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Effects of stretch and pressure on the characteristics of premixed swirling tubular methane-air flames
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Proceedings of the
Proceedings of the Combustion Institute 32 (2009) 1149–1156
Combustion Institute www.elsevier.com/locate/proci
Effects of stretch and pressure on the characteristics of premixed swirling tubular methane-air flames Yuyin Zhang a,*, Satoru Ishizuka b, Huayang Zhu c, Robert J. Kee c a
Department of Mechanical Engineering, Tokyo Denki University, 2-2 Kanda-Nishikicho, Chiyoda-ku, Tokyo 101-8457, Japan b Hiroshima University, Higashi-Hiroshima 739-8527, Japan c Colorado School of Mines, Golden, CO 80401, USA
Abstract This paper uses tubular flame similarity and computational models to investigate the characteristics of premixed methane-air flames with high swirl rates. As the swirl rate increases, thus increasing centrifugal forces within the flow field, pressure variations can be large. Results show that the radial pressure field significantly affects flame structure and overall burning characteristics. Molecular species transport is affected by pressure-diffusion and absolute pressure in the reaction zone, which can be significantly reduced. To assist isolating and interpreting swirl rate effects, results are compared with comparable flames in planar unstrained and opposed-flow twin flame settings. Results show that swirl rate can influence methane-air flames differently from comparable propane-air flames. These differences are explained in terms of the pressure fields and the first Damkohler number. Ó 2009 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Tubular flame; Swirl; Stretch rate; Pressure-diffusion; Premixed methane-air
1. Introduction Tubular flames have been studied over two decades from a fundamental viewpoint [1,2], and recently we have identified the importance of pressure-diffusion in swirling propane-air flames [3]. Swirl-type tubular flames may be regarded as elementary flames, which are well suited to explore and quantify the effects of stretch, curvature, and pressure-diffusion. For example, very high local swirl rates may be present in turbulent
*
Corresponding author. Fax: +81 3 5280 3569. E-mail address: [email protected] Zhang).
(Y.
eddies, thus affecting overall combustion characteristics. In addition to fundamental interest, tubular flames are attracting growing interest in the context of practical combustion technology. According to the Rayleigh criterion, swirl-type tubular flames can be stably established between the lean and rich flammability limits [2]. Various types of tubular flame burners have been developed and demonstrated for a variety of applications, including stabilizing a main-jet flame, burning low-heat-value byproducts from steel making, and burning liquid heavy oils [4]. Tubular flames are currently being incorporated into a fuel reforming system for a fuel–cell application. A new concept of rapidly mixed tubular flame combustion has also been proposed for its safety (i.e.,
1540-7489/$ - see front matter Ó 2009 The Combustion Institute. Published by Elsevier Inc. All rights reserved. doi:10.1016/j.proci.2008.06.066
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Y. Zhang et al. / Proceedings of the Combustion Institute 32 (2009) 1149–1156
no flash-back) and low NOx emissions characteristics [5]. There are alternative means to establish a tubular flame for particular applications [6]. For both scientific and technological reasons, it is important to improve fundamental understanding of tubular flame characteristics. In a previous effort for propane-air flames, we have shown that the pressure diffusion of a rate-controlling species opposes ordinary diffusion [3]. The molecular weight of the rate-controlling species, propane in the lean mixture and oxygen in the rich mixture, is greater than the mean molecular weight of the mixture. Consequently, flame temperature decreases with increasing rotation for both lean and rich propane-air mixtures. However, as reported in this paper, the situation is different for methane-air mixtures. In lean methane-air combustion, methane is the rate-controlling species, with a smaller molecular weight than the mixture. As a result, there are significant differences between methane and propane tubular flames. Yamamoto et al. studied both methane and propane in weakly stretched tubular flames, including the effects of pressure-diffusion [7,8]. However, they used a global one-step reaction and a simplified diffusion model. This paper incorporates elementary kinetics and multicomponent diffusion, thus providing much more physical and chemical detail. Stretch, curvature, rotationinduced pressure drop, and pressure-diffusion have complex, coupled, influences on flame behavior. The paper compares swirling tubular flames with planar unstretched flames, stretched opposed-flow flames, and tubular non-swirling flames to separate and quantify the relative effects of stretch, curvature, and rotation rate.
2. Model summary Figure 1 illustrates the principal features of the swirling tubular flame model. It considers an outer porous wall (at r = R) that rotates with a velocity wR. Combustible premixed gases are injected radially inward through the porous wall at a velocity vR. A cylindrical flame is established within the tube. In tubular similarity, the single independent variable is the radius r. The software implementation is a modification of the OPPDIF software [9]. The computation uses a hybrid Newton solution algorithm and an adaptive meshing method with very fine resolution (micron scale) near flame front where gradients are high. Mathematical details of the model, the governing equations, and solution algorithms may be found in previous papers [3,10,11]. The diffusion velocities, which are central to the thrust of this paper,
Fig. 1. Tubular flame model and boundary conditions. Dependent variables are radial velocity v, scaled axial velocity U = u/z, circumferential velocity w, temperature T, and mass fractions Yk. K 1 X W j Dkj X k W j–k dX j 1 dp DT 1 dT k ; þ ðX j Y j Þ p dr dr qY k T dr
Vk ¼
ð1Þ
include the effects of pressure and thermal diffusion, where, p is the pressure, Xk are the mole fractions, Dkj are the ordinary multicomponent diffusion coefficients, W is the mean molecular weight, and DTk are the thermal diffusion coefficients. Methane kinetics is represented using GRIMECH 3.0 [12]. This mechanism considers 53 species and 325 elementary reactions, including NOx kinetics. Thermodynamic and transport properties, as well as reaction rates, are evaluated using CHEMKIN [11,13,14]. Tubular flames are influenced by the coupled influence of stretch and curvature. To assist isolating these effects and understand their individual contributions, we consider two planar flame configurations. An unstretched planar premixed flame is modeled with the PREMIX software [10] and a stretched opposed-flow twin flame is modeled with the OPPDIF software [15].
