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Study of “hyperbolic” diffusion flames: Appearance of instability caused by an interaction of stretched diffusion flames
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Proceedings of the
Proceedings of the Combustion Institute 33 (2011) 1129–1136
Combustion Institute www.elsevier.com/locate/proci
Study of “hyperbolic” diffusion flames: Appearance of instability caused by an interaction of stretched diffusion flames Yuji Nakamura a,⇑, Ryosuke Nozaki a, Akio Kitajima b a
Division of Mechanical and Space Engineering, Hokkaido University, Japan b Energy Technology Research Institute, AIST, Japan
Abstract An appearance of dynamic combustion instability due to the interaction of curved-stretched diffusion flames is studied experimentally. A pair of “hyperbolic” diffusion flames, made by four slot burners to form four “crossed” vertical and horizontal interfacial planes of fuel and oxidizer, is utilized for the present purpose. Two types of diffusion flame are obtained: the flames can be formed around each fuel stream (we define the flame as “normal diffusion flame (NDF)” mode in the present study) or formed within each oxidizer stream (so called “inverse diffusion flame (IDF)” mode). It is observed that the diffusion flame in the normal diffusion flame mode seems more stable than that in the inverse diffusion flame mode under the conditions studied. Under specific conditions, the flame fluctuation is amplified at the transient point from one mode to the other. According to the numerical simulation for the inverse diffusion flame mode, a small leakage of oxygen into the hot vitiated fuel gas occurs at the flame tip, where the reaction zone becomes wider due to the lowest Damkohler number. Once such two flame tips approach substantially, the leaked oxygen is merged, and reactivity is dramatically improved to induce ignition-like behavior, leading to dynamic flame instability. This result clearly reveals the possibility of an instability mode induced by the interaction of curved-stretched diffusion flames. Ó 2010 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Flame–flame interaction; Diffusion flame; Stretched flame; Ignition
1. Introduction An unstable combustion behavior, which is often preceded by the sudden acceleration/deceleration of combustion at the local scale, is one ⇑ Corresponding author. Address: Division of Mechanical and Space Engineering, Graduate School of Engineering, Hokkaido University, N13 W8, Kita-ku, Sapporo 060-8628, Japan. Fax: +81 11 706 6386. E-mail address: [email protected] (Y. Nakamura).
of the important issues in practical combustion systems. Strong fluctuation may cause undesired noise then eventually induce severe mechanical damage, so it must be avoided. To this end, further understanding of the potential cause of such an unstable combustion behavior, namely instability, in a combustion system is a necessary task. Combustion instability has been widely studied in the past, and its basics are found in major textbooks and review articles e.g., [1,2]. Nevertheless, little attention has been paid so far to the unstable combustion behavior caused by the interaction of
1540-7489/$ - see front matter Ó 2010 The Combustion Institute. Published by Elsevier Inc. All rights reserved. doi:10.1016/j.proci.2010.06.113
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neighboring flames, especially in diffusion flames, which are used for a variety of practical combustors. During the combustion process in the combustor (thus, a turbulent flame is considered in the following), the local flamelet is affected by various size of eddies, is stretched and curved and then interacts with others. In this way, one can show that the interaction of not only stretched but also curved flames is one of the fundamental processes in actual combustion systems. Of course it is not necessary to study further on this issue if the flames always steadily exist (called the “stable” state in this work) away from any instability due to the interaction; however, there is no concrete evidence at present. A motivation of the present study is to look for the possibility of causing instability due to the interaction of curved-stretched diffusion flames. So far, the detailed structure of single stretched diffusion flames has been studied extensively with a one-dimensional stagnation flow field [3–6] and 2-D field [7–9], mostly for the purpose of understanding a key process that leads to extinction. Not only the flame stretch (400 s1 [6]) but also the flame curvature could lead to extinction due to the non-Lewis number effect [7,9], preferential diffusion [10], and the Damkohler number effect [8]. Nevertheless, few studies have examined their interaction systematically, possibly because of the difficulty in realizing such interactions in a simple way; obviously, conventional counterflow diffusion flames are not suitable for this purpose. Yang et al. [11] proposed a special counterflow burner to form stationary adjacent curvedstretched flames. They utilized this burner to examine the extension of the extinction limit based on the flame interaction with relatively diluted fuel and oxidizer (for example, the fuel concentration in the fuel flow is less than 9%) and moderate strain rate (<35 s1) [12]. In this study, to enforce their interaction under stronger stretched fields, a higher strain rate is employed (>40 s1) with “hyperbolic” flames (a pair of highly-curved diffusion flames). Hyperbolic (diffusion) flames are obtained by arranging four slot burners properly; two of them are aligned, and they are crossed to form four “crossed” vertical and horizontal interfacial planes of fuel and oxidizer between the upper/ lower burners. Our burner system is somewhat similar to what was proposed by Yang et al. [11]; however, it has a unique function to control the “offset” of the upper/lower burners. By imposing the offset, two types of hyperbolic diffusion flames are successfully obtained without a notable change in the flow field under a fixed fuel/oxidizer condition (i.e., nearly identical stretch field and maximum temperature); one is that the flames are formed around each fuel stream (the so called “normal diffusion flame (NDF)” mode), and the other is that the flames are formed within each
