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The stabilization of a methane–air edge flame within a mixing layer in a narrow channel
Combustion and Flame 157 (2010) 201–203
Contents lists available at ScienceDirect
Combustion and Flame j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / c o m b u s t fl a m e
Brief Communication
The stabilization of a methane–air edge flame within a mixing layer in a narrow channel Min Jung Lee, Nam Il Kim * School of Mechanical Engineering, Chung-Ang University, Dongjak, Seoul 156-76, Republic of Korea
a r t i c l e
i n f o
Article history: Received 6 May 2009 Received in revised form 23 July 2009 Accepted 25 September 2009 Available online 23 October 2009
a b s t r a c t The flame stabilization mechanism of a methane–air edge flame formulated in a narrow channel was experimentally investigated and compared with a simple analytical model. Non-premixed flames were classified into premixed flame modes and edge flame modes. The correlation between the propagation velocity and the fuel concentration gradient in a narrow channel was investigated and the applicability of ordinary edge-flame theory was appraised. Ó 2009 The Combustion Institute. Published by Elsevier Inc. All rights reserved.
1. Introduction The structure of triple flames in fuel–air mixing layers was first observed by Phillips [1]. Since Dold [2] reported on the importance of triple-flame structures, various studies have been conducted, and these have been summarized by Chung [3]. Chung et al. have studied the characteristics of lifted diffusion flames using smallscale fuel jets [4–6]. Analytical solutions of the propagation velocity for triple flames were derived by Liñán et al. [7,8]. And Kim et al. [9,10] have reported on the existence of the critical fuel concentration gradient for maximum propagation velocity. Various flame structures in fuel–air mixing layers, namely edge flames, continue to be studied and summarized [11]. Recently, the application of non-premixed flames to microcombustors has been suggested [12–14]. However, it remains unclear whether edge-flame theory in an open space applies to mixing layers in a narrow channel. This study aims to experimentally stabilize various non-premixed flames in a narrow channel and to compare experimental results with edge-flame theory. This study will increase understanding of the dynamics of non-premixed flames in a narrow channel. 2. Experimental method A fuel–air mixing layer was formulated in a test burner as shown in Fig. 1. Methane (>99.99%) and dry-air were injected through a contraction nozzle (cross-sectional contraction ratio of 40) to enhance flow distribution uniformity in the test section and to avoid flame attachment on a splitting plate caused by the * Corresponding author. Address: School of Mechanical Engineering, Chung-Ang University, 221, Heukseok, Dongjak, Seoul 156-76, Republic of Korea. Fax: +82 2 825 5753. E-mail address: [email protected] (N.I. Kim).
wake downstream of the plate. With this effort, velocity could be decoupled from mass diffusion to the extent possible. The test section consisted of quartz plates; the length (y-direction) was 20 cm; the width (x-direction) W was 1.5 cm; and the gap was 0.5 cm. The experimental parameters were the fuel–air ratio (FA-ratio) in the volume base and the mean velocity Vm in the channel. Fuel concentration was measured using gas chromatography and the sampling flow rate was sufficiently small. 3. Results and discussion Overall flame behaviors are shown in Fig. 1a–d. By adjusting the Vm and the FA-ratio, the flame can be stabilized at a suitable location. Direct photos are shown in Fig. 2a and b for the constant fuel flow rates QF and for the Vm, respectively. Depending on the cases, various flame configurations were observed; e.g., tribrachial, single-edged, and premixed. The flame distance h was measured for fixed QF and Vm as shown in Fig. 2c. A velocity profile in a rectangular channel is usually determined by the flow rate and the no-slip condition on the wall, and it is redirected when a flame is formulated in the channel. Thus, the mean velocity is most meaningful, and many previous studies used mean velocity as the flame propagation velocity in channels [1,10,16]. Therefore, mean velocity in the channel was used as a characteristic velocity to solve a two-dimensional species-conservation equation. The equation governing fuel transfer in the channel can be ^ ¼ y=xc , as follows: simplified using ^ x ¼ x=xc and y
2 @Y F Dfuel @ Y F : ¼ ^ @y V m xc @ ^x2
ð1Þ
where xc = YF,inW and the YF,in is the inlet mass fraction. The Dfuel is a modified fuel mass diffusion coefficient which will be determined later. Although the mixing layer starts slightly earlier, it is expected
0010-2180/$ - see front matter Ó 2009 The Combustion Institute. Published by Elsevier Inc. All rights reserved. doi:10.1016/j.combustflame.2009.09.019
202
M.J. Lee, N.I. Kim / Combustion and Flame 157 (2010) 201–203
Test section
a
[cm]
1
1.5
YF,x=0
20
stoichiometric line
20
a
15
0.1
analytical experiment (Vm=44.4 cm/s) FA=0.047 , y= variable FA=variable, y= 5 cm
b 0.01 0.01
0.1
1
10
100
y D *fuel / V m xc
y
10
y=0
b
c
analytical Experiment (Vm=44.4 cm/s, FA=0.047) y=15cm y=10cm y=5cm
1
5 5
fuel
d
air
0
unit : [cm]
0 Fig. 1. Test burner and superposed photos of overall flame behavior: (a) Vm = 12.59 cm/s, FA = 0.19; (b) Vm = 35.21 cm/s, FA = 0.06; (c) Vm = 44.25 cm/s, FA = 0.047; and (d) Vm = 48.78 cm/s, FA = 0.042.
" ! !# 1 1 ^x 1 þ ^x YF ¼ erf pffiffiffiffiffiffi þ erf pffiffiffiffiffiffi : 2 ^ ^ 2 ky 2 ky
ð2aÞ
When the FA-ratio is small (xc W), this problem can be simplified as a solid conduction problem of thermal conductivity k ¼ Dfuel =V m xc . The exact solution can be determined as follows [15]:
c
cm 10
3
ð3Þ
here, erf is the error-function. The fuel concentration on the left wall YF,x=0 can then be evaluated by substituting x = 0 as shown in Fig. 3a. Measured concentrations were adjusted to the analytical results by modifying Dfuel 1:6 DCH4 0:35 cm2 =s. The analytical fuel distribution in the x-direction can then be estimated as shown in
ð2bÞ
a
2
Fig. 3. Comparison of analytical and experimental results: (a) fuel concentration on the left boundary and adjustment of the experimental fuel concentration and (b) comparison of the horizontal distribution of the fuel concentration between theoretical and experimental results.
to be small because it will be squeezed through contraction. Additionally, the disturbance of the mixing origin will also be reflected by the modification of Dfuel . The boundary conditions can be simplified as follows:
Y F ¼ 1ðx xc Þ; Y F ¼ 0 ðxc < xÞ ðif y ¼ 0Þ; @Y F ¼ 0 ðat x ¼ 0 or x ¼ WÞ: @x
1
Quenching
QF=114 cm3/min 3
QF=95.4 cm /min 3
20
QF=76.3 cm /min Vm=43.5 cm/s Vm=40.5 cm/s Vm=37.9 cm/s
h [cm]
5
b10
10
5
0 0.02 FA-ratio
0.3 0.1 0.05 Fuel-air ratio (volume base)
Fig. 2. Direct photos showing variation of the fuel–air ratio (FA): (a) fixed fuel flow rates (QF = 76.3 cm3/min); (b) fixed mean velocity (Vm = 40.5 cm/s); and (c) lifted flame heights for variation of the fuel–air ratio.
M.J. Lee, N.I. Kim / Combustion and Flame 157 (2010) 201–203
All experimental results were converged into a curve as shown in Fig. 4, with two distinct flame stabilization modes in the narrow channel. One was governed by the flow redirection by premixed curved flames near the boundary wall at higher mean velocity, like a premixed flame in a narrow tube [16]. The other was governed by the FCG, which was determined by the development of the mixing layer in the channel. The experimental results clearly show a correlation between the propagation velocity of the edge flame and the FCG. Thus, edge-flame theory in an open space is applicable even though its value in this experiment was much smaller than that found in previous studies [3,9]. Such a deviation from previous studies may be attributed to heat loss, shear stress, or dead space near the wall.
3
QF=114 cm /min
80
3
QF=95.4 cm /min 3
QF=76.3 cm /min
70
Vm, V f [cm/s]
Vm=37.9 cm/s Vm=40.5 cm/s
60
203
Vm=43.5 cm/s 50
40
Acknowledgments This research was supported by a Chung-Ang University Research Scholarship Grant.
Vm[cm/ s] = ( 47 ± 2) − 20.5× FCG[1/ cm]
30
0.0
0.3
0.6
Fuel concentration gradient (FCG) [1/cm] Fig. 4. Correlation between mean velocity Vm (or propagation velocity Vf) in the channel and the fuel concentration gradient (FCG) at the stoichiometric condition.
