Yiguang Ju, Hongsheng Guo, Kaoru Maruta and Takashi Niioka. Institute of Fluid Science, Tohoku University, ABSTRACT

Transcription

1 1 Structure and Extinction Limit for Nonadiabatic Methane/Air Premixed Flame Yiguang Ju, Hongsheng Guo, Kaoru Maruta and Takashi Niioka Institute of Fluid Science, Tohoku University, Katahira 2-1-1, Sendai 98-77, Japan ABSTRACT Extinction limit and ammability limit of stretched methane-air premixed ames are investigated numerically with detailed chemistry. Attention is paid to the eects of radiation heat loss on extinction mechanism. The predicted temperature dips agree well with the experimental data. The results show that radiation reduces ame temperature in two dierent regimes, indirect heat conduction loss and direct radiation loss. It is found that there are two distinct extinction limits, a radiation extinction limit at low stretch rate and a stretch extinction limit at high stretch rate. Flammability for stretched ame is obtained by producing a C-shaped extinction curve. INTRODUCTION Understanding of the structure and the mechanism of extinction is frequently based on the one-dimensional, planar propagation ame and on the countow ame. It is known that both radiation and stretch greatly aect the structure and extinction of laminar ames. For one-dimensional, planar propagation ame, Spalding[1] showed that extinction can be produced by radiation heat loss. On the other hand, experimental study on counterow premixed ame revealed that ame can be extinguished by only increasing the stretch rates[2]. The combined eect of radiation and stretch has been investigated theoretically and experimentally using counterow premixed ame[3,4]. However, interaction between radiation eect and stretch eect at low stretch rate is not particularly addressed. Recently, Understanding of extinction mechanism at low stretch rate and relation between the counterow ame and the planar propagation ame becomes very important for accurate determination of the ammability. Numerical study based on the one-step overall reaction and constant transport properties was conducted by Platt and Tien[4]. Their results showed that there exists a radiation limit at low stretch rate. Recent experiment in microgravity[5] made it clear that ame does quench at two dierent stretch rates. Therefore, it is necessary to understand the mechanism of these two distinct extinctions using detailed chemistry. The purpose of this study is to investigate numerically the ame structure and extinction mechanism of methane-air premixed ames in low stretch rate near lean limit. First, comparison of radiation cooling of separated ames between experiment and numerical simulation is made. Radiation distribution function is introduced to evaluate the radiative heat loss on the ame structure. Then, correlations between ame temperature and stretch rate for various equivalence ratios are obtained. Finally, a C-shaped extinction curve is presented. THEORETICAL MODEL The ame conguration analyzed in this study is the symmetrical counterow laminar premixed ame. Detailed descriptions on this ame and its mathematical model have been made in the previous studies[7,8]. In this study, the burner separation distance is xed at 1 cm for all calculations. Only one-half of the domain is solved due to the symmetry of twin ames. For radiation calculation, assumption of optical thin limit has been frequently used in examining the radiation eect on laminar ames[5]. In the present study, particular attention is paid to the ame structure and extinction mechanism in the fuel lean condition. Even at low stretch rate, ame separation