Y. Zhang et al. / Proceedings of the Combustion Institute 32 (2009) 1149–1156
Although the results and insights derived from the study are general, the examples in the paper consider a tubular flame with a burner diameter d = 3 cm and the inlet mixture at 300 K and 1 atm. The stretch rate is given as e = 4 vR/d, which is varied through changing radial injection velocity vR. In the opposed-flow twin flames, the stretch rate is calculated as e = 2 vL/L, where L is the distance between two nozzles and vL is the injection velocity. In the case of a non-swirling tubular flame, the pressure is varied by specifying the inlet pressure. But for a swirling tubular flame, the pressure variation and pressure-diffusion change with the rotation rate. 3. Results and discussion There can be significant centrifugal forces in a swirl-type tubular flame with high rotation rates. These forces cause significant radial pressure gradients. When the pressure gradients are sufficiently high, the pressure-diffusion of species is significant. In propane-air premixed tubular flames increasing rotation rate shifts the flame position toward the centerline and the flame temperature decreases [3]. The reason for this behavior is that the supply of the rate-controlling species (propane for lean and oxygen for rich mixtures) into the flame front is suppressed as the rotation rate increases. The result is a decreasing supply of chemical enthalpy to the flame, decreasing the heat release rate. What is the equivalent situation for a methaneair flame? Results shown in Fig. 2 reveal important trends of a methane-air premixed tubular flame at equivalence ratio / = 0.7. In this case, the radial inlet velocity is vR = 191 cm/s, which corresponds to an axial stretch rate of e = 4 vR/ d = 255 s1. Wall rotation velocities wR are varied in the range 0 6 wR =vR 6 16. As the rotation velocity increases, the pressure at the flame front (here, flame position is defined as the position of the maximum heat release rate, RHRR) drops, the maximum flame temperature decreases and
Fig. 2. Maximum flame temperature and pressure at the flame front as functions of rotation velocity.
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the flame diameter shrinks slightly (i.e., the position of maximum HRR shifts slightly toward the centerline). This trend is similar to that of propane-air reported previously. However, there is an apparent conflict with the mechanism of pressure-diffusion discussed previously [3]. Because molecular weight of methane (the rate-controlling species in this case) is smaller than the mean molecular weight, pressure-diffusion acts in the same direction as ordinary diffusion. Thus, including pressure-diffusion would be expected to cause the flame to shift toward the inlet (Fig. 3) and the flame temperature should rise due to the enhanced chemical enthalpy supply to the reacting zone. To understand this apparently ‘‘conflicting phenomenon,” we separately analyze the effect of the pressure itself, pressure-diffusion, and the effects of the stretch and curvature. 3.1. Pressure As rotation velocity increases, pressure decreases in the reaction zone. First consider how this pressure drop affects the reaction rates. The effect of pressure on flame temperature for a stretched (but without curvature) premixed planar flame is examined in the context of an opposedflow twin flame (modeled with OPPDIF ). Further, a one-dimensional planar flame (without stretch or curvature) is modeled using PREMIX . In both cases the inlet temperature is 300K and the methane-air equivalence ratio is / = 0.7. Figure 4 illustrates the effect of pressure on flame temperature. The temperature of the planar flame (non-stretched, without curvature) varies only slightly with pressure. However, flame temperature of the opposed-flow flame (stretched but without curvature), decreases significantly as pressure decreases, and the influence of pressure is more significant at a larger stretch rate. Although chemical reaction rates may depend on pressure, the flame temperature does not depend
Fig. 3. Radial dependence of diffusive mass fluxes for the rate-controlling species. Profiles are shown for situations that include and exclude pressure-diffusion.
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Fig. 4. Effect of pressure on maximum flame temperature for opposed-flow twin flames at different stretch rates, compared to one-dimensional planar flame.
directly on the reaction rates. Flame temperature depends on the time required for completion of reactions and the residence time of the reacting species in the reaction zone, which decreases with the stretch rate. In other words, decreasing pressure affects flame temperature by reducing residence time in the reaction zone. These effects can be characterized in terms of the first Damkohler number, Da ¼
sf 1=flow velocity : / sc 1=chemical reaction rate
ð2Þ
In this expression sf is a characteristic aerodynamic time and sc is a characteristic chemical reaction time. For lean methane-air flames at fixed stretch rate, others have also reported the observation that flame temperature increases with increasing pressure. Hassan et al. [16] reported this result for freely propagating spherical flames and Nishioka et al. [17] reported the effect in tubular flames. As indicated in Fig. 4, the opposedflow flame temperature at low strain rate (35 s1) is slightly different from the planar case. The temperature for the opposed-flow flame is slightly higher than that for the completely unstrained flame due to the non-unity Lewis number effect [19,20]. However, the temperature difference is less than 6 K, which is very small compared to the flame temperature of 1850 K.
Fig. 5. Stretch effect on flame temperature for opposedflow twin flames and non-swirling tubular flames at various pressures.
when Lewis number is smaller than unity [18,19]. For pressures below 1 atm, flame temperature falls sharply and monotonically. This behavior is the result of decreasing Da at lower pressures. The lower panel of Fig. 5 represents a non-swirling tubular flame (stretched, with curvature). In this case, as the stretch rate increases, the flame temperature first rises and then turns to fall for all pressures considered. As with the opposed-flow flame, this behavior can be interpreted with the Damkohler number, Eq. (2). Figure 6 shows flame temperature as a function of stretch rate. It is evident that the temperature
3.2. Stretch rate and curvature Tubular flames are formed in axially stretched flow, with the flame surface forming a cylindrical tube. Figure 5 shows maximum flame temperature as a function of stretch rate at different pressures. Consider first the upper panel, which represents opposed-flow twin flames (stretched, without curvature). With pressures above 1 atm, as stretch rate increases, flame temperature rises slightly at low stretch rate, but then falls at larger stretch rates. Such behavior is typical in combustion
0
50
100
150
200
250
Fig. 6. The effect of stretch on maximum flame temperature for opposed-flow flames and non-swirling tubular flames at various pressures.