oxidizer stream (the so called “inverse diffusion flame (IDF)” mode). In this way, an interaction of curved-stretched diffusion flames can be examined systematically. 2. Experiment To examine the effect of the interaction of stretched and/or curved diffusion flames, four slot burners were used to form four fuel–oxidizer interfacial planes in the combustion zone, and the actual apparatus is schematically illustrated in Fig. 1. Two “combined” (slot) burners were made; each one consists of two (single) aligned slot burners. Then these burners were crossed to form a stagnation-point flow. The fuel was injected from the diagonally located streams, and the oxidizer was injected from the other two. Eventually, four “crossed” shape fuel–oxidizer interfacial planes were formed between the burners. The upper/lower burners were made of stainless steel with a thin metal sheet inside it to separate the volume in half, which was identical to the two aligned slot burners. At all burner ports, a rectangular piece of sintered metal (SMC EBS100M; 5 mm thickness) was installed [5 mm in width (x) and 20 mm in depth (y)] to eject uniform flow into the combustion domain. Ceramic balls (each dia. = 2 mm) were installed inside the burner to remove the large eddies. The upper burner was firmly connected with the outer frame, whereas the lower burner was placed over the mechanical stage (xz) to enable adjustment of the offset and gap length between the two burners. The flow rate of fuel and oxidizer were controlled by flow meters (KOFLOC RK1650 series). After the flow control system, gases were distributed into the four burners properly, as shown in Fig. 1. The fuel and oxidizer used in this study were methane and oxygen, respectively, and the
Fig. 1. A schematic illustration of burner system.
Y. Nakamura et al. / Proceedings of the Combustion Institute 33 (2011) 1129–1136
diluent was nitrogen. Throughout the study, the ratio of the induced amount of fuel and oxygen was set to a half in volume, and the ratio of the total volume flow rates of fuel and oxidizer flow was set to unity. Considering the representative case of X CH4 ¼ 0:4, X O2 ¼ 0:8, a stoichiometric mixture fraction, Zst, can be calculated as 0.43, which is less than 0.51, the fraction at which the flame stays at the boundary of the fuel–air interface (Zst = [(Lefuel/Leoxidizer)1/2 + 1]1) e.g., [13,14]. This condition ensured that our flame was inherently formed slightly within the oxidizer stream. To avoid any disturbance caused by the buoyancy-induced flow, a stabilizer plate was placed near each burner. The offset distance (Loff) and gap distance between the burners (Lg), the gas flow velocity (Uj), and the fuel/oxidizer concentrations (X CH4 /X O2 ) were varied to investigate the flame interaction behavior. A digital camera (Canon EF-S 18-55U) was used to obtain still images. To increase the signal-to-noise ratio, the images were always taken in a dark room with a lens aperture (f-number) and shutter speed of F8 and 1/1000 s, respectively. 3. Analysis In addition to the experiment, numerical simulation in the two-dimensional (2-D) configuration was performed for further discussion. Figure 2 schematically shows the numerical model adopted in this study. Four burner ports were arranged at the upper/lower numerical boundaries, and uniform fuel and oxidizer flow was ejected into the numerical domain to form a stagnation-point flow field. The Fire Dynamic Simulator (FDS) developed at The National Institute of Standards and Technology (NIST) was used for the present analysis [15]. Although FDS was originally developed to simulate large-scale phenomena, the DNS mode, which does not apply any turbulent model to evaluate the transport term, was employed in the present study. To capture any possible flame motion in time properly, a time-dependent analy-
Fig. 2. Adopted numerical model.
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sis was made. A global one-step reaction model is used for simplicity, and the adopted reaction constants were obtained from Puri and Seshadri [16]. The calculation was performed with a conventional personal computer, and a typical productive run required only a half day. 4. Results and discussion 4.1. Observation of interacting curved-stretched diffusion flames Figure 3 shows a direct still image of typical “hyperbolic” diffusion flames at a selected condition. As indicated, the flame color is mostly blue near the center part, and the luminous flame appears downstream. A pair of hyperbolic flames was successfully formed under higher stretched conditions, without any apparent local extinction at center as shown in previous studies [11,12]. A bright flame base (with a tribrachial flame structure [17]) is clearly shown to hold the downstream flame-tail. Because the typical stagnation-point flow is formed in the present burner system, the strain rate (here, it is identical to the bulk velocity gradient), j, of the hyperbolic flame could be represented by j = (Uj,upper + Uj,lower)/Lg [12], and this value was used as a characteristic strain rate in this study. In general, the strain rate must be evaluated as a local quantity; however, using this “averaged” value could be a measure of the strain rate for a qualitative discussion. A pair of hyperbolic flames appears more clearly once the burner offset is varied, as shown in Fig. 4. When the offset is negative (the center of lower burner is shifted to the left), a pair of hyperbolic flames is formed around the diagonally-allocated fuel stream; namely, the NDF mode appears. Changing the offset to positive (the center of lower burner is shifted to the right), a pair of hyperbolic flames is then formed within the oxidizer stream; namely, the IDF mode appears. During this change, the flames experience the “zero offset” condition at which the two flames are close to each other (nearly merged) and the reconnection of the flamelet near the center part occurs to form one “crossed” flame. In this way, we could see systematically the change from the interaction of NDFs to that of IDFs with this burner system. In Fig. 4, one important feature is shown: in the negative offset mode where the NDF mode appears, blue emission can be seen near the center, suggesting that a highly-reactive zone would be formed there. On the contrary, in the positive offset mode where the IDF mode appears, such emission cannot be seen; rather, a clear “blank” zone is observed, suggesting that the oxidation reaction may not be as much active there. This trend is identical to what was observed in Yang’s work [12], where a large amount of OH
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Fig. 3. Direct photographs of obtained hyperbolic flames at zero offset (Loff = 0), (a) Uj = 0.33 m/s, X O2 = 0.8, Xfuel = 0.4, Lg = 20 mm, (b) Uj = 0.5 m/s, X O2 = 0.8, Xfuel = 0.4, Lg = 10 mm.