2 2 distance in the vicinity of extinction point is very small. Therefore, it is justiable to employ the optical thin model as a simplication. By assuming only CO2, H2O, CO and CH4 are emitting species, the volumetric heat ux for energy equation can be written as _q r = 4K p (T 4 T 4 1 ) ; (1) K p = P CO2 K CO2 + P H2O K H2O + P CO K CO + P CH4 K CH4 : (2) Where is the Stefan-Boltzmann constant, and T and T1 are respectively local and ambient temperatures. K p denotes the averaged Planck mean absorption coecient of the mixture. P i and K i are respectively the partial pressure and Planck mean absorption coecient of species i. Data of the Planck mean absorption coecient of the emitting species are obtained from Ref.[9]. The detailed chemical mechanism used in the numerical calculation is the C1 chemistry presented by Kee et al.[1], which includes 58 elementary reactions and 18 reacting species. Nitrogen is treated inert here. Transport properties are calculated from CHEMKIN database[11]. Thermal diusions of H and H2 are also included. The governing equation is solved by employing the modied Newton algorithm developed by Smooke[12] and Kee et al.[1]. Near the extinction limit, particularly at the extinction point, the Jacobian of the dierential equation system becomes singular. To alleviate this diculty, arclength continuation algorithm developed by Giovangigli and Smooke[7] is used. The normalization condition is given by s = dt [T (s) ds T (s )] + da ds [a(s) a(s )] : (3) The solution procedure used here is somewhat deviates from that in Ref.[7]. Stretch rate is constantly solved together with other variables. Near the extinction limit, da=ds is set to zero. On the other hand, o the extinction limit, dt =ds is set to zero. These procedure can proceed smoothly through the whole solution branch. RADIATION COOLING AND TEMPERATURE DIP To examine the radiation cooling and to demonstrate the validity of the present theoretical models, especially the radiation model, a comparison between the experimental data and the predicted results is made. The boundary conditions used here are the same as that in the experiment. Separation distance between burners is 2 cm. Velocity at the burner exit plane is kept at a constant value of 2 cm/s. The volumetric percentages,, of methane in air are respectively 6.53, 6.18 and Temperature (K) Ω=6.53 Ω=6.18 Ω=5.88 Experiment (Liu et al. 1986) Predicted data Axial coordinate, x (cm) Figure 1 Comparison of axial temperature proles between experiment and prediction for typical methane percentage,, in air Since the temperature measurementwas done with thermocouples with.5 mm diameter, a radiation correction of the measured temperature has been made here by using the expression suggested in Ref.[4].

3 3 The corrected axial temperature proles and predicted axial temperature proles are shown in Fig.1. It can be seen that, both the experimental data and the predicted data show that there is a temperature dip with its minim at the stagnation plane for each curve. Since the radiation heat loss is proportional to the volume of the emitting gas, as shown in Fig.1, As the separation distance between the twin ames increases, the magnitude of this temperature dip also increases. As a result, this temperature dip induces a heat conduction loss downstream of the reaction zone. Therefore, radiation cooling to premixed ame consists of two parts, a direct radiation heat loss through gas emitting within and before the reaction zone and an indirect conduction heat loss due to the existence of temperature dip caused by radiation downstream of the reaction zone. At high stretch rate, since reaction zone is very thin and diusion of emitting species is suppressed, the indirect conduction heat loss plays an important role to ame cooling. At low stretch rate, however, since ame thickens and diusion processes becomes dominant, direct radiation heat loss within and before the reaction zone may becomes very important. 15 b Flame temperature (K) d a Ω=4.9 (Φ=.491) Stretch extinction limit Radiation extinction limit c Stretch rate (1/s) Figure 2 Flame temperature prole plotted as a function of stretch rate FLAME STRUCTURE AND EXTINCTION MECHANISM Figure 2 shows the variation of the ame temperature (maximum temperature) with stretch rate for methane percentage in air = 4:9. Starting from point a, with the increase of stretch rate, ame temperature increases dramatically. This increase of temperature is attributed to the Lewis eect. Since Lewis number of fuel lean methane air mixture is slightly less than unit, an increase of stretch rate causes a larger energy gains due to the increase of the decient reactant through diusion than the energy loss to external streamlines through conduction. As shown in Fig.2, at stretch rate of 32 1/s (point b), ame temperature reaches its maxim. With a further increase of stretch rate, ame is pushed to the stagnation plane and reaction cannot be completed because of the reduced residence time. As a result, ame temperature decreases and eventually leads to extinction at point c. This extinction is caused by stretch eect, so we call it "stretch extinction" hereafter. On the other hand, a decrease of stretch rate from point a results in a continuous drop of ame temperature. At point d, a new extinction point emerges. Since this extinction is mainly caused by the radiation heat loss, we name it "radiation extinction limit", as a distinction to the stretch extinction limit.