Y. Zhang et al. / Proceedings of the Combustion Institute 32 (2009) 1149–1156
depends on curvature and pressure, with significant differences between tubular, non-swirling, flames and opposed-flow flames. Flame curvature is the principle difference between these flames. Figure 7 shows flame temperature as a function of pressure at two stretch rates. At smaller stretch rates, there is relatively little difference between the two flames for the whole pressure range. However, at larger stretch rates the differences are significant, and the differences are accentuated at lower pressures. This is because that at low stretch rate the flame curvature is reduced (the flame is closer to the wall), and thus the flame temperature approaches that of the opposed-flow flames (without curvature). At larger stretch rate, the flame front shifts toward the centerline, resulting in larger flame curvature. Larger flame curvature contributes to the less decrease in flame temperature due to pressure fall, compared to the opposedflow twin flames. These results are consistent with the experimental results of Law et al. [20,21] and those of Peters [22] and Hawkes and Chen [23], who argued that when curvature is large, tangential diffusion is dominant within thin reaction zones of premixed methane-air turbulent flames. To further assist interpretation of stretch rate and pressure effects on flame temperature, Damkohler numbers are computed using the following definition: Da ¼
qi;max sf 1=e : ¼ ¼ sc q=qi;max qe
ð3Þ
In this form, qi, max is the maximum net rate of progress for the ith reaction and q is the local mass density. The stretch rate is computed as e = 4 vR/d for the tubular flame and e = 2 vL/L for the opposed-flow flames. Because the flame temperature is most sensitive to the chain-branching reaction [15,16]
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H þ O2 OH þ O;
ð4Þ
this reaction is used to evaluate Da. Figure 8 illustrates the first Damkohler number Da as a function of stretch rate at different pressures. The Damkohler number decreases with increasing stretch rate and decreasing pressure for tubular flames and opposed-flow flames. However, at a fixed stretch rate and pressure, Da of the tubular flame is always greater than that of the opposedflow flames. This indicates that for lean methane-air mixtures, the flame temperature of the tubular flame is higher than that for the nonstretched opposed-flow flames. This behavior is likely caused by the contribution of the positive flame curvature to Da [20]. In addition to stretch rate and pressure effects, Fig. 8 shows that Da is also affected by the flame curvature. Therefore, it may be possible to generalize the Damkohler number to include the effects of the curvature and tangential diffusion. 3.3. Pressure-diffusion Highly swirling reacting flow may be influenced by pressure-diffusion because of the associated large centrifugal forces. To assist understanding the effects of pressure-diffusion on flame structure, swirling tubular flames are computed at a small stretch rate (e = 64 s1) so as to minimize the stretch effect. Figure 9 shows flame temperature Tf, flame position RHRR, and local pressure at the flame front pHRR as functions of rotation rate for two equivalence ratios. As the equivalence ratio increases toward stoichiometric, the flame moves closer to the wall. At / = 0.70 (upper panel) wall rotation rate has only a small effect on flame temperature and flame position. However, at / = 0.55 (lower panel) the effects
[s-1 ] Fig. 7. The effect of pressure on flame temperature for opposed-flow flames and non-swirling tubular flames at different stretch rates.
Fig. 8. Effect of stretch rate on Damkohler number for no-swirl tubular flames and opposed-flow flames.
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Fig. 10. Diffusive mass fluxes for the rate-controlling species (CH4) as a function of radius. Profiles are shown for models that include and exclude pressure-diffusion.
Fig. 9. Effect of wall rotation on flame temperature, position of maximum heat release rate (RHRR), and flame front pressure pHRR in swirling tubular flames with small stretch rate for two equivalence ratios. The dashed lines show results that exclude pressure-diffusion term in Eq. (1).
