Energy Fuels 2009, 23, 4236–4244 Published on Web 07/20/2009
: DOI:10.1021/ef900138u
A Study on Flame Extinction Characteristics along a C-Curve Dae Geun Park,† Jin Han Yun,‡ Jeong Park,*,† and Sang In Keel‡ †
School of Mechanical Engineering, Pukyong National University, San 100, Yongdang-dong, Nam-gu, Busan 608-739, Korea, and ‡ Eco-Machinery Research Division, Korea Institute of Machinery & Materials, 171 Jang-dong, Yuseong-gu, Daejeon 305-343, Korea Received February 17, 2009. Revised Manuscript Received June 19, 2009
A study has been conducted both experimentally and numerically to clarify impacts of curtain flow and velocity ratio on low strain rate flame extinction and to further display transition of shrinking flame disk to flame-hole. Critical mole fractions at flame extinction are provided in terms of velocity ratio, nitrogen curtain flow rate, and global strain rate. Flame extinction modes are grouped into four on a C-curve, which is characterized by a flame-hole, the shrinking of edge flame, and edge flame oscillation. It is seen that varying curtain flow rate does not impact on edge flame oscillation, flame extinction, and even flame extinction modes. Variation of velocity ratio extends to the low strain rate flame extinction modes beyond the turning point. It is found that the expanding and shrinking flames always have negative flame propagation speed; it is also recognized that the decrease of flame radius is prone to extinguish due to the dominant role of radial conduction heat loss. The examination of energy fraction is also presented to stress the role of radial conduction heat loss, particularly at the outer flame edge part. A variety of research efforts have also been focused on clarifying the dynamic aspects of edge flame.6-13 However most of these researches have been focused on the responses of a flame hole at high strain rate flames. Low strain rate flame extinction corresponds to a limit relevant to heat losses, whereas high strain rate flame is caused by flame stretch. Microgravity experiments suggested that flame extinction at low strain rate diffusion flame might be responsible for radiative heat loss.14 This could be reasonable in one-dimensional flame system where the flame radius is relatively large and thus the flame presumes to behave like a one-dimensional flame. However most experiments might be conducted with a finite burner diameter in opposed jet diffusion flame. A ring-shaped flame disk, in which the outer concentration field consists of partially premixed mixtures, is established in an opposed-jet diffusion flame. Then an edge flame, which is intrinsically dynamic, essentially forms at the boundary edge of the ring-shaped flame disk. Furthermore, an appreciable heat loss reduces critical Lewis number for edge flame oscillation at appropriately high strain rate flames and at low strain rate flames.15-18 Notably, radial conduction
Introduction Edge flame intrinsically has dynamic properties, and its dynamic flame response is well understood in the middle branch of S-curve flame response.1 That is, the flame surface forms a hole at the place where scalar dissipation rate exceeds some critical value in a turbulent jet diffusion flame. The scalar dissipation rate at the edge of the flame hole decreases as the flame hole evolves downstream. Then the edge flame, moved to the middle branch of S-curve, is finally forwarded to the upper-branch through a reignition process (advanced wave) or to the lower branch through extinction process (extinction wave). These phenomena have been well described in the numerical works of the previous study2 where unsteady step variations of imposed scalar dissipation rate near the extinction limit produced flame extinctions or reignitions. Edge flame has therefore been a hot issue, particularly at high strain rate flames, for two decades because of these ubiquitous phenomena, either with a positive flame propagation velocity or a negative one. The temporal evolution of their topological structures were numerically described for a flame disk, which is a small burning element serving as an ignition source to reignite the extinguished area in turbulent flame, and flame hole at high strain rate flames.3 The existence of multiple solutions of vigorously burning flames at identical conditions was displayed when there is no inert gas flow curtain; a disk diffusion flame and an edge flame at appropriately high strain flames.4 In recent years numerous numerical works have been devoted to the study of such local extinction and reignition events in turbulent diffusion flames using flamelet modeling.2,5
(6) Im, H. G.; Chen, J. H. Combust. Flame 1999, 119, 436. (7) Lyons, K. M.; Watson, K. A.; Carter, C. D.; Donbar, J. M. Combust. Flame 2005, 142, 308. (8) Lee, B. J.; Chung, S. H. Combust. Flame 1997, 109, 163. (9) Lee, J.; Won, S. H.; Jin, S. H.; Chung, S. H. Combust. Flame 2003, 135, 449. (10) Upatnieks, A.; Driscoll, J. F.; Rasmussen, C. C.; Ceccio, S. L. Combust. Flame 2004, 138, 259. (11) Santoro, V. S.; Li~ nan, A.; Gomez, A. Proc. Combust. Inst. 2000, 28, 2039. (12) Shay, M. L.; Ronney, P. D. Combust. Flame 1998, 112, 171. (13) Carnell, W. F.Jr.; Renfro, M. W. Combust. Flame 2005, 141, 350. (14) Maruta, K.; Yoshida, M.; Guo, H.; Ju, Y.; Niioka, T. Combust. Flame 1998, 112, 181. (15) Short, M.; Liu, Y. Combust. Theory Model. 2004, 8, 425. (16) Kurdyumov, V. N.; Matalon, M. Combust. Flame 2004, 139, 329. (17) Park, J. S.; Hwang, D. J.; Park, J.; Kim, J. S.; Kim, S.; Keel, S. I.; Kim, T. K.; Noh, D. S. Comust. Flame 2006, 146, 612. (18) Oh, C. B.; Hamins, A.; Bundy, M.; Park, J. Combust. Theory Model. 2008, 12, 283.
