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Proceedings of the Combustion Institute 33 (2011) 1105–1112

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CombustionInstitute

Transition of flat flames to turbulent motion inducedby external laser irradiation

June Sung Park, Osamu Fujita *, Yuji Nakamura, Hiroyuki Ito

Hokkaido University, Kita13 Nishi8, Kita-ku, Sapporo, Hokkaido, Japan

Available online 8 August 2010

Abstract

Experiments with flames premixed C2H4/CO2-O2 (Le < 1) in a tube have been conducted. The mixturewas ignited at the top, open end of the tube, and a flame front propagated downward toward the closed endof tube. To investigate details of motion of flame tip fluctuations at the initial moment of irradiating theCO2 laser light, a completely flat flame front was considered a default flame, corresponding to the primaryacoustic instability as reported by Searby [1]. The laser exposure to the mixture induced local flame frontdeformation, resulting in a strong turbulent flame transforming eventually via the secondary acoustic insta-bility. To elucidate the effect of the flame curvature, the flame velocity and curvature prior to establishmentof the secondary acoustic instability were analyzed using a high speed camera. The results showed a suddenacceleration of the flame tip front during the advancing period. This was followed by a time lag between theflame velocity and curvature, indicating an increase in the flame velocity even with the decreasing flamecurvature. These behaviors can be explained by selective acceleration at the center of the flame by an acous-tic field and diffusive-thermal effects at a critical curvature beyond which flame extinction occurs.� 2010 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Keywords: Acoustic instability; External laser irradiation method; Flame curvature; Diffusive-thermal instability;Pressure gradient

1. Introduction

Acoustic instability of premixed flames propa-gating in a combustion tube has been investigatedextensively for more than a century. This researchhas particularly been motivated by an interest inthe growth mechanisms of acoustic instabilityand the acoustic feedback. The first suggestion,the criterion of acoustic instability, was developedby Rayleigh [2]. It was shown that if changes inheat release are in phase with the acoustic waves,the thermal energy will amplify the acoustic

1540-7489/$ - see front matter � 2010 The Combustion Institdoi:10.1016/j.proci.2010.06.101

* Corresponding author. Fax: +81 11 706 6385.E-mail address: ofujita@eng.hokudai.ac.jp (O. Fujita).

waves. To attain the Rayleigh criteria, it is consid-ered that the interaction between the combustionintensity and pressure wave is important. Therehave been two well-known aspects of attemptsto understand this interaction, the response ofthe chemical reactions to pressure waves and theperiodic fluctuation of the total flame areainduced by acoustic-related factors [3].

In 1992, Searby reported classic flame propa-gation in a tube [1]. Here definitions of differentand unique flame front behaviors were developed.Four distinct regimes were categorized into: (1) acurved shape with a large cell and no sound justafter ignition, (2) a primary acoustic instabilitywith a flat flame surface, (3) a violent secondaryacoustic instability, and (4) turbulent motion.

ute. Published by Elsevier Inc. All rights reserved.

Fig. 1. Schematic outline of the experimental setup.

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Following these observations, Searby and Roch-werger presented theoretical and experimentalverification of the primary thermo-acoustic insta-bility based on a stability diagram, predicting thebehaviors of downwardly propagating flames intubes [4].

It was shown that in the primary acousticinstability, featuring a flat flame surface withmoderate acoustic intensity, pressure fluctuationsgive rise to fluctuations in the burning intensityand modulate the local heat release rates, and thatthe energy input balances with a damping lossin the system. For 1-dimensional considerations,the experimental results are well explained bythe theories of the flat flame structure.

For the more active burning states of the sec-ondary acoustic instability which overcome thenatural damping losses to the tube, an oscillatingcellular structure of very short duration isobserved. Finally, the flame propagates with astrong turbulent motion. According to Searby[1], the periodic changes of the flame surface areain the secondary acoustic instability is in phasewith the acoustic waves.

It should, however, be noted that these peri-odic changes of surface area are caused by theoscillatory motion of cellular structures inherentlypresent in a given premixed gas condition (mix-ture strength and mixture ratio). In the Searbywork, therefore, the generation process of cellstructure is not controlled and the transitionprocess from the primary acoustic instability tothe secondary acoustic instability is not welldescribed, and further detailed investigation ofthe transition phenomena is essential for anunderstanding of the differences between theprimary and secondary instability as well as tounderstand the transition from laminar to turbu-lent flame under the effects of the acoustic field.