Fig. 3b with ^xY F;x¼0 and YF/YF,x=0. Measured results were well matched, implying that this simple analytical estimation is valid for the experimental results. All experimental results shown in Fig. 2 were replotted with the FCG and the flame propagation velocity Vf, which was assumed to be close to mean velocity for a stationary flame in the channel [1,10]. Here, a simple numerical calculation of Eq. (1) was used to evaluate the FCG at the stoichiometric point. This is because Eq. (3), which employs the semi-infinite assumption, is not applicable when the FA-ratio is relatively large.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16]
H. Phillips, Proc. Combust. Inst. 10 (1965) 1277–1283. J.W. Dold, Combust. Flame 76 (1989) 71–88. S.H. Chung, Proc. Combust. Inst. 31 (2007) 877–892. S.H. Chung, B.J. Lee, Combust. Flame 86 (1991) 62–72. B.J. Lee, S.H. Chung, Combust. Flame 109 (1997) 163–172. Y.S. Ko, S.H. Chung, Combust. Flame 118 (1999) 151–163. G.R. Ruetsch, L. Vervisch, A. Liñán, Phys. Fluids 7 (6) (1995) 1447–1454. E. Fernández-Tarrazo, M. Vera, A. Liñán, Combust. Flame 144 (2006) 261–276. N.I. Kim, J.I. Seo, K.C. Oh, H.D. Shin, Proc. Combust. Inst. 30 (2005) 367–374. N.I. Kim, J.I. Seo, Y.T. Guahk, H.D. Shin, Combust. Flame 146 (2006) 168–179. J. Buckmaster, Prog. Energy Combust. 28 (5) (2002) 435–475. C. Miesse, R. Masel, M. Short, M.A. Shannon, Proc. Combust. Inst. 30 (2005) 2499–2507. K.V. Dobrego, I.M. Kozlov, V.V. Vasiliev, J.-P. Martin, P. Gillon, Int. J. Heat Mass Transfer 51 (2008) 1962–1969. B. Xu, Y. Ju, Proc. Combust. Inst. 32 (2009) 1375–1382. H.S. Carslaw, J.G. Jaeger, Conduction of Heat in Solids, second ed., Oxford University Press, 1959. pp. 50–56, 99–101. N.I. Kim, K. Maruta, Combust. Flame 146 (2006) 283–301.
Contents lists available at ScienceDirect
Combustion and Flame j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / c o m b u s t fl a m e
Brief Communication
The stabilization of a methane–air edge flame within a mixing layer in a narrow channel Min Jung Lee, Nam Il Kim * School of Mechanical Engineering, Chung-Ang University, Dongjak, Seoul 156-76, Republic of Korea
a r t i c l e
i n f o
Article history: Received 6 May 2009 Received in revised form 23 July 2009 Accepted 25 September 2009 Available online 23 October 2009
a b s t r a c t The flame stabilization mechanism of a methane–air edge flame formulated in a narrow channel was experimentally investigated and compared with a simple analytical model. Non-premixed flames were classified into premixed flame modes and edge flame modes. The correlation between the propagation velocity and the fuel concentration gradient in a narrow channel was investigated and the applicability of ordinary edge-flame theory was appraised. Ó 2009 The Combustion Institute. Published by Elsevier Inc. All rights reserved.
1. Introduction The structure of triple flames in fuel–air mixing layers was first observed by Phillips [1]. Since Dold [2] reported on the importance of triple-flame structures, various studies have been conducted, and these have been summarized by Chung [3]. Chung et al. have studied the characteristics of lifted diffusion flames using smallscale fuel jets [4–6]. Analytical solutions of the propagation velocity for triple flames were derived by Liñán et al. [7,8]. And Kim et al. [9,10] have reported on the existence of the critical fuel concentration gradient for maximum propagation velocity. Various flame structures in fuel–air mixing layers, namely edge flames, continue to be studied and summarized [11]. Recently, the application of non-premixed flames to microcombustors has been suggested [12–14]. However, it remains unclear whether edge-flame theory in an open space applies to mixing layers in a narrow channel. This study aims to experimentally stabilize various non-premixed flames in a narrow channel and to compare experimental results with edge-flame theory. This study will increase understanding of the dynamics of non-premixed flames in a narrow channel. 2. Experimental method A fuel–air mixing layer was formulated in a test burner as shown in Fig. 1. Methane (>99.99%) and dry-air were injected through a contraction nozzle (cross-sectional contraction ratio of 40) to enhance flow distribution uniformity in the test section and to avoid flame attachment on a splitting plate caused by the * Corresponding author. Address: School of Mechanical Engineering, Chung-Ang University, 221, Heukseok, Dongjak, Seoul 156-76, Republic of Korea. Fax: +82 2 825 5753. E-mail address: [email protected] (N.I. Kim).
wake downstream of the plate. With this effort, velocity could be decoupled from mass diffusion to the extent possible. The test section consisted of quartz plates; the length (y-direction) was 20 cm; the width (x-direction) W was 1.5 cm; and the gap was 0.5 cm. The experimental parameters were the fuel–air ratio (FA-ratio) in the volume base and the mean velocity Vm in the channel. Fuel concentration was measured using gas chromatography and the sampling flow rate was sufficiently small. 3. Results and discussion Overall flame behaviors are shown in Fig. 1a–d. By adjusting the Vm and the FA-ratio, the flame can be stabilized at a suitable location. Direct photos are shown in Fig. 2a and b for the constant fuel flow rates QF and for the Vm, respectively. Depending on the cases, various flame configurations were observed; e.g., tribrachial, single-edged, and premixed. The flame distance h was measured for fixed QF and Vm as shown in Fig. 2c. A velocity profile in a rectangular channel is usually determined by the flow rate and the no-slip condition on the wall, and it is redirected when a flame is formulated in the channel. Thus, the mean velocity is most meaningful, and many previous studies used mean velocity as the flame propagation velocity in channels [1,10,16]. Therefore, mean velocity in the channel was used as a characteristic velocity to solve a two-dimensional species-conservation equation. The equation governing fuel transfer in the channel can be ^ ¼ y=xc , as follows: simplified using ^ x ¼ x=xc and y
2 @Y F Dfuel @ Y F : ¼ ^ @y V m xc @ ^x2
ð1Þ
where xc = YF,inW and the YF,in is the inlet mass fraction. The Dfuel is a modified fuel mass diffusion coefficient which will be determined later. Although the mixing layer starts slightly earlier, it is expected
0010-2180/$ - see front matter Ó 2009 The Combustion Institute. Published by Elsevier Inc. All rights reserved. doi:10.1016/j.combustflame.2009.09.019
202
M.J. Lee, N.I. Kim / Combustion and Flame 157 (2010) 201–203
Test section
a
[cm]
1
1.5
YF,x=0
20
stoichiometric line
20
a
15
0.1
analytical experiment (Vm=44.4 cm/s) FA=0.047 , y= variable FA=variable, y= 5 cm
b 0.01 0.01
0.1
1
10
100
y D *fuel / V m xc
y
10
y=0
b
c
analytical Experiment (Vm=44.4 cm/s, FA=0.047) y=15cm y=10cm y=5cm
1
5 5
fuel
d
air
0
unit : [cm]
0 Fig. 1. Test burner and superposed photos of overall flame behavior: (a) Vm = 12.59 cm/s, FA = 0.19; (b) Vm = 35.21 cm/s, FA = 0.06; (c) Vm = 44.25 cm/s, FA = 0.047; and (d) Vm = 48.78 cm/s, FA = 0.042.
" ! !# 1 1 ^x 1 þ ^x YF ¼ erf pffiffiffiffiffiffi þ erf pffiffiffiffiffiffi : 2 ^ ^ 2 ky 2 ky
ð2aÞ
When the FA-ratio is small (xc W), this problem can be simplified as a solid conduction problem of thermal conductivity k ¼ Dfuel =V m xc . The exact solution can be determined as follows [15]:
c
cm 10
3
ð3Þ
here, erf is the error-function. The fuel concentration on the left wall YF,x=0 can then be evaluated by substituting x = 0 as shown in Fig. 3a. Measured concentrations were adjusted to the analytical results by modifying Dfuel 1:6 DCH4 0:35 cm2 =s. The analytical fuel distribution in the x-direction can then be estimated as shown in
ð2bÞ
a
2
Fig. 3. Comparison of analytical and experimental results: (a) fuel concentration on the left boundary and adjustment of the experimental fuel concentration and (b) comparison of the horizontal distribution of the fuel concentration between theoretical and experimental results.
to be small because it will be squeezed through contraction. Additionally, the disturbance of the mixing origin will also be reflected by the modification of Dfuel . The boundary conditions can be simplified as follows:
Y F ¼ 1ðx xc Þ; Y F ¼ 0 ðxc < xÞ ðif y ¼ 0Þ; @Y F ¼ 0 ðat x ¼ 0 or x ¼ WÞ: @x
1
Quenching
QF=114 cm3/min 3
QF=95.4 cm /min 3
20
QF=76.3 cm /min Vm=43.5 cm/s Vm=40.5 cm/s Vm=37.9 cm/s
h [cm]
5
b10
10
5
0 0.02 FA-ratio
0.3 0.1 0.05 Fuel-air ratio (volume base)
Fig. 2. Direct photos showing variation of the fuel–air ratio (FA): (a) fixed fuel flow rates (QF = 76.3 cm3/min); (b) fixed mean velocity (Vm = 40.5 cm/s); and (c) lifted flame heights for variation of the fuel–air ratio.
M.J. Lee, N.I. Kim / Combustion and Flame 157 (2010) 201–203
All experimental results were converged into a curve as shown in Fig. 4, with two distinct flame stabilization modes in the narrow channel. One was governed by the flow redirection by premixed curved flames near the boundary wall at higher mean velocity, like a premixed flame in a narrow tube [16]. The other was governed by the FCG, which was determined by the development of the mixing layer in the channel. The experimental results clearly show a correlation between the propagation velocity of the edge flame and the FCG. Thus, edge-flame theory in an open space is applicable even though its value in this experiment was much smaller than that found in previous studies [3,9]. Such a deviation from previous studies may be attributed to heat loss, shear stress, or dead space near the wall.
3
QF=114 cm /min
80
3
QF=95.4 cm /min 3
QF=76.3 cm /min
70
Vm, V f [cm/s]
Vm=37.9 cm/s Vm=40.5 cm/s
60
203
Vm=43.5 cm/s 50
40
Acknowledgments This research was supported by a Chung-Ang University Research Scholarship Grant.
Vm[cm/ s] = ( 47 ± 2) − 20.5× FCG[1/ cm]
30
0.0
0.3
0.6
Fuel concentration gradient (FCG) [1/cm] Fig. 4. Correlation between mean velocity Vm (or propagation velocity Vf) in the channel and the fuel concentration gradient (FCG) at the stoichiometric condition.
Fig. 3b with ^xY F;x¼0 and YF/YF,x=0. Measured results were well matched, implying that this simple analytical estimation is valid for the experimental results. All experimental results shown in Fig. 2 were replotted with the FCG and the flame propagation velocity Vf, which was assumed to be close to mean velocity for a stationary flame in the channel [1,10]. Here, a simple numerical calculation of Eq. (1) was used to evaluate the FCG at the stoichiometric point. This is because Eq. (3), which employs the semi-infinite assumption, is not applicable when the FA-ratio is relatively large.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16]
H. Phillips, Proc. Combust. Inst. 10 (1965) 1277–1283. J.W. Dold, Combust. Flame 76 (1989) 71–88. S.H. Chung, Proc. Combust. Inst. 31 (2007) 877–892. S.H. Chung, B.J. Lee, Combust. Flame 86 (1991) 62–72. B.J. Lee, S.H. Chung, Combust. Flame 109 (1997) 163–172. Y.S. Ko, S.H. Chung, Combust. Flame 118 (1999) 151–163. G.R. Ruetsch, L. Vervisch, A. Liñán, Phys. Fluids 7 (6) (1995) 1447–1454. E. Fernández-Tarrazo, M. Vera, A. Liñán, Combust. Flame 144 (2006) 261–276. N.I. Kim, J.I. Seo, K.C. Oh, H.D. Shin, Proc. Combust. Inst. 30 (2005) 367–374. N.I. Kim, J.I. Seo, Y.T. Guahk, H.D. Shin, Combust. Flame 146 (2006) 168–179. J. Buckmaster, Prog. Energy Combust. 28 (5) (2002) 435–475. C. Miesse, R. Masel, M. Short, M.A. Shannon, Proc. Combust. Inst. 30 (2005) 2499–2507. K.V. Dobrego, I.M. Kozlov, V.V. Vasiliev, J.-P. Martin, P. Gillon, Int. J. Heat Mass Transfer 51 (2008) 1962–1969. B. Xu, Y. Ju, Proc. Combust. Inst. 32 (2009) 1375–1382. H.S. Carslaw, J.G. Jaeger, Conduction of Heat in Solids, second ed., Oxford University Press, 1959. pp. 50–56, 99–101. N.I. Kim, K. Maruta, Combust. Flame 146 (2006) 283–301.