*To whom correspondence should be addressed. E-mail: jeongpark@ pknu.ac.kr. Telephone: þ82-51-629-6140. Fax: þ82-51-629-6150. (1) Buckmaster, J.; Jackson, T. L. Proc. Combust. Inst. 2000, 28, 1957. (2) Mauss, F.; Keller, D.; Peter, N. Proc. Combust. Inst. 1990, 23, 693. (3) Lu, Z.; Ghosal, S. J. Fluid Mech. 2004, 513, 287–307. (4) Lee, J. ; Frouzakis, C. E. ; Boulouchos, K. Proc. Combust. Inst. 2000, 28, 801. (5) Pitsch, H.; Cha, C. M.; Fedotov, S. Combust. Theory Modelling 2003, 7, 317. r 2009 American Chemical Society
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heat loss in addition to radiation heat loss may then play an important role of edge flame oscillation and flame extinction at low strain rate flames of the ring-shaped flame disk.17,18 Our research is motivated from the feature of two extinctions in the C-curve of Figure 1. That is, high strain rate flame extinction is caused by flame stretch, in that high strain flame extinguishes through a flame-hole. However low strain rate flame extinction is due to a limit defined by heat losses.1 The previous study also showed that low strain rate flame is caused by the shrinkage of the edge flame formed at the outer part of the flame disk.17,18 Is there any coexistent regime of flame hole and shrinking flame disk when the flame extinguishes at global strain rates around the turning point? What is the main mechanism of flame extinction and edge flame oscillation at shrinking flame disks? What is the role of the buoyancy effects in flame extinction and edge flame oscillation at low strain rate flames in normal gravity? Experiments and numerical simulations are conducted to clarify the above-mentioned questions at varying velocity ratio, global strain rate, and nitrogen curtain flow rate.
Figure 1. Flame response on a C-curve and flame extinction modes through a transition.
Experimental Methods Figure 2 shows the schematic of the system of experimental setup, flow control, and measurement. The counterflow burner with the inner nozzle diameters of 18.0 mm is installed in a compartment in order to prevent external disturbance. The water jacket of the upper nozzle is used to cool down the burner surface. Exhaust gases are sucked through a couple of pipes by a vacuum pump. Nitrogen curtain flow, supplied by the outer duct nozzle of the lower burner, is employed to prevent external flame disturbance and to remove the redundant outer flame held by a wake flow. The volume flow rate of nitrogen curtain flow varies from 4 to 12 L/min to change the local strain rate near the outer flame edge and clarify effects of curtain flow rate in flame extinction. Fuel is supplied from the upper duct nozzle to force the flame not to be positioned near the upper duct nozzle since the flame zone forms in the oxidizer side. A series of fine-mesh steel screens are positioned to impose plug-flow velocity profiles at the exits of the burner duct nozzles. The fuel used is a high grade of methane with a purity of 99.95%, and that of nitrogen is also 99.95%. The mass flow rates of fuel, air, and diluents are regulated by the individual mass flow controllers. The separation distance between reactant duct nozzles is fixed to 15.0 mm, in that the flame is more prone to heat loss to burner rim due to buoyancy effects. This selection may highlight the important role of lateral heat loss in flame extinction at low strain rate flames. The velocity ratio between fuel flow and air flow is from 3 to 5. The global strain rate in the present experiments is from 10 to 110 s-1. Experiments are implemented by increasing added nitrogen flow rate, while maintaining a constant global strain rate. A software-based package is utilized to manipulate these procedures. The global strain is defined as follows:19 pffiffiffiffiffi ! pffiffiffiffiffi ! Vf F Ff 2Va 2Vr Vf ag ¼ 1þ pffiffiffiffifffi ¼ 1þ pffiffiffiffi ð1Þ ffi L L V a Fa Vr Fa
Figure 2. Schematic drawing of burner and flow systems.
