a study on flame extinction characteristics along a c-curve

4236r 2009 American Chemical Society pubs.acs.org/EF

Energy Fuels 2009, 23, 4236–4244 : DOI:10.1021/ef900138uPublished on Web 07/20/2009

A Study on Flame Extinction Characteristics along a C-Curve

Dae Geun Park,† Jin Han Yun,‡ Jeong Park,*,† and Sang In Keel‡

†School ofMechanical Engineering, Pukyong National University, San 100, Yongdang-dong, Nam-gu, Busan 608-739, Korea, and‡Eco-Machinery Research Division, Korea Institute of Machinery & Materials, 171 Jang-dong, Yuseong-gu,

Daejeon 305-343, Korea

Received February 17, 2009. Revised Manuscript Received June 19, 2009

A study has been conducted both experimentally and numerically to clarify impacts of curtain flow andvelocity ratio on low strain rate flame extinction and to further display transition of shrinking flame disk toflame-hole. Critical mole fractions at flame extinction are provided in terms of velocity ratio, nitrogencurtain flow rate, and global strain rate. Flame extinctionmodes are grouped into four on aC-curve, whichis characterized by a flame-hole, the shrinking of edge flame, and edge flame oscillation. It is seen thatvarying curtain flow rate does not impact on edge flame oscillation, flame extinction, and even flameextinction modes. Variation of velocity ratio extends to the low strain rate flame extinction modes beyondthe turning point. It is found that the expanding and shrinking flames always have negative flamepropagation speed; it is also recognized that the decrease of flame radius is prone to extinguish due to thedominant role of radial conduction heat loss. The examination of energy fraction is also presented to stressthe role of radial conduction heat loss, particularly at the outer flame edge part.

Introduction

Edge flame intrinsically has dynamic properties, and itsdynamic flame response is well understood in the middlebranch of S-curve flame response.1 That is, the flame surfaceforms a hole at the place where scalar dissipation rate exceedssome critical value in a turbulent jet diffusion flame. The scalardissipation rate at the edge of the flame hole decreases as theflame hole evolves downstream. Then the edge flame, movedto the middle branch of S-curve, is finally forwarded to theupper-branch through a reignition process (advancedwave) orto the lower branch through extinction process (extinctionwave). These phenomena have been well described in thenumerical works of the previous study2 where unsteady stepvariations of imposed scalar dissipation rate near the extinc-tion limit produced flame extinctions or reignitions. Edgeflame has therefore been a hot issue, particularly at high strainrate flames, for two decades because of these ubiquitousphenomena, either with a positive flame propagation velocityor a negative one. The temporal evolution of their topologicalstructureswere numerically described for a flamedisk,which isa small burning element serving as an ignition source toreignite the extinguished area in turbulent flame, and flamehole at high strain rate flames.3 The existence of multiplesolutions of vigorously burning flames at identical conditionswas displayed when there is no inert gas flow curtain; a diskdiffusion flame and an edge flame at appropriately high strainflames.4 In recent years numerous numerical works have beendevoted to the study of such local extinction and reignitionevents in turbulent diffusion flames using flameletmodeling.2,5

A variety of research efforts have also been focused onclarifying the dynamic aspects of edge flame.6-13 Howevermost of these researches have been focused on the responses ofa flame hole at high strain rate flames.

Low strain rate flame extinction corresponds to a limitrelevant to heat losses,whereas high strain rate flame is causedby flame stretch. Microgravity experiments suggested thatflame extinction at low strain rate diffusion flame might beresponsible for radiative heat loss.14 This could be reasonablein one-dimensional flame system where the flame radius isrelatively large and thus the flame presumes to behave like aone-dimensional flame. However most experiments might beconducted with a finite burner diameter in opposed jet diffu-sion flame. A ring-shaped flame disk, in which the outerconcentration field consists of partially premixed mixtures,is established in an opposed-jet diffusion flame. Then an edgeflame, which is intrinsically dynamic, essentially forms at theboundary edge of the ring-shaped flame disk. Furthermore,an appreciable heat loss reduces critical Lewis number foredge flame oscillation at appropriately high strain rate flamesand at low strain rate flames.15-18Notably, radial conduction

*To whom correspondence should be addressed. E-mail: [email protected]. Telephone: þ82-51-629-6140. Fax: þ82-51-629-6150.(1) Buckmaster, J.; Jackson, T. L.Proc. Combust. Inst. 2000, 28, 1957.(2) Mauss, F.; Keller, D.; Peter, N.Proc. Combust. Inst. 1990, 23, 693.(3) Lu, Z.; Ghosal, S. J. Fluid Mech. 2004, 513, 287–307.(4) Lee, J. ; Frouzakis, C. E. ; Boulouchos, K. Proc. Combust. Inst.

