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air turbulent premixed flames at high pressure and high temperature
Proceedings of the
Proceedings of the Combustion Institute 30 (2005) 827–834
Combustion Institute www.elsevier.com/locate/proci
Burning velocity correlation of methane/air turbulent premixed flames at high pressure and high temperature Hideaki Kobayashia,*, Katsuhiro Seyamab, Hirokazu Hagiwaraa, Yasuhiro Ogamia a b
Institute of Fluid Science, Tohoku University, Sendai, Miyagi 980-8577, Japan Koube Steel Ltd., 2-3-1 Arai-cho-Shinhama, Takasago, Hyogo 676-8670, Japan
Abstract Turbulent burning velocities for methane/air mixtures at pressures ranging from atmospheric pressure up to 1.0 MPa and mixture temperatures of 300 and 573 K were measured, which covers the typical operating conditions of premixed-type gas-turbine combustors. A bunsen-type flame stabilized in a high-pressure chamber was used, and OH-PLIF visualization was performed with the pressure and mixture temperature being kept constant. In addition to a burner with an outlet diameter of 20 mm for the high-pressure experiments, a large-scale burner with an outlet diameter of 60 mm was used at atmospheric pressure to extend the turbulence Reynolds number based on the Taylor microscale, Rk, as a common parameter to compare the pressure and temperature effects. It was confirmed that Rk over 100 could be attained and that u 0 /SL could be extended even at atmospheric pressure. Based on the contours of the mean progress variable Æcæ = 0.1 determined using OH-PLIF images, turbulent burning velocity was measured. ST/SL was also found to be greatly affected by pressure for preheated mixtures at 573 K. The bending tendency of the ST/SL curves with u 0 /SL was seen regardless of pressure and mixture temperature and the Rk region where the bending occurs corresponded well to the region where the smallest scale of flame wrinkling measured as a fractal inner-cutoff approaches the characteristic flame instability scale and becomes almost constant. A power law of ST/SL with (P/P0)(u 0 /SL) was clearly seen when ST was determined using Æcæ = 0.1 contours, and the exponent was close to 0.4, indicating agreement with the previous results using the mean flame cone method and the significant pressure effects on turbulent burning velocity. 2004 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Turbulent burning velocity; High pressure; High temperature; Mean progress variable
1. Introduction Recently, research and development of premixed-type gas-turbine combustors have been
*
Corresponding author. Fax: +81 22 217 5323. E-mail address: [email protected] (H. Kobayashi).
widely performed because of their advantage of low NOx emission and low CO2 generation, especially in the case of using natural-gas-based fuel. However, premixed-type combustors tend to generate combustion induced oscillation and, in some cases, this causes serious damage to the combustor. Acoustic effects in the combustor and subsequent equivalence ratio variations seem to play an important role in such combustion oscillation;
1540-7489/$ - see front matter 2004 The Combustion Institute. Published by Elsevier Inc. All rights reserved. doi:10.1016/j.proci.2004.08.098
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however, the essential mechanism of the oscillation remains unclear. One of the most significant reasons for this is the lack of information on turbulent premixed flame in a high-pressure, hightemperature environment, although a large number of studies on turbulent premixed flames have been performed [1,2]. Combustion oscillation generates high-frequency pressure change up to several hundred hertz and a change in turbulence characteristics. Therefore, research on the effects of the pressure and temperature of turbulent premixed flames and burning velocity is important for elucidating the oscillation mechanism even for the steady condition of pressure. The authors of this paper have previously performed experimental studies on high-pressure turbulent premixed flames using a burner stabilized flame in a high-pressure chamber, keeping the chamber pressure constant, and succeeded in measuring turbulent burning velocity and the scale of the smallest wrinkling of the turbulent flame front [3,6]. Moreover, experiments have also been performed to measure the scale of wrinkling for a high-temperature premixture at high pressure, and a scale relation model between the smallest scale of flame wrinkling, turbulence length scale, and intrinsic flame instability has been proposed [7]. The aim of the present study was to extend further the measurement of turbulent burning velocity at high pressure and high temperature. In our previous measurement of turbulent burning velocity, we used an angle method for the mean flame cone determined by laser tomography using fine seeding particles and a laser sheet [3,5]. However, in the case of turbulent premixed flames, the flame region, i.e., mean flame brush, has a certain thickness, and this thickness varies along the flame cone as is reviewed by Lipatnikov and Chomiak [8]. In this case, a more suitable way to determine the turbulent burning velocity is to use the turbulent flame front determined by employing the mean progress variable, Æcæ. Therefore, measurement of turbulent burning velocity at high-pressure and high-temperature in Æcæ space is the main purpose of this study. Another purpose of this study was to investigate the relationship between the smallest scale of flame wrinkling and turbulent burning velocity. When the flame structure is in the flamelet regime, turbulent burning velocity is basically determined by the total flame area and local laminar burning velocity, meaning that the flame wrinkling scale plays an important role in the determination of burning velocity. In our previous study [7], the above-stated scale relation based on the turbulence Reynolds number, Rk, which is based on Taylor microscale, kg, exists at high-pressure but is not well confirmed at ordinary pressure. This is due to the limited range of Rk when a smallscale burner is used. To confirm the general role of Rk for turbulent premixed flames, a large-scale