4 4 Flame separation distance (cm) 1.5 Ω=4.9 (Φ=.491) d a b c Stretch rate (1/s) Figure 3 Flame separation distance plotted as a function of stretch rate The corresponding ame separation distance of Fig.2 is shown in Fig.3. Here, the ame position is dened by the location with maximum CH concentration. It can be seen that, at point a (stretch rate is about 6. 1/s), ame separation distance reaches its maximum. Either an increase or a decrease of stretch rate will result in a decrease of ame separation distance. The behavior of the increasing ame separation distance with the decrease of stretch rate has been well known. However, the behavior of decreasing ame separation with the decrease of stretch rate is new. At point a, there is a large temperature dip on the temperature prole. Indirect conduction heat loss downstream of the reaction zone reduces ame temperature and causes ame to narrow its separation distance. On the other hand, near the extinction point d, ame eventually moves onto the stagnation plane with the decrease of stretch rate. Flame separation distance is so small that there is no temperature dip behind the reaction zone. Thus, the indirect conduction heat loss can be negligible. However, the direct radiation heat loss within and before the reaction zone becomes increasingly important as the stretch rate decrease. At stretch rate of.99 1/s. ame is extinguished in the way of incomplete combustion caused by the direct radiation heat loss. Therefore, the direct mechanisms for stretch extinction and radiation extinction of the stretched ames are very dierent, although they share a common phenomenon of the incomplete combustion at the extinction limits..3 6 Fration of radiation heat loss.2.1 d a b Ω=4.9 (Φ=.491) c 4 2 Radiation heat loss (J/m 2 s) Stretch rate (1/s) Figure 4 Radiation fraction, f r (), plotted as a function of stretch rate

5 5 as Toevaluate the distribution of the radiation heat loss, a radiation distribution function f r (x) is dened f r (x) = Z x Z 1 _q rdx= 1 _q cdxi : (4) Where _q r and _q c are respectively the volumetric radiation heat loss and chemical heat release per second. Therefore, f r (x) represents the fraction of radiation heat loss from left boundary to location x in the total chemical heat release. As x approaches to zero, f r () denotes the total radiation fraction in the total chemical heat release. The variation of radiation fraction with stretch rate is shown in Fig.4. At stretch extinction limit (point c), radiation fraction is less than 1%. At point a, where ame separation distance reaches its maxim, radiation fraction increases to 12%. This radiant heat loss is so high that ame loses its ability to propagate upstream. A further decrease of stretch rate results in a decrease of ame separation distance (see Fig.3) and a dramatic increase of radiation fraction. At radiation extinction limit (point d), the radiation heat loss even reaches 25% in the total chemical heat release. Therefore, stretch extinction and radiation extinction occur in two dierent extremes. The dashed line in Fig.4 represents the total radiation heat loss. It can be clearly seen that total radiation heat loss increases with increasing ame separation distance (abc in Fig.3). At point a, both ame separation distance and radiation heat loss take their maximum values. Although a further decrease of stretch rate causes an increase of radiation fraction, the total radiation heat loss still decreases due to the decreasing ame separation. The increasing dependence of radiation fraction on decreasing stretch rate is attributed to the decrease of total chemical heat release. Since chemical heat release depends on the mass burning rate, as the stretch rate goes down, the mass burning rate decreases and thus leads to a decrease of chemical heat release. On the other hand, since radiation heat loss depends on the volume and the temperature of emitting gas, decrease of stretch rate will leads to an increase of total radiation heat loss if the ame separation distance does not change. To compensate the decrease of chemical heat release and to reduce radiation heat loss, ame will adjust its location to narrow its separation. In addition, for methane-air ame, Lewis-eect plays an increasingly positive contribution to enhance the chemical reaction as reaction zone moves towards the stagnation plane. Therefore, strictly speaking, the emerge of radiation extinction limit is the result of competition between radiation eect and Lewis eect. To demonstrate the dierence of the distributions of radiation heat loss over the ames at dierent stretch rates, variations of radiation distribution function and chemical heat release with axial distance are plotted in Fig.5. For stretch rate a = 1 1/s, radiation heat loss before and within the reaction zone, which directly reduces ame temperature, is less than 1% of the total chemical heat release. Thus, most of the radiation heat loss occurs downstream of the reaction zone and only weakly aects the ame temperature through the indirect conduction heat loss. However, for stretch rate a = 1. 1/s, Figure 5 shows that, all the radiation heat loss occurs before and within the reaction zone. Thus, direct radiation heat loss is the true mechanism inducing the radiation extinction at low stretch rate. Flame temperature proles correlated with stretch rate near ammability of counterow premixed ame is shown in Fig.6. It can be seen that each stable ame in the range of volumetric fuel percentage between 4.23 and 4.6 has two extinction limits, the radiation limit and stretch limit.