are more pronounced. As rotation rate increases, the flame temperature first rises and then decreases. This behavior is caused by higher curvature and lower pressure in the / = 0.55 flame, which is positioned nearer the centerline. The / = 0.70 flame, positioned closer to the wall, experiences a relatively small pressure decrease and relatively low pressure gradient in the flame zone. Thus, according to the Eq. (1), the effects of rotation should be less important in the / = 0.70 flame. To further investigate the effect of pressure, the / = 0.55 flame is modeled without including the pressure-diffusion term in Eq. (1). As seen in the lower panel of Fig. 9, neglecting pressure-diffusion causes the flame to move closer to the centerline and the flame temperature is significantly decreased. To further understand the effects of pressurediffusion, a flame was modeled with the exclusion and the inclusion of the pressure-diffusion term in Eq. (1). The / = 0.55 flame was at high rotation rate (wR = 70 m/s) and low stretch rate (e = 64 s1). Figure 10 shows radial profiles of the methane (rate-controlling species) diffusion mass flux. When the pressure-diffusion term is neglected, the diffusive mass flux decreases and the peak shifts toward the centerline, which causes a smaller chemical enthalpy supply to the flame. It is also found including pressure-diffusion significantly extends the extinction limit at high rotation rate. These results demonstrate that pressure-diffusion enhances mass diffusion of the rate-controlling species to the flame and thus contributes to increased flame temperature at high rotation rate and small stretch rate. Interestingly, this trend is
opposite to the case for propane-air [3] for both rich and lean flames, where the pressure-diffusion causes reduced flame temperature as a result of suppressing the chemical enthalpy supply to the flame at high rotation rate. A reduction of pressure in the flame zone (as a result of high rotation) reduces chemical reaction rate, which tends to reduce flame temperature. Therefore, the flame temperature depends on a balance between the effects of pressure-diffusion and pressure itself. To put it concretely, in the case / = 0.55, the flame temperature rises slightly as the rotation rate increases up to about wR = 60 m/s. This indicates that the pressure-diffusion effect slightly dominates effect of pressure drop. However, when the rotation rate increases further, the pressure-diffusion (positive effect) cannot overcome the effect of reduced pressure (negative effect). Thus the flame temperature begins to decrease. These results are quite different from those predicted by Yamamoto [8], who reported that the temperature of a lean methane-air tubular flame should increase monotonically with increasing rotation rate. The difference may result from that Yamamoto did not account for the effect of reduced pressure in the flame. For a swirling tubular flame with a large stretch rate, such as shown in Fig. 2 (e = 255 s1), the flame forms near the centerline, even at an equivalence rate of / = 0.70. In this case, as the rotation rate increases, pressure falls in the flame zone, which causes Damkohler number to decrease significantly. Consequently, the flame temperature falls in spite of the ‘‘positive” pressure-diffusion effect. In this context ‘‘positive” means that the pressure-diffusion effect increases the supply of the rate-controlling species to the flame, thus enhancing the combustion. For methane-air flames, the effects of pressurediffusion are generally small except near blow-off and high rotation. In other cases, however, pressure-diffusion can be significant because pressure-diffusion is proportional not only to the pressure gradient, but also to the difference
Y. Zhang et al. / Proceedings of the Combustion Institute 32 (2009) 1149–1156
between the molar and mass fractions of the ratecontrolling species. For example, the pressurediffusion effect in propane-air flames is more important than it is in methane flames [3]. 4. Summary and conclusions The characteristics of lean premixed methaneair swirling tubular flames have been investigated using computational models. As reported in our previous research, pressure-diffusion can influences flame characteristics significantly. In the present study, we further address the influence of pressure variations and pressure itself in the flame zone. To isolate particular physical processes, a variety of other flames are modeled and compared with swirling tubular flames. The other flames include planar unstretched flames, opposed-flow flames that include stretch but not curvature, and non-swirling tubular flames that include stretch and curvature but not rotation. This research has greatly clarified the flame characteristics of swirling tubular flames. Some specific observations and conclusions are summarized below: (1) Based on comparing with one-dimensional flat flames, it is confirmed that the flame temperature is nearly insensitive to pressure variations in the range from 0.5 to 3.0 atm. (2) For stretched flames, including premixed opposed-flow twin flames and non-swirling tubular flames, pressure variations influence the flame temperature through the first Damkohler number. As pressure decreases, the maximum rate of progress of the key reaction is reduced, resulting in a decrease of the first Damkohler number and eventually a reduction in flame temperature. (3) For swirling tubular flames, the flame is influenced not only by stretch and curvature, but also by pressure-diffusion and by pressure itself. (a) When the flame is far from the rotational axis, the pressure gradient and the pressure drop within the flame zone are small. Consequently the flame temperature remains nearly independent of rotational velocity. (b) When the flame is situated near the rotational axis, pressure diffusion and pressure itself influence flame temperature significantly. At a large stretch rate, reduced pressure is a dominant factor, inducing a significant decrease in the first Damkohler number, which results in a monotonically decreasing flame temperature as a function of increasing rotational velocity. When the stretch rate is
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small, pressure-diffusion dominates and pressure-diffusion of a rate-controlling species (here, methane) increases the flame temperature as a function of increasing the rotational velocity. However, further increase of the rotational velocity causes a significant pressure drop within the reaction zone, resulting in reduced flame temperature through a reduction of the first Damkohler number. (4) In contrast to lean and rich propane-air swirling tubular flames, an increase in flame temperature due to pressure-diffusion can occur in lean methane/air flames. The increase occurs, however, only when the flame position is close to the rotational axis and the stretch rate is small. The flame temperature decreases monotonically with increasing rotation rate when the stretch rate is large. This flame temperature reduction is attributed to reduced pressure, which serves to reduce the first Damkohler number.
Acknowledgement This work was supported by the New Energy and Industrial Technology Development Organization (NEDO), Japan.
References [1] S. Ishizuka, Proc. Combust. Inst. 20 (1984) 287–294. [2] S. Ishizuka, Prog. Energy Combust. Sci. 19 (1993) 187–226. [3] Y. Zhang, S. Ishizuka, H. Zhu, R. Kee, Proc. Combust. Inst. 31 (2007) 1101–1107. [4] D. Shimokuri, S. Ishizuka, Proc. Combust. Inst. 30 (2005) 399–406. [5] S. Ishizuka, T. Motodamari, D. Shimokuri, Proc. Combust. Inst. 31 (2007) 1085–1092. [6] R. Kee, A. Colclasure, H. Zhu, Y. Zhang, Combust. Flame 152 (2008) 114–124. [7] K. Yamamoto, T. Hirano, S. Ishizuka, Proc. Combust. Inst. 26 (1996) 1129–1135. [8] K. Yamamoto, Combust. Flame 118 (1999) 431–444. [9] A.E. Lutz, R.J. Kee, J.F. Grcar, F.M. Rupley, OPPDIF: A Fortran Program for Computing Opposed-Flow Diffusion Flames, Tech. Rep. SAND96-8243, Sandia National Laboratories, 1996. [10] J.F. Grcar, R.J. Kee, M.D. Smooke, J.A. Miller, Proc. Combust. Inst. 21 (1986) 1773–1782. [11] R. Kee, M. Coltrin, P. Glarborg, Chemically Reacting Flow: Theory and Practice, John Wiley, Hoboken, NJ, 2003. [12] G. Smith, D. Golden, M. Frenklach, N. Moriarty, B. Eiteneer, M. Goldenberg, C. Bowman, R.