Fig. 4. Effect of offset on the observed flame shape. Conditions: Uj = 0.5 m/s, X O2 = 0.8, Xfuel = 0.4, Lg = 10 mm.
was produced near the center in the NDF mode compared to the IDF mode. Throughout the experiment, the hyperbolic flames looked rather stable in the NDF mode
compared to the IDF mode. The interacting flames behaved differently depending on the condition. Most flames tended to be stabilized; however, occasionally the strongly-amplified
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fluctuation with noise was clearly notified. Although the appearance of this unstable status was quite sensitive to the conditions, it clearly implied the existence of an interaction-induced instability. To confirm the possibility of the existence of an observed instability mode, 2-D numerical analysis was performed. 4.2. Numerical results to identify instability induced by interaction According to the numerical results, we could successfully reproduce two kinds of combustion states, as observed in the experiment: a steady state (a pair of hyperbolic flames is stationary) and an unsteady state (periodic ignition-like behavior due to the flame interaction; details will be discussed later). Figure 5 shows the mapping of the predicted status under a variety conditions imposed in this numerical study. As shown in the figure, the range to show the above-mentioned unsteady behavior is relatively limited, showing that it may hard to realize experimentally (i.e., it is relatively sensitive to the conditions imposed). However, it is confirmed that the experimentally observed unstable status is also found around the range. Thus, it is now ensured that this unsteady state should correspond to the instability as observed in the experiment. Figure 6 shows the numerically obtained 2-D distributions of the major dependent variables under steady conditions, as indicated in Fig. 5. It is clearly shown that the flow field is identical to that of stagnation-point flow in (a), the high temperature zone shows “crossed” shape in (b), and the reaction zone covers the oxidizer streams to separate the fuel and oxidizer regime in (c)–(e). From this figure, two important features are noted. One is that the distribution of oxygen is broadened at the curved point [flame tip; see (d)], and the other is that the connection of the fuel zone (namely, “hot fuel-bridge” formation) is along one diagonal line from lower-left to upper-right in (e). Because the hyperbolic flame
Fig. 5. Mapping of steady/unsteady conditions.
Fig. 6. 2-D distributions of major quantities at steady condition from the numerical simulations (see Fig. 5) at Uj = 0.8 m/s, X O2 = 0.6, Xfuel = 0.3, Lg = 20 mm. (a) Vector plot of velocity, (b) color maps of temperature [300 K (blue) 2800 K (red)], (c) heat release rate (0.0 kW/m3 (blue) 6.5 105 (red) kW/m3), (d) oxygen mass fraction [0.0 (blue) 0.8 (red)], (e) fuel mass fraction [0.0 (blue) 0.3 (red)]. (For interpretation of the references in color in this figure legend, the reader is referred to the web version of this article.)
is located within the oxidizer, the ejected fuel is not entirely consumed, and thus, fuel remains as a mixture with the combustion product to form a vitiated fuel gas at the center zone. Figure 7 indicates the time-sequence of flame behavior under unsteady conditions, as indicated in Fig. 5. These figures clearly show that timedependent or, more precisely, periodic behavior can be obtained in this system. The temperature at the center sharply increases similar to ignition. After such an abrupt temperature rise is diminished, a sharp rise in temperature is again achieved after a certain time passes to show the periodic temperature fluctuation. Now the question is why this abrupt change in temperature, which is ignition-like behavior, is achieved. Importantly, at the onset of the ignition-like behavior, it is shown that a small amount of oxygen is leaked through the flame tip from both of
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Fig. 7. Time-sequence of 2-D temperature [left; 300 K (blue) 2800 K (red)] and oxygen mass fraction [right; 0.0 (blue) 0.1 (red)] in unsteady condition (see in Fig. 5) at Uj = 0.8 m/s, X O2 = 0.8, Xfuel = 0.4, Lg = 20 mm. Plotted Dt is 10 ms. (For interpretation of the references in color in this figure legend, the reader is referred to the web version of this article.)