6 6 Radiation distribution function, fr(x) Ω=4.9 (Φ=.491) a=1 1/s a=1. 1/s 1.5 Axial coodinate, x (cm) Chemical heat release (J/m s ) Figure 5 Radiation distribution function f r (x) and chemical heat release for stretch rate a =1 1/s and a=1. 1/s 14 Ω=4.6 Flame temperature (K) Stretch rate (1/s) Figure 6 Flame temperature proles plotted as a function of stretch rate for various fuel percentages in air EXTINCTION CURVE Variation of extinction limit dened by the stretch rate, where extinction occurs, with equivalence ratio is shown in Fig.7. Numerical calculation is made by using two dierent data of the Planck mean absorption coecients, in which data given be Tien[9] (model I) is widely accepted while data given in Ref.[13] (model II)is reported to far under estimate the gas emitting. Experimental data was obtained in normal and microgravity[6,14]. It can be seen that, for adiabatic ame, extinction limit decreases monotonically with the decrease of equivalence ratio. However, for nonadiabatic ame, numerical results obtained using the two dierent radiation models show that there are two branches of extinction limits. The upper branch is the stretch extinction branch while the low branch represents the radiation extinction branch. The emerging point of the two branches denotes the ammability limit of the stretched ames. As shown in Fig.7, radiation heat loss almost has no eect on the stretch extinction limit at high equivalence ratio. For equivalence ratio below.5, however, radiation dramatically aects both the stretch extinction limit and the radiation extinction limits. Since radiation is under evaluated by the model II, the predicted ammability of stretched ames is smaller than that calculated by the received model I. Although there is

7 REFERENCES 7 a little discrepancy between the experimental data and the predicted data, considering the simple model of radiation and the eect of burner diameter in experiment, the agreement is quite good. Velocity gradient, 2v/d (1/s) Adiabatic flame Radiation model I[9] Radiation model II[13] Experiment[6,14] Equivalence ratio Figure 7 Comparison of extinction limits as a function of equivalence ratio obtained by experiments and numerical calculations using two dierent radiation models CONCLUSION Flame regimes and extinction limits of premixed methane-air ames with radiation heat loss are calculated numerically with detailed chemistry. the present calculation reproduced well the temperature dip measured in the experiment. Furthermore, the present results showed that radiation heat loss has a signicant eects on ame structure and extinction limit through two dierent ways, indirect heat conduction loss downstream the reaction zone and direct radiation heat loss within and before the reaction zone. At high stretch rate, indirect conduction heat loss is the main route to aect the ame temperate. At low stretch rate, however, the direct radiation heat loss is the dominant mechanism to quench the ame. The results further showed that, for equivalence ratio between.42 and.49, the ame temperature prole is O-shaped and there are two extinction limits for each stable ame, a radiation limit at low stretch rate and the stretch limit at high stretch rate. The radiation limit is the result of competition between radiation eect and Lewis eect. It is found that ammability of stretched methane-air premixed ame is far less than that of one-dimensional, planar propagation ame. The present results agree well with the experimental data. References [1] Spalding, D.B., Proc. Soc. London, A24, 83-1(1957). [2] Tsuji, JSME-ASME Joint Thermal Engr. Conf. P.11, [3] Sohrab, S.H. and Law, C.K., Int. J. Heat Mass Transf., 27:291-3, [4] Liu, G.E., Ye, Z.Y. and Sohrab S.H., Combust. Flame 64:193-21(1986). [5] Platt J.A. and Tien J.S., Chemical and Physical Processes in Combustion, 199 Fall Technical Meeting, Easten Section of the Combustion Institute, 199. [6] Maruta, K., Yoshida, M., Ju, Y. and Niioka, T., Twenty-Sixth Symp.(Int.) on Combustion, 1996, to appear. [7] Giovangigli, V. and Smooke, M.D., Combust. Sci. and Tech. 53:23-49, 1987.

8 REFERENCES 8 [8] Kee, R.J., Miller, J.A., Evans, G.H. and Dixon-Lewis,G., Twenty-Second Symp. (Int.), p.1479, [9] Tien, C.L., Advances in Heat Transfer, vol.5, , [1] Kee, R.J., et al., Sandia Report, SAND85-824(1985). [11] Kee, R.J., et al., Sandia Report, SAND (1986). [12] Smooke, M.D., Journal of Computational Physics, 48, 72-15(1982). [13] Kuznetsov, V.R. and Sabelnikov, V.A., Turbulence and Combustion, Hemisphere Publishing Corporation, New York, p.27-28, 199. [14] Law, C.K., Zhu, D.L., and Yu, G., Twenty-First Symp. (Int.), p.1419, 1986.