Burner wall temperature is measured with a K-type thermocouple in order to elucidate heat losses to the upper burner rim due to buoyancy effects. Buoyancy effects in flame extinction are then evaluated through the comparison between the experimental and numerical results. Time-averaged wall temperature is taken with the data acquired during 10 s using a data acquisition system (Graphtec, GL500).
Numerical Strategies A time-dependent two-dimensional axisymmetric configuration is employed in the present computation to treat counterflow non-premixed flame. Because the fluid velocity treated here is very low in comparison to the velocity of acoustic wave propagation, a set of model-free equations with a low Mach number approximation is used.20 The governing equations to be solved may be written as follows: DF þr 3 ðFuÞ ¼ 0 ð2Þ Dt DðFuÞ þr 3 ðFuuÞ ¼ -rp1 þr 3 u½ðruÞþðruÞT Dt 2 - ðr 3 uÞIþðF -F0 Þg 3
Where Vr is defined as Vr = Vf/Va, which is the velocity ratio between the exit velocities of the upper and lower duct nozzles. The parameters V and F denote the velocity and density of the reactant stream at the duct boundary, respectively; L is the duct separation distance; and the subscripts a and f represent the air and fuel streams, respectively. The dynamic behavior of oscillating flame is captured by a digital media camera and analyzed by a matlab-based program.
ð3Þ
ðDFYi Þ þr 3 ðFuYi Þ ¼ r 3 ðFDim rYi ÞþWi ωi , ði Dt ¼ 1, 2, :::, NÞ
(19) Chellian, H. K.; Law, C. K.; Ueda, K.; Smooke, M. D.; Williams, F. A. Proc. Combust. Inst. 1990, 23, 503.
(20) Oh, C. B.; Lee, C.; Park, J. Combust. Flame 2004, 138, 225.
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Fcp
DT þu 3 rT Dt
: DOI:10.1021/ef900138u
¼ r 3 ðλrTÞþF -
n X
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n X i ¼1
A nonuniform 401 101 grid system is used for the computational domain of 40 70 mm, which yields the minimal grid spacing of 0.01 mm in the axial direction and that of 0.2 mm in the radial direction in the region of interest. Because a global reaction mechanism was used in the computations, the smallest length scale in these laminar flames was in the heat release rate region. Generally, at least 10 grid points are needed to resolve the heat release rate region. A grid sensitivity test was conducted for a number of limiting flame conditions in which three grid sizes (dx) were examined: 0.005, 0.01, and 0.05 mm. The results for dx = 0.01 mm were within 0.15 and 0.10% for the maximum temperature and extinction limits, respectively, of the results obtained using dx = 0.005 mm for the simulation of normal gravity flames (ag = 25 s-1). Symmetry boundary conditions were applied for the velocities, species mass fractions, and temperature on the centerline. The uniform inflow velocity profile was enforced on each nozzle outlet, and a slip boundary condition was applied to the outside boundary. The top and bottom sides were treated as an outflow boundary, because the incoming flow escaped mainly from the upper boundary in normal gravity. No-slip and Neumann boundary conditions were used for the velocity on the burner walls and its gradient, respectively. The inflow temperatures for the fuel, air, and curtain streams were set to 298 K, and the wall temperature was also assumed to be 298 K.