the hyperbolic flames and merged at the center, where hot vitiated fuel gas is present. Once the leaked oxygen becomes substantial, it is allowed
to achieve highly-reactive state there at certain time and the local temperature increases suddenly. This situation is physically identical to the ignition
Y. Nakamura et al. / Proceedings of the Combustion Institute 33 (2011) 1129–1136
induced by oxygen injection into a hot fuel stream as a beneficial technique to avoid local extinction [18]. Interestingly, this abrupt change in temperature of interacting diffusion flames is somewhat identical to what was predicted by Petrov & Ghoneim [19], which never be realized in experiment. In this sense, this work is the first ever to made it experimentally. Once the ignition-like behavior is identified, the volume expansion at the center prohibits further oxygen penetration. Then, the flame returns to the “original” hyperbolic shape because the continuous supply of fuel/oxidizer pushes the flame back to the stagnation-point. Then the oxygen leakage occurs again to catch the second ignition. In this way, the periodic ignition-like behavior as shown in our numerical study is obtained. If this is correct, the frequency of the ignition-like behavior should hold a certain correlation with the relaxation time scale (to the original hyperbolic flame shape), namely, the inverse of velocity gradient. In Fig. 8, the numerically-predicted frequency is plotted against the bulk velocity gradient, which is the same as a characteristic strain rate in the present stagnation-point flow, j. As suspected, all numerical data plots nearly follow a single (linear) line, suggesting that the frequency can be simply characterized by the given strain rate. According to Fig. 8, if one can assume that the linear trend continues, the zero-frequency, such as the minimum value of the strain rate to induce the instability mode caused by the curved-stretched flame interaction, is obtained by 45 s1, which is much less than the critical value to cause extinction in an ordinary 1-D flame system [6]. Because the merging process of leaked oxygen is the key factor leading to the ignition as observed, it is believed that a certain range of characteristic strain rate, i.e., that of bulk velocity gradient, should be preferable to meet the instability condition. To be more specific, in order to achieve it, we need to create the combustion field which has sufficiently low Damkohler number at the tip but highenough Damkohler number at the flame base to avoid the blow-off. Obviously the condition to
Fig. 8. Frequency of ignition-like behavior vs. given strain rate from the numerical simulations.
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meet these requirement simultaneously is limited; this is why the range leading to periodic ignition-like behavior might be limited as shown in Fig. 5. Lastly, we should notify that the present periodic ignition-like behavior might appear preferentially in the IDF mode, not in the NDF mode. As seen in Fig. 4, in the NDF mode, the center part stays in the moderate reactive condition, and thus, continuous gentle oxidation takes place. It is suspected that moderate fuel leakage at the flame tip would continuously occur to provide fuel to the “oxygen bridge”. In this way, the center part might not be ready to show temporal ignition; rather, it is already ignited to form steady combustion field there. On the contrary, in the IDF mode, the center part shows less reactivity and would be ready to ignite when the ignition condition is temporary achieved there. These differences between the NDF and IDF modes might be due to the difference in the flame curvature at the tip because the momentum of the jet from the oxidizer is higher than that from fuel in the present study, and the stagnation planes formed in left/ right sides are not at the same height. We would like to work on this phenomenon experimentally as well as numerically, especially focusing on the effect of the momentum of the jets, to confirm the key factor leading to the instability during the interaction of curved-stretched diffusion flames. 5. Conclusions To examine the existence of any unstable combustion behavior, called instability in this study, due to the interaction of curved-stretched diffusion flames, which often occur in turbulent diffusion combustion, a pair of “hyperbolic” diffusion flames was made by four slot burners. Two types of hyperbolic flames were obtained with the present burner system: a flame forms to surround the fuel stream (so called “normal diffusion flame” mode) or forms within the oxidizer stream (so called “inverse diffusion flame” mode). The hyperbolic flame seems more stable in the normal diffusion flame mode compared to the inverse diffusion flame mode. At the transient point from one mode to the other, the flame fluctuation is amplified under the specific conditions. According to the numerical analysis, in the case of the inverse diffusion flame, a small leakage of oxygen into hot vitiated fuel gas occurs at the flame tip, which should give the lowest Damkohler number as well as the maximum curvature. Due to the flame–flame interaction, the leaked oxygen is merged to cause an ignition-like behavior, i.e., instability. This result clearly reveals the possibility of an instability mode induced by the interaction of curvedstretched diffusion flames.
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Acknowledgments This work is partially supported by a grant-inaid for challenging exploratory research (MEXT, Japan), the Tanikawa-Netsugijyutu Foundation, and the Mazda Foundation. The authors express our sincere thanks for their support and contributions.
References [1] F.A. Williams, Combustion Theory, second ed., Addison-Wesley, New York, 1985. [2] C.K. Law, C.J. Sung, Prog. Energ. Combust. Sci. 26 (2000) 459–505. [3] S. Ishizuka, H. Tsuji, Proc. Combust. Inst. 18 (1981) 695–703. [4] N. Peters, R.J. Kee, Combust. Flame 68 (1987) 71. [5] S.L. Olson, J.S. Tien, Combust. Flame 70 (1987) 161. [6] H.K. Chelliah, C.K. Law, T. Ueda, M.D. Smooke, F.A. Williams, Proc. Combust. Inst. 23 (1990) 503– 511.