burner was used for the experiment at ordinary pressure. 2. Experimental apparatus and procedure The High-Pressure Combustion Test Facility at the Institute of Fluid Science, Tohoku University, including an electrical air-heater to preheat supplied air before mixing with fuel in the chamber, was used [4,7]. The total power of the heater was 10 kW. In addition to a stainless steel nozzle-type burner with an outlet diameter of 20 mm, a newly constructed circular outlet burner with an outlet diameter of 60 mm, as shown in Fig. 1, was used. In this study, the former burner is referred to as O.D.20 or the O.D.20 burner and the latter as O.D.60 or the O.D.60 burner. In the previous study, the significant role of turbulence Reynolds number based on the Taylor microscale, Rk, was confirmed for discussion of the relationship between turbulence scale and the smallest scale of flame wrinkling. When the O.D.20 burner was used at atmospheric pressure, it was found that Rk is small and the range is limited. Also, the integral scale of turbulence was small, making it
Fig. 1. Schematic of the O.D.60 burner, used at ordinary pressure and room temperature to increase the range of the turbulence Reynolds number, Rk.
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difficult to separate the turbulence effect and the intrinsic flame instability effect. The small-scale burner, O.D.20, also eliminates the range of u 0 / SL to allow comparison of the ST/SL data with those in a high-pressure environment [7]. In this study, the O.D.60 burner was used only at atmospheric pressure because of its huge heat release when it was used at high pressure. For both burners, turbulence was generated by perforated plates upstream of the nozzle outlet. Several kinds of plates with hole diameters, d, of 1, 2, 3, 3.5, and 4 mm for the O.D.20 burner, and 9.0 and 10.5 mm for the O.D.60 burner were used. A methane(CH4)/air mixture was used for the experiments. The temperature of the mixture was 300 and 573 K at pressures of 0.1, 0.5, and 1.0 MPa for the O.D.20 burner. The equivalence ratio, /, was 0.9. In the previous study, leaner mixtures (/ = 0.6 and / = 0.8) were used at high pressure and high temperature. However, the data on the laminar burning velocity, SL, are limited, and it was still difficult to determine the correct value of SL numerically, resulting in difficulties in estimating the characteristic time scale and flame instability length scale. For accuracy of discussion of the ST/SL variations with pressure and mixture temperature, we thus decided to use only mixture at / = 0.9. Laminar burning velocity and the effects of pressure and temperature were estimated using the following equation [9]: S L ¼ S L0 ðT =T 0 Þm ðP =P 0 Þn ;
ð1Þ
where P and T are the pressure and temperature of the mixture, and T0, P0, and SL0 are, respectively, 300 K, 0.1 MPa, and laminar burning velocity at those conditions as reference values. The temperature exponent, m, and pressure exponent, n, used here were 1.9 and 0.5, respectively, based on our own experimental data [4] and numerical analysis based on the PREMIX code [10] (including CHEMKIN-II database [11] and GRI-Mech ver.2.11 mechanism [12]). The reference value, SL0, was taken from the experimental data by Law [13]. For temperature control, automatic feedback of the electrical power to the heater was activated based on the temperature measured by a thermocouple at the burner outlet, and thus temperature variation at the outlet was kept less than ±5 K. For OH-PLIF measurement, a high-resolution ICCD camera (ANDOR Technology, DH53418F) with a 1024 · 1024 pixel CCD was used. Thus, the pixel resolution was 54 lm at the measurement plane for the O.D.20 burner and 100 lm for O.D.60 burner because of the large observation area for the larger burner. A Nd-YAG laser (Spectra Physics, GCR-25010) and a dye laser with a frequency doubler (Lumonics, HD-500 and HT-1000) were used. A
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blended branch of Q1(9) and Q2(8) for (1, 0) bands of the OH radical was selected for the OH excitation, and almost all OH-LIF emission from the (0, 0) band was detected using a UV lens (Nikkon, UV-105 mm, F4.5S), a low-pass filter (WG-295), and a broad band-pass filter (UG-5). Thickness of the laser sheet was less than 50 lm at the flame position, and the maximum energy of a single laser shot was 11 mJ. Because of the huge size of the image data using the high-resolution ICCD camera, a total of fifty OH-PLIF images were analyzed for each experimental condition. After binarization, taking into account the bimodal characteristics of OHPLIF images, the instantaneous flame front was determined. In this study, for the measurement of turbulent burning velocity, ST, two-dimensional mean progress variable Æcæ profiles were calculated using the OH-PLIF images, and then an angle method and area method were used for the Æcæ contours. The precise procedure is presented and discussed in the next section. To investigate the relationship between the smallest scale of flame wrinkling and turbulent burning velocity, fractal analysis was performed, and inner-cutoff, ei, was calculated for the data of the O.D.60 burner using the circle method [14]. The caliper method [15] was also used, and comparison of the results showed that the fractal dimension slightly depends on the selected method but that the inner-cutoff was not affected by the methods. We consider this to be due to the image resolution being high enough to accurately estimate the smallest scale of flame wrinkling. Turbulence measurement was performed for the airflow using a constant-temperature hot-wire anemometer (Dantec, Streamline 90N) at the center of the burner outlet. Calibration methods, the probes, (i.e., a tungsten probe with a sensor 5 lm in diameter at room temperature and a platinum/iridium probe with a sensor 12.7 lm in diameter at high temperature), and the spectral analysis were the same as those in a previous study [7]. The transverse integral scale of turbulence, lg, was evaluated by integrating the Eulerian time correlation of velocity data, assuming TaylorÕs hypothesis and isotropy of turbulence. The transverse Taylor microscale, kg, was calculated from the energy spectrum of the turbulence to the calculate the turbulence Reynolds number, Rk. 3. Results and discussion 3.1. OH-PLIF images of flames for different size burners and the effect of pressure and temperature Figures 2A and B show the OH-PLIF image of methane/air turbulent premixed flames of / = 0.9 for the O.D.60 burner at atmospheric
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Fig. 2. OH-PLIF images for different burner sizes and effect of pressure and mixture temperature (/ = 0.9): (A) O.D.60 burner: 0.1 MPa, 300 K, u 0 = 0.92 m/s, Rk = 89.2; (B) O.D.20 burner: 0.5 MPa, 573 K, u 0 = 0.67 m/s, Rk = 60.3.
pressure and room temperature, and that for the O.D.20 burner at 0.5 MPa and a mixture temperature of 573 K. Compared to the images using the O.D.20 burner as shown in our previous paper (Fig. 1A in [6]), the flame front is very corrugated, and many broken unburned gas islands are seen. However, the tip of the flame wrinkling is not as sharp as that of the image shown for the case at high pressure in Fig. 2B. Turbulence Reynolds numbers Rk, of the condition in Fig. 2A is 89.2, and that of the condition in Fig. 2B is 60.3, meaning that the approaching flow of mixture has a distinct inertial subrange in the turbulence spectrum [7]. By using the O.D.60 burner, it was confirmed that the range of the turbulence Reynolds number can be extended, and that discussion of the flame characteristics based on Rk is possible over a wide range of pressures and temperatures. 3.2. Turbulent burning velocity measurement at high-pressure and high-temperature Figure 3 the shows the Borghi diagram of turbulent flame structure refined by Peters [16], in which all data in these experiments are plotted. Regardless of pressure, temperature, and burner size, the flame structure is in the flamelet regime, though several data at high u 0 /SL are in thin reaction zones. The progress variable c is defined when local temperature was used as cðx; yÞ ¼ ½T ðx; yÞ T u =½T b T u ;
ð2Þ
where T is the temperature, subscripts u and b are the unburned and burned sides, respectively, and x and y are the coordinates in two-dimensional images. Strictly speaking, c varies gradually in
Fig. 3. Borghi diagram modified by Peters [16] in which all data of this experiment are plotted. d, Ka, Kad, and Re are laminar flame thicknesses represented by a/SL, where a is the thermal diffusivity of unburned mixture, turbulent Karlovitz number, second Karlovitz number, and turbulence Reynolds number based on integral scale of turbulence, respectively.
the direction normal to the local flame front. However, if the scale of the flame thickness is very thin compared with the global scale of the flames, it is reasonable to consider that the instantaneous flame front is sufficiently thin to assume that c is a step function, i.e., c = 0 on the unburned side and c = 1 on the burned side, especially at high pressure. Because the OH radical concentration quickly increases at the flame front for a premixed flame, the binarized images of OH-PLIF can be used for the instantaneous boundary between c = 0 and c = 1. Thus, in this study, the mean progress variable was defined in the two-dimensional space as hci ¼
N X
cn ðx; yÞ=N;
ð3Þ
n¼1
where N is the number of images. Figures. 4A and B show Æcæ contours and mean flame cones calculated using fifty images of OHPLIF in total for the O.D.60 burner at 0.1 MPa and 300 K, and those for the O.D.20 burner at 0.5 MPa and 573 K. As the number of images is limited due to the huge size of image data for the fine resolution ICCD camera, the Æcæ contour is not yet smooth. However, the tip angle of each Æcæ contour can be determined and, by using the mean velocity at the nozzle outlet, the turbulent burning velocity, ST, depending on Æcæ can be calculated. In this figure, images of the mean flame cone are also shown. The procedure to determine the mean flame cone and ST is the same as that used in a previous study [3] for the images of the laser tomography for small seeding particles. The following equation was used: S T ¼ U sinðh=2Þ;
ð4Þ
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Fig. 5. Effect of the methods to measure turbulent burning velocity: 0.1 MPa, 300 K, O.D.60 burner.