ðcpi Dim rYi 3 rTÞ
Wi hoi w_ i þq_ r
ð5Þ
i ¼1
p0 ¼ FR0 T
N X Yi i ¼1
Wi
ð6Þ
where p0 and p1 represent the thermodynamic and hydrodynamic pressures, respectively. In addition, u denotes the velocity vector; T is the temperature; F is the density; Yi is the mass fraction of species i; hoi is the heat of formation of · species i; ωi is the production rate of species i; Dim is the mixture-averaged diffusion coefficient; cpi is the specific heat of species i; R0 is the universal gas constant; and q_ r is the radiative heat flux term. A QUICK21 and a second-order central difference schemes are used to discretize the convection and the diffusion terms of the governing equations on staggered grid system. To obtain a stable solution for the reacting flow field with stiff density variation, a predictor-corrector scheme22 is employed. For the time integration of the species and energy equations, a second-order Adams-Bashforth scheme for the predictor step and a second-order Quasi-Crank-Nicolson scheme for the corrector step were used, respectively. A second-order Adams-Bashforth scheme is used in both the predictor and corrector steps for the time integration of momentum equation. The efficient algebraic computation for the velocitypressure correction was performed using a HSMAC method,23 which is modified to consider the density variation. For the calculation of the thermodynamic and transport properties, we adopted the CHEMKIN-II and TRANFIT packages.24,25 A optically thin model14 was adopted to describe the radiative heat flux term in the energy equation. The details in numerical methods are found elsewhere.26 A three-step irreversible reaction mechanism27 for methane oxidation was used in the two-dimensional computation. The reaction mechanism used in this study was CH4 þ1:5O2 f COþ2H2 O
Results and Discussion Figure 3 shows variations of critical nitrogen mole fraction at flame extinction with global strain rate for (a) various velocity ratios at the nitrogen curtain flow rate of 8 L/min and (b) various nitrogen curtain flow rates at the velocity ratio of 5. In Figure 3 flame extinction behaviors are typically those of a C-curve. That is, the high strain rate flame extinction is responsible for flame stretch, whereas low strain rate flame extinction is attributed by heat loss.1 The critical nitrogen mole fractions at flame extinction collapse into one curve at high strain rate flames for all curtain flow rates and all velocity ratios. This implies that high strain rate flame extinction may pursue the one-dimensional flame response. Critical mole fraction at flame extinction decreases with increase of velocity ratio at low strain rate flames in Figure 3a. This tendency is consistent with that of the previous studies with the nozzle diameter of 26.0 mm, and these extinction behaviors were shown to be mainly caused by radial conduction heat loss, rather than radiative heat loss.14,17,18 Meanwhile, varying curtain flow rate may have two contrary effects at low strain rate flames. The increase of curtain flow rate at low strain rate flames increases the local strain rate, particularly at the outer flame edge. Indeed, the responses such as flame extinction and edge flame oscillation can be affected by the change of local strain rate since low strain rate flame extinction and its edge flame oscillation begin at the outer flame edge.17,18 This implies that the low strain rate flame is effectively more sustainable to flame extinction on the C-curve since the flame strength at the outer flame edge increases. On the contrary, the increase of curtain flow rate at low strain rate flames may reduce the population of reactive species near the flame edge. As a result in Figure 3b, effects of curtain flow rate do not appear in the behavior of critical mole fraction at flame extinction because the aforementioned effects maybe canceled out each other. However, the detailed explanation on effects of velocity ratio
COþ0:5O2 f CO2 CO2 f COþ0:5O2 and the associated reaction rates were -d½CH4 =dt ¼ 1011:68 expð-23500=TÞ½CH4 0:7 ½O2 0:8 -d½CO=dt ¼ 1012:35 expð-19200=TÞ½CO½H2 O0:5 ½O2 0:25 -d½CO2 =dt ¼ 1012:50 expð-20500=TÞ½CO½H2 O0:5 ½O2 0:25 with the reaction rates in units of kmol/m3 3 s. (21) Leonard, B. P. Comput. Methods Appl. Mech. Eng. 1979, 19, 59. (22) Najm, H. N.; Wyckoff, P. S.; Knio, O. M. J. Comput. Phys. 1998, 143, 381. (23) Hirt, C. W.; Cook, J. L. J. Comput. Phys. 1972, 10, 324. (24) Kee, R. J.; Rupley, F. M.; Miller, J. A. SAND89-8009B, 1989. (25) Kee, R. J.; Dixon-Lewis, G.; Warnatz, J.; Coltrin, M. E.; Miller, J. A. SAND86-8246, 1986. (26) Oh, C. B.; Lee, C. E.; Park, J. Combust. Flame 2004, 138, 225. (27) Dryer, F. L.; Glassman, I. Proc. Combust. Inst. 1972, 14, 987– 1003.
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Figure 4. Representative photos of temporal evolution of flame extinction correspondent to the individual regime at the global strain rates of (a) 15, (b) 40, and (c) 55 s-1 for the velocity ratio of 4 and the curtain flow rate of 8 L/min. Table 1. The Classification of Flame Extinction Modes Considering Whether Edge Flame Oscillates and Flame Hole Formsa ag, s-1
Figure 3. Variations of critical nitrogen mole fraction at flame extinction with global strain rate for (a) various velocity ratios at the nitrogen curtain flow rate of 8 L/min and (b) various nitrogen curtain flow rates at the velocity ratio of 5.