[7] S.H. Chung, C.K. Law, Combust. Sci. Technol. 37 (1984) 21. [8] S. Ishizuka, Y. Sakai, Proc. Combust. Inst. 21 (1986) 1821–1828. [9] H.G. Im, C.K. Law, R.L. Axelbaum, Proc. Combust. Inst. 23 (1990) 551–558. [10] T. Takagi, Z. Xu, Combust. Flame 96 (1994) 50–59. [11] S.Y. Yang, B.K. Lee, S.H. Chung, Combust. Flame 136 (2004) 246–248. [12] S.Y. Yang, S.K. Ryu, B.K. Lee, S.H. Chung, Combust. Theor. Model. 13 (2009) 235–250. [13] S.H. Chung, C.K. Law, Combust. Flame 52 (1983) 59–79. [14] A. Kitajima, T. Hatanaka, M. Takeuchi, H. Torikai, T. Miyadera, Combust. Flame 142 (2005) 72– 88. [15]. [16] I.K. Puri, K. Seshadri, Combust. Flame 65 (1986) 137–150. [17] H. Phillips, Proc. Combust. Inst. 10 (1965) 1277– 1283. [18] A.H. Lefebvre, Gas Turbine Combustion, second ed., Tayler & Francis, 1999 (Chapter 5). [19] C.A. Petrov, A.F. Ghoniem, Combust. Flame 115 (1998) 180–194.
Proceedings of the
Proceedings of the Combustion Institute 33 (2011) 1129–1136
Combustion Institute www.elsevier.com/locate/proci
Study of “hyperbolic” diffusion flames: Appearance of instability caused by an interaction of stretched diffusion flames Yuji Nakamura a,⇑, Ryosuke Nozaki a, Akio Kitajima b a
Division of Mechanical and Space Engineering, Hokkaido University, Japan b Energy Technology Research Institute, AIST, Japan
Abstract An appearance of dynamic combustion instability due to the interaction of curved-stretched diffusion flames is studied experimentally. A pair of “hyperbolic” diffusion flames, made by four slot burners to form four “crossed” vertical and horizontal interfacial planes of fuel and oxidizer, is utilized for the present purpose. Two types of diffusion flame are obtained: the flames can be formed around each fuel stream (we define the flame as “normal diffusion flame (NDF)” mode in the present study) or formed within each oxidizer stream (so called “inverse diffusion flame (IDF)” mode). It is observed that the diffusion flame in the normal diffusion flame mode seems more stable than that in the inverse diffusion flame mode under the conditions studied. Under specific conditions, the flame fluctuation is amplified at the transient point from one mode to the other. According to the numerical simulation for the inverse diffusion flame mode, a small leakage of oxygen into the hot vitiated fuel gas occurs at the flame tip, where the reaction zone becomes wider due to the lowest Damkohler number. Once such two flame tips approach substantially, the leaked oxygen is merged, and reactivity is dramatically improved to induce ignition-like behavior, leading to dynamic flame instability. This result clearly reveals the possibility of an instability mode induced by the interaction of curved-stretched diffusion flames. Ó 2010 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Flame–flame interaction; Diffusion flame; Stretched flame; Ignition
1. Introduction An unstable combustion behavior, which is often preceded by the sudden acceleration/deceleration of combustion at the local scale, is one ⇑ Corresponding author. Address: Division of Mechanical and Space Engineering, Graduate School of Engineering, Hokkaido University, N13 W8, Kita-ku, Sapporo 060-8628, Japan. Fax: +81 11 706 6386. E-mail address: [email protected] (Y. Nakamura).
of the important issues in practical combustion systems. Strong fluctuation may cause undesired noise then eventually induce severe mechanical damage, so it must be avoided. To this end, further understanding of the potential cause of such an unstable combustion behavior, namely instability, in a combustion system is a necessary task. Combustion instability has been widely studied in the past, and its basics are found in major textbooks and review articles e.g., [1,2]. Nevertheless, little attention has been paid so far to the unstable combustion behavior caused by the interaction of
1540-7489/$ - see front matter Ó 2010 The Combustion Institute. Published by Elsevier Inc. All rights reserved. doi:10.1016/j.proci.2010.06.113
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neighboring flames, especially in diffusion flames, which are used for a variety of practical combustors. During the combustion process in the combustor (thus, a turbulent flame is considered in the following), the local flamelet is affected by various size of eddies, is stretched and curved and then interacts with others. In this way, one can show that the interaction of not only stretched but also curved flames is one of the fundamental processes in actual combustion systems. Of course it is not necessary to study further on this issue if the flames always steadily exist (called the “stable” state in this work) away from any instability due to the interaction; however, there is no concrete evidence at present. A motivation of the present study is to look for the possibility of causing instability due to the interaction of curved-stretched diffusion flames. So far, the detailed structure of single stretched diffusion flames has been studied extensively with a one-dimensional stagnation flow field [3–6] and 2-D field [7–9], mostly for the purpose of understanding a key process that leads to extinction. Not only the flame stretch (400 s1 [6]) but also the flame curvature could lead to extinction due to the non-Lewis number effect [7,9], preferential diffusion [10], and the Damkohler number effect [8]. Nevertheless, few studies have examined their interaction