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Cellular and sporadic flame regimes of low-Lewis-number stretched premixed flames
Available online at www.sciencedirect.com
Proceedings of the
Proceedings of the Combustion Institute 34 (2013) 981–988
Combustion Institute www.elsevier.com/locate/proci
Cellular and sporadic flame regimes of low-Lewis-number stretched premixed flames Roman Fursenko a,d,⇑, Sergey Minaev a,d, Hisashi Nakamura b, Takuya Tezuka b, Susumu Hasegawa b, Koichi Takase b, Xing Li b, Masato Katsuta c, Masao Kikuchi c, Kaoru Maruta b a
Khristianovich Institute of Theoretical and Applied Mechanics, SB RAS, Novosibirsk, Russia Institute of Fluid Science, Tohoku University, 2-1-1 Katahira, Aoba, Sendai 980-8577, Japan c Tsukuba Space Center, Japan Aerospace Exploration Agency, Sengen, Tsukuba, Ibaraki 305-8505, Japan d Far Eastern Federal University, Vladivostok, Russia b
Available online 14 September 2012
Abstract 3D structure and dynamical behavior of low-Lewis-number stretched premixed flames are numerically simulated within the framework of a thermo-diffusive model with one-step chemical reaction. The results are compared with microgravity experiments at qualitative level. The influence of Lewis number, equivalence ratio, and heat loss intensity on flame structure is investigated. It is experimentally and numerically found that lean counterflow flames can appear as a set of separate ball-like flames in a state of chaotic motion. It is shown that the time averaged flame balls coordinate may be considered as important characteristic similar to coordinate of continuous flame front. Numerical simulations reveal essential incompleteness of combustion at high level of heat losses. This incompleteness occurs in the process of lean mixtures combustion and is caused by fuel leakage through the gaps among ball-like flames. Ó 2012 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Counterflow flames; Premixed cellular flames; Heat losses; Flame balls; Thermal-diffusion instability
1. Introduction Increasing interest for clean and effective combustion technologies encourages investigations of lean premixed flames due to less pollutant emission and higher efficiency. Difficulties arising in the fundamental investigations of near-limit lean ⇑ Corresponding author. Address: Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch of Russian, Academy of Sciences, Institutskaya st. 4/1, Novosibirsk 630090, Russia. Fax: +7 (383) 3307268. E-mail address: [email protected] (R. Fursenko).
premixed flames are attributed not only to complex interaction of transport, chemical processes and radiative heat losses, but also to complex spatial structure of combustion wave subject to thermal-diffusive instability. The fuel-lean, near-limit laminar flames are sensitive to radiative heat losses which intensify thermo-diffusion instability resulting in the formation of non-planar cellular structures. Numerical simulations of the flame dynamics in straight [1,2] and divergent [3] channels showed that under the influence of radiative heat losses the low-Lewis-number flames break up to separate flame cells while being in a state of chaotic self-motion and splitting. In such
1540-7489/$ - see front matter Ó 2012 The Combustion Institute. Published by Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.proci.2012.08.014
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systems, the combustion wave consists of separate cap-like fragments which sometimes close upon themselves to form seemingly spherical structures, that are allied to “flame balls” found in microgravity experiments [4,5]. It is necessary to notice that at normal gravity the combustion wave lifting up in narrow tube sometimes can take “flame ball” shape [6]. Such combustion wave may be termed a “sporadic combustion wave” to distinguish its special structure that is different from conventional continuous flame structure. One of the unusual features of sporadic combustion wave is incomplete burning of fuel that remains in the combustion products [3]. The numerical simulations of non-stationary structure of sporadic combustion wave meet with formidable difficulties due to their chemical complexity [7,8] and wide range of spatiotemporal scales involved. Therefore reduced 3D reaction-diffusion model is reasonable in this case since it allows qualitative description of collective dynamics of flame balls constituting sporadic combustion wave. Due to the overwhelming influence of buoyancy [9], experimental investigations of the counterflow lean lowLewis-number flames under micro gravity conditions seem to be very promising [10]. For instance, absolute flammability limits and the peculiarities of thermo-diffusive instabilities can be examined in details [11–13] in this flame geometry. The present study is an attempt to make a qualitative comparison between the results of micro gravity experiments and numerical simulations of counterflow low-Lewis-number premixed flames at low stretch rates in order to distinguish general parameters determining dynamics of sporadic combustion wave. 2. Experiment Twenty seconds microgravity condition during the parabolic flight by Diamond Air Service Company, Nagoya, Japan [14] was utilized in this study. Airplane, MU300 which manufactured by Mitsubishi was employed for flight experiments. Experimental system is illustrated in Fig. 1. One pair of 3 cm diameter counterflow burners
Fig. 1. Schematic of experimental system.
was set in a combustion chamber, the distance between the burners 2L was 3 cm. The counterflow burners were made of brazen circular pipe with a porous plate inside. Nearly flat flow velocity profile can be obtained by this arrangement at low velocity conditions. Automatic experimental system which consists of PC, digital mass-flow-controllers, AD/DA converters and trigger circuit were used in the experiments. In every experiment, the nominal stretch rate a = U/L where U is flow velocity at the burner exit was maintained at a corresponding constant value. The CH4/O2/Xe mixture with X O2 =X Xe ¼ 0:141, where X O2 and X Xe are mole fractions of O2 and Xe correspondingly, was used in experiments. During the experiment, the mixture content was changed linearly with time and the quasi-steady trend of flame depending on the varying equivalence ratio was examined. Several seconds before the start of microgravity, flow velocity at the burner exit and mixture composition for each experiment were established. The mixture was then ignited by pilot flame. The pilot flame was removed immediately after ignition and the fuel concentration was gradually decreased in 20-s microgravity duration. Two video cameras were fixed in horizontal and vertical directions to record flame behavior. Accuracy of airplane microgravity experiment was verified by comparison of present data with previous one obtained during JAMIC (Drop tower) experiments [11]. The airplane’s and Drop tower’s experimental data were in good agreement with each other and the test points scattering in these experiments was less than 1%. Figure 2 shows experimental photos of counterflow flames. Two counterflow burners issuing fresh mixture are located on the right and the left sides of the frames. Experimental observations at the nominal stretch rate a = 1.038 (1/s) showed that for respectively high equivalence ratios 0:46 < /, the continuous cellular flames existed (Fig. 2a). Geometrically cellular flame is a surface with smooth maxima extending into the fresh mixture region. Such structures are typical for the flames subjected to the thermo-diffusion instability [1]. With the reduction of /, the cellular flames broke into the separate cells which were in a state of chaotic motion (Fig. 2b and c). Further decrease of equivalence ratio led to the decrease of each cell size (Fig. 2b and c) and finally to the flame extinction. For the flames represented by the set of moving cells, the measurement of the distance between the flames based on separately taken experimental frame would be incorrect. The following technique was applied for experimental measurements of average distance between the flames. A consecutive series of video frames within some interval Dt were selected. The interval Dt was chosen so that within this interval the variation of equivalence ratio did not exceed 3% of the average
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Fig. 2. Experimental photos of counterflow flames for a = 1.038 and / ¼ 0:47 (a), / ¼ 0:4 (b), / ¼ 0:38 (c) and stack superposition of 90 consequtive frames with time interval 0.016 s obtained for a = 1.03, / ¼ 0:4 0:02 (d).
equivalence ratio for the given interval. Further the series of the frames was stacked by ImageStacker software in order to obtain the superposition of the frames. The resulting averaged image is shown in Fig. 2d and the flame representation looks as two bright strips. As it is seen from Fig. 2d, the external borders of the strips are sharp and fringeless. These borders are marked by black dashed lines in Fig. 2d. The distance between the flames was determined as the distance between the external borders of the strips. Dependences of the distance between the sporadic combustion waves on equivalence ratio are shown in Fig. 3a. The experiments showed that the distance between the flames decreases with decrease of equivalence ratio. For further comparison of the experimental results with results of numerical simulations the dependency of non-dimensional flame speed on dimensionless fuel concentration 1/r 1 is plotted in Fig. 3b. To estimate the average cells size the dimensional and non-dimensional spatial scales are depicted in Fig. 2. The definitions of non-dimensional variables are introduced in the next section. 3. Numerical simulations The 3D configuration considered in the present study is back-to-back counterflow premixed flames. In this configuration the air–fuel mixtures are issued from two opposed burners placed in
positions y = ±Ly forming two flames near the stagnation plane y = 0. It is assumed that the stagnation plane y = 0 is a plane of symmetry. The following conventional framework of the model is employed: one-step irreversible exothermic reaction with Arrhenius kinetics, reactant composition far from stoichiometric, and radiative heat loss. With these assumptions, the appropriately nondimensionalized set of equations for temperature and deficient reactant concentration reads ~rT ¼ r2 T hðT 4 r4 Þ þ ð1 rÞW ðT ; CÞ Tt þ V ð1Þ C t þ V~rC ¼ Le1 r2 C W ðT ; CÞ
ð2Þ
Here T is the scaled temperature in units of Tb, the adiabatic temperature of combustion products; C is the scaled concentration of the deficient reactant in units of C0 of the value in the fresh mixture; x, y, z is non-dimensional spatial coordinates in units lth = Dth/Ub, the thermal width of flame, where Dth is the thermal diffusivity of the mixture and Ub is the velocity of a planar adiabatic flame in the high activation energy limit; t is the scaled time in units Dth =U 2b ; r = T0/Tb where T0 is the fresh mixture temperature; Le = Dth/Dmol is the Lewis number, where Dmol is the deficient reactant molecular diffusivity. Dimensionless flow velocity ~ ¼ ðax=2; vector in units Ub is given by formula V ay; az=2Þ where a is the non-dimensional stretch rate. Normalized chemical reaction rate
Fig. 3. Experimental dependences of the distance between the flames d on equivalence ratio / (a) and experimental dependency of nondimensional flame speed on dimensionless fuel concentration 1=r 1 (b).
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has the following form W(T, C) = (1 r)2 N2C exp(N(1 1/T))/2Le where N = Ta/Tb is the scaled activation energy, Ta being the activation temperature. At large N non-dimensional velocity of a well-settled planar adiabatic flame is close to unity in these variables. Unit value of non-dimensional flame speed corresponds to the dimensional velocity Ub = B exp(Ta/2Tb) of a planar adiabatic flame in the high activation energy limit. The activation temperature Ta and pre-exponential factor B in above formula were chosen to fit the dependence of Ub on equivalence ratio calculated by detailed reaction mechanism GRI-Mech 3.0. The term h(T4 r4) in Eq. (1) represents radiative heat losses where h is scaled Stefan– Boltzmann constant in units of qb cp lP U b =4T 3b lth ; lP is the Planck mean absorption length; cp, specific heat; qb, burned gas density. Since the results of the work [13] demonstrate that at medium to low values of the stretch rate, the radiative heat loss has a particularly strong impact on the counterflow premixed fuel-lean, methane–air flames. Therefore the radiative heat loss is assumed as the primary form of loss in the present numerical investigations. At the same time, the chemical kinetics of methane–air or hydrocarbon–air combustion consists of two major steps, one to form CO from the fuel and the other to convert CO to CO2. The relatively slow second reaction step may affect the near-limit behavior of hydrocarbon flames. Further numerical investigations with more complex chemistry seem to be necessary for more detailed examination of the flame structure. Equations (1) and (2) are considered in the rectangular domain Lx 6 x 6 Lx, 0 6 y 6 Ly, Lz 6 z 6 Lz and subject to the following boundary conditions Inletðy ¼ Ly Þ : T ¼ r; C ¼ 1
ð3Þ
Symmetryðy ¼ 0Þ : @T =@y ¼ 0; @C=@y ¼ 0
ð4Þ
x ¼ Lx ; z ¼ Lz : T ¼ r; C ¼ 0:
ð5Þ
Notice that asymmetrical flame configurations which may appear in experiments with two counterflow burners cannot be reproduced due to restrictions imposed by symmetric boundary conditions (4). The set of governing equations (1) and (2) was solved numerically by explicit finite-difference scheme. At initial moment, the computational domain is filled by fresh mixture with temperature r. In the numerical simulations, the flame was ignited by specifying the high temperature zone near the stagnation plane. Five sets of the orthogonal grids of 256 192 256, 320 240 320, 384 288 384, 400 304 400 and 416 320 416 were employed. Convergence tests showed that the results of calculations for the three
last-named finer grids are qualitatively the same and quantity difference in flame speed Vf = ayf of adiabatic flame (h = 0) is less than 0.2%. Figure 4 shows the dependency of flame speed on grid resolution for four tested grids. The solutions presented below correspond to the 384 288 384 grid and they were evaluated for Ly = 60, Lx = Lz = 40, r = 0.2, N = 10.5. Numerical tests of the planar stretched adiabatic flames (h = 0) show that for the computation domain 80 60 80 in units of lth = Dth/Ub, the used grid provides at least 5 points within the flame reaction zone. In this paper, we utilized the parallelism provided by Graphics Processing Unit (GPU) to speed up numerical computations. In the absence of radiative heat losses (h = 0) as well as for small heat-loss rates the flame assumes a pebbly cellular structure evolving in time and resembling structures obtained in papers [15,16]. Figure 5a depicts equiscalar surface C = 0.15 that is close to the flame surface and the concentration distribution in z = 0 plane was calculated for Le = 0.3, a = 0.067 and h = 0.0. In the near adiabatic case, the flame represents by continuous flame surface separating unburned gas and combustion products. The temperature T rapidly rises across the flame front from r to unity, while the concentration C drops from unity to zero. The mean flame front position characterized by average y coordinate of the flame surface is well-defined. As one would expect, at small heat-loss rates the flame consumes the deficient reactant completely (Fig. 5a). The flame propagation velocity Vf = ayf is equal to the absolute value of flow velocity at the flame front yf, and it is equal to 2.6 for Le = 0.3 and 1.3 for Le = 0.5. Thus the propagation velocity of the cellular flame appears to be significantly higher than the velocity of the associated planar flame (Vf = 0.94) due to increasing of the flame surface caused by thermal-diffusion instability. Notice that for the flames settled far from the stagnation
Fig. 4. Dependency of flame speed Vf calculated for Le = 0.3, a = 0.067, h = 0 on computational cells size.
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Fig. 5. Equiscalar surfaces C = 0.15 (top) and concentration distributions in z = 0 plane (bottom) calculated for Le = 0.3 and h = 0, a = 0.067 (a); h = 0.6, a = 0.033 (b); h = 0.8, a = 0.033 (c). Flow direction is shown by arrows. Vectors ~ x;~ z belong to stagnation plane.
plane, the increase of the stretch rate a leads to the decreasing of the distance between the flames, but the flame propagation velocity remains almost constant. This result coincides with theoretical predictions [17] obtained for the planar flame propagating in divergent channel. Under further increase of heat losses, the flame front structure gradually changed in the same manner as it was described in [15] for the lean low-Lewis-number flame propagating in the straight channel. At first, the cells size increases, after that the cellular flame does suffer local extinction at some of its cusps, accompanied by a noticeable escape of the unconsumed reactant through the emerging gaps. At a sufficiently large value of heat losses, the cellular flame disintegrates into a group of nearly identical cells resembling flame balls (see Fig. 5b and c). Their mutual arrangement however is not frozen but involves fluctuations, sporadic detachments of the leading flamelet from the others, followed by its disintegration and formation of the secondary flamelets nearly identical to the primary one. As a rule after the splitting, one of the ball-like flames is moved downstream with the flow and eventually disappears due to gradual depletion of the mixture. The typical evolution of ball-like flames is shown in Fig. 6, where the equiscalar surfaces of temperature are plotted in successive moments. In spite of this moving, splitting and extinguishing of ball-like flames, the equiscalar surfaces of fuel before combustion zone are represented by smooth surfaces (see Fig. 5). These surfaces being
Fig. 6. Temporal sequence of equiscalar surfaces T = 0.8 with Dt = 4.0 calculated for Le = 0.3, a = 0.033 h = 0.8.
time averaged over characteristics intervals of several ball-like flame disintegrations are almost flat. Thus, it makes possible to attribute averaged flame front position to an array of ball-like flames constituting sporadic combustion waves. It allows to determine average flame velocity in both numerical and experimental investigations. Dependences of the flame propagation velocity on heat losses intensity calculated for different stretch rates are shown in Fig. 7a. As it may be
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Fig. 7. Dependences of the flame propagation velocity Vf and concentration of unconsumed reactants Cres on heat loss intensity (a, c) and on dimensionless fuel concentration 1=r 1 (b, d).
seen from Fig. 7a the flame velocity decreases with rise of heat losses intensity h. This is consistent with previous investigations [1,3] on low-Lewisnumber flames with radiative heat losses propagating in the straight tube and in divergent channel. Taking formula for the flame speed Vf = ayf into account, the increase of the parameter h corresponding to Vf reduction leads to the shift of the average flame front position towards the stagnation plane at the fixed stretch rate a. Note that for chosen parameters and Le = 0.3 the planar flame extinction limit is h = 0.06 whereas the sporadic combustion wave extinguishes at h = 1.3. Thus sporadic combustion waves can exist in sub critical lean mixtures with fuel concentration less than extinction limits of flat flame. Taking into account dependence of the nondimensional heat losses intensity h on parameters characterizing mixture contents h (1 r)/ r exp(N(r)) the dependence of the flame front speed on dimensionless fuel concentration 1/ r 1 = Tb/T0 1 was calculated (Fig. 7b). Notice that flame velocity in Fig. 7b was calculated for distant flames located far from stagnation plane. The flame speed of distant flames remains almost constant with variation of stretch rate. As it may be concluded from Fig. 7b the
flame front velocity is increasing function of nondimensional parameter 1/r 1. Since the distance between the counterflow flames is proportional to Vf at fixed stretch rate, the distance between the flames rise with increase of equivalence ratio which is proportional to 1/r 1. This result coincides with experimental observations presented in previous section (see Fig. 3). Figure 8 depicts side view of seven overlapped slices of chemical reaction rate distribution. The experimental flame image presented in Fig. 2 has been obtained by CCD camera (Photron MC 2.1) with image intensifier. Luminescence from the methane flame in Fig. 2 was mainly caused by CH and C2 chemiluminescence which occurs in thin zone near the maximum heat release surface. The calculated maximal heat release surfaces are presented in Fig. 8. Since the increase of heat loss intensity have the same effect on flame structure as decreasing of the equivalence ratio, it may be concluded that numerical results qualitatively reproduce experimental data presented in Fig. 2. In particular it is seen that flame cells size decreases with rise of heat loss intensity whereas the gap between the cells increases. In order to compare characteristic size of the cells forming sporadic combustion wave the average cells size was determined on the basis of 2D flame representation presented in
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Fig. 8. Side view of seven overlapped slices with chemical reaction rate distribution calculated for Le = 0.3 and a = 0.067, h = 0 (a), a = 0.067, h = 0.3 (b), a = 0.033, h = 0.6 (c), a = 0.033 h = 0.8 (d). Flow direction is shown by arrows. Stagnation plane is marked by white dashed line.
Fig. 8. The characteristic size of ball-like flames observed in numerical simulations may be estimated as 1–2.5 cm that roughly corresponds to the experimental observations (see Fig. 2). Figure 7c and d shows dependencies of the concentration of unconsumed reactants on heat loss intensity and non-dimensional fuel concentration, correspondingly. At comparatively high radiative heat losses that are typical for lean mixtures, the incomplete fuel consumption is observed and the fuel leakage increases with heat-losses intensification (see Fig. 7a and b). The nondimensional heat losses h increases with decreasing of non-dimensional fuel concentration and therefore concentration of the unburned fuel in combustion products increases (Fig. 7b). This effect induces by broadening of the gap between the flame balls at high heat losses (see Fig. 5). As it may be seen from Fig. 3, the average ball-like flames radius decreases with increase of the heatlosses that coincides with theoretical predictions [5] obtained for the isolated flame ball in free space. Numerical simulations showed that the flame can be established in stagnation flow field in the wide range of problem parameters such as stretch rate, mixture contents and heat-loss intensity (see Fig. 7a and b). The flame speed and regions of existence of the flame strongly depend on Lewis number as seen in Fig. 7a and b. Decreasing of the Lewis number leads to increase of the quenching heat losses value (see Fig. 7a) due to effect of thermal-diffusion instability which becomes stronger with decreasing of Lewis number. Such flame front behavior was predicted theoretically for non-adiabatic cellular flame [18,19]. Notice that the minimal propagation velocity of the lean low-Lewis-number flame (for example Vfmin = 0.4 for Le = 0.5 (see Fig. 7b) is less than the critical velocity Vcr = e1/2 0.6 of the planar nonadiabatic flame. 4. Concluding remarks Numerical simulations and experimental observations of low-Lewis-number stretched pre-
mixed flames detect that combustion wave of lean low-Lewis-number premixtures can consist of separate combustion zones resembling flame balls. The experiments and the numerical simulations coincide in the conclusion that the decrease of equivalence ratio leads to the decrease of average distance between the flames. Also both experiments and simulations showed that decrease of equivalence ratio leads to decrease of separate flame cells’ size. Numerical simulations reveal essential incompleteness of combustion at high level of heat losses. This incompleteness occurs in the process of lean mixtures’ combustion and is caused by fuel leakage through the gaps among ball-like flames. The uncertainty in evaluation of total heat release related to incompleteness of combustion and complex spatial-temporary structure of reaction zone creates difficulties in analytical estimation of propagation velocity of sporadic combustion waves. As it was demonstrated in paper [20] the supposition about complete consumption of fuel would made problem tractable and allowed estimation of propagation velocity of combustion wave constituted of planar array of ball-like flames. It seems perspective to explore a similar model for the steadily propagating sporadic combustion wave that in contrast with classical planar laminar flame would be unbound on restriction about complete fuel consumption and admitted fuel leakage through array of ball-like flames. Recent numerical investigations of low-Lewis-number flames propagating in divergent channel [3] and the results of this paper demonstrate possibility to apply the concept on flame front of sporadic combustion wave even in case when the combustion wave consists of separate ball-like flames being in the state of chaotic motion. It seems interesting to verify theoretical prediction about incompleteness combustion related with sporadic structure of combustion wave of lean low-Lewisnumber premixed gases in future experiments. Interestingly, in spite of the fact of combustion incompleteness the propagation velocity of sporadic combustion wave may exceed propagation velocity of plane adiabatic flame of the same mixture content.
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Acknowledgments The authors are grateful to the Tohoku University and Siberian Branch of Russian Academy of Sciences (Integration project No. 38) for financial support.
References [1] L. Kagan, G. Sivashinsky, Combust. Flame 108 (1997) 220–226. [2] S. Minaev, L. Kagan, G. Joulin, G. Sivashinsky, Combust. Theor. Model. 5 (2001) 609–622. [3] R. Fursenko, S. Minaev, Combust. Theor. Model. doi:10.1080/13647830.2011.570378. [4] P.D. Ronney, Combust. Flame 82 (1990) 1–14. [5] P.D. Ronney, M.S. Wu, H.G. Pearlman, K.J. Weiland, AIAA J. 36 (1998) 1361–1368. [6] Y.L. Shoshin et al., Proc. Combust. Inst. 33 (2011) 1211–1216. [7] E. Ferna´ndez-Tarrazo et al., Proc. Combust. Inst. 33 (2011) 1203–1210.
[8] Z. Chen et al., Proc. Combust. Inst. 33 (2011) 1219– 1226. [9] P.D. Ronney, Space Forum 4 (1998) 49–98. [10] C.K. Law, D.L. Shu, G. Yu, Proc. Combust. Inst. 21 (1986) 1419–1426. [11] K. Maruta, M. Yoshida, Y. Ju, T.K. Niioka, Proc. Combust. Inst. 26 (1996) 1283–1289. [12] K. Maruta, Y. Ju, A. Honda, T. Niioka, Proc. Combust. Inst. 27 (1998) 2611–2617. [13] Y. Ju, H. Guo, K. Maruta, F. Liu, J. Fluid Mech. 342 (1997) 315–334. [14] Available at http://www.das.co.jp/new_html_e/service/01.html. [15] L. Kagan, S. Minaev, G. Sivashinsky, Math. Comput. Simulat. 65 (2004) 511–520. [16] B. Denet, P. Haldenwang, Combust. Sci. Technol. 86 (1992) 199–221. [17] S. Minaev, R. Fursenko, Y. Ju, C.K. Law, J. Fluid Mech. 488 (2003) 225–244. [18] G. Joulin, G.I. Sivashinsky, Combust. Sci. Technol. 31 (1983) 75–90. [19] J. Yuan, Y. Ju, C.K. Law, Phys. Fluids 17 (2005) 074106. [20] F.A. Williams, J.F. Grcar, Proc. Combust. Inst. 32 (2009) 1351–1357.
Proceedings of the
Proceedings of the Combustion Institute 34 (2013) 981–988
Combustion Institute www.elsevier.com/locate/proci
Cellular and sporadic flame regimes of low-Lewis-number stretched premixed flames Roman Fursenko a,d,⇑, Sergey Minaev a,d, Hisashi Nakamura b, Takuya Tezuka b, Susumu Hasegawa b, Koichi Takase b, Xing Li b, Masato Katsuta c, Masao Kikuchi c, Kaoru Maruta b a
Khristianovich Institute of Theoretical and Applied Mechanics, SB RAS, Novosibirsk, Russia Institute of Fluid Science, Tohoku University, 2-1-1 Katahira, Aoba, Sendai 980-8577, Japan c Tsukuba Space Center, Japan Aerospace Exploration Agency, Sengen, Tsukuba, Ibaraki 305-8505, Japan d Far Eastern Federal University, Vladivostok, Russia b
Available online 14 September 2012
Abstract 3D structure and dynamical behavior of low-Lewis-number stretched premixed flames are numerically simulated within the framework of a thermo-diffusive model with one-step chemical reaction. The results are compared with microgravity experiments at qualitative level. The influence of Lewis number, equivalence ratio, and heat loss intensity on flame structure is investigated. It is experimentally and numerically found that lean counterflow flames can appear as a set of separate ball-like flames in a state of chaotic motion. It is shown that the time averaged flame balls coordinate may be considered as important characteristic similar to coordinate of continuous flame front. Numerical simulations reveal essential incompleteness of combustion at high level of heat losses. This incompleteness occurs in the process of lean mixtures combustion and is caused by fuel leakage through the gaps among ball-like flames. Ó 2012 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Counterflow flames; Premixed cellular flames; Heat losses; Flame balls; Thermal-diffusion instability
1. Introduction Increasing interest for clean and effective combustion technologies encourages investigations of lean premixed flames due to less pollutant emission and higher efficiency. Difficulties arising in the fundamental investigations of near-limit lean ⇑ Corresponding author. Address: Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch of Russian, Academy of Sciences, Institutskaya st. 4/1, Novosibirsk 630090, Russia. Fax: +7 (383) 3307268. E-mail address: [email protected] (R. Fursenko).
premixed flames are attributed not only to complex interaction of transport, chemical processes and radiative heat losses, but also to complex spatial structure of combustion wave subject to thermal-diffusive instability. The fuel-lean, near-limit laminar flames are sensitive to radiative heat losses which intensify thermo-diffusion instability resulting in the formation of non-planar cellular structures. Numerical simulations of the flame dynamics in straight [1,2] and divergent [3] channels showed that under the influence of radiative heat losses the low-Lewis-number flames break up to separate flame cells while being in a state of chaotic self-motion and splitting. In such
1540-7489/$ - see front matter Ó 2012 The Combustion Institute. Published by Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.proci.2012.08.014
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R. Fursenko et al. / Proceedings of the Combustion Institute 34 (2013) 981–988
systems, the combustion wave consists of separate cap-like fragments which sometimes close upon themselves to form seemingly spherical structures, that are allied to “flame balls” found in microgravity experiments [4,5]. It is necessary to notice that at normal gravity the combustion wave lifting up in narrow tube sometimes can take “flame ball” shape [6]. Such combustion wave may be termed a “sporadic combustion wave” to distinguish its special structure that is different from conventional continuous flame structure. One of the unusual features of sporadic combustion wave is incomplete burning of fuel that remains in the combustion products [3]. The numerical simulations of non-stationary structure of sporadic combustion wave meet with formidable difficulties due to their chemical complexity [7,8] and wide range of spatiotemporal scales involved. Therefore reduced 3D reaction-diffusion model is reasonable in this case since it allows qualitative description of collective dynamics of flame balls constituting sporadic combustion wave. Due to the overwhelming influence of buoyancy [9], experimental investigations of the counterflow lean lowLewis-number flames under micro gravity conditions seem to be very promising [10]. For instance, absolute flammability limits and the peculiarities of thermo-diffusive instabilities can be examined in details [11–13] in this flame geometry. The present study is an attempt to make a qualitative comparison between the results of micro gravity experiments and numerical simulations of counterflow low-Lewis-number premixed flames at low stretch rates in order to distinguish general parameters determining dynamics of sporadic combustion wave. 2. Experiment Twenty seconds microgravity condition during the parabolic flight by Diamond Air Service Company, Nagoya, Japan [14] was utilized in this study. Airplane, MU300 which manufactured by Mitsubishi was employed for flight experiments. Experimental system is illustrated in Fig. 1. One pair of 3 cm diameter counterflow burners
Fig. 1. Schematic of experimental system.
was set in a combustion chamber, the distance between the burners 2L was 3 cm. The counterflow burners were made of brazen circular pipe with a porous plate inside. Nearly flat flow velocity profile can be obtained by this arrangement at low velocity conditions. Automatic experimental system which consists of PC, digital mass-flow-controllers, AD/DA converters and trigger circuit were used in the experiments. In every experiment, the nominal stretch rate a = U/L where U is flow velocity at the burner exit was maintained at a corresponding constant value. The CH4/O2/Xe mixture with X O2 =X Xe ¼ 0:141, where X O2 and X Xe are mole fractions of O2 and Xe correspondingly, was used in experiments. During the experiment, the mixture content was changed linearly with time and the quasi-steady trend of flame depending on the varying equivalence ratio was examined. Several seconds before the start of microgravity, flow velocity at the burner exit and mixture composition for each experiment were established. The mixture was then ignited by pilot flame. The pilot flame was removed immediately after ignition and the fuel concentration was gradually decreased in 20-s microgravity duration. Two video cameras were fixed in horizontal and vertical directions to record flame behavior. Accuracy of airplane microgravity experiment was verified by comparison of present data with previous one obtained during JAMIC (Drop tower) experiments [11]. The airplane’s and Drop tower’s experimental data were in good agreement with each other and the test points scattering in these experiments was less than 1%. Figure 2 shows experimental photos of counterflow flames. Two counterflow burners issuing fresh mixture are located on the right and the left sides of the frames. Experimental observations at the nominal stretch rate a = 1.038 (1/s) showed that for respectively high equivalence ratios 0:46 < /, the continuous cellular flames existed (Fig. 2a). Geometrically cellular flame is a surface with smooth maxima extending into the fresh mixture region. Such structures are typical for the flames subjected to the thermo-diffusion instability [1]. With the reduction of /, the cellular flames broke into the separate cells which were in a state of chaotic motion (Fig. 2b and c). Further decrease of equivalence ratio led to the decrease of each cell size (Fig. 2b and c) and finally to the flame extinction. For the flames represented by the set of moving cells, the measurement of the distance between the flames based on separately taken experimental frame would be incorrect. The following technique was applied for experimental measurements of average distance between the flames. A consecutive series of video frames within some interval Dt were selected. The interval Dt was chosen so that within this interval the variation of equivalence ratio did not exceed 3% of the average
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Fig. 2. Experimental photos of counterflow flames for a = 1.038 and / ¼ 0:47 (a), / ¼ 0:4 (b), / ¼ 0:38 (c) and stack superposition of 90 consequtive frames with time interval 0.016 s obtained for a = 1.03, / ¼ 0:4 0:02 (d).
equivalence ratio for the given interval. Further the series of the frames was stacked by ImageStacker software in order to obtain the superposition of the frames. The resulting averaged image is shown in Fig. 2d and the flame representation looks as two bright strips. As it is seen from Fig. 2d, the external borders of the strips are sharp and fringeless. These borders are marked by black dashed lines in Fig. 2d. The distance between the flames was determined as the distance between the external borders of the strips. Dependences of the distance between the sporadic combustion waves on equivalence ratio are shown in Fig. 3a. The experiments showed that the distance between the flames decreases with decrease of equivalence ratio. For further comparison of the experimental results with results of numerical simulations the dependency of non-dimensional flame speed on dimensionless fuel concentration 1/r 1 is plotted in Fig. 3b. To estimate the average cells size the dimensional and non-dimensional spatial scales are depicted in Fig. 2. The definitions of non-dimensional variables are introduced in the next section. 3. Numerical simulations The 3D configuration considered in the present study is back-to-back counterflow premixed flames. In this configuration the air–fuel mixtures are issued from two opposed burners placed in
positions y = ±Ly forming two flames near the stagnation plane y = 0. It is assumed that the stagnation plane y = 0 is a plane of symmetry. The following conventional framework of the model is employed: one-step irreversible exothermic reaction with Arrhenius kinetics, reactant composition far from stoichiometric, and radiative heat loss. With these assumptions, the appropriately nondimensionalized set of equations for temperature and deficient reactant concentration reads ~rT ¼ r2 T hðT 4 r4 Þ þ ð1 rÞW ðT ; CÞ Tt þ V ð1Þ C t þ V~rC ¼ Le1 r2 C W ðT ; CÞ
ð2Þ
Here T is the scaled temperature in units of Tb, the adiabatic temperature of combustion products; C is the scaled concentration of the deficient reactant in units of C0 of the value in the fresh mixture; x, y, z is non-dimensional spatial coordinates in units lth = Dth/Ub, the thermal width of flame, where Dth is the thermal diffusivity of the mixture and Ub is the velocity of a planar adiabatic flame in the high activation energy limit; t is the scaled time in units Dth =U 2b ; r = T0/Tb where T0 is the fresh mixture temperature; Le = Dth/Dmol is the Lewis number, where Dmol is the deficient reactant molecular diffusivity. Dimensionless flow velocity ~ ¼ ðax=2; vector in units Ub is given by formula V ay; az=2Þ where a is the non-dimensional stretch rate. Normalized chemical reaction rate
Fig. 3. Experimental dependences of the distance between the flames d on equivalence ratio / (a) and experimental dependency of nondimensional flame speed on dimensionless fuel concentration 1=r 1 (b).
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has the following form W(T, C) = (1 r)2 N2C exp(N(1 1/T))/2Le where N = Ta/Tb is the scaled activation energy, Ta being the activation temperature. At large N non-dimensional velocity of a well-settled planar adiabatic flame is close to unity in these variables. Unit value of non-dimensional flame speed corresponds to the dimensional velocity Ub = B exp(Ta/2Tb) of a planar adiabatic flame in the high activation energy limit. The activation temperature Ta and pre-exponential factor B in above formula were chosen to fit the dependence of Ub on equivalence ratio calculated by detailed reaction mechanism GRI-Mech 3.0. The term h(T4 r4) in Eq. (1) represents radiative heat losses where h is scaled Stefan– Boltzmann constant in units of qb cp lP U b =4T 3b lth ; lP is the Planck mean absorption length; cp, specific heat; qb, burned gas density. Since the results of the work [13] demonstrate that at medium to low values of the stretch rate, the radiative heat loss has a particularly strong impact on the counterflow premixed fuel-lean, methane–air flames. Therefore the radiative heat loss is assumed as the primary form of loss in the present numerical investigations. At the same time, the chemical kinetics of methane–air or hydrocarbon–air combustion consists of two major steps, one to form CO from the fuel and the other to convert CO to CO2. The relatively slow second reaction step may affect the near-limit behavior of hydrocarbon flames. Further numerical investigations with more complex chemistry seem to be necessary for more detailed examination of the flame structure. Equations (1) and (2) are considered in the rectangular domain Lx 6 x 6 Lx, 0 6 y 6 Ly, Lz 6 z 6 Lz and subject to the following boundary conditions Inletðy ¼ Ly Þ : T ¼ r; C ¼ 1
ð3Þ
Symmetryðy ¼ 0Þ : @T =@y ¼ 0; @C=@y ¼ 0
ð4Þ
x ¼ Lx ; z ¼ Lz : T ¼ r; C ¼ 0:
ð5Þ
Notice that asymmetrical flame configurations which may appear in experiments with two counterflow burners cannot be reproduced due to restrictions imposed by symmetric boundary conditions (4). The set of governing equations (1) and (2) was solved numerically by explicit finite-difference scheme. At initial moment, the computational domain is filled by fresh mixture with temperature r. In the numerical simulations, the flame was ignited by specifying the high temperature zone near the stagnation plane. Five sets of the orthogonal grids of 256 192 256, 320 240 320, 384 288 384, 400 304 400 and 416 320 416 were employed. Convergence tests showed that the results of calculations for the three
last-named finer grids are qualitatively the same and quantity difference in flame speed Vf = ayf of adiabatic flame (h = 0) is less than 0.2%. Figure 4 shows the dependency of flame speed on grid resolution for four tested grids. The solutions presented below correspond to the 384 288 384 grid and they were evaluated for Ly = 60, Lx = Lz = 40, r = 0.2, N = 10.5. Numerical tests of the planar stretched adiabatic flames (h = 0) show that for the computation domain 80 60 80 in units of lth = Dth/Ub, the used grid provides at least 5 points within the flame reaction zone. In this paper, we utilized the parallelism provided by Graphics Processing Unit (GPU) to speed up numerical computations. In the absence of radiative heat losses (h = 0) as well as for small heat-loss rates the flame assumes a pebbly cellular structure evolving in time and resembling structures obtained in papers [15,16]. Figure 5a depicts equiscalar surface C = 0.15 that is close to the flame surface and the concentration distribution in z = 0 plane was calculated for Le = 0.3, a = 0.067 and h = 0.0. In the near adiabatic case, the flame represents by continuous flame surface separating unburned gas and combustion products. The temperature T rapidly rises across the flame front from r to unity, while the concentration C drops from unity to zero. The mean flame front position characterized by average y coordinate of the flame surface is well-defined. As one would expect, at small heat-loss rates the flame consumes the deficient reactant completely (Fig. 5a). The flame propagation velocity Vf = ayf is equal to the absolute value of flow velocity at the flame front yf, and it is equal to 2.6 for Le = 0.3 and 1.3 for Le = 0.5. Thus the propagation velocity of the cellular flame appears to be significantly higher than the velocity of the associated planar flame (Vf = 0.94) due to increasing of the flame surface caused by thermal-diffusion instability. Notice that for the flames settled far from the stagnation
Fig. 4. Dependency of flame speed Vf calculated for Le = 0.3, a = 0.067, h = 0 on computational cells size.
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Fig. 5. Equiscalar surfaces C = 0.15 (top) and concentration distributions in z = 0 plane (bottom) calculated for Le = 0.3 and h = 0, a = 0.067 (a); h = 0.6, a = 0.033 (b); h = 0.8, a = 0.033 (c). Flow direction is shown by arrows. Vectors ~ x;~ z belong to stagnation plane.
plane, the increase of the stretch rate a leads to the decreasing of the distance between the flames, but the flame propagation velocity remains almost constant. This result coincides with theoretical predictions [17] obtained for the planar flame propagating in divergent channel. Under further increase of heat losses, the flame front structure gradually changed in the same manner as it was described in [15] for the lean low-Lewis-number flame propagating in the straight channel. At first, the cells size increases, after that the cellular flame does suffer local extinction at some of its cusps, accompanied by a noticeable escape of the unconsumed reactant through the emerging gaps. At a sufficiently large value of heat losses, the cellular flame disintegrates into a group of nearly identical cells resembling flame balls (see Fig. 5b and c). Their mutual arrangement however is not frozen but involves fluctuations, sporadic detachments of the leading flamelet from the others, followed by its disintegration and formation of the secondary flamelets nearly identical to the primary one. As a rule after the splitting, one of the ball-like flames is moved downstream with the flow and eventually disappears due to gradual depletion of the mixture. The typical evolution of ball-like flames is shown in Fig. 6, where the equiscalar surfaces of temperature are plotted in successive moments. In spite of this moving, splitting and extinguishing of ball-like flames, the equiscalar surfaces of fuel before combustion zone are represented by smooth surfaces (see Fig. 5). These surfaces being
Fig. 6. Temporal sequence of equiscalar surfaces T = 0.8 with Dt = 4.0 calculated for Le = 0.3, a = 0.033 h = 0.8.
time averaged over characteristics intervals of several ball-like flame disintegrations are almost flat. Thus, it makes possible to attribute averaged flame front position to an array of ball-like flames constituting sporadic combustion waves. It allows to determine average flame velocity in both numerical and experimental investigations. Dependences of the flame propagation velocity on heat losses intensity calculated for different stretch rates are shown in Fig. 7a. As it may be
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Fig. 7. Dependences of the flame propagation velocity Vf and concentration of unconsumed reactants Cres on heat loss intensity (a, c) and on dimensionless fuel concentration 1=r 1 (b, d).
seen from Fig. 7a the flame velocity decreases with rise of heat losses intensity h. This is consistent with previous investigations [1,3] on low-Lewisnumber flames with radiative heat losses propagating in the straight tube and in divergent channel. Taking formula for the flame speed Vf = ayf into account, the increase of the parameter h corresponding to Vf reduction leads to the shift of the average flame front position towards the stagnation plane at the fixed stretch rate a. Note that for chosen parameters and Le = 0.3 the planar flame extinction limit is h = 0.06 whereas the sporadic combustion wave extinguishes at h = 1.3. Thus sporadic combustion waves can exist in sub critical lean mixtures with fuel concentration less than extinction limits of flat flame. Taking into account dependence of the nondimensional heat losses intensity h on parameters characterizing mixture contents h (1 r)/ r exp(N(r)) the dependence of the flame front speed on dimensionless fuel concentration 1/ r 1 = Tb/T0 1 was calculated (Fig. 7b). Notice that flame velocity in Fig. 7b was calculated for distant flames located far from stagnation plane. The flame speed of distant flames remains almost constant with variation of stretch rate. As it may be concluded from Fig. 7b the
flame front velocity is increasing function of nondimensional parameter 1/r 1. Since the distance between the counterflow flames is proportional to Vf at fixed stretch rate, the distance between the flames rise with increase of equivalence ratio which is proportional to 1/r 1. This result coincides with experimental observations presented in previous section (see Fig. 3). Figure 8 depicts side view of seven overlapped slices of chemical reaction rate distribution. The experimental flame image presented in Fig. 2 has been obtained by CCD camera (Photron MC 2.1) with image intensifier. Luminescence from the methane flame in Fig. 2 was mainly caused by CH and C2 chemiluminescence which occurs in thin zone near the maximum heat release surface. The calculated maximal heat release surfaces are presented in Fig. 8. Since the increase of heat loss intensity have the same effect on flame structure as decreasing of the equivalence ratio, it may be concluded that numerical results qualitatively reproduce experimental data presented in Fig. 2. In particular it is seen that flame cells size decreases with rise of heat loss intensity whereas the gap between the cells increases. In order to compare characteristic size of the cells forming sporadic combustion wave the average cells size was determined on the basis of 2D flame representation presented in
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Fig. 8. Side view of seven overlapped slices with chemical reaction rate distribution calculated for Le = 0.3 and a = 0.067, h = 0 (a), a = 0.067, h = 0.3 (b), a = 0.033, h = 0.6 (c), a = 0.033 h = 0.8 (d). Flow direction is shown by arrows. Stagnation plane is marked by white dashed line.
Fig. 8. The characteristic size of ball-like flames observed in numerical simulations may be estimated as 1–2.5 cm that roughly corresponds to the experimental observations (see Fig. 2). Figure 7c and d shows dependencies of the concentration of unconsumed reactants on heat loss intensity and non-dimensional fuel concentration, correspondingly. At comparatively high radiative heat losses that are typical for lean mixtures, the incomplete fuel consumption is observed and the fuel leakage increases with heat-losses intensification (see Fig. 7a and b). The nondimensional heat losses h increases with decreasing of non-dimensional fuel concentration and therefore concentration of the unburned fuel in combustion products increases (Fig. 7b). This effect induces by broadening of the gap between the flame balls at high heat losses (see Fig. 5). As it may be seen from Fig. 3, the average ball-like flames radius decreases with increase of the heatlosses that coincides with theoretical predictions [5] obtained for the isolated flame ball in free space. Numerical simulations showed that the flame can be established in stagnation flow field in the wide range of problem parameters such as stretch rate, mixture contents and heat-loss intensity (see Fig. 7a and b). The flame speed and regions of existence of the flame strongly depend on Lewis number as seen in Fig. 7a and b. Decreasing of the Lewis number leads to increase of the quenching heat losses value (see Fig. 7a) due to effect of thermal-diffusion instability which becomes stronger with decreasing of Lewis number. Such flame front behavior was predicted theoretically for non-adiabatic cellular flame [18,19]. Notice that the minimal propagation velocity of the lean low-Lewis-number flame (for example Vfmin = 0.4 for Le = 0.5 (see Fig. 7b) is less than the critical velocity Vcr = e1/2 0.6 of the planar nonadiabatic flame. 4. Concluding remarks Numerical simulations and experimental observations of low-Lewis-number stretched pre-
mixed flames detect that combustion wave of lean low-Lewis-number premixtures can consist of separate combustion zones resembling flame balls. The experiments and the numerical simulations coincide in the conclusion that the decrease of equivalence ratio leads to the decrease of average distance between the flames. Also both experiments and simulations showed that decrease of equivalence ratio leads to decrease of separate flame cells’ size. Numerical simulations reveal essential incompleteness of combustion at high level of heat losses. This incompleteness occurs in the process of lean mixtures’ combustion and is caused by fuel leakage through the gaps among ball-like flames. The uncertainty in evaluation of total heat release related to incompleteness of combustion and complex spatial-temporary structure of reaction zone creates difficulties in analytical estimation of propagation velocity of sporadic combustion waves. As it was demonstrated in paper [20] the supposition about complete consumption of fuel would made problem tractable and allowed estimation of propagation velocity of combustion wave constituted of planar array of ball-like flames. It seems perspective to explore a similar model for the steadily propagating sporadic combustion wave that in contrast with classical planar laminar flame would be unbound on restriction about complete fuel consumption and admitted fuel leakage through array of ball-like flames. Recent numerical investigations of low-Lewis-number flames propagating in divergent channel [3] and the results of this paper demonstrate possibility to apply the concept on flame front of sporadic combustion wave even in case when the combustion wave consists of separate ball-like flames being in the state of chaotic motion. It seems interesting to verify theoretical prediction about incompleteness combustion related with sporadic structure of combustion wave of lean low-Lewisnumber premixed gases in future experiments. Interestingly, in spite of the fact of combustion incompleteness the propagation velocity of sporadic combustion wave may exceed propagation velocity of plane adiabatic flame of the same mixture content.
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Acknowledgments The authors are grateful to the Tohoku University and Siberian Branch of Russian Academy of Sciences (Integration project No. 38) for financial support.
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