Fig. 4. Æcæ contours and mean flame cones calculated using fifty OH-PLIF images (/ = 0.9): (A) O.D.60 burner: 0.1 MPa, 300 K, u 0 = 0.92 m/s, Rk = 89.2; (B) O.D.20 burner: 0.5 MPa, 573 K, u 0 = 0.67 m/s, Rk = 60.3.
where U and h are the mean flow rate at the nozzle outlet and tip angle of the Æcæ contours, respectively. We can see that the contour of Æcæ = 0.5 corresponds well to the mean flame cone using OH-PILF images, except for the region around the flame tip. The difference between Æcæ = 0.5 contour and the mean flame cone is caused by the difference in dealing with the tip region in the calculation code. However, because the angle method in this study does not use this tip region to measure the turbulent burning velocity, we can say that the burning velocities measured using the mean flame cone and the angle method correspond very well to those measured for the Æcæ = 0.5 contour. It is seen that the cone angles determined by Æcæ = 0.1 and the Æcæ = 0.05 contours are larger than those by Æcæ = 0.5, meaning that the turbulent burning velocities determined at Æcæ = 0.1 and Æcæ = 0.05 are larger than that at Æcæ = 0.5. As is seen in Figs. 4A and B, the contour of Æcæ = 0.1 is located at almost the same place as that of Æcæ = 0.05. In fact, the difference in the cone angle between Æcæ = 0.1 and Æcæ = 0.05 contours was less than several percentage points when the data scattering is considered, and thus the difference in turbulent burning velocity is very small. Therefore, we decided to use Æcæ = 0.1 contours for the measurement of turbulent burning velocity based on the angle method using Eq. (4). However, in some cases of small flame height, especially for the O.D.60 burner experiment, the cone angle of the Æcæ = 0.1 contour was not clearly
detected. In this case, the approximation of Æcæ = 0.1 contour to a polynomial curve whose order is higher than second was performed assuming axisymmetry of the contours, and then the total flame area was determined. Figure 5 shows the effects of methods to measure the turbulent burning velocity, i.e., the angle method and area method, indicating that the difference is sufficiently small. Thus, both methods were used depending on the Æcæ = 0.1 contour images. In this figure, we can see that, even at atmospheric pressure (0.1 MPa), high u 0 /SL over 3.0 could be attained. In our previous experiment using the O.D.20 burner at ordinary pressure, the maximum u 0 /SL was 1.5 as shown in Fig. 6 of [3,5], indicating the effectiveness of using the large-scale burner for the turbulent flame experiments at atmospheric pressure. Figure 6 shows the variations of ST/SL with u 0 / SL and the effects of pressure and mixture temper-
Fig. 6. Variations of turbulent burning velocity, ST, with turbulence intensity, u 0 , normalized by laminar burning velocity, SL, and effects of pressure and mixture temperature.
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ature up to 1.0 MPa and 573 K. We can see that the effect of pressure is significant even for a preheated mixture and that when ST and u 0 are normalized by SL at the mixture temperature, the variation of ST/SL with u 0 /SL is identical at each pressure, meaning that the pressure is the predominant parameter. This figure also implies a significant effect of the laminar burning velocity on the flame characteristics of turbulent combustion at high pressure and high temperature. 3.3. Correlation of turbulent burning velocity at high pressure and high temperature From Fig. 6, it is seen that the variation of ST/SL with u 0 /SL is not linear. This ÔbendingÕ tendency in the higher u 0 /SL region has been known and is interpreted as being the effect of such factors as flame stretch in highly turbulent flows [17]. In the case of turbulent premixed flames in the flamelet regime, turbulent burning velocity is determined by the total area of the flame front, meaning that the scale of flame front wrinkling is one of the predominant parameters of the flame area. Especially when the fractal characteristics of the instantaneous turbulent flame front are considered, the smallest scale of flame wrinkling corresponds to the inner-cutoff scale and is one of the three predominant parameters, i.e., inner-cutoff scale, outercutoff scale, and fractal dimension. In our previous research, it was found that, at high-pressure, the fractal inner-cutoff, ei, and average length scale of the vortex tube diameter in turbulent flows, lv, defined as lv = 12gk (where gk is the Kolmogorov scale) based on DNS [18], decreased with Rk, regardless of pressure and mixture temperature. The magnitude of ei was close to lv when lv was larger than the characteristic instability scale and corresponded to the maximum growth rate of Darrieus–Landau flame instability combined with the diffusive-thermal effects, li [7,19]. When Rk increased further and lv became smaller than li, ei became almost constant, while, at atmospheric pressure, the abovementioned relationship between lv, li, and ei was not clear because of the limited range of Rk, i.e., experimental limitation due to the small burner. In this study, using the O.D.60 burner, the range of Rk could be extended, and thus the comparison of ei, lv, and li was successful. Figure 7A shows the variations. We can clearly see the decrease in ei with Rk and that ei becomes almost constant when lv becomes smaller than li, indicating that the scale relation of ei, lv , and li for Rk variation exists even at atmospheric pressure. In Fig. 7B, the variation of ST/SL with Rk is also shown. It is interesting to see that the bending region of ST/SL corresponds well to the region of Rk where ei becomes almost constant. This characteristic was also seen at high pressure and
Fig. 7. Variation of the relation between ST/SL and characteristic length scales of turbulent premixed flame at 0.1 MPa and 300 K: (A) characteristic length scales; (B) turbulent burning velocity.