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Hanson, S. Song, W. Gardiner, V. Lissianski, Z. Qin, GRI-Mech—An Optimized Detailed Chemical Reaction Mechanism for Methane Combustion, Tech. Rep. available at http://www.me.berkeley.edu/ gri_mech, Gas Research Institute, 1999. [13] R.J. Kee, F.M. Rupley, E. Meeks, J.A. Miller, Chemkin-III: A Fortran Chemical Kinetics Package for the Analysis of Gas-phase Chemical and Plasma Kinetics, Tech. Rep. SAND96-8216, Sandia National Laboratories, 1996. [14] R.J. Kee, G. Dixon-Lewis, J. Warnatz, M.E. Coltrin, J.A. Miller, A FORTRAN Computer Code Package for the Evaluation of Gas-phase Multicomponent Transport Properties, Tech. Rep. SAND86-8246, Sandia National Laboratories, 1986.
[15] R. Kee, J. Miller, G.H. Evans, Proc. Combust. Inst. 22 (1988) 1479–1494. [16] M. Hassan, K. Aung, G. Faeth, Combust. Flame 115 (1998) 539–550. [17] M. Nishioka, K. Inagaki, S. Ishizuka, T. Takeno, Combust. Flame 86 (1991) 90–100. [18] H. Tsuji, I. Yamaoka, Proc. Combust. Inst. 19 (1982) 1533–1540. [19] J. Sato, Proc. Combust. Inst. 19 (1982) 1541–1548. [20] C. Law, P. Cho, M. Mizomoto, H. Yoshida, Proc. Combust. Inst. 21 (1986) 1803–1809. [21] C. Law, C. Sung, Prog. Energy Combust. Sci. 26 (2000) 459–505. [22] N. Peters, J. Fluid Mech. 19 (1999) 107–132. [23] E. Hawkes, J. Chen, Proc. Combust. Inst. 30 (2005) 30.
Proceedings of the
Proceedings of the Combustion Institute 32 (2009) 1149–1156
Combustion Institute www.elsevier.com/locate/proci
Effects of stretch and pressure on the characteristics of premixed swirling tubular methane-air flames Yuyin Zhang a,*, Satoru Ishizuka b, Huayang Zhu c, Robert J. Kee c a
Department of Mechanical Engineering, Tokyo Denki University, 2-2 Kanda-Nishikicho, Chiyoda-ku, Tokyo 101-8457, Japan b Hiroshima University, Higashi-Hiroshima 739-8527, Japan c Colorado School of Mines, Golden, CO 80401, USA
Abstract This paper uses tubular flame similarity and computational models to investigate the characteristics of premixed methane-air flames with high swirl rates. As the swirl rate increases, thus increasing centrifugal forces within the flow field, pressure variations can be large. Results show that the radial pressure field significantly affects flame structure and overall burning characteristics. Molecular species transport is affected by pressure-diffusion and absolute pressure in the reaction zone, which can be significantly reduced. To assist isolating and interpreting swirl rate effects, results are compared with comparable flames in planar unstrained and opposed-flow twin flame settings. Results show that swirl rate can influence methane-air flames differently from comparable propane-air flames. These differences are explained in terms of the pressure fields and the first Damkohler number. Ó 2009 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Tubular flame; Swirl; Stretch rate; Pressure-diffusion; Premixed methane-air
1. Introduction Tubular flames have been studied over two decades from a fundamental viewpoint [1,2], and recently we have identified the importance of pressure-diffusion in swirling propane-air flames [3]. Swirl-type tubular flames may be regarded as elementary flames, which are well suited to explore and quantify the effects of stretch, curvature, and pressure-diffusion. For example, very high local swirl rates may be present in turbulent
*
Corresponding author. Fax: +81 3 5280 3569. E-mail address: [email protected] Zhang).
(Y.
eddies, thus affecting overall combustion characteristics. In addition to fundamental interest, tubular flames are attracting growing interest in the context of practical combustion technology. According to the Rayleigh criterion, swirl-type tubular flames can be stably established between the lean and rich flammability limits [2]. Various types of tubular flame burners have been developed and demonstrated for a variety of applications, including stabilizing a main-jet flame, burning low-heat-value byproducts from steel making, and burning liquid heavy oils [4]. Tubular flames are currently being incorporated into a fuel reforming system for a fuel–cell application. A new concept of rapidly mixed tubular flame combustion has also been proposed for its safety (i.e.,
1540-7489/$ - see front matter Ó 2009 The Combustion Institute. Published by Elsevier Inc. All rights reserved. doi:10.1016/j.proci.2008.06.066
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Y. Zhang et al. / Proceedings of the Combustion Institute 32 (2009) 1149–1156
no flash-back) and low NOx emissions characteristics [5]. There are alternative means to establish a tubular flame for particular applications [6]. For both scientific and technological reasons, it is important to improve fundamental understanding of tubular flame characteristics. In a previous effort for propane-air flames, we have shown that the pressure diffusion of a rate-controlling species opposes ordinary diffusion [3]. The molecular weight of the rate-controlling species, propane in the lean mixture and oxygen in the rich mixture, is greater than the mean molecular weight of the mixture. Consequently, flame temperature decreases with increasing rotation for both lean and rich propane-air mixtures. However, as reported in this paper, the situation is different for methane-air mixtures. In lean methane-air combustion, methane is the rate-controlling species, with a smaller molecular weight than the mixture. As a result, there are significant differences between methane and propane tubular flames. Yamamoto et al. studied both methane and propane in weakly stretched tubular flames, including the effects of pressure-diffusion [7,8]. However, they used a global one-step reaction and a simplified diffusion model. This paper incorporates elementary kinetics and multicomponent diffusion, thus providing much more physical and chemical detail. Stretch, curvature, rotationinduced pressure drop, and pressure-diffusion have complex, coupled, influences on flame behavior. The paper compares swirling tubular flames with planar unstretched flames, stretched opposed-flow flames, and tubular non-swirling flames to separate and quantify the relative effects of stretch, curvature, and rotation rate.
2. Model summary Figure 1 illustrates the principal features of the swirling tubular flame model. It considers an outer porous wall (at r = R) that rotates with a velocity wR. Combustible premixed gases are injected radially inward through the porous wall at a velocity vR. A cylindrical flame is established within the tube. In tubular similarity, the single independent variable is the radius r. The software implementation is a modification of the OPPDIF software [9]. The computation uses a hybrid Newton solution algorithm and an adaptive meshing method with very fine resolution (micron scale) near flame front where gradients are high. Mathematical details of the model, the governing equations, and solution algorithms may be found in previous papers [3,10,11]. The diffusion velocities, which are central to the thrust of this paper,
Fig. 1. Tubular flame model and boundary conditions. Dependent variables are radial velocity v, scaled axial velocity U = u/z, circumferential velocity w, temperature T, and mass fractions Yk. K 1 X W j Dkj X k W j–k dX j 1 dp DT 1 dT k ; þ ðX j Y j Þ p dr dr qY k T dr
Vk ¼
ð1Þ
include the effects of pressure and thermal diffusion, where, p is the pressure, Xk are the mole fractions, Dkj are the ordinary multicomponent diffusion coefficients, W is the mean molecular weight, and DTk are the thermal diffusion coefficients. Methane kinetics is represented using GRIMECH 3.0 [12]. This mechanism considers 53 species and 325 elementary reactions, including NOx kinetics. Thermodynamic and transport properties, as well as reaction rates, are evaluated using CHEMKIN [11,13,14]. Tubular flames are influenced by the coupled influence of stretch and curvature. To assist isolating these effects and understand their individual contributions, we consider two planar flame configurations. An unstretched planar premixed flame is modeled with the PREMIX software [10] and a stretched opposed-flow twin flame is modeled with the OPPDIF software [15].
Y. Zhang et al. / Proceedings of the Combustion Institute 32 (2009) 1149–1156
Although the results and insights derived from the study are general, the examples in the paper consider a tubular flame with a burner diameter d = 3 cm and the inlet mixture at 300 K and 1 atm. The stretch rate is given as e = 4 vR/d, which is varied through changing radial injection velocity vR. In the opposed-flow twin flames, the stretch rate is calculated as e = 2 vL/L, where L is the distance between two nozzles and vL is the injection velocity. In the case of a non-swirling tubular flame, the pressure is varied by specifying the inlet pressure. But for a swirling tubular flame, the pressure variation and pressure-diffusion change with the rotation rate. 3. Results and discussion There can be significant centrifugal forces in a swirl-type tubular flame with high rotation rates. These forces cause significant radial pressure gradients. When the pressure gradients are sufficiently high, the pressure-diffusion of species is significant. In propane-air premixed tubular flames increasing rotation rate shifts the flame position toward the centerline and the flame temperature decreases [3]. The reason for this behavior is that the supply of the rate-controlling species (propane for lean and oxygen for rich mixtures) into the flame front is suppressed as the rotation rate increases. The result is a decreasing supply of chemical enthalpy to the flame, decreasing the heat release rate. What is the equivalent situation for a methaneair flame? Results shown in Fig. 2 reveal important trends of a methane-air premixed tubular flame at equivalence ratio / = 0.7. In this case, the radial inlet velocity is vR = 191 cm/s, which corresponds to an axial stretch rate of e = 4 vR/ d = 255 s1. Wall rotation velocities wR are varied in the range 0 6 wR =vR 6 16. As the rotation velocity increases, the pressure at the flame front (here, flame position is defined as the position of the maximum heat release rate, RHRR) drops, the maximum flame temperature decreases and
Fig. 2. Maximum flame temperature and pressure at the flame front as functions of rotation velocity.
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the flame diameter shrinks slightly (i.e., the position of maximum HRR shifts slightly toward the centerline). This trend is similar to that of propane-air reported previously. However, there is an apparent conflict with the mechanism of pressure-diffusion discussed previously [3]. Because molecular weight of methane (the rate-controlling species in this case) is smaller than the mean molecular weight, pressure-diffusion acts in the same direction as ordinary diffusion. Thus, including pressure-diffusion would be expected to cause the flame to shift toward the inlet (Fig. 3) and the flame temperature should rise due to the enhanced chemical enthalpy supply to the reacting zone. To understand this apparently ‘‘conflicting phenomenon,” we separately analyze the effect of the pressure itself, pressure-diffusion, and the effects of the stretch and curvature. 3.1. Pressure As rotation velocity increases, pressure decreases in the reaction zone. First consider how this pressure drop affects the reaction rates. The effect of pressure on flame temperature for a stretched (but without curvature) premixed planar flame is examined in the context of an opposedflow twin flame (modeled with OPPDIF ). Further, a one-dimensional planar flame (without stretch or curvature) is modeled using PREMIX . In both cases the inlet temperature is 300K and the methane-air equivalence ratio is / = 0.7. Figure 4 illustrates the effect of pressure on flame temperature. The temperature of the planar flame (non-stretched, without curvature) varies only slightly with pressure. However, flame temperature of the opposed-flow flame (stretched but without curvature), decreases significantly as pressure decreases, and the influence of pressure is more significant at a larger stretch rate. Although chemical reaction rates may depend on pressure, the flame temperature does not depend
Fig. 3. Radial dependence of diffusive mass fluxes for the rate-controlling species. Profiles are shown for situations that include and exclude pressure-diffusion.
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Fig. 4. Effect of pressure on maximum flame temperature for opposed-flow twin flames at different stretch rates, compared to one-dimensional planar flame.
directly on the reaction rates. Flame temperature depends on the time required for completion of reactions and the residence time of the reacting species in the reaction zone, which decreases with the stretch rate. In other words, decreasing pressure affects flame temperature by reducing residence time in the reaction zone. These effects can be characterized in terms of the first Damkohler number, Da ¼
sf 1=flow velocity : / sc 1=chemical reaction rate
ð2Þ
In this expression sf is a characteristic aerodynamic time and sc is a characteristic chemical reaction time. For lean methane-air flames at fixed stretch rate, others have also reported the observation that flame temperature increases with increasing pressure. Hassan et al. [16] reported this result for freely propagating spherical flames and Nishioka et al. [17] reported the effect in tubular flames. As indicated in Fig. 4, the opposedflow flame temperature at low strain rate (35 s1) is slightly different from the planar case. The temperature for the opposed-flow flame is slightly higher than that for the completely unstrained flame due to the non-unity Lewis number effect [19,20]. However, the temperature difference is less than 6 K, which is very small compared to the flame temperature of 1850 K.
Fig. 5. Stretch effect on flame temperature for opposedflow twin flames and non-swirling tubular flames at various pressures.
when Lewis number is smaller than unity [18,19]. For pressures below 1 atm, flame temperature falls sharply and monotonically. This behavior is the result of decreasing Da at lower pressures. The lower panel of Fig. 5 represents a non-swirling tubular flame (stretched, with curvature). In this case, as the stretch rate increases, the flame temperature first rises and then turns to fall for all pressures considered. As with the opposed-flow flame, this behavior can be interpreted with the Damkohler number, Eq. (2). Figure 6 shows flame temperature as a function of stretch rate. It is evident that the temperature
3.2. Stretch rate and curvature Tubular flames are formed in axially stretched flow, with the flame surface forming a cylindrical tube. Figure 5 shows maximum flame temperature as a function of stretch rate at different pressures. Consider first the upper panel, which represents opposed-flow twin flames (stretched, without curvature). With pressures above 1 atm, as stretch rate increases, flame temperature rises slightly at low stretch rate, but then falls at larger stretch rates. Such behavior is typical in combustion
0
50
100
150
200
250
Fig. 6. The effect of stretch on maximum flame temperature for opposed-flow flames and non-swirling tubular flames at various pressures.
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depends on curvature and pressure, with significant differences between tubular, non-swirling, flames and opposed-flow flames. Flame curvature is the principle difference between these flames. Figure 7 shows flame temperature as a function of pressure at two stretch rates. At smaller stretch rates, there is relatively little difference between the two flames for the whole pressure range. However, at larger stretch rates the differences are significant, and the differences are accentuated at lower pressures. This is because that at low stretch rate the flame curvature is reduced (the flame is closer to the wall), and thus the flame temperature approaches that of the opposed-flow flames (without curvature). At larger stretch rate, the flame front shifts toward the centerline, resulting in larger flame curvature. Larger flame curvature contributes to the less decrease in flame temperature due to pressure fall, compared to the opposedflow twin flames. These results are consistent with the experimental results of Law et al. [20,21] and those of Peters [22] and Hawkes and Chen [23], who argued that when curvature is large, tangential diffusion is dominant within thin reaction zones of premixed methane-air turbulent flames. To further assist interpretation of stretch rate and pressure effects on flame temperature, Damkohler numbers are computed using the following definition: Da ¼
qi;max sf 1=e : ¼ ¼ sc q=qi;max qe
ð3Þ
In this form, qi, max is the maximum net rate of progress for the ith reaction and q is the local mass density. The stretch rate is computed as e = 4 vR/d for the tubular flame and e = 2 vL/L for the opposed-flow flames. Because the flame temperature is most sensitive to the chain-branching reaction [15,16]
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H þ O2 OH þ O;
ð4Þ
this reaction is used to evaluate Da. Figure 8 illustrates the first Damkohler number Da as a function of stretch rate at different pressures. The Damkohler number decreases with increasing stretch rate and decreasing pressure for tubular flames and opposed-flow flames. However, at a fixed stretch rate and pressure, Da of the tubular flame is always greater than that of the opposedflow flames. This indicates that for lean methane-air mixtures, the flame temperature of the tubular flame is higher than that for the nonstretched opposed-flow flames. This behavior is likely caused by the contribution of the positive flame curvature to Da [20]. In addition to stretch rate and pressure effects, Fig. 8 shows that Da is also affected by the flame curvature. Therefore, it may be possible to generalize the Damkohler number to include the effects of the curvature and tangential diffusion. 3.3. Pressure-diffusion Highly swirling reacting flow may be influenced by pressure-diffusion because of the associated large centrifugal forces. To assist understanding the effects of pressure-diffusion on flame structure, swirling tubular flames are computed at a small stretch rate (e = 64 s1) so as to minimize the stretch effect. Figure 9 shows flame temperature Tf, flame position RHRR, and local pressure at the flame front pHRR as functions of rotation rate for two equivalence ratios. As the equivalence ratio increases toward stoichiometric, the flame moves closer to the wall. At / = 0.70 (upper panel) wall rotation rate has only a small effect on flame temperature and flame position. However, at / = 0.55 (lower panel) the effects
[s-1 ] Fig. 7. The effect of pressure on flame temperature for opposed-flow flames and non-swirling tubular flames at different stretch rates.
Fig. 8. Effect of stretch rate on Damkohler number for no-swirl tubular flames and opposed-flow flames.
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Fig. 10. Diffusive mass fluxes for the rate-controlling species (CH4) as a function of radius. Profiles are shown for models that include and exclude pressure-diffusion.
Fig. 9. Effect of wall rotation on flame temperature, position of maximum heat release rate (RHRR), and flame front pressure pHRR in swirling tubular flames with small stretch rate for two equivalence ratios. The dashed lines show results that exclude pressure-diffusion term in Eq. (1).
are more pronounced. As rotation rate increases, the flame temperature first rises and then decreases. This behavior is caused by higher curvature and lower pressure in the / = 0.55 flame, which is positioned nearer the centerline. The / = 0.70 flame, positioned closer to the wall, experiences a relatively small pressure decrease and relatively low pressure gradient in the flame zone. Thus, according to the Eq. (1), the effects of rotation should be less important in the / = 0.70 flame. To further investigate the effect of pressure, the / = 0.55 flame is modeled without including the pressure-diffusion term in Eq. (1). As seen in the lower panel of Fig. 9, neglecting pressure-diffusion causes the flame to move closer to the centerline and the flame temperature is significantly decreased. To further understand the effects of pressurediffusion, a flame was modeled with the exclusion and the inclusion of the pressure-diffusion term in Eq. (1). The / = 0.55 flame was at high rotation rate (wR = 70 m/s) and low stretch rate (e = 64 s1). Figure 10 shows radial profiles of the methane (rate-controlling species) diffusion mass flux. When the pressure-diffusion term is neglected, the diffusive mass flux decreases and the peak shifts toward the centerline, which causes a smaller chemical enthalpy supply to the flame. It is also found including pressure-diffusion significantly extends the extinction limit at high rotation rate. These results demonstrate that pressure-diffusion enhances mass diffusion of the rate-controlling species to the flame and thus contributes to increased flame temperature at high rotation rate and small stretch rate. Interestingly, this trend is
opposite to the case for propane-air [3] for both rich and lean flames, where the pressure-diffusion causes reduced flame temperature as a result of suppressing the chemical enthalpy supply to the flame at high rotation rate. A reduction of pressure in the flame zone (as a result of high rotation) reduces chemical reaction rate, which tends to reduce flame temperature. Therefore, the flame temperature depends on a balance between the effects of pressure-diffusion and pressure itself. To put it concretely, in the case / = 0.55, the flame temperature rises slightly as the rotation rate increases up to about wR = 60 m/s. This indicates that the pressure-diffusion effect slightly dominates effect of pressure drop. However, when the rotation rate increases further, the pressure-diffusion (positive effect) cannot overcome the effect of reduced pressure (negative effect). Thus the flame temperature begins to decrease. These results are quite different from those predicted by Yamamoto [8], who reported that the temperature of a lean methane-air tubular flame should increase monotonically with increasing rotation rate. The difference may result from that Yamamoto did not account for the effect of reduced pressure in the flame. For a swirling tubular flame with a large stretch rate, such as shown in Fig. 2 (e = 255 s1), the flame forms near the centerline, even at an equivalence rate of / = 0.70. In this case, as the rotation rate increases, pressure falls in the flame zone, which causes Damkohler number to decrease significantly. Consequently, the flame temperature falls in spite of the ‘‘positive” pressure-diffusion effect. In this context ‘‘positive” means that the pressure-diffusion effect increases the supply of the rate-controlling species to the flame, thus enhancing the combustion. For methane-air flames, the effects of pressurediffusion are generally small except near blow-off and high rotation. In other cases, however, pressure-diffusion can be significant because pressure-diffusion is proportional not only to the pressure gradient, but also to the difference
Y. Zhang et al. / Proceedings of the Combustion Institute 32 (2009) 1149–1156
between the molar and mass fractions of the ratecontrolling species. For example, the pressurediffusion effect in propane-air flames is more important than it is in methane flames [3]. 4. Summary and conclusions The characteristics of lean premixed methaneair swirling tubular flames have been investigated using computational models. As reported in our previous research, pressure-diffusion can influences flame characteristics significantly. In the present study, we further address the influence of pressure variations and pressure itself in the flame zone. To isolate particular physical processes, a variety of other flames are modeled and compared with swirling tubular flames. The other flames include planar unstretched flames, opposed-flow flames that include stretch but not curvature, and non-swirling tubular flames that include stretch and curvature but not rotation. This research has greatly clarified the flame characteristics of swirling tubular flames. Some specific observations and conclusions are summarized below: (1) Based on comparing with one-dimensional flat flames, it is confirmed that the flame temperature is nearly insensitive to pressure variations in the range from 0.5 to 3.0 atm. (2) For stretched flames, including premixed opposed-flow twin flames and non-swirling tubular flames, pressure variations influence the flame temperature through the first Damkohler number. As pressure decreases, the maximum rate of progress of the key reaction is reduced, resulting in a decrease of the first Damkohler number and eventually a reduction in flame temperature. (3) For swirling tubular flames, the flame is influenced not only by stretch and curvature, but also by pressure-diffusion and by pressure itself. (a) When the flame is far from the rotational axis, the pressure gradient and the pressure drop within the flame zone are small. Consequently the flame temperature remains nearly independent of rotational velocity. (b) When the flame is situated near the rotational axis, pressure diffusion and pressure itself influence flame temperature significantly. At a large stretch rate, reduced pressure is a dominant factor, inducing a significant decrease in the first Damkohler number, which results in a monotonically decreasing flame temperature as a function of increasing rotational velocity. When the stretch rate is
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small, pressure-diffusion dominates and pressure-diffusion of a rate-controlling species (here, methane) increases the flame temperature as a function of increasing the rotational velocity. However, further increase of the rotational velocity causes a significant pressure drop within the reaction zone, resulting in reduced flame temperature through a reduction of the first Damkohler number. (4) In contrast to lean and rich propane-air swirling tubular flames, an increase in flame temperature due to pressure-diffusion can occur in lean methane/air flames. The increase occurs, however, only when the flame position is close to the rotational axis and the stretch rate is small. The flame temperature decreases monotonically with increasing rotation rate when the stretch rate is large. This flame temperature reduction is attributed to reduced pressure, which serves to reduce the first Damkohler number.
Acknowledgement This work was supported by the New Energy and Industrial Technology Development Organization (NEDO), Japan.
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