Tsuchimoto et al. have conducted experimentsto investigate oscillation phenomena in upwardpropagating flames [5]. They formed flame sur-faces with a convex structure towards theunburned mixture of freely propagating flamesusing a novel technique, a CO2 laser method[5,6]. It was found that the intentionally-deformedflame surface could modify the subsequent flamepropagation behavior, and it was possible toinduce unstable motion of the flame front. Theexternal laser irradiation preheats the unburnedmixture locally in front of the reaction zone, andthe flame propagation velocity increases locally,and here the flame front acquires a stronglycurved shape. Further, the authors found that itwas possible to initiate the transition from the pri-mary acoustic instability to the secondary acousticinstability of downward propagating flat flames ina tube by utilizing the CO2 laser method [7]. Theseresults showed that the method could be apromising technique to study the transition pro-cess in detail without unwanted flow disturbances.

In the present paper, observations of the tran-sient process of downward propagating tubeflames will be made by using the method andhighly detailed time-resolved imaging. Based onthe observations, an attempt will be made toexplain the background to the growth mechanismof the acoustic instability, related to the couplingof the chemical reaction intensity and/or the oscil-lation of the flame area with the acoustic pressurefluctuations.

Special focus will be placed on the effects offlame tip curvatures on the change of flame veloc-ity in the transient regime just prior to the onset ofthe secondary acoustic instability. The discussionpresents a detailed description of oscillation phe-nomena of curved flame fronts actively inducedby the CO2 laser method.

2. Experimental configuration

The experimental apparatus is schematicallyoutlined in Fig. 1. The propagation tube (transpar-ent acrylic tube, inner diameter 50 mm and length450 mm) is aligned vertically and is filled with thetested gas (Table 1) at atmospheric pressure. Ethyl-ene gas is the main absorption medium of CO2 laserlight according to the NIST chemical database [8].Carbon dioxide was selected as an inert gas toreduce the burning velocity. Since the Lewisnumber (Le ¼ a=DO2, a: thermal diffusivity of themixture, DO2: mass diffusivity of insufficient com-ponent) is less than unity, the flame front may beunstable with some disturbance on the flame sur-face. There is an automatic opening system pow-ered by an electro-magnet and a mechanicalspring at the upper end of the tube. When the sparkigniter is activated, the exhaust part is simulta-neously opened. The premixed gas inside thetube is continuously exposed to the laser beam(beam diameter 3.3 mm, SYNRAD Firester v20,

Table 1Composition of the tested gas.

C2H4 O2 CO2 Le U SL

9% 21% 70% 0.79 1.29 25.1

U: Equivalence ratio, Le: Lewis No., SL:1D laminarburning velocity (cm/s, CHEMKIN3.7, Premix code,GRI-Mech3.0).

J.S. Park et al. / Proceedings of the Combustion Institute 33 (2011) 1105–1112 1107

wavelength 10.6 lm) in the time 0.6 seconds afteractivating the igniter, then the CO2 laser beam pre-heats the unburned mixture just ahead of the flamesurface locally at the center. A mechanical shutter isset in the laser path to control the exposure timingof the laser beam. The time-dependent behaviors ofthe oscillating flame fronts are captured by a highspeed camera (2500 fps, exposure time 397 ls).The onset of the laser exposure is defined ast = 0.0 s. A microphone is placed at the bottomto observe the sound pressure fluctuation.

3. Results and discussion

3.1. Flame dynamics

Figure 2 shows downward propagating flatflames during the flame propagation inside thetransparent tube (applied laser power 0 W), simi-lar to those of primary acoustic instability flames[1]. Upon ignition, a curved flame front with avery low curvature propagates downwardly dueto hydrodynamic instability. And then, the flamefront quickly becomes flat, within 0.4 s, at theupper part of the tube. This flat flame is selectedas the default flame to investigate the transitionprocess to the secondary instability. In this condi-tion, the mean flame velocity is 14.9 cm/s.

In the experiments, the CO2 laser beam is irra-diated into the tube. Then, ethylene among themixture components absorbs laser energy just in

Fig. 2. Still images of the temporal evolution of flamefronts without laser power.

front of the flame surface at the center. Preheatedunburned mixture may increase the local flamevelocity. As the applied laser power increases,the acceleration of the local flame velocity is pro-nounced. In the case of low laser power (�4 W),the flame front is slightly deformed and attains alow flame curvature, and it continues to propagatewithout any other acceleration, although data forthis is not presented in the paper. This mode ofpropagation arises as the curvature here is insuffi-cient to induce any instability mechanism such asa diffusive-thermal effect [5,6].

Figure 3 depicts the temporal variation of theflame tip position with a laser power of 0–18 W.For laser power 0 W, the flat flame front propa-gates to the bottom of the tube with periodicoscillations. This flame behavior corresponds tothe primary acoustic instability as reported inRef. [1]. In the case of 18 W laser power, the slopeof the flame tip position after 75 ms increases (75–120 ms), that is, a periodic and sudden accelera-tion of the flame tip position appears. After this,there is a sudden decrease in the slope of the flametip position with increasing oscillation amplitude.This flame behavior is akin to the secondaryacoustic instability (120–148 ms). Finally, explo-sive turbulent motion appears with strong noise.Qualitatively the same characteristics are observedalong the propagation direction with the laserpower of 6 and 12 W.

This following part of this section describes thetransition phenomena (defined as “regime 1” asindicated in Fig. 4b) from a flat flame surface (pri-mary acoustic instability) to strong turbulentmotion through the secondary acoustic instabilitytriggered by active controls of the flame curvatures.

Figure 4a shows characteristic flame behaviors.In this study, only a mixture with Le < 1 was usedas shown in Table 1. Thus, when the flame fronthas a large positive curvature (convex) towardsfresh mixture, it is subject to non-equidiffusioneffects (diffusive-thermal instability), which result

Fig. 3. Flame tip position vs. time with various laserpower inputs.

Fig. 4. Still images of transient flame motion (a), and temporal variations in the flame position and velocity (b) with alaser power 18 W.

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J.S. Park et al. / Proceedings of the Combustion Institute 33 (2011) 1105–1112 1109

in increases in the combustion velocity at theflame tip by selective increases in the flame tiptemperature. As shown in Fig. 4a, the flame tipshows extremely unstable behaviors in the tran-sient regime (regime 1), showing unique structurelike “ice cream”. This flame tip condition is one ofthe main concerns in this study in the discussionof the transition from the primary to the second-ary acoustic instability. The gradual increase inthe area of the flame surface could make it suscep-tible to inducing acceleration of the burned gasflow. In regime 2, the flame front shows a suddendecrease in the mean flame velocity (see Fig. 4b).And, corrugated flame front structures areobserved with an increasing flame surface area.This flame (with corrugated flame front structure)corresponds to the secondary acoustic instability.Finally in regime 3, the flame front shows strongturbulent motion with a breakdown of its cellularstructures.

Acoustic influences on the flame propagationare inevitable in a tube, and acoustic waves couldaffect the flame front behaviors even without thelaser irradiation as suggested by Fig. 3. Therefore,the analysis is conducted within each cycle offlame front fluctuation to establish how the flametip movement is affected by the changes in theflame curvature at every cycle.

Figure 4b depicts the position of the flame tipand its velocity with a laser power of 18 W. Theflame front shows a flat surface until 80 ms, whichis fluctuating mainly due to the acoustic waves. Inall the experiments, the frequency of the flamevelocity change shows values very similar to thatof the acoustic waves. The measured oscillationfrequency (from Fast Fourier Transform, FFT)shows a peak value at 185.4 Hz. During the firstacceleration in regime 1, the flame velocity showsextremely unstable oscillation with the gradualincrease in oscillation amplitude. The flame tippropagates downward toward the bottom of thetube with both negative and positive velocities.It is natural that the positive velocity is higherthan the negative. But, it must be noted that theincrease in the flame velocity at advancing wavesexceeds the decrease at retreating waves consider-ably when compared with those of the flat flame(�80 ms) and with regime 2. This implies thatthere are effects to enhance flame propagation thatare unique to regime 1. One such possible effect isthe diffusive-thermal effect. In regime 1, the flamefront is everywhere convex and its front curvatureincreases cycle by cycle, while in the other regimes,the flat flame regime (primary instability) andregime 2, have flat fronts on average. This differ-ence may cause the differences in diffusive-thermaleffect leading to the unique selective accelerationof the flame tip and the increases in flame surfacearea cycle by cycle in regime 1. A previousstudy by Kadowaki [11] proposed that in anon-equidiffusion field, the increased flame tip

temperature induced by the curvature effect pro-motes the flame propagation due to the character-istic of the reaction rate. More detailed discussionof the curvature effects will be made in Figs. 5and 6 with the measurements of the flame tipcurvatures.

After the enhanced burning state of regime 1,the amplitude of the first cycle of the flame veloc-ity at the advancing wave in regime 2 is muchsmaller than that of the previous cycle in regime1. Here there is more active retreating thanadvancing waves accompanied by increasingamplitudes of velocity fluctuations and corruga-tion motion during the period of regime 2.

Finally in regime 3, a strong turbulent motionappears with the breakdown of the cellular struc-tures. The maximum flame velocity according tothe high speed camera image is approximately2500 cm/s, about 100 times the 1D laminar burn-ing velocity.

As discussed above, when the flame fronts havehighly curved shapes, the resulting flame behavioris sensitively subject to the diffusive-thermal effect,and the flame curvatures at the flame apex weremeasured. Figure 5 shows (a) the method of mea-suring the flame tip curvatures, (b) the time his-tory of the flame tip velocity and the measuredflame tip curvature, and (c) the flat flame position(indicated in Fig. 5a), the velocities of the flatflame and curved flame tip, and the normalizedluminous intensity (I/I0), all in regime 1 and witha laser power of 18 W. The temporal variationof the luminous intensity (I) was determined bythe total sum of the gray level of RGB in all thepixels, and it is normalized with the gray level ofthe flat flame (I0, 0 W). Figure 5b shows that thereis some phase shifting between the flame velocityand curvature, and the time delay becomes largeras the maximum curvature increases, cycle bycycle.

For a further understanding, quantitative com-parisons are given in Fig. 5c. The position of theflat flame surface may be thought of as an indica-tor of when pressure changes because it corre-sponds to the average flow motion of the gas inthe tube caused by the acoustic waves, while theflame tip velocity as well as the flat flame velocity(see Fig. 5c) has a consistent phase delay (�p/2) inrelation to the change in the flat surface position.Both the position of the flat surface and normal-ized luminous intensity nearly coincide duringregime 1. If it is assumed that the measured lumi-nosity corresponds to the heat release, the totalheat release of the system may be modulated withthe pressure fluctuations. Then, the obtainedexperimental results in regime 1 could show atransient process to the secondary acoustic insta-bility. To understand the advancing waves inmore detail, the dependence of the flame tip veloc-ity on the flame curvature is investigated in regime1 by using Eq. (1) defined as,

Fig. 5. (a) The definition of flame front curvature, (b) temporal variations of flame tip velocity and flame frontcurvature, and (c) the position of flat flame surface, normalized luminosity and the velocity of flat flame surface andcurved flame in regime 1 with a laser power of 18 W.

Fig. 6. Variation of Fn with varying flame tip curvaturein regime 1.

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F n ¼V f þ 2jV Cycle njjV Cycle nj

; ð1Þ

where V f is the flame velocity. V Cycle n the mini-mum velocity of the flame tip at each cycle, andthe subscript n is the cycle number as indicatedin Fig. 5b. This value, Fn, is the non-dimensionalflame tip velocity, and presents how the flametip velocity evolves from V Cycle n during each cyclen. Three cycles were selected for the analysis asindicated in Fig. 5b.

Figure. 6 shows the calculated results of Eq. (1)with varying flame tip curvatures. The dottedarrow presents the direction of the changes of thephenomena. In the figure, F n increases from 1 tothe maximum curvature. After the maximum cur-vature, the trajectory of F n shows a negative slope

J.S. Park et al. / Proceedings of the Combustion Institute 33 (2011) 1105–1112 1111

of flame evolution. It is apparent that the maximumflame tip curvature increases as the cycle numberincreases. Further, it is noted that every trajectoryplaces in the positive curvature range and it shiftstoward lager curvatures, cycle by cycle. This sug-gests that a cycle in regime 1 is always subject tothe diffusive-thermal effect independent of whetherit is advancing or retreating and that the effect mustbe enhanced as the cycle number increases. Thiscould cause the increased energy input leading tothe growth in acoustic instability. The absolute gra-dient of F n changes right after the maximum curva-ture becomes larger with the increasing cyclenumber, which is caused by increased acousticacceleration. Increased acoustic accelerationcauses faster growth of the flame tip curvature,which reaches the critical value (or critical stretchrate) in a short period. When the phase of the max-imum curvature advances more, the acceleration ofthe flame tip velocity becomes larger at the momentof the maximum curvature as can be understoodfrom Fig. 5b.

3.2. Physical model of the transition process

The following presents a plausible mechanismof the transition process (regime 1) accompaniedby the oscillatory propagation based on the dis-cussion so far. Figure 7 shows the conceptualdescription of the process in one cycle. The exter-nal laser irradiation preheats the unburned mix-ture ahead of the reaction zone, and then thelocal flame speed is increased in this area. Thisprojection of the flame tip is augmented by diffu-

Fig. 7. Hypothesis for the flame

sive-thermal effects due to increases in the flametip curvature, causing sudden accelerations andincreases in the burned gas temperatures behindthe flame tip. In other words, the density of theburned gas behind the flame tip becomes lower,as does its inertia. Then, this high temperatureburned gas is susceptible to being acceleratedselectively by the negative pressure gradient.When the flame tip curvature reaches a criticalvalue (critical stretch rate), it does not evolve fur-ther. This is seen as the incomplete reaction withincreasing flame stretch terminates the increasein the flame tip velocity [9,10]. Simultaneously,the other flame front, other than at the flame tip(see Fig. 7 at the maximum flame velocity) main-tains the propagation. This process may be thecause of the phase delay of the flame tip velocityversus the curvature change. For the retreatingwaves, the positive pressure gradient forces theflame surface to decelerate. But, the diffusive-ther-mal effect is still controlling the flame tip propaga-tion. Thus, the absolute value of the decrease inflame tip velocity is much smaller than that ofthe increase in flame tip velocity.

We proposed a hypothesis to explain the tran-sient regime (regime 1) through the diffusive-ther-mal effect and the acoustic waves. Although thisprocess is artificially initiated by the formationof an initial curvature with the laser irradiationmethod, the described process allows for the gen-erality of the evolution process from the flat flameto the secondary acoustic instability once a distur-bance, i.e. the initial curvature, for some reasonaffects the flat flame.

tip acceleration mechanism.

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4. Concluding remarks

This paper investigates the transition process(regime 1) of the downward propagating of ethyl-ene premixed flames in a tube from the primaryto the secondary acoustic instability, which hasnever been observed in detail in the previous litera-tures. The CO2 laser method employed here couldsuccessfully control the initiation of the transitionprocess by development of an artificial disturbance,which makes it possible to observe the phenomenaprecisely. In the regime 1, a unique structure (icecream shape) at the flame front is formed underthe presence of acoustic field (regime 1 in Fig. 4a).In this regime, a flame tip grows extremely fast asa result of stronger advancing waves than retreat-ing waves at each cycle. Since the flame front curva-tures in the regime always have positive value(Fig. 5), the flame tip should be subject to the diffu-sive-thermal effect, which can explain the fastgrowth of flame tip in regime 1. This growth cycleis modulated with acoustic cycle and it can resultin the enhanced acoustic amplitude to reach the sec-ondary acoustic instability regime.

Acknowledgements

This study was supported by Grants-in-Aid forScientific Research (KIBAN(B) #18360095 andKIBAN(B) #21360090) from MEXT Japan.

Appendix A. Supplementary data

Supplementary data associated with this articlecan be found, in the online version, at doi:10.1016/j.proci.2010.06.101.

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