temperature. Although the mechanism of the ÔbendingÕ related to the smallest scale of flame wrinkling is not clear at present, when fractal characteristics of turbulent flame front are considered, a convincing explanation of this feature is that the limit of the smallest scale of flame wrinkling causes a certain limit of area increase when the Rk or u 0 /SL becomes very high. In our previous paper, an experimentally obtained general correlation of ST/SL as an equation of power law for (P/P0) (u 0 /SL), where P0 is atmospheric pressure, 0.1 MPa, was proposed [5]. In this study, a similar correlation was examined for ST/SL determined at Æcæ = 0.1 contours. Fig. 8A shows all the data at high pressure and high temperature obtained in this experiment using the parameter, (P/P0) (u 0 /SL), on a log scale. The linear correlation of ST/SL, except for smaller (P/P0) (u 0 /SL) data at each pressure and temperature, is seen. The existence of these data regions of non-linear variation on a log scale was also seen in the previous study using laser tomography and mean flame cone. Figure 8B shows that the correlation of the data before bending was removed in the region of smaller Rk. The distinct linear correlation between ST/SL and (P/P0) (u 0 /SL) is seen regardless of
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tics, laminar burning velocity, and thermal properties of the mixture including Lewis number. Thus, the correlation can be used not only for actual combustors operated at high pressure and high temperature but also for verification of turbulent combustion models including the pressure and temperature effects. Also, it will be useful for further investigation of combustion induced oscillation mechanism of premixed-type gas-turbine combustors. 4. Conclusions Measurement of turbulent burning velocities for a methane/air mixture in a high-pressure, high-temperature environment was performed using Bunsen-type burner stabilized flames and OH-PLIF in a high-pressure chamber with the pressure and mixture temperature being maintained at constant levels. The pressure range was 0.1–1.0 MPa, and the mixture temperature was 300 and 573 K. The following results were obtained:
Fig. 8. General correlation of turbulent burning velocity at high pressure and high temperature: (A) all data of this experiment; (B) the correlation in the region where smaller Rk before ÔbendingÕ was removed, i.e., in the region where the smallest scale of flame wrinkling is almost constant. The equation with coefficient of 2.9 is from previous study [6].
pressure and mixture temperature and the correlation shown in Fig. 8B is written as S T= S L ¼ 5:04 ½ðP =P 0 Þðu0 =S L Þ0:38 :
ð5Þ
In Fig. 8B, the correlation obtained in the previous study is also shown, indicating that the difference in the coefficient 5.04 (it was 2.9 in the previous study [5]) is seen due to the increase in the thickness of the flame zones downstream, while the exponent 0.38 is the same as that in the previous study in which the mechanism is interpreted to be based on the intrinsic instability of the flame front at high pressure. Therefore, the effect of pressure on ST/SL is essentially described by a power law for (P/P0) (u 0 /SL) even at high temperature, and the exponent is close to 0.4, regardless of Æcæ contours to determine ST. Based on examination of the relation between turbulent energy spectrum, smallest scale of flame wrinkling, flame instability scale, and bending characteristics of ST/SL, we can say that Eq. (5) can be well applied in the region of 12gk < li, which is determined from turbulence characteris-
1. By using a large-scale burner (O.D.60), the maximum turbulence Reynolds number based on the Taylor microscale, Rk, of more than 100 could be attained even at atmospheric pressure, and comparison with experimental results under high-pressure conditions could be performed based on Rk and u 0 /SL. 2. ST/SL measured based on Æcæ contours was affected by the pressure as well as that based on mean flame cones, as previously reported [3]. At each pressure, variations of ST/SL with u 0 /SL were identical regardless of mixture temperature when the laminar burning velocity, SL, was correctly estimated. 3. The scale relation between the averaged vortex tube diameter of turbulence, the smallest scale flame wrinkling scale measured as a fractal inner-cutoff, and the characteristic flame instability scale was confirmed even at atmospheric pressure using a large-scale burner (O.D.60). 4. A bending tendency of the ST/SL curves with increasing u 0 /SL was seen, regardless of pressure and temperature. Moreover, the Rk region of the bending corresponded to the region where the smallest scale of flame wrinkling approaches the characteristic flame instability scale and becomes almost constant, indicating that the total flame area and the scale of flame wrinkling play important roles in the determination of turbulent burning velocity, even at high pressure and high temperature. 5. A power law of ST/SL with (P/P0) (u 0 /SL) was confirmed for ST based on Æcæ = 0.1 contours, and the exponent was close to 0.4. This indicates agreement with the power law seen in the previous measurement using the mean
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flame cone, and the significant effects of pressure on turbulent burning velocity for a high temperature mixture.