4 L/min
8 L/min
12 L/min
Vr = 3 regime I regime II regime III regime IV turning point
e20 25 30-40 45e 40
e20 25 30-40 45e 40
e20 25 30-40 45e 40
Vr = 4 regime I regime II regime III regime IV turning point
e20 25-30 35-50 55e 40
e20 25-30 35-50 55e 40
e20 25-30 35-50 55e 40
Vr = 5 regime I regime II regime III regime IV turning point
e25 30 35-70 75e 35-40
e25 30 35-70 75e 35-40
e25 30 35-70 75e 35-40
a Regime I: Flame extinction through the shrinkage of the outer edge flame with edge flame oscillation and without a flame-hole in shrinking flame-disks. Regime II: Flame extinction through a flame hole and the shrinkage of the outer edge flame with edge flame oscillation in shrinking flame-disks. Regime III Flame extinction through a flame hole and the shrinkage of the outer edge flame without edge flame oscillation in shrinking flame-disk. Regime IV: Flame extinction through a flame hole without the shrinkage and oscillation of edge flame in flame-disks.
and curtain flow rate can be given through numerical simulation later. Meanwhile, the previous study17 indicated that low strain rate flames always show a growing oscillation mode prior to flame extinction. But it should be noticed that for various velocity ratios the largest global strain rates for edge flame oscillation were less than the global strain rates of the turning points in the C-curves. This implicitly represents that there exists a shrinking flame-disk without edge flame oscillation on the C-curve. On the contrary, it may be conceptually believed that a flame-hole is formed at the flame center if high strain rate counterflow diffusion flame extinguishes. However, experimental evidence on this point may have been seldom clarified elsewhere. Further, it has not been provided elsewhere whether a flame-hole and a shrinking flame-disk appear simultaneously. We took all the pictures according to global strain rate as varying velocity ratio and curtain flow rate. Figure 4 displays the representative photos of temporal evolution of flame extinction correspondent to the individual regime at the global strain rates of (a) 15, (b) 40, and (c) 55 s-1 for the velocity ratio of 4 and the curtain flow rate of 8 L/min. As shown in Figure 4a, the extinction at low strain rate flame
begins from the outer flame edge and is forwarded to the flame center while the flame oscillates. In Figure 4b there is a dark region with the lowest flame intensity at a finite distance from the flame center, whereas the flame extinction still progressed from the outer flame edge to the flame center without flame oscillation. It is also seen that the flame extinguishes through a flame-hole on the flame surface without flame oscillation. Particularly, Figure 4b is relevant to the transition from a shrinking flame-disk to a flame-hole in flame extinction. We can classify the flame extinction modes based on the displayed features. Table 1 illustrates the classification of flame extinction modes considering whether edge flame oscillates and flame-hole forms. As shown in Table 1, varying curtain flow rate affects the classified regimes little. Regime I corresponds to the flame extinction through the shrinkage of the outer edge flame with edge flame oscillation and without a flame-hole in shrinking flame-disks. Regime II is the flame extinction 4239
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Figure 6. Traveling-velocities of expanding and shrinking edge flames at the last stage prior to the extinction according to curtain flow rate at the global strain rate of 15 s-1 and the velocity ratio of 4.
hole at the flame center. It is also found that regime III is not confined prior to the turning point but extended to high strain rate flames beyond the turning point, particularly at the velocity ratios of 4 and 5. Regime IV, in which the flame extinction is caused by flame-hole, migrates to a larger global strain rate as velocity ratio increases. As shall be shown later through numerical simulation in detail, this is attributed to the extension of the regime in low strain rate flame due to radial conduction heat loss. Figure 5 illustrates (a) temporal variation of the flame-disk radius through edge flame oscillation and (b) that during the shrinking period of edge flame oscillation at the global strain rate of 15 s-1, the velocity ratio of 4, the critical nitrogen mole fraction of 0.639, and the curtain flow rate of 8 L/min. The oscillating flame is shown to be accelerated while the flame reaches the extinction. Furthermore, the temporal variation of flame-disk radius for the last shrinking flame is quite different from those for the shrinking flames during the other periods. This means that the last shrinking flame can not be sustained anymore. It is understood that the temporal behaviors of edge flame during the shrinking periods are typically those of a retreating wave in Figure 5 since both the flow velocity and the edge traveling-velocity are negative. However a direct answer can not be given to whether the expanding edge flames are advancing waves or retreating waves. Figure 6 compares the traveling-velocities of expanding and shrinking edge flames at the last stage prior to the extinction according to curtain flow rate at the global strain rate of 15 s-1 and the velocity ratio of 4. If the flame is positioned at the stagnation plane, the edge flame propagation velocity is expressed as Vf = drf/dt - arf, where rf is the flame radius. Here, a is the local strain rate at the outer flame edge of flame-disk, thus the last term becomes the gas flow velocity. However the actual edge flame propagation velocity is approximated to Vf = drf/dt - Carf since the flame is established in the oxidizer-side. Here C is dependent upon the flame location, the flame radius, the global strain rate, the velocity ratio, and the curtain flow rate. However, C can be approximated to unity since the radial flow velocity at the flame edge is similar to that at on the same radial location on the stagnation plane. In our experimental ranges the orders of gas flow
Figure 5. (a) Temporal variation of the flame-disk radius through edge flame oscillation and (b) that during the shrinking period of edge flame oscillation at the global strain rate of 15 s-1, the velocity ratio of 4, the critical nitrogen mole fraction of 0.639, and the curtain flow rate of 8 L/min.
through a flame-hole and the shrinkage of the outer edge flame with edge flame oscillation in shrinking flame-disks. Regime III is the flame extinction through a flame-hole and the shrinkage of the outer edge flame without edge flame oscillation in shrinking flame-disk. Regime IV is the flame extinction through a flame-hole without the shrinkage and oscillation of edge flame in flame-disks. It should be noted that regimes II and III appear during the transition from a shrinking flame-disk to a flame-hole. Meanwhile the turning points and the individual regimes are affected little by curtain flow rate as shown in Table 1. The global strain rates for regimes I and II are less than those of the turning points at all velocity ratios and curtain flow rates. A flame-hole forms at low strain rate flames prior to the turning point even if the flame-hole is not the main mechanism of flame extinction at the low strain rate flame. It should be noted that the location of flame-hole formation is not the flame center but a finite distance from the flame center at high strain rate flames beyond the turning point in our experimental range (15110 s-1). This implies that the flame extinction responses on the C-curve can not be described by a one-dimensional approach, and a larger global strain rate out of the experimental range may be required for the formation of a flame 4240
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Figure 7. (a) Temporal variations of heat release rate contours at conditions of Vr=3, XN2=0.82, QN2=4 L/min, ag=25 s-1, and L=15 mm in normal-gravity. (b) Temporal variations of heat release rate contours at conditions of Vr =3, XN2 =0.82, QN2 =12 L/min, ag =25 s-1, and L=15 mm in normal-gravity. (c) Temporal variations of heat release rate contours at conditions of Vr =5, XN2 =0.77, XN2 =4 L/min, ag = 25 s-1, and L=15 mm in normal-gravity. 4241
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velocity are of O (10 cm/s), whereas all the edge travelingvelocities in Figure 6 are of O (10 mm/s). It is seen that the edge flame propagation velocities are always negative, even during the expanding period at low strain rate oscillating flames. Figure 6 also shows that during the shrinking period the traveling-speed of edge flame increases as flame radius decreases. This implies that edge traveling-speed increases due to the increase of radial heat conduction loss since the radial conduction heat loss is relevant to the inverse of flame radius,17 as shall be also shown through the numerical simulation later. Figure 6 also demonstrates that the flame radius, which may be an indicator of flame stabilization, has to increase in order to have a zero edge traveling-velocity (a stationary flame). Meanwhile, it is found that in our experiment range the flame is stabilized for the flame radius more than 7.5 mm, whereas the flame oscillates for that less than 7.5 mm from the inspection of the flame radius in regimes I and II from Table 1. This implies that there exists a critical flame radius for edge flame oscillation. However, this critical radius of 7.5 mm may be limited in our experiment. In the foregoing statements we addressed that radial conduction heat loss is relevant to the inverse of flame radius and small flame radius accelerates edge traveling-velocity. Then we can explain the reason why curtain flow rate did not impact critical nitrogen mole fractions at low strain rate flames in Figure 3. At low strain rate flame the increase of curtain flow rate causes the increase of the local strain rate, in that it contributes to flame stabilization. However, as shown in Figure 6 the edge traveling-speed also increases as cutrtain flow rate increases. Furthermore the increase of curtain flow rate forces the reactive species to be reduced in the flame zone. These play a role of flame destabilization. It is therefore understood that the cancellation of these contrary effects did not impact the response of critical nitrogen mole fraction to curtain flow rate. We have addressed the main reason of edge flame oscillation, flame extinction, and even the transition of the aforementioned regimes to heat loss effects at low strain rate flames. However, the detailed explanation has not yet been given. Now we will display the importance of radial conduction heat loss in edge flame oscillation and also evaluate buoyancy effects through numerical simulation. Figure 7 shows temporal variations of heat release rate contours at conditions of (a) Vr = 3, XN2 = 0.82, QN2 = 4L/min ; (b) Vr = 3, XN2 = 0.82, QN2 = 12 L/min; and (c) Vr = 5, XN2 = 0.77, QN2 = 4L/min for ag = 25 s-1 and L = 15 mm in normalgravity. In Figure 7 the heat release rate has the unit of W/m3. The flame conditions were taken just at flame extinction. The time zero is taken at the flame condition where the flame radius is a minimum during the temporal evolution. All the flames oscillate just at flame extinction as shown in Figure 7. It should be noted that the fuel Lewis numbers are 1.008 in panels a and b in Figure 7 and 1.013 in panel c, respectively. This implies that those flames may not oscillate without the help of appreciable heat losses since the fuel Lewis numbers is near unity.15-17 In Figure 7 the increase of curtain flow rate does not change the amplitude of edge flame oscillation, whereas the increase of velocity ratio produces the increase of the amplitude of edge flame oscillation. These are consistent with the experimental evidence that the increase of velocity ratio lowered the critical nitrogen mole fractions at extinction in Figure 3a and that the increase of curtain flow rate does not change the critical nitrogen mole fractions at extinction in Figure 3b. The comparison of the individual
Figure 8. Temporal variations of energy fractions at (a) flame center and (b) near flame edge at the flame condition of Vr=3, ag=25 s-1, XN2=0.82, and QN2=4 L/min.
fractional contribution to chemical energy term in the energy equation may be required in order to verify which heat loss terms contribute to the edge flame oscillation importantly in those flame disks in Figure 7. The energy equation can be expressed as follows:
where Cx and Cr are the axial and radial convection terms, Dx and Dr are the axial and radial diffusion terms, Mx and Mr are the axial and radial interdiffusion terms, Ra is the radiation heat loss terms, and CS is the chemical source term, respectively. Figure 8 shows temporal variations of energy fractions at (a) flame center and (b) near flame edge at the flame condition of Vr=3, ag=25 s-1, XN2=0.82, and QN2=4 L/min. Figures 9 and 10 are the same plot at the flame condition of Vr = 5, ag =25 s-1, XN2 =0.82, and QN2 =12 L/min and at 4242
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Figure 9. Temporal variations of energy fractions at (a) flame center and (b) near flame edge at the flame condition of Vr=3, ag=25 s-1, XN2=0.82, and QN2=12 L/min.
Figure 10. Temporal variations of energy fractions at (a) flame center and (b) near flame edge at the flame condition of Vr=5, ag= 25 s-1, XN2=0.77, and QN2=4 L/min.
the flame condition of Vr=5, ag=25 s-1, XN2=0.77, and QN2= 4 L/min, respectively. These energy fractions are compared along the surface of maximum heat release rate in these figures. The flame edge location was taken where radial conduction heat loss is a maximum. The transient terms in all cases are negligible, even in the unsteady state. At the center points in Figures 8a, 9a, and 10a, axial conduction heat loss term is dominant, whereas the radiation heat loss shows a minor contribution and the others are negligible. The contribution of radiation heat loss may be a little larger if the flame condition is selected at lower global strain rate. That is, flame response is determined mainly by the balance between chemical energy and axial conduction heat loss at the flame center. The contribution of axial and radial conduction heat losses prevails at the flame edges in Figures 8b, 9b, and 10b. In all cases axial convection heat losses are negligible, and this means that buoyancy effects do not contribute to edge flame oscillation and flame extinction so much. It is therefore seen that at the outer flame edges radial and axial conduction heat losses play important roles of flame extinction and edge flame oscillation at low strain rate flames. This is the reason why the outer edge flames in flame-disks oscillate at the low strain-rate
flames as shown in Table 1. It is also seen that curtain flow rate is not effective in the energy fractions from the comparison of Figures 8b and 9b. However, radial convection terms at the flame edges are positive differently from those at flame centers. This is because radial convection heat is transferred outwardly along the surface from the flame center and is accumulated at the individual location. As a result, the maximum heat absorption should be in the case of a maximum flame radius at the elapsed time of 0.2 s. The maximum and minimum flame radii are not so much different in panels a and b in Figure 7, whereas those are quite different in panel c. Therefore, in Figures 8b and 9b the contributions of radial convection term are nearly the same, whereas in Figure 10b the contribution of the radial convection term shows a definite maximum at the maximum flame radius (the elapsed time of 0.2 s). Even if this affects the contributions of axial and radial diffusion terms a little bit in Figure 10b, the global feature is not changed compared to those in Figures 8b and 9b. That is, the contribution of axial and radial conduction heat losses prevails at the outer flame edges. In general, maximum flame temperature as an indicator of flame strength, based on onedimensional flame response, is determined by the balance between chemical energy and conduction heat loss normal to 4243
Energy Fuels 2009, 23, 4236–4244
: DOI:10.1021/ef900138u
Geun Park et al.
the flame surface. Additive heat loss such as radial conduction heat loss and radiation heat loss therefore deteriorates the flame strength. Figures 8b, 9b, and 10b definitely show that radial conduction heat loss is the main reason to deteriorate flame strength at the flame edges, in that edge flame oscillation and flame extinction are caused by radial conduction heat loss as was shown in Table 1 and Figure 4. This is the direct reason why low strain rate flames show the shrinkage of edge flame with and without edge flame oscillation.
reactive species near the flame edge. Variation of curtain flow rate does not impact on edge flame oscillation and flame extinction because of the cancellation of these effects as is confirmed experimentally and numerically. It is also seen that the edge flame propagation velocities are always negative during shrinking and even expanding periods at low strain rate oscillating-flames. During the shrinking period the traveling-speed of edge flame increases as flame radius decreases, in that radial conduction heat loss increases in decrease of flame radius as is also confirmed numerically. This implies that the decrease of flame radius is prone to extinguish due to the dominant role of radial conduction heat loss. The comparison among energy fractions according to velocity ratio and curtain flow rate definitely stresses the important role of radial conduction heat loss. At the flame center, the axial conduction heat loss term is dominant, whereas the radiation heat loss shows a minor contribution and the others are negligible. The flame response is determined by the balance among chemical energy, mainly axial conduction heat loss, and partly radiation heat loss. At the outer flame edge axial and radial conduction heat losses prevail, whereas the radial convection heat transfer plays a role of heat absorption and the others are negligible. Notably, buoyancy effects may not impact on edge flame oscillation so much since axial convection heat loss is negligible in all cases and the change of axial flame location through varying velocity ratio do not modify the tendencies of energy fraction. The balance between chemical energy and conduction heat loss normal to the flame surface is broken at the outer flame edge. The additive radial conduction heat loss therefore deteriorates the flame strength. Consequently, radial conduction heat loss is the main reason to deteriorate flame strength at the flame edges, in that edge flame oscillation and flame extinction are caused by radial conduction heat loss.
Concluding Remarks Experimental and numerical studies on the characteristics of flame extinction have been conducted at low strain rate flames, and the following conclusion is obtained. Flame extinction modes on a C-curve can be classified into four for the present burner diameter: flame extinction through the shrinkage of the outer edge flame with edge flame oscillation and without a flame-hole in shrinking flame-disks (regime I), flame extinction through a flame-hole and the shrinkage of the outer edge flame with edge flame oscillation in shrinking flame-disks (regime II), flame extinction through a flame hole and the shrinkage of the outer edge flame without edge flame oscillation in shrinking flame-disk (regime III), and flame extinction through a flame hole without the shrinkage and oscillation of edge flame in flame-disks (regime IV). Particularly, the global strain rates for regimes I and II are less than those of turning point at all velocity ratios and curtain flow rates. The global strain rates for regimes III and IV are extend to those beyond the turning point as velocity ratio increases. This is because the increase in velocity ratio increases radial conduction heat loss at the outer flame edge part, as is confirmed in numerical simulation. In our experimental range up to the global strain rate of 110 s-1, the location of the formation of a flame-hole is not the flame center but a finite distance from the flame center. Much larger global strain rate may be required for the formation of a flame-hole at the flame center. The increase of curtain flow rate at low strain rate flames increases the local strain rate, particularly at the outer flame edge, in that the flame becomes more sustainable to flame extinction. On the contrary, the increase of curtain flow rate at low strain rate flames may reduce the population of
Acknowledgment. This work was by Pukyong National University Research Fund in 2009 (0012000200811400).
Note Added after ASAP Publication. Figure 3 was incorrect in the version of this paper published ASAP July 20, 2009; the correct version published ASAP July 27, 2009.
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