2000, 28, 801.(5) Pitsch, H.; Cha, C. M.; Fedotov, S. Combust. Theory Modelling

2003, 7, 317.

(6) Im, H. G.; Chen, J. H. Combust. Flame 1999, 119, 436.(7) Lyons, K. M.; Watson, K. A.; Carter, C. D.; Donbar, J. M.

Combust. Flame 2005, 142, 308.(8) Lee, B. J.; Chung, S. H. Combust. Flame 1997, 109, 163.(9) Lee, J.; Won, S. H.; Jin, S. H.; Chung, S. H.Combust. Flame 2003,

135, 449.(10) Upatnieks, A.; Driscoll, J. F.; Rasmussen, C. C.; Ceccio, S. L.

Combust. Flame 2004, 138, 259.(11) Santoro, V. S.; Li~n�an, A.; Gomez, A. Proc. Combust. Inst. 2000,

28, 2039.(12) Shay, M. L.; Ronney, P. D. Combust. Flame 1998, 112, 171.(13) Carnell,W. F.Jr.; Renfro,M.W.Combust. Flame 2005, 141, 350.(14) Maruta, K.; Yoshida, M.; Guo, H.; Ju, Y.; Niioka, T. Combust.

Flame 1998, 112, 181.(15) Short, M.; Liu, Y. Combust. Theory Model. 2004, 8, 425.(16) Kurdyumov, V.N.;Matalon,M.Combust. Flame 2004, 139, 329.(17) Park, J. S.; Hwang, D. J.; Park, J.; Kim, J. S.; Kim, S.; Keel, S. I.;

Kim, T. K.; Noh, D. S. Comust. Flame 2006, 146, 612.(18) Oh, C. B.; Hamins, A.; Bundy, M.; Park, J. Combust. Theory

Model. 2008, 12, 283.

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Energy Fuels 2009, 23, 4236–4244 : DOI:10.1021/ef900138u Geun Park et al.

heat loss in addition to radiation heat loss may then play animportant role of edge flame oscillation and flame extinctionat low strain rate flames of the ring-shaped flame disk.17,18

Our research is motivated from the feature of two extinc-tions in the C-curve of Figure 1. That is, high strain rate flameextinction is caused by flame stretch, in that high strain flameextinguishes through a flame-hole. However low strain rateflame extinction is due to a limit defined by heat losses.1 Theprevious study also showed that low strain rate flame is causedby the shrinkage of the edge flame formed at the outer part ofthe flame disk.17,18 Is there any coexistent regime of flame holeand shrinking flamediskwhen the flame extinguishes at globalstrain rates around the turning point? What is the mainmechanism of flame extinction and edge flame oscillation atshrinking flame disks?What is the role of the buoyancy effectsin flame extinction and edge flameoscillationat low strain rateflames in normal gravity? Experiments and numerical simula-tions are conducted to clarify the above-mentioned questionsat varying velocity ratio, global strain rate, and nitrogencurtain flow rate.

Experimental Methods

Figure 2 shows the schematic of the system of experimentalsetup, flow control, and measurement. The counterflow burnerwith the inner nozzle diameters of 18.0 mm is installed in acompartment in order to prevent external disturbance. The waterjacket of the upper nozzle is used to cool down the burner surface.Exhaust gases are sucked through a couple of pipes by a vacuumpump.Nitrogen curtain flow, supplied by the outer duct nozzle ofthe lower burner, is employed to prevent external flame distur-bance and to remove the redundant outer flame held by a wakeflow. The volume flow rate of nitrogen curtain flow varies from 4to 12 L/min to change the local strain rate near the outer flameedge and clarify effects of curtain flow rate in flame extinction.Fuel is supplied from the upper duct nozzle to force the flame notto be positioned near the upper duct nozzle since the flame zoneforms in the oxidizer side. A series of fine-mesh steel screens arepositioned to impose plug-flow velocity profiles at the exits of theburner duct nozzles. The fuel used is a high grade ofmethanewitha purity of 99.95%, and that of nitrogen is also 99.95%. Themassflow rates of fuel, air, and diluents are regulated by the individualmass flow controllers. The separation distance between reactantduct nozzles is fixed to 15.0mm, in that the flame ismore prone toheat loss to burner rim due to buoyancy effects. This selectionmay highlight the important role of lateral heat loss in flameextinction at low strain rate flames. The velocity ratio betweenfuel flow and air flow is from 3 to 5.