Acknowledgments The authors are grateful to Prof. T. Niioka and for helpful discussions. We also acknowledge the assistance of Mr. S. Hasegawa for help in designing the apparatus. This research was supported by the Grant-in-Aid for Scientific Research of the Ministry of Education, Culture, Sports, Science and Technology, Japan.
References [1] F.A. Williams, Combustion Theory, second ed., Addison-Wesley, Redwood City, CA, 1985, p. 411. [2] D. Bradley, A.K.C. Lau, M. Lawes, Philos. Trans. R. Soc. London Ser. A 338 (1992) 359–387. [3] H. Kobayashi, T. Tamura, K. Maruta, T. Niioka, F.A. Williams, Proc. Combust. Inst. 26 (1996) 389–396. [4] H. Kobayashi, T. Nakashima, T. Tamura, K. Maruta, T. Niioka, Combust. Flame 108 (1997) 104–117. [5] H. Kobayashi, Y. Kawabata, K. Maruta, Proc. Combust. Inst. 27 (1998) 941–948. [6] H. Kobayashi, H. Kawazoe, Proc. Combust. Inst. 28 (2000) 375–382. [7] H. Kobayashi, T. Kawahata, K. Seyama, T. Fujimori, J.-S. Kim, Proc. Combust. Inst. 29 (2002) 1793–1800.
[8] A.N. Lipatnikov, J. Chomiak, Prog. Energy Combust. Sci. 28 (2002) 1–74. [9] M. Metghalchi, J.C. Keck, Combust. Flame 38 (1980) 143–157. [10] R.J. Kee, J.F. Grcar, M.D. Smooke, J.A. Miller, Report No. SAND89-8009, Sandia National Laboratories, 1993. [11] R.J. Kee, F.M. Rupley, J.A. Miller, Report No. SAND85-8240, Sandia National Laboratories, 1991. [12] C.T. Bowman, R.K. Hanson, D.F. Davidson, W.C. Gardiner Jr., V. Lissianski, G.P. Smith, D.M. Golden, M. Frenklach, H. Wang, M. Goldenberg, GRI-Mech 2.11, Gas Research Institute, 1995. Available from:
Comment Ralph Aldredge, UC Davis, USA. What mechanism do you attribute to bending of the ST/SL versus u 0 /SL curve, with increasing u 0 /SL? Do you find that this mechanism is more important for large pressure-conditions than for atmospheric? Reply. From the point of view of fractal characteristics of the turbulent flame front, the bending of the u 0 /SL is related to the phenomenon that the smallest scale of flame wrinkle, i.e., the fractal inner cutoff, becomes constant because total flame area is determined by inner cutoff scale, outer cutoff scale, and fractal
dimension. Fractal dimension is almost constant at high turbulent Reynolds number, so that we need more data especially on the fractal outer cutoff of the flame wrinkles in order to confirm it. The mechanism of the bending is identical even at atmospheric pressure. However, at high pressure, the range of turbulence Reynolds number based on the Taylor microscale is wide and the actual high-pressure combustors tends to be operated at higher turbulent Reynolds number after bending, meaning that the prediction of ST/SL may be easier than the case at atmospheric pressure.
Proceedings of the Combustion Institute 30 (2005) 827–834
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Burning velocity correlation of methane/air turbulent premixed flames at high pressure and high temperature Hideaki Kobayashia,*, Katsuhiro Seyamab, Hirokazu Hagiwaraa, Yasuhiro Ogamia a b
Institute of Fluid Science, Tohoku University, Sendai, Miyagi 980-8577, Japan Koube Steel Ltd., 2-3-1 Arai-cho-Shinhama, Takasago, Hyogo 676-8670, Japan
Abstract Turbulent burning velocities for methane/air mixtures at pressures ranging from atmospheric pressure up to 1.0 MPa and mixture temperatures of 300 and 573 K were measured, which covers the typical operating conditions of premixed-type gas-turbine combustors. A bunsen-type flame stabilized in a high-pressure chamber was used, and OH-PLIF visualization was performed with the pressure and mixture temperature being kept constant. In addition to a burner with an outlet diameter of 20 mm for the high-pressure experiments, a large-scale burner with an outlet diameter of 60 mm was used at atmospheric pressure to extend the turbulence Reynolds number based on the Taylor microscale, Rk, as a common parameter to compare the pressure and temperature effects. It was confirmed that Rk over 100 could be attained and that u 0 /SL could be extended even at atmospheric pressure. Based on the contours of the mean progress variable Æcæ = 0.1 determined using OH-PLIF images, turbulent burning velocity was measured. ST/SL was also found to be greatly affected by pressure for preheated mixtures at 573 K. The bending tendency of the ST/SL curves with u 0 /SL was seen regardless of pressure and mixture temperature and the Rk region where the bending occurs corresponded well to the region where the smallest scale of flame wrinkling measured as a fractal inner-cutoff approaches the characteristic flame instability scale and becomes almost constant. A power law of ST/SL with (P/P0)(u 0 /SL) was clearly seen when ST was determined using Æcæ = 0.1 contours, and the exponent was close to 0.4, indicating agreement with the previous results using the mean flame cone method and the significant pressure effects on turbulent burning velocity. 2004 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Turbulent burning velocity; High pressure; High temperature; Mean progress variable
1. Introduction Recently, research and development of premixed-type gas-turbine combustors have been
*
Corresponding author. Fax: +81 22 217 5323. E-mail address: [email protected] (H. Kobayashi).
widely performed because of their advantage of low NOx emission and low CO2 generation, especially in the case of using natural-gas-based fuel. However, premixed-type combustors tend to generate combustion induced oscillation and, in some cases, this causes serious damage to the combustor. Acoustic effects in the combustor and subsequent equivalence ratio variations seem to play an important role in such combustion oscillation;
1540-7489/$ - see front matter 2004 The Combustion Institute. Published by Elsevier Inc. All rights reserved. doi:10.1016/j.proci.2004.08.098
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however, the essential mechanism of the oscillation remains unclear. One of the most significant reasons for this is the lack of information on turbulent premixed flame in a high-pressure, hightemperature environment, although a large number of studies on turbulent premixed flames have been performed [1,2]. Combustion oscillation generates high-frequency pressure change up to several hundred hertz and a change in turbulence characteristics. Therefore, research on the effects of the pressure and temperature of turbulent premixed flames and burning velocity is important for elucidating the oscillation mechanism even for the steady condition of pressure. The authors of this paper have previously performed experimental studies on high-pressure turbulent premixed flames using a burner stabilized flame in a high-pressure chamber, keeping the chamber pressure constant, and succeeded in measuring turbulent burning velocity and the scale of the smallest wrinkling of the turbulent flame front [3,6]. Moreover, experiments have also been performed to measure the scale of wrinkling for a high-temperature premixture at high pressure, and a scale relation model between the smallest scale of flame wrinkling, turbulence length scale, and intrinsic flame instability has been proposed [7]. The aim of the present study was to extend further the measurement of turbulent burning velocity at high pressure and high temperature. In our previous measurement of turbulent burning velocity, we used an angle method for the mean flame cone determined by laser tomography using fine seeding particles and a laser sheet [3,5]. However, in the case of turbulent premixed flames, the flame region, i.e., mean flame brush, has a certain thickness, and this thickness varies along the flame cone as is reviewed by Lipatnikov and Chomiak [8]. In this case, a more suitable way to determine the turbulent burning velocity is to use the turbulent flame front determined by employing the mean progress variable, Æcæ. Therefore, measurement of turbulent burning velocity at high-pressure and high-temperature in Æcæ space is the main purpose of this study. Another purpose of this study was to investigate the relationship between the smallest scale of flame wrinkling and turbulent burning velocity. When the flame structure is in the flamelet regime, turbulent burning velocity is basically determined by the total flame area and local laminar burning velocity, meaning that the flame wrinkling scale plays an important role in the determination of burning velocity. In our previous study [7], the above-stated scale relation based on the turbulence Reynolds number, Rk, which is based on Taylor microscale, kg, exists at high-pressure but is not well confirmed at ordinary pressure. This is due to the limited range of Rk when a smallscale burner is used. To confirm the general role of Rk for turbulent premixed flames, a large-scale
burner was used for the experiment at ordinary pressure. 2. Experimental apparatus and procedure The High-Pressure Combustion Test Facility at the Institute of Fluid Science, Tohoku University, including an electrical air-heater to preheat supplied air before mixing with fuel in the chamber, was used [4,7]. The total power of the heater was 10 kW. In addition to a stainless steel nozzle-type burner with an outlet diameter of 20 mm, a newly constructed circular outlet burner with an outlet diameter of 60 mm, as shown in Fig. 1, was used. In this study, the former burner is referred to as O.D.20 or the O.D.20 burner and the latter as O.D.60 or the O.D.60 burner. In the previous study, the significant role of turbulence Reynolds number based on the Taylor microscale, Rk, was confirmed for discussion of the relationship between turbulence scale and the smallest scale of flame wrinkling. When the O.D.20 burner was used at atmospheric pressure, it was found that Rk is small and the range is limited. Also, the integral scale of turbulence was small, making it
Fig. 1. Schematic of the O.D.60 burner, used at ordinary pressure and room temperature to increase the range of the turbulence Reynolds number, Rk.
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difficult to separate the turbulence effect and the intrinsic flame instability effect. The small-scale burner, O.D.20, also eliminates the range of u 0 / SL to allow comparison of the ST/SL data with those in a high-pressure environment [7]. In this study, the O.D.60 burner was used only at atmospheric pressure because of its huge heat release when it was used at high pressure. For both burners, turbulence was generated by perforated plates upstream of the nozzle outlet. Several kinds of plates with hole diameters, d, of 1, 2, 3, 3.5, and 4 mm for the O.D.20 burner, and 9.0 and 10.5 mm for the O.D.60 burner were used. A methane(CH4)/air mixture was used for the experiments. The temperature of the mixture was 300 and 573 K at pressures of 0.1, 0.5, and 1.0 MPa for the O.D.20 burner. The equivalence ratio, /, was 0.9. In the previous study, leaner mixtures (/ = 0.6 and / = 0.8) were used at high pressure and high temperature. However, the data on the laminar burning velocity, SL, are limited, and it was still difficult to determine the correct value of SL numerically, resulting in difficulties in estimating the characteristic time scale and flame instability length scale. For accuracy of discussion of the ST/SL variations with pressure and mixture temperature, we thus decided to use only mixture at / = 0.9. Laminar burning velocity and the effects of pressure and temperature were estimated using the following equation [9]: S L ¼ S L0 ðT =T 0 Þm ðP =P 0 Þn ;
ð1Þ
where P and T are the pressure and temperature of the mixture, and T0, P0, and SL0 are, respectively, 300 K, 0.1 MPa, and laminar burning velocity at those conditions as reference values. The temperature exponent, m, and pressure exponent, n, used here were 1.9 and 0.5, respectively, based on our own experimental data [4] and numerical analysis based on the PREMIX code [10] (including CHEMKIN-II database [11] and GRI-Mech ver.2.11 mechanism [12]). The reference value, SL0, was taken from the experimental data by Law [13]. For temperature control, automatic feedback of the electrical power to the heater was activated based on the temperature measured by a thermocouple at the burner outlet, and thus temperature variation at the outlet was kept less than ±5 K. For OH-PLIF measurement, a high-resolution ICCD camera (ANDOR Technology, DH53418F) with a 1024 · 1024 pixel CCD was used. Thus, the pixel resolution was 54 lm at the measurement plane for the O.D.20 burner and 100 lm for O.D.60 burner because of the large observation area for the larger burner. A Nd-YAG laser (Spectra Physics, GCR-25010) and a dye laser with a frequency doubler (Lumonics, HD-500 and HT-1000) were used. A
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blended branch of Q1(9) and Q2(8) for (1, 0) bands of the OH radical was selected for the OH excitation, and almost all OH-LIF emission from the (0, 0) band was detected using a UV lens (Nikkon, UV-105 mm, F4.5S), a low-pass filter (WG-295), and a broad band-pass filter (UG-5). Thickness of the laser sheet was less than 50 lm at the flame position, and the maximum energy of a single laser shot was 11 mJ. Because of the huge size of the image data using the high-resolution ICCD camera, a total of fifty OH-PLIF images were analyzed for each experimental condition. After binarization, taking into account the bimodal characteristics of OHPLIF images, the instantaneous flame front was determined. In this study, for the measurement of turbulent burning velocity, ST, two-dimensional mean progress variable Æcæ profiles were calculated using the OH-PLIF images, and then an angle method and area method were used for the Æcæ contours. The precise procedure is presented and discussed in the next section. To investigate the relationship between the smallest scale of flame wrinkling and turbulent burning velocity, fractal analysis was performed, and inner-cutoff, ei, was calculated for the data of the O.D.60 burner using the circle method [14]. The caliper method [15] was also used, and comparison of the results showed that the fractal dimension slightly depends on the selected method but that the inner-cutoff was not affected by the methods. We consider this to be due to the image resolution being high enough to accurately estimate the smallest scale of flame wrinkling. Turbulence measurement was performed for the airflow using a constant-temperature hot-wire anemometer (Dantec, Streamline 90N) at the center of the burner outlet. Calibration methods, the probes, (i.e., a tungsten probe with a sensor 5 lm in diameter at room temperature and a platinum/iridium probe with a sensor 12.7 lm in diameter at high temperature), and the spectral analysis were the same as those in a previous study [7]. The transverse integral scale of turbulence, lg, was evaluated by integrating the Eulerian time correlation of velocity data, assuming TaylorÕs hypothesis and isