric heat source term of radi-ation is given as

_qr ¼XN -band

j¼1

DmXN

n¼1

xnkn

XM

m¼1

Ij;n;m � 4pIbj

!ð13Þ

Fig. 1. Comparison of the predicted radiation flux at theoutside hollow sphere boundary with theory for a grayemitting media with unity radiation power. Bothboundaries are black.

For spherical flame simulation, due to thepressure change and the pressure inducedcompression wave, we employed the unsteadycompressible Navier–Stokes equations formulti-species reactive flow. The central differencescheme and the Euler scheme were employed forthe diffusion and time integrations, respectively.The convective flux is calculated by the HLLCRiemann solver [39]. To numerically resolvethe moving flame front, an adaptive mesh refine-ment algorithm was developed. The mesh addi-tion and removal are based on the first andsecond order gradients of the temperature andmajor species distributions. Adaptive mesh ofeight-level was used and the moving reactionzone was always fully covered by finest meshesof 30 lm in width. This adaptive algorithm ismuch more efficient than that used in theCHEMKIN package [40]. For methane oxida-tion, the GRI-MECH 3.0 mechanism [41] wasused and the detailed transport and thermody-namic properties were predicted from theCHEMKIN database [40]. To initiate the com-putation, a hot spot with radius of 1.5 mmand temperature of 1800 K was set in the centerinitially to mimic the spark ignition in experi-ments. The same as experiments, the stretchedflame speed was first obtained from the flamefront (point of maximum heat release) historyand then was linearly extrapolated to zerostretch rate to obtain the unstretched flamespeed [25]. The present numerical code repre-sents the most advanced unsteady, radiative,1D flame modeling and it would be availablefor free download on our website.

4. Results and discussion

4.1. Validation of radiation model and radiation inspherical geometry

To validate the radiation model presentedfrom Eq. (5) to Eq. (13) in a spherical geometry,we first compare the net radiation flux at the out-side black boundary of a hollow sphere with innerand outer radii r1 and r2 (Fig. 1). The medium inthe hollow sphere has a unity emissive power andno externally incident intensity at boundaries. Fora given r2 � r1, the ratio of r1/r2 represents thecurvature of the hollow sphere. The normalizedradiation fluxes are plotted as a function ofr2 � r1 for two different r1/r2 ratios and comparedwith the analytical solution [42]. It is seen that forboth cases, the present numerical results agreeextremely well with the theory. In addition, theresults show that the increase of hollow spherecurvature at a given optical thickness has less radi-ation loss. This is obvious because the emittinggas volume becomes smaller at smaller r1/r2.

To validate the FSNB-CK model for spectralradiation, we calculated the volumetric radiationheat loss for water vapor (at 1000 K) in a hollowsphere. At r1/r2 = 1, the hollow sphere becomes aslab, so that the results can be compared withthose in [33] in which the radiation heat loss wascalculated from the SNB model using a ray trac-ing method. Figure 2 shows that the presentFSNB-CK model can well reproduce the resultsin [33]. However, unlike the method in [33], thepresent method only requires computation timeproportional to the grid number without loss ofaccuracy. Therefore, the present FSNB-CK modelis accurate and computationally efficient. The vol-umetric heat loss for a solid sphere (r1 = 0) is alsoshown in Fig. 2. It is seen that comparing to theslab radiation, the heat loss in the solid spherecase is much larger near the outside boundary.

Fig. 2. Comparison of predicted volumetric heat loss forspectral dependent H2O vapor radiation in a hollowsphere with a uniform temperature distribution andblack boundaries.

Fig. 3. (a) Schlieren photographs of CH4 � {0.3O2 +0.2He + 0.5CO2} flames at different equivalence ratios at1 atm; (b) measured and predicted laminar flame speedsof CH4 � {0.3O2 + 0.2He + 0.5CO2} flames as a func-tion of equivalence ratio at 1 atm.

Z. Chen et al. / Proceedings of the Combustion Institute 31 (2007) 2693–2700 2697

However, the radiation heat loss at the center ofthe sphere becomes smaller. Therefore, the radia-tion geometry has a great impact on the local radi-ation heat loss. This will become clearer in thefollowing flame speed comparisons.

4.2. Effect of radiation absorption on flame speed atelevated pressures

Figure 3a shows Schlieren photographs ofCH4 � {0.3O2 + 0.2He + 0.5CO2} flames at dif-ferent equivalence ratios at 1 atm. For fast-burn-ing mixtures (stoichiometric or nearstoichiometric mixtures, / = 0.8 in Fig. 3a), buoy-ancy effect is not observed from flame images andthe flame front is spherically symmetric. For leanmixtures, the effect of buoyancy is noticeable andthe flame front reaches the top edge of the photo-graph before reaching the bottom. Here, we definethe 1-g downward flammability limit, Ud, as in thelimiting mixture in which the flame can propagatethroughout the whole chamber.For the presentCH4 � {0.3O2 + 0.2He + 0.5CO2} mixture, thedownward flammability limit is Ud = 0.50. Belowthis limit, e.g. for leaner mixtures (/ = 0.49 inFig. 3a), the flame cannot propagate downwardagainst buoyancy forces. After reaching the topof the inner chamber, the flame spreads out andpropagates downward. Although the mixture atthis condition is still flammable, the flame frontlocation is hard to determine and flame speed dataare not extracted for these cases. At elevated pres-sures, buoyancy effect is enhanced with theincrease of mixture density. For example, at5 atm the downward flammability limit becomesUd = 0.57.

Figure 3b shows measured and predicted flamespeeds of CH4 � {0.3O2 + 0.2He + 0.5CO2} flamesat different equivalence ratios at 1 atm. For compar-isons, three radiation models were employed. Firstis the optically thin model (OPTM) in which no

radiation absorption is considered. The second isthe SNB gray band model in 1D planar geometry(SNB-GB1D) [21,33,42] in which gray gas modelis used at each band (375 bands in total) and radia-tion absorption is solved in the one-dimensionalslab rather than in spherical geometry. The thirdone is the present FSNB-CK model in which spec-tral radiation is solved in the spherical coordinate.Furthermore, the volumetric radiation heat lossesand temperature distributions predicted fromOPTM, SNB-GB1D and FSNB-CK for flames atequivalence ratio of 0.6 and flame radius of2.4 cm are plotted in Fig. 4.

Figure 3b shows that the optically thin modelunder predict the flame speed. This is becauseOPTM model over predicts the radiation heat lossand the flame temperature decreases significantlyin the burned zone (Fig. 4). However, for the

Fig. 4. Temperature and volumetric heat loss distribu-tions in spherical CH4 � {0.3O2 + 0.2He + 0.5CO2}flame at U = 0.6 and P = 1 atm.

Fig. 5. Measured and predicted laminar flame speeds ofCH4 � {0.3O2 + 0.2He + 0.5CO2} flames as a functionof equivalence ratio at 2 atm.

Fig. 6. Measured and predicted laminar flame speeds ofCH4 � {0.3O2 + 0.2He + 0.5CO2} flames as a functionof equivalence ratio at 5 atm.

2698 Z. Chen et al. / Proceedings of the Combustion Institute 31 (2007) 2693–2700

FSNB-CK model, it is seen that because of radia-tion absorption, the radiation heat loss in theburned zone becomes much smaller. There is a sig-nificant amount of radiation heat loss that is reab-sorbed by the unburned mixture (see the part withnegative heat loss in Fig. 4) from the burned zone.This means that the radiation absorption in CO2

diluted flames increases the flame speed by reduc-ing the net heat loss and that the optically thinmodel is not applicable. As the equivalence ratiodecreases, it is seen from Fig. 3b that radiationabsorption plays an increasing role in increasingthe flame speed and extending the flammabilitylimit. On the other hand, the SNB gray bandmodel in 1D geometry significantly over-predictsthe flame speed. This over-prediction comes fromtwo sources. One is that the employment of one-dimensional radiation geometry in which moreradiation emission in the burned gas than that inthe spherical flame was calculated (compare theradiation predicted by FSNB-CK(planar) andFSNB-CK(spherical) in Fig. 4); and the secondis that the gray narrow band assumption increasesthe radiation absorption (compare the radiationpredicted by FSNB-CK(planar) and SNB-GB1Din Fig. 4). The present FSNB-CK model greatlyimproved the flame speed prediction. A slightover-prediction may be resulted from the linearextrapolation method for flame speed because,strictly speaking, the radiation enhancement doesnot linearly increase with the flame radius. Thisimprovement is because the radiation in sphericalflame geometry is appropriately solved and thespectral radiation in each band is accurately treat-ed by using the cumulative function of k-distribu-tion from the direct Laplace transform instead ofa simple gray assumption [4].

Theoretical analysis in [18] shows that radia-tion absorption has less effect as pressure increasesbecause the total chemical heat release increaseswith the pressure. In order to examine the effectof pressure, the radiation absorption effect and

comparison of different radiation model forCH4 + {0.3O2 + 0.2He + 0.5CO2} mixtures at2 atm is shown in Fig. 5. It is seen that radiationabsorption becomes much stronger than that at1 atm. Different from the theory [18], the presentresult shows that radiation absorption increaseswith pressure. This is because an infinite opticalthickness was assumed in the theory so that allthe radiation heat loss from the burned zone willbe absorbed by the unburned mixture. In the pres-ent experiment, the optical thickness is finite(about 1.0–6.0 estimated from OPTM) so thatthe increase of pressure enlarges the optical thick-ness and radiation absorption. Again, for thesame reason, it is clearly seen that the presentFSNB-CK model predicts the flame speed muchbetter than SNB-GB1D. With a further increaseof pressure, Fig. 6 shows that the radiationabsorption effect further increases.

To further demonstrate the pressure effect onradiation absorption, the normalized flame speedincrease due to radiation absorption at differentequivalence ratio is plotted in Fig. 7. It is seen thatthe radiation absorption enhancement on flamespeed is linearly dependent on pressure. This line-ar dependence is caused by the increase of optical

Fig. 7. Effects of radiation absorption on flame speed atdifferent pressure and equivalence ratios.

Fig. 8. The predicted effective Boltzmann number versusflame size at 1 atm.

Z. Chen et al. / Proceedings of the Combustion Institute 31 (2007) 2693–2700 2699

thickness. In addition, Fig. 7 shows that with thedecrease of equivalence ratio, the effect of radia-tion absorption on flame speed becomes more sig-nificant. Therefore, it can be concluded thatalthough the pressure increase leads to anincreased chemical heat release, the effect of radi-ation absorption on flame speed enhancement stillincreases and becomes increasingly important forlean flames.

As discussed above, the radiation absorptiondepends on the optical thickness. Therefore, it willbe interesting to show how the radiation absorp-tion enhancement on flame speed depends onflame size so that a flamelet model can be usedto correct the radiation absorption effect in turbu-lence modeling. According to the theory [14], theflame speed is related with the Boltzmann num-ber, B, by

ðSL=S0LÞ lnðSL=S0

LÞ ¼ B;

B ¼ ErðT 4ad � T 4

0Þ=ð2Rq0S0LCpT 2

adÞð14Þ

where E, R, r, and Cp denote the activation ener-gy, universal gas constant, Stefan–Boltzmannconstant, and the specific heat, respectively. Tad

is the adiabatic flame temperature, and q0 andT0 are the unburned gas density and temperature.Therefore, B represents the radiation absorptioneffect on the increase of flame speeds. The effectiveB numbers estimated from theory [18] andcomputation [by using SL from simulation andthe first equation of Eq. (14)] as a function offlame size are plotted in Fig. 8. Note that incalculating the B number, the flame stretch effectis already excluded by comparing the radiativeflames with the adiabatic flames. It is seen thatthe radiation absorption effect predicted by thetheory is two-order magnitude higher than thatpredicted by the FSNB-CK model. In addition,the theory predicts a constant B number withthe increase of flame radius. This is also becauseof the assumption of large optical thickness. TheFSNB-CK model predicts a negative B numberat small flame radius and an increasing depen-dence of B on the flame radius. This means that

at small flame radius, although radiation absorp-tion can enhance the flame speed, the final flamespeed remains below the adiabatic flame speed.However, with the increase of flame radius, theoptical thickness increases, yielding an increasein B number. Again, for the optically thin model,the predicted B number is much lower. At highpressures, similar trends are also found exceptthat the B number becomes positive at 2 atm.Therefore, by computing the B number for a givenoptical thickness, the radiation absorption effectcan be employed in flamelet model for turbulentmodeling.

5. Conclusions

The spectral dependent radiation absorptioneffect on flame speed enhancement was measuredby using CO2 diluted CH4–O2 mixtures at normaland elevated pressures. A new accurate FSNB-CKmodel was developed and validated for radiationcomputation of spherical propagating flames.The following conclusions were drawn from thisstudy:

1. Radiation absorption increases the flame speedand extends the flammability limit. Thisenhancement effect also increases with pres-sure. The spectral dependent radiation absorp-tion needs to be included in any quantitativepredictions of flame speed and flammabilitylimit with CO2 addition.

2. The present radiation model can well reproducethe theoretical radiation flux at hollow sphereboundaries and the measured flame speed. TheSNB narrow-band gray model over-predictsthe flame speed while the optically thin modelsignificantly under-predicts the flame speed.

3. The radiation absorption effect increases withflame size and pressure. The theory based ongray gas model over-predicts the radiationabsorption by two-orders. The effective Boltz-mann number is extracted from the presentradiation modeling and can be applied to flam-elet modeling in turbulent flow.

2700 Z. Chen et al. / Proceedings of the Combustion Institute 31 (2007) 2693–2700

4. Flame geometry has a significant effect onflame radiation. In spherical flame modeling,the one-dimensional slab radiation modelover-predicts the radiation absorption.

Acknowledgments

This work was partially supported by NASAMicrogravity Research grant (NNC04GA59G)and DOE Project (DE-FG26-06NT42716).

References

[1] Y. Ju, T. Niioka, K. Maruta, Appl. Mech. Rev. 54(2001) 257.

[2] C.K. Law, F.N. Egolfopoulos, Proc. Combust. Inst.23 (1990) 413.

[3] M. Sibulkin, A. Frendi, Combust. Flame 82 (1990)334.

[4] K.N. Lakshmisha, P.J. Paul, H.S. Mukunda, Proc.Combust. Inst. 23 (1990) 433.

[5] A. Abbud-Madrid, P.D. Ronney, Proc. Combust.Inst. 23 (1990) 423.

[6] J.A. Platt, J.S. T’ien, in: Fall Technical Meeting,Eastern Section of the Combustion Institute, 1990.

[7] K. Maruta, M. Yoshida, Y. Ju, T. Niioka, Proc.Combust. Inst. 26 (1996) 1283.

[8] C.J. Sung, C.K. Law, Proc. Combust. Inst. 26 (1996)865.

[9] H. Guo, Y. Ju, K. Maruta, T. Niioka, F. Liu,Combust. Flame 109 (1997) 639.

[10] Y. Ju, H. Guo, K. Maruta, F. Liu, J. Fluid Mech.342 (1997) 315.

[11] J. Buckmaster, Combust. Theory Model. 1 (1997) 1.[12] Y. Ju, H. Guo, K. Maruta, T. Niioka, Combust.

Flame 113 (1998) 113.[13] Y. Ju, G. Masuya, F. Liu, H. Guo, K. Maruta, T.

Niioka, Proc. Combust. Inst. 27 (1998) 2151.[14] Y. Ju, C.K. Law, K. Maruta, T. Niioka, Proc.

Combust. Inst. 28 (2000) 1891.[15] D.B. Spalding, Proc. R. Soc. (Lond.) A240 (1957) 83.[16] J. Buckmaster, Combust. Flame 26 (1976) 151.[17] G. Joulin, P. Clavin, Acta Astronaut. 3 (1976) 223.[18] G. Joulin, B. Deshaies, Combust. Sci. Technol. 47

(1986) 299.[19] D. Lozinski, J. Buckmaster, P.D. Ronney, Combust.

Flame 97 (1994) 301.[20] Y. Ju, G. Masuya, P.D. Ronney, Proc. Combust.

Inst. 27 (1998) 2619.

[21] H. Guo, Y. Ju, K. Maruta, T. Niioka, F. Liu,Combust. Sci. Technol. 135 (1998) 49.

[22] M.S. Wu, P.D. Ronney, Y. Ju, in: 38th AerospaceSciences Meeting and Exhibit, AIAA 2000-0851,2000.

[23] J. Ruan, H. Kobayashi, T. Niioka, Y. Ju, Combust.Flame 124 (2001) 225.

[24] A. Abbud-Madrid, P.D. Ronney, AIAA J. 31(1993) 2179.

[25] X. Qin, Y. Ju, Proc. Combust. Inst. 30 (2005)233.

[26] L.S. Rothman, C.P. Rinsland, A. Goldman, S.T.Massie, D.P. Edwards, J.M. Flaud, A. Perrin, C.Camy-Peyret, V. Dana, J.V. Mandin, J. Schroeder,A. McCann, R.R. Gamache, R.B. Wattson, K.Yoshino, K.V. Chance, K.W. Jucks, L.R. Brown,V. Nemtchinov, P. Varanasi, J. Quant. Spect.Radiative Transfer 60 (1998) 665.

[27] N. Jacquinet-Husson et al., J. Quant. Spect. Radi-ative Transfer 62 (1999) 205.

[28] A. Soufiani, J. Taine, Intl. J. Heat Mass Transfer 40(1997) 987.

[29] W.L. Grosshandler, Radical, Int. J. Heat MassTransfer 23 (1980) 1147.

[30] M.K. Denison, B.W. Webb, J. Heat Transfer 117(1995) 359.

[31] M.F. Modest, H. Zhang, J. Heat Transfer 124(2002) 30.

[32] M.F. Modest, S.P. Bharadwaj, in: Proceedings ofthe ICHMT, 3rd International Symposium OnRadiative Transfer, Antalya, Turkey, 2001.

[33] T.K. Kim, J.A. Menart, H.S. Lee, J. Heat Transfer113 (1991) 946.

[34] H. Bedir, J.S. Tien, H.S. Lee, Combust. TheoryModel. 1 (1997) 395.

[35] A.A. Lacis, V.A. Oinas, J. Geophys. Res. 96 (1991)9027.

[36] F. Liu, G.J. Smallwood, O.L. Gulder, J. Quant.Spect. Radiative Transfer 68 (2001) 401.

[37] W.A. Fiveland, J. Heat Transfer 106 (1984)699.

[38] D.B. Ludwig, W. Malkmus, J.E. Reardon, J.A.L.Thomson, NASA SP3080, 1973.

[39] E.F. Toro, M. Spruce, W. Speares, Shock Waves 4(1994) 25.

[40] R.J. Kee, J.F. Grcar, M.D. Smooke, J.A. Miller,Sandia Report, SAND85-8240, Sandia NationalLaboratories, 1985.

[41] Available at http://www.me.berkeley.edu/gri_mech/.[42] H. Greenspan, C.N. Kelber, D. Okrent (Eds.),

Comput. Methods Reactor Phys., Gordon andBreach, New York, 1968.

Comment

Derek Bradley, Leeds University, UK Can your anal-ysis be applied to the conditions of very large flame radii,such as might occur in atmospheric explosions?

Reply. Yes. Since the optical thickness increases withflame radius, for the conditions of very large flame radii,

the radiation emission and re-absorption become evenmore important. Therefore, the spectrally dependentradiation absorption effect on flame speed enhancementmust be considered.