The global strain rate in the present experiments is from 10 to110 s-1. Experiments are implemented by increasing addednitrogen flow rate, while maintaining a constant global strainrate. A software-based package is utilized to manipulate theseprocedures. The global strain is defined as follows:19

ag ¼ 2Va

L1þ Vf

ffiffiffiffiffiFfpVa

ffiffiffiffiffiFap !

¼ 2VrVf

L1þ

ffiffiffiffiffiFfpVr

ffiffiffiffiffiFap !

ð1Þ

Where Vr is defined as Vr = Vf/Va, which is the velocity ratiobetween the exit velocities of the upper and lower duct nozzles.The parameters V and F denote the velocity and density of thereactant stream at the duct boundary, respectively; L is the ductseparation distance; and the subscripts a and f represent the airand fuel streams, respectively.

The dynamic behavior of oscillating flame is captured by adigital media camera and analyzed by a matlab-based program.

Burnerwall temperature ismeasuredwith aK-type thermocouplein order to elucidate heat losses to the upper burner rim due tobuoyancy effects. Buoyancy effects in flame extinction are thenevaluated through the comparison between the experimental andnumerical results. Time-averaged wall temperature is taken withthe data acquired during 10 s using a data acquisition system(Graphtec, GL500).

Numerical Strategies

A time-dependent two-dimensional axisymmetric config-uration is employed in the present computation to treatcounterflow non-premixed flame. Because the fluid velocitytreated here is very low in comparison to the velocity ofacoustic wave propagation, a set ofmodel-free equationswitha low Mach number approximation is used.20 The governingequations to be solved may be written as follows:

DFDt

þr 3 ðFuÞ ¼ 0 ð2Þ

DðFuÞDt

þr 3 ðFuuÞ ¼ -rp1þr 3 u½ðruÞþðruÞT

-2

3ðr 3 uÞI�þðF-F0Þg ð3Þ

ðDFYiÞDt

þr 3 ðFuYiÞ ¼ r 3 ðFDimrYiÞþWiωi, ði

¼ 1, 2, :::,NÞ ð4Þ

Figure 1. Flame response on a C-curve and flame extinction modesthrough a transition.

Figure 2. Schematic drawing of burner and flow systems.

(19) Chellian,H.K.; Law,C.K.;Ueda,K.; Smooke,M.D.;Williams,F. A. Proc. Combust. Inst. 1990, 23, 503. (20) Oh, C. B.; Lee, C.; Park, J. Combust. Flame 2004, 138, 225.

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FcpDTDt

þu 3rT

� �¼ r 3 ðλrTÞþF

Xni¼1

ðcpiDimrYi 3rTÞ

-Xni¼1

Wihoi _wiþ _qr ð5Þ

p0 ¼ FR0TXNi¼1

Yi

Wi

� �ð6Þ

where p0 and p1 represent the thermodynamic and hydrody-namic pressures, respectively. In addition, u denotes thevelocity vector; T is the temperature; F is the density; Yi isthe mass fraction of species i; hi

o is the heat of formation ofspecies i; ω

·i is the production rate of species i; Dim is the

mixture-averaged diffusion coefficient; cpi is the specific heatof species i; R0 is the universal gas constant; and _qr is theradiative heat flux term.

AQUICK21 and a second-order central difference schemesare used to discretize the convection and the diffusion terms ofthe governing equations on staggered grid system. To obtain astable solution for the reacting flow field with stiff densityvariation, a predictor-corrector scheme22 is employed. Forthe time integration of the species and energy equations, asecond-order Adams-Bashforth scheme for the predictor stepand a second-order Quasi-Crank-Nicolson scheme for thecorrector step were used, respectively. A second-orderAdams-Bashforth scheme is used in both the predictor andcorrector steps for the time integration of momentum equa-tion. The efficient algebraic computation for the velocity-pressure correction was performed using a HSMAC meth-od,23 which is modified to consider the density variation. Forthe calculation of the thermodynamic and transport proper-ties, we adopted the CHEMKIN-II and TRANFIT pack-ages.24,25 A optically thinmodel14 was adopted to describe theradiative heat flux term in the energy equation. The details innumerical methods are found elsewhere.26 A three-step irre-versible reaction mechanism27 for methane oxidation wasused in the two-dimensional computation. The reaction me-chanism used in this study was

CH4þ1:5O2 f COþ2H2O

COþ0:5O2 f CO2

CO2 f COþ0:5O2

and the associated reaction rates were

-d½CH4�=dt ¼ 1011:68expð-23500=TÞ½CH4�0:7½O2�0:8

-d½CO�=dt ¼ 1012:35expð-19200=TÞ½CO�½H2O�0:5½O2�0:25

-d½CO2�=dt ¼ 1012:50expð-20500=TÞ½CO�½H2O�0:5½O2�0:25

with the reaction rates in units of kmol/m33 s.

A nonuniform 401 � 101 grid system is used for thecomputational domain of 40 � 70 mm, which yields theminimal grid spacing of 0.01 mm in the axial direction andthat of 0.2 mm in the radial direction in the region of interest.Because a global reaction mechanism was used in the compu-tations, the smallest length scale in these laminar flameswas inthe heat release rate region. Generally, at least 10 grid pointsare needed to resolve the heat release rate region. A gridsensitivity test was conducted for a number of limiting flameconditions inwhich three grid sizes (dx) were examined: 0.005,0.01, and 0.05mm. The results for dx=0.01mmwere within0.15 and 0.10% for the maximum temperature and extinctionlimits, respectively, of the results obtained using dx = 0.005mm for the simulation of normal gravity flames (ag= 25 s-1).Symmetry boundary conditions were applied for the veloci-ties, speciesmass fractions, and temperature on the centerline.The uniform inflow velocity profile was enforced on eachnozzle outlet, anda slipboundary conditionwas applied to theoutside boundary. The top and bottom sides were treatedas an outflow boundary, because the incoming flow escapedmainly from the upper boundary in normal gravity. No-slipandNeumann boundary conditionswere used for the velocityon the burner walls and its gradient, respectively. The inflowtemperatures for the fuel, air, and curtain streams were setto 298 K, and the wall temperature was also assumed to be298 K.

Results and Discussion

Figure 3 shows variations of critical nitrogen mole frac-tion at flame extinction with global strain rate for (a) variousvelocity ratios at the nitrogen curtain flow rate of 8 L/minand (b) various nitrogen curtain flow rates at the velocityratio of 5. In Figure 3 flame extinction behaviors aretypically those of a C-curve. That is, the high strain rateflame extinction is responsible for flame stretch, whereas lowstrain rate flame extinction is attributed by heat loss.1 Thecritical nitrogen mole fractions at flame extinction collapseinto one curve at high strain rate flames for all curtain flowrates and all velocity ratios. This implies that high strain rateflame extinction may pursue the one-dimensional flameresponse. Criticalmole fraction at flame extinction decreaseswith increase of velocity ratio at low strain rate flames inFigure 3a. This tendency is consistent with that of theprevious studies with the nozzle diameter of 26.0 mm, andthese extinction behaviors were shown to be mainly causedby radial conduction heat loss, rather than radiative heatloss.14,17,18 Meanwhile, varying curtain flow rate may havetwo contrary effects at low strain rate flames. The increase ofcurtain flow rate at low strain rate flames increases the localstrain rate, particularly at the outer flame edge. Indeed, theresponses such as flame extinction and edge flame oscillationcan be affected by the change of local strain rate since lowstrain rate flame extinction and its edge flame oscillationbegin at the outer flame edge.17,18 This implies that the lowstrain rate flame is effectively more sustainable to flameextinction on the C-curve since the flame strength at theouter flame edge increases. On the contrary, the increase ofcurtain flow rate at low strain rate flames may reduce thepopulation of reactive species near the flame edge.As a resultin Figure 3b, effects of curtain flow rate do not appear in thebehavior of critical mole fraction at flame extinction becausethe aforementioned effects maybe canceled out each other.However, the detailed explanation on effects of velocity ratio

(21) Leonard, B. P. Comput. Methods Appl. Mech. Eng. 1979, 19, 59.(22) Najm,H.N.;Wyckoff, P. S.; Knio, O.M. J. Comput. Phys. 1998,

143, 381.(23) Hirt, C. W.; Cook, J. L. J. Comput. Phys. 1972, 10, 324.(24) Kee, R. J.; Rupley, F. M.; Miller, J. A. SAND89-8009B, 1989.(25) Kee, R. J.; Dixon-Lewis, G.; Warnatz, J.; Coltrin, M. E.; Miller,

J. A. SAND86-8246, 1986.(26) Oh, C. B.; Lee, C. E.; Park, J. Combust. Flame 2004, 138, 225.(27) Dryer, F. L.; Glassman, I. Proc. Combust. Inst. 1972, 14, 987–

1003.

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and curtain flow rate can be given through numericalsimulation later.

Meanwhile, the previous study17 indicated that low strainrate flames always show a growing oscillation mode prior toflame extinction. But it should be noticed that for variousvelocity ratios the largest global strain rates for edge flameoscillation were less than the global strain rates of the turningpoints in the C-curves. This implicitly represents that thereexists a shrinking flame-diskwithout edge flame oscillation onthe C-curve. On the contrary, it may be conceptually believedthat a flame-hole is formed at the flame center if high strainrate counterflow diffusion flame extinguishes. However, ex-perimental evidence on this point may have been seldomclarified elsewhere. Further, it has not been provided else-wherewhether a flame-hole and a shrinking flame-disk appearsimultaneously. We took all the pictures according to globalstrain rate as varying velocity ratio and curtain flow rate.Figure 4 displays the representative photos of temporalevolution of flame extinction correspondent to the individualregime at the global strain rates of (a) 15, (b) 40, and (c) 55 s-1

for the velocity ratio of 4 and the curtain flow rate of 8 L/min.As shown in Figure 4a, the extinction at low strain rate flame

begins from the outer flame edge and is forwarded to the flamecenter while the flame oscillates. In Figure 4b there is a darkregion with the lowest flame intensity at a finite distance fromthe flame center, whereas the flame extinction still progressedfrom the outer flame edge to the flame center without flameoscillation. It is also seen that the flame extinguishes through aflame-hole on the flame surface without flame oscillation.Particularly, Figure 4b is relevant to the transition from ashrinking flame-disk to a flame-hole in flame extinction. Wecan classify the flame extinctionmodes based on the displayedfeatures. Table 1 illustrates the classification of flame extinc-tion modes considering whether edge flame oscillates andflame-hole forms. As shown in Table 1, varying curtain flowrate affects the classified regimes little. Regime I correspondsto the flame extinction through the shrinkage of the outer edgeflame with edge flame oscillation and without a flame-hole inshrinking flame-disks. Regime II is the flame extinction

Figure 3. Variations of critical nitrogen mole fraction at flameextinction with global strain rate for (a) various velocity ratios atthe nitrogen curtain flow rate of 8 L/min and (b) various nitrogencurtain flow rates at the velocity ratio of 5.

Figure 4. Representative photos of temporal evolution of flameextinction correspondent to the individual regime at the globalstrain rates of (a) 15, (b) 40, and (c) 55 s-1 for the velocity ratio of4 and the curtain flow rate of 8 L/min.

Table 1. The Classification of Flame Extinction Modes Considering

Whether Edge Flame Oscillates and Flame Hole Formsa

ag, s-1

4 L/min 8 L/min 12 L/min

Vr = 3regime I e20 e20 e20regime II 25 25 25regime III 30-40 30-40 30-40regime IV 45e 45e 45eturning point 40 40 40

Vr = 4regime I e20 e20 e20regime II 25-30 25-30 25-30regime III 35-50 35-50 35-50regime IV 55e 55e 55eturning point 40 40 40

Vr = 5regime I e25 e25 e25regime II 30 30 30regime III 35-70 35-70 35-70regime IV 75e 75e 75eturning point 35-40 35-40 35-40

aRegime I: Flame extinction through the shrinkage of the outer edgeflame with edge flame oscillation and without a flame-hole in shrinkingflame-disks. Regime II: Flame extinction through a flame hole and theshrinkage of the outer edge flamewith edge flameoscillation in shrinkingflame-disks. Regime III Flame extinction through a flame hole and theshrinkage of the outer edge flame without edge flame oscillation inshrinking flame-disk. Regime IV: Flame extinction through a flame holewithout the shrinkage and oscillation of edge flame in flame-disks.

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through a flame-hole and the shrinkage of the outer edgeflame with edge flame oscillation in shrinking flame-disks.Regime III is the flame extinction through a flame-hole andthe shrinkage of the outer edge flame without edge flameoscillation in shrinking flame-disk. Regime IV is the flameextinction through a flame-hole without the shrinkage andoscillation of edge flame in flame-disks. It should be notedthat regimes II and III appear during the transition from ashrinking flame-disk to a flame-hole. Meanwhile the turningpoints and the individual regimes are affected little by curtainflow rate as shown in Table 1. The global strain rates forregimes I and II are less than those of the turning points at allvelocity ratios and curtain flow rates. A flame-hole forms atlow strain rate flames prior to the turning point even if theflame-hole is not the main mechanism of flame extinction atthe low strain rate flame. It should be noted that the locationof flame-hole formation is not the flame center but a finitedistance from the flame center at high strain rate flamesbeyond the turning point in our experimental range (15-110 s-1). This implies that the flame extinction responses onthe C-curve can not be described by a one-dimensionalapproach, and a larger global strain rate out of the experi-mental range may be required for the formation of a flame

hole at the flame center. It is also found that regime III is notconfined prior to the turning point but extended to high strainrate flames beyond the turning point, particularly at thevelocity ratios of 4 and 5. Regime IV, in which the flameextinction is caused by flame-hole, migrates to a larger globalstrain rate as velocity ratio increases. As shall be shown laterthroughnumerical simulation in detail, this is attributed to theextension of the regime in low strain rate flame due to radialconduction heat loss.

Figure 5 illustrates (a) temporal variation of the flame-diskradius through edge flame oscillation and (b) that during theshrinking period of edge flame oscillation at the global strainrate of 15 s-1, the velocity ratio of 4, the critical nitrogenmolefraction of 0.639, and the curtain flow rate of 8 L/min. Theoscillating flame is shown to be accelerated while the flamereaches the extinction.Furthermore, the temporal variationofflame-disk radius for the last shrinking flame is quite differentfrom those for the shrinking flames during the other periods.This means that the last shrinking flame can not be sustainedanymore.

It is understood that the temporal behaviors of edge flameduring the shrinking periods are typically those of a retreat-ingwave in Figure 5 since both the flow velocity and the edgetraveling-velocity are negative. However a direct answer cannot be given to whether the expanding edge flames areadvancing waves or retreating waves. Figure 6 comparesthe traveling-velocities of expanding and shrinking edgeflames at the last stage prior to the extinction according tocurtain flow rate at the global strain rate of 15 s-1 and thevelocity ratio of 4. If the flame is positioned at the stagnationplane, the edge flame propagation velocity is expressed asVf = drf/dt - arf, where rf is the flame radius. Here, a is thelocal strain rate at the outer flame edge of flame-disk, thusthe last term becomes the gas flow velocity. However theactual edge flame propagation velocity is approximated toVf = drf/dt - Carf since the flame is established in theoxidizer-side. Here C is dependent upon the flame location,the flame radius, the global strain rate, the velocity ratio,and the curtain flow rate. However, C can be approximatedto unity since the radial flow velocity at the flame edge issimilar to that at on the same radial location on the stagna-tion plane. In our experimental ranges the orders of gas flow

Figure 6. Traveling-velocities of expanding and shrinking edgeflames at the last stage prior to the extinction according to curtainflow rate at the global strain rate of 15 s-1 and the velocity ratio of 4.

Figure 5. (a) Temporal variation of the flame-disk radius throughedge flame oscillation and (b) that during the shrinking period ofedge flame oscillation at the global strain rate of 15 s-1, the velocityratio of 4, the critical nitrogen mole fraction of 0.639, and thecurtain flow rate of 8 L/min.

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Figure 7. (a) Temporal variations of heat release rate contours at conditions ofVr=3,XN2=0.82,QN2

=4 L/min, ag=25 s-1, and L=15mm innormal-gravity. (b) Temporal variations of heat release rate contours at conditions of Vr=3, XN2

=0.82, QN2=12 L/min, ag=25 s-1, and

L=15 mm in normal-gravity. (c) Temporal variations of heat release rate contours at conditions of Vr=5, XN2=0.77, XN2

=4 L/min, ag=25 s-1, and L=15 mm in normal-gravity.

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velocity are of O (10 cm/s), whereas all the edge traveling-velocities in Figure 6 are of O (10 mm/s). It is seen that theedge flame propagation velocities are always negative, evenduring the expanding period at low strain rate oscillatingflames. Figure 6 also shows that during the shrinking periodthe traveling-speed of edge flame increases as flame radiusdecreases. This implies that edge traveling-speed increasesdue to the increase of radial heat conduction loss since theradial conduction heat loss is relevant to the inverse of flameradius,17 as shall be also shown through the numericalsimulation later. Figure 6 also demonstrates that the flameradius, which may be an indicator of flame stabilization, hasto increase in order to have a zero edge traveling-velocity (astationary flame). Meanwhile, it is found that in our experi-ment range the flame is stabilized for the flame radius morethan 7.5 mm, whereas the flame oscillates for that less than7.5 mm from the inspection of the flame radius in regimes Iand II from Table 1. This implies that there exists a criticalflame radius for edge flame oscillation. However, thiscritical radius of 7.5 mm may be limited in our experiment.In the foregoing statements we addressed that radial con-duction heat loss is relevant to the inverse of flame radiusand small flame radius accelerates edge traveling-velocity.Thenwe can explain the reasonwhy curtain flow rate did notimpact critical nitrogen mole fractions at low strain rateflames in Figure 3. At low strain rate flame the increase ofcurtain flow rate causes the increase of the local strain rate,in that it contributes to flame stabilization. However, asshown in Figure 6 the edge traveling-speed also increases ascutrtain flow rate increases. Furthermore the increase ofcurtain flow rate forces the reactive species to be reduced inthe flame zone. These play a role of flame destabilization. Itis therefore understood that the cancellation of these con-trary effects did not impact the response of critical nitrogenmole fraction to curtain flow rate.

We have addressed the main reason of edge flame oscilla-tion, flame extinction, and even the transition of the afore-mentioned regimes to heat loss effects at low strain rateflames. However, the detailed explanation has not yet beengiven. Now we will display the importance of radial conduc-tion heat loss in edge flame oscillation and also evaluatebuoyancy effects through numerical simulation. Figure 7shows temporal variations of heat release rate contours atconditionsof (a)Vr=3,XN2

=0.82,QN2=4L/min ; (b)Vr=

3, XN2= 0.82,QN2

= 12 L/min; and (c) Vr = 5, XN2= 0.77,

QN2= 4L/min for ag = 25 s-1 and L = 15 mm in normal-

gravity. In Figure 7 the heat release rate has the unit ofW/m3.The flame conditions were taken just at flame extinction. Thetime zero is taken at the flame condition where the flameradius is a minimum during the temporal evolution. All theflames oscillate just at flame extinctionas shown inFigure 7. Itshould be noted that the fuel Lewis numbers are 1.008 inpanels a and b in Figure 7 and 1.013 in panel c, respectively.This implies that those flames may not oscillate without thehelp of appreciable heat losses since the fuel Lewis numbers isnear unity.15-17 In Figure 7 the increase of curtain flow ratedoes not change the amplitude of edge flame oscillation,whereas the increase of velocity ratio produces the increaseof the amplitude of edge flame oscillation. These are consis-tent with the experimental evidence that the increase ofvelocity ratio lowered the critical nitrogen mole fractions atextinction in Figure 3a and that the increase of curtain flowrate does not change the critical nitrogen mole fractions atextinction in Figure 3b. The comparison of the individual

fractional contribution to chemical energy term in the energyequation may be required in order to verify which heat lossterms contribute to the edge flame oscillation importantly inthose flame disks in Figure 7. The energy equation can beexpressed as follows:

whereCx andCr are the axial and radial convection terms,Dx

and Dr are the axial and radial diffusion terms, Mx and Mr

are the axial and radial interdiffusion terms, Ra is theradiation heat loss terms, andCS is the chemical source term,respectively.

Figure 8 shows temporal variations of energy fractions at(a) flame center and (b) near flame edge at the flame conditionofVr=3, ag=25 s-1,XN2

=0.82, andQN2=4L/min. Figures 9

and 10 are the same plot at the flame condition ofVr=5, ag=25 s-1, XN2

=0.82, and QN2=12 L/min and at

Figure 8.Temporal variations of energy fractions at (a) flame centerand (b) near flame edge at the flame condition ofVr=3, ag=25 s-1,XN2

=0.82, and QN2=4 L/min.

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the flame conditionofVr=5,ag=25 s-1,XN2=0.77, andQN2

=4 L/min, respectively. These energy fractions are comparedalong the surface of maximum heat release rate in thesefigures. The flame edge location was taken where radialconduction heat loss is a maximum. The transient terms inall cases are negligible, even in the unsteady state.At the centerpoints in Figures 8a, 9a, and 10a, axial conduction heat lossterm is dominant, whereas the radiation heat loss shows aminor contribution and the others are negligible. The con-tribution of radiation heat loss may be a little larger if theflame condition is selected at lower global strain rate. That is,flame response is determined mainly by the balance betweenchemical energy and axial conduction heat loss at the flamecenter.

The contribution of axial and radial conduction heat lossesprevails at the flame edges in Figures 8b, 9b, and 10b. In allcases axial convection heat losses are negligible, and thismeans that buoyancy effects do not contribute to edge flameoscillation and flame extinction so much. It is therefore seenthat at the outer flame edges radial and axial conduction heatlosses play important roles of flame extinction and edge flameoscillation at low strain rate flames. This is the reasonwhy theouter edge flames in flame-disks oscillate at the low strain-rate

flames as shown inTable 1. It is also seen that curtain flow rateis not effective in the energy fractions from the comparison ofFigures 8b and 9b. However, radial convection terms at theflame edges are positive differently from those at flamecenters. This is because radial convection heat is transferredoutwardly along the surface from the flame center and isaccumulated at the individual location. As a result, themaximum heat absorption should be in the case of a max-imum flame radius at the elapsed time of 0.2 s. The maximumandminimum flame radii are not somuch different in panels aand b in Figure 7, whereas those are quite different in panel c.Therefore, in Figures 8b and 9b the contributions of radialconvection term are nearly the same, whereas in Figure 10bthe contribution of the radial convection term shows a definitemaximum at the maximum flame radius (the elapsed time of0.2 s). Even if this affects the contributions of axial and radialdiffusion terms a little bit in Figure 10b, the global feature isnot changed compared to those in Figures 8b and 9b. That is,the contribution of axial and radial conduction heat lossesprevails at the outer flame edges. In general, maximum flametemperature as an indicator of flame strength, based on one-dimensional flame response, is determined by the balancebetween chemical energy and conduction heat loss normal to

Figure 9.Temporal variations of energy fractions at (a) flame centerand (b) near flame edge at the flame condition ofVr=3, ag=25 s-1,XN2

=0.82, and QN2=12 L/min.

Figure 10. Temporal variations of energy fractions at (a) flamecenter and (b) near flame edge at the flame condition of Vr=5, ag=25 s-1, XN2

=0.77, and QN2=4 L/min.

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the flame surface.Additive heat loss such as radial conductionheat loss and radiation heat loss therefore deteriorates theflame strength. Figures 8b, 9b, and 10b definitely show thatradial conduction heat loss is the main reason to deteriorateflame strengthat the flame edges, in that edge flameoscillationand flame extinction are caused by radial conduction heat lossas was shown in Table 1 and Figure 4. This is the direct reasonwhy low strain rate flames show the shrinkage of edge flamewith and without edge flame oscillation.

Concluding Remarks

Experimental and numerical studies on the characteristicsof flame extinction have been conducted at low strain rateflames, and the following conclusion is obtained.

Flame extinction modes on a C-curve can be classified intofour for the present burner diameter: flame extinction throughthe shrinkage of the outer edge flame with edge flame oscilla-tion andwithout a flame-hole in shrinking flame-disks (regimeI), flame extinction through a flame-hole and the shrinkage ofthe outer edge flame with edge flame oscillation in shrinkingflame-disks (regime II), flame extinction through a flame holeand the shrinkage of the outer edge flame without edge flameoscillation in shrinking flame-disk (regime III), and flameextinction through a flame hole without the shrinkage andoscillation of edge flame in flame-disks (regime IV). Particu-larly, the global strain rates for regimes I and II are less thanthose of turning point at all velocity ratios and curtain flowrates. The global strain rates for regimes III and IV are extendto those beyond the turning point as velocity ratio increases.This is because the increase in velocity ratio increases radialconduction heat loss at the outer flame edge part, as isconfirmed in numerical simulation. In our experimental rangeup to the global strain rate of 110 s-1, the location of theformation of a flame-hole is not the flame center but a finitedistance from the flame center. Much larger global strain ratemay be required for the formation of a flame-hole at the flamecenter. The increase of curtain flow rate at low strain rateflames increases the local strain rate, particularly at the outerflame edge, in that the flame becomes more sustainable toflame extinction. On the contrary, the increase of curtain flowrate at low strain rate flames may reduce the population of

reactive species near the flame edge. Variation of curtain flowrate does not impact on edge flame oscillation and flameextinction because of the cancellation of these effects as isconfirmed experimentally and numerically.

It is also seen that the edge flame propagation velocities arealways negative during shrinking and even expanding periodsat low strain rate oscillating-flames. During the shrinkingperiod the traveling-speed of edge flame increases as flameradius decreases, in that radial conductionheat loss increases indecrease of flame radius as is also confirmed numerically. Thisimplies that the decrease of flame radius is prone to extinguishdue to the dominant role of radial conduction heat loss.

The comparison among energy fractions according tovelocity ratio and curtain flow rate definitely stresses theimportant role of radial conduction heat loss. At the flamecenter, the axial conduction heat loss term is dominant,whereas the radiation heat loss shows a minor contributionand the others are negligible. The flame response is deter-mined by the balance among chemical energy, mainly axialconduction heat loss, and partly radiation heat loss. At theouter flame edge axial and radial conduction heat lossesprevail, whereas the radial convection heat transfer plays arole of heat absorption and the others are negligible. No-tably, buoyancy effects may not impact on edge flameoscillation so much since axial convection heat loss isnegligible in all cases and the change of axial flame locationthrough varying velocity ratio do not modify the tendenciesof energy fraction. The balance between chemical energyand conduction heat loss normal to the flame surface isbroken at the outer flame edge. The additive radial conduc-tion heat loss therefore deteriorates the flame strength.Consequently, radial conduction heat loss is the mainreason to deteriorate flame strength at the flame edges, inthat edge flame oscillation and flame extinction are causedby radial conduction heat loss.

Acknowledgment. This work was by Pukyong National Uni-versity Research Fund in 2009 (0012000200811400).

Note Added after ASAP Publication. Figure 3 was in-correct in the version of this paper published ASAP July20, 2009; the correct version published ASAP July 27, 2009.

a study on flame extinction characteristics along a c-curve

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