systematically, possibly because of the difficulty in realizing such interactions in a simple way; obviously, conventional counterflow diffusion flames are not suitable for this purpose. Yang et al. [11] proposed a special counterflow burner to form stationary adjacent curvedstretched flames. They utilized this burner to examine the extension of the extinction limit based on the flame interaction with relatively diluted fuel and oxidizer (for example, the fuel concentration in the fuel flow is less than 9%) and moderate strain rate (<35 s1) [12]. In this study, to enforce their interaction under stronger stretched fields, a higher strain rate is employed (>40 s1) with “hyperbolic” flames (a pair of highly-curved diffusion flames). Hyperbolic (diffusion) flames are obtained by arranging four slot burners properly; two of them are aligned, and they are crossed to form four “crossed” vertical and horizontal interfacial planes of fuel and oxidizer between the upper/ lower burners. Our burner system is somewhat similar to what was proposed by Yang et al. [11]; however, it has a unique function to control the “offset” of the upper/lower burners. By imposing the offset, two types of hyperbolic diffusion flames are successfully obtained without a notable change in the flow field under a fixed fuel/oxidizer condition (i.e., nearly identical stretch field and maximum temperature); one is that the flames are formed around each fuel stream (the so called “normal diffusion flame (NDF)” mode), and the other is that the flames are formed within each
oxidizer stream (the so called “inverse diffusion flame (IDF)” mode). In this way, an interaction of curved-stretched diffusion flames can be examined systematically. 2. Experiment To examine the effect of the interaction of stretched and/or curved diffusion flames, four slot burners were used to form four fuel–oxidizer interfacial planes in the combustion zone, and the actual apparatus is schematically illustrated in Fig. 1. Two “combined” (slot) burners were made; each one consists of two (single) aligned slot burners. Then these burners were crossed to form a stagnation-point flow. The fuel was injected from the diagonally located streams, and the oxidizer was injected from the other two. Eventually, four “crossed” shape fuel–oxidizer interfacial planes were formed between the burners. The upper/lower burners were made of stainless steel with a thin metal sheet inside it to separate the volume in half, which was identical to the two aligned slot burners. At all burner ports, a rectangular piece of sintered metal (SMC EBS100M; 5 mm thickness) was installed [5 mm in width (x) and 20 mm in depth (y)] to eject uniform flow into the combustion domain. Ceramic balls (each dia. = 2 mm) were installed inside the burner to remove the large eddies. The upper burner was firmly connected with the outer frame, whereas the lower burner was placed over the mechanical stage (xz) to enable adjustment of the offset and gap length between the two burners. The flow rate of fuel and oxidizer were controlled by flow meters (KOFLOC RK1650 series). After the flow control system, gases were distributed into the four burners properly, as shown in Fig. 1. The fuel and oxidizer used in this study were methane and oxygen, respectively, and the
Fig. 1. A schematic illustration of burner system.
Y. Nakamura et al. / Proceedings of the Combustion Institute 33 (2011) 1129–1136
diluent was nitrogen. Throughout the study, the ratio of the induced amount of fuel and oxygen was set to a half in volume, and the ratio of the total volume flow rates of fuel and oxidizer flow was set to unity. Considering the representative case of X CH4 ¼ 0:4, X O2 ¼ 0:8, a stoichiometric mixture fraction, Zst, can be calculated as 0.43, which is less than 0.51, the fraction at which the flame stays at the boundary of the fuel–air interface (Zst = [(Lefuel/Leoxidizer)1/2 + 1]1) e.g., [13,14]. This condition ensured that our flame was inherently formed slightly within the oxidizer stream. To avoid any disturbance caused by the buoyancy-induced flow, a stabilizer plate was placed near each burner. The offset distance (Loff) and gap distance between the burners (Lg), the gas flow velocity (Uj), and the fuel/oxidizer concentrations (X CH4 /X O2 ) were varied to investigate the flame interaction behavior. A digital camera (Canon EF-S 18-55U) was used to obtain still images. To increase the signal-to-noise ratio, the images were always taken in a dark room with a lens aperture (f-number) and shutter speed of F8 and 1/1000 s, respectively. 3. Analysis In addition to the experiment, numerical simulation in the two-dimensional (2-D) configuration was performed for further discussion. Figure 2 schematically shows the numerical model adopted in this study. Four burner ports were arranged at the upper/lower numerical boundaries, and uniform fuel and oxidizer flow was ejected into the numerical domain to form a stagnation-point flow field. The Fire Dynamic Simulator (FDS) developed at The National Institute of Standards and Technology (NIST) was used for the present analysis [15]. Although FDS was originally developed to simulate large-scale phenomena, the DNS mode, which does not apply any turbulent model to evaluate the transport term, was employed in the present study. To capture any possible flame motion in time properly, a time-dependent analy-
Fig. 2. Adopted numerical model.
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sis was made. A global one-step reaction model is used for simplicity, and the adopted reaction constants were obtained from Puri and Seshadri [16]. The calculation was performed with a conventional personal computer, and a typical productive run required only a half day. 4. Results and discussion 4.1. Observation of interacting curved-stretched diffusion flames Figure 3 shows a direct still image of typical “hyperbolic” diffusion flames at a selected condition. As indicated, the flame color is mostly blue near the center part, and the luminous flame appears downstream. A pair of hyperbolic flames was successfully formed under higher stretched conditions, without any apparent local extinction at center as shown in previous studies [11,12]. A bright flame base (with a tribrachial flame structure [17]) is clearly shown to hold the downstream flame-tail. Because the typical stagnation-point flow is formed in the present burner system, the strain rate (here, it is identical to the bulk velocity gradient), j, of the hyperbolic flame could be represented by j = (Uj,upper + Uj,lower)/Lg [12], and this value was used as a characteristic strain rate in this study. In general, the strain rate must be evaluated as a local quantity; however, using this “averaged” value could be a measure of the strain rate for a qualitative discussion. A pair of hyperbolic flames appears more clearly once the burner offset is varied, as shown in Fig. 4. When the offset is negative (the center of lower burner is shifted to the left), a pair of hyperbolic flames is formed around the diagonally-allocated fuel stream; namely, the NDF mode appears. Changing the offset to positive (the center of lower burner is shifted to the right), a pair of hyperbolic flames is then formed within the oxidizer stream; namely, the IDF mode appears. During this change, the flames experience the “zero offset” condition at which the two flames are close to each other (nearly merged) and the reconnection of the flamelet near the center part occurs to form one “crossed” flame. In this way, we could see systematically the change from the interaction of NDFs to that of IDFs with this burner system. In Fig. 4, one important feature is shown: in the negative offset mode where the NDF mode appears, blue emission can be seen near the center, suggesting that a highly-reactive zone would be formed there. On the contrary, in the positive offset mode where the IDF mode appears, such emission cannot be seen; rather, a clear “blank” zone is observed, suggesting that the oxidation reaction may not be as much active there. This trend is identical to what was observed in Yang’s work [12], where a large amount of OH
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Fig. 3. Direct photographs of obtained hyperbolic flames at zero offset (Loff = 0), (a) Uj = 0.33 m/s, X O2 = 0.8, Xfuel = 0.4, Lg = 20 mm, (b) Uj = 0.5 m/s, X O2 = 0.8, Xfuel = 0.4, Lg = 10 mm.
Fig. 4. Effect of offset on the observed flame shape. Conditions: Uj = 0.5 m/s, X O2 = 0.8, Xfuel = 0.4, Lg = 10 mm.
was produced near the center in the NDF mode compared to the IDF mode. Throughout the experiment, the hyperbolic flames looked rather stable in the NDF mode
compared to the IDF mode. The interacting flames behaved differently depending on the condition. Most flames tended to be stabilized; however, occasionally the strongly-amplified
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fluctuation with noise was clearly notified. Although the appearance of this unstable status was quite sensitive to the conditions, it clearly implied the existence of an interaction-induced instability. To confirm the possibility of the existence of an observed instability mode, 2-D numerical analysis was performed. 4.2. Numerical results to identify instability induced by interaction According to the numerical results, we could successfully reproduce two kinds of combustion states, as observed in the experiment: a steady state (a pair of hyperbolic flames is stationary) and an unsteady state (periodic ignition-like behavior due to the flame interaction; details will be discussed later). Figure 5 shows the mapping of the predicted status under a variety conditions imposed in this numerical study. As shown in the figure, the range to show the above-mentioned unsteady behavior is relatively limited, showing that it may hard to realize experimentally (i.e., it is relatively sensitive to the conditions imposed). However, it is confirmed that the experimentally observed unstable status is also found around the range. Thus, it is now ensured that this unsteady state should correspond to the instability as observed in the experiment. Figure 6 shows the numerically obtained 2-D distributions of the major dependent variables under steady conditions, as indicated in Fig. 5. It is clearly shown that the flow field is identical to that of stagnation-point flow in (a), the high temperature zone shows “crossed” shape in (b), and the reaction zone covers the oxidizer streams to separate the fuel and oxidizer regime in (c)–(e). From this figure, two important features are noted. One is that the distribution of oxygen is broadened at the curved point [flame tip; see (d)], and the other is that the connection of the fuel zone (namely, “hot fuel-bridge” formation) is along one diagonal line from lower-left to upper-right in (e). Because the hyperbolic flame
Fig. 5. Mapping of steady/unsteady conditions.
Fig. 6. 2-D distributions of major quantities at steady condition from the numerical simulations (see Fig. 5) at Uj = 0.8 m/s, X O2 = 0.6, Xfuel = 0.3, Lg = 20 mm. (a) Vector plot of velocity, (b) color maps of temperature [300 K (blue) 2800 K (red)], (c) heat release rate (0.0 kW/m3 (blue) 6.5 105 (red) kW/m3), (d) oxygen mass fraction [0.0 (blue) 0.8 (red)], (e) fuel mass fraction [0.0 (blue) 0.3 (red)]. (For interpretation of the references in color in this figure legend, the reader is referred to the web version of this article.)
is located within the oxidizer, the ejected fuel is not entirely consumed, and thus, fuel remains as a mixture with the combustion product to form a vitiated fuel gas at the center zone. Figure 7 indicates the time-sequence of flame behavior under unsteady conditions, as indicated in Fig. 5. These figures clearly show that timedependent or, more precisely, periodic behavior can be obtained in this system. The temperature at the center sharply increases similar to ignition. After such an abrupt temperature rise is diminished, a sharp rise in temperature is again achieved after a certain time passes to show the periodic temperature fluctuation. Now the question is why this abrupt change in temperature, which is ignition-like behavior, is achieved. Importantly, at the onset of the ignition-like behavior, it is shown that a small amount of oxygen is leaked through the flame tip from both of
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Fig. 7. Time-sequence of 2-D temperature [left; 300 K (blue) 2800 K (red)] and oxygen mass fraction [right; 0.0 (blue) 0.1 (red)] in unsteady condition (see in Fig. 5) at Uj = 0.8 m/s, X O2 = 0.8, Xfuel = 0.4, Lg = 20 mm. Plotted Dt is 10 ms. (For interpretation of the references in color in this figure legend, the reader is referred to the web version of this article.)
the hyperbolic flames and merged at the center, where hot vitiated fuel gas is present. Once the leaked oxygen becomes substantial, it is allowed
to achieve highly-reactive state there at certain time and the local temperature increases suddenly. This situation is physically identical to the ignition
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induced by oxygen injection into a hot fuel stream as a beneficial technique to avoid local extinction [18]. Interestingly, this abrupt change in temperature of interacting diffusion flames is somewhat identical to what was predicted by Petrov & Ghoneim [19], which never be realized in experiment. In this sense, this work is the first ever to made it experimentally. Once the ignition-like behavior is identified, the volume expansion at the center prohibits further oxygen penetration. Then, the flame returns to the “original” hyperbolic shape because the continuous supply of fuel/oxidizer pushes the flame back to the stagnation-point. Then the oxygen leakage occurs again to catch the second ignition. In this way, the periodic ignition-like behavior as shown in our numerical study is obtained. If this is correct, the frequency of the ignition-like behavior should hold a certain correlation with the relaxation time scale (to the original hyperbolic flame shape), namely, the inverse of velocity gradient. In Fig. 8, the numerically-predicted frequency is plotted against the bulk velocity gradient, which is the same as a characteristic strain rate in the present stagnation-point flow, j. As suspected, all numerical data plots nearly follow a single (linear) line, suggesting that the frequency can be simply characterized by the given strain rate. According to Fig. 8, if one can assume that the linear trend continues, the zero-frequency, such as the minimum value of the strain rate to induce the instability mode caused by the curved-stretched flame interaction, is obtained by 45 s1, which is much less than the critical value to cause extinction in an ordinary 1-D flame system [6]. Because the merging process of leaked oxygen is the key factor leading to the ignition as observed, it is believed that a certain range of characteristic strain rate, i.e., that of bulk velocity gradient, should be preferable to meet the instability condition. To be more specific, in order to achieve it, we need to create the combustion field which has sufficiently low Damkohler number at the tip but highenough Damkohler number at the flame base to avoid the blow-off. Obviously the condition to
Fig. 8. Frequency of ignition-like behavior vs. given strain rate from the numerical simulations.
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meet these requirement simultaneously is limited; this is why the range leading to periodic ignition-like behavior might be limited as shown in Fig. 5. Lastly, we should notify that the present periodic ignition-like behavior might appear preferentially in the IDF mode, not in the NDF mode. As seen in Fig. 4, in the NDF mode, the center part stays in the moderate reactive condition, and thus, continuous gentle oxidation takes place. It is suspected that moderate fuel leakage at the flame tip would continuously occur to provide fuel to the “oxygen bridge”. In this way, the center part might not be ready to show temporal ignition; rather, it is already ignited to form steady combustion field there. On the contrary, in the IDF mode, the center part shows less reactivity and would be ready to ignite when the ignition condition is temporary achieved there. These differences between the NDF and IDF modes might be due to the difference in the flame curvature at the tip because the momentum of the jet from the oxidizer is higher than that from fuel in the present study, and the stagnation planes formed in left/ right sides are not at the same height. We would like to work on this phenomenon experimentally as well as numerically, especially focusing on the effect of the momentum of the jets, to confirm the key factor leading to the instability during the interaction of curved-stretched diffusion flames. 5. Conclusions To examine the existence of any unstable combustion behavior, called instability in this study, due to the interaction of curved-stretched diffusion flames, which often occur in turbulent diffusion combustion, a pair of “hyperbolic” diffusion flames was made by four slot burners. Two types of hyperbolic flames were obtained with the present burner system: a flame forms to surround the fuel stream (so called “normal diffusion flame” mode) or forms within the oxidizer stream (so called “inverse diffusion flame” mode). The hyperbolic flame seems more stable in the normal diffusion flame mode compared to the inverse diffusion flame mode. At the transient point from one mode to the other, the flame fluctuation is amplified under the specific conditions. According to the numerical analysis, in the case of the inverse diffusion flame, a small leakage of oxygen into hot vitiated fuel gas occurs at the flame tip, which should give the lowest Damkohler number as well as the maximum curvature. Due to the flame–flame interaction, the leaked oxygen is merged to cause an ignition-like behavior, i.e., instability. This result clearly reveals the possibility of an instability mode induced by the interaction of curvedstretched diffusion flames.
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Acknowledgments This work is partially supported by a grant-inaid for challenging exploratory research (MEXT, Japan), the Tanikawa-Netsugijyutu Foundation, and the Mazda Foundation. The authors express our sincere thanks for their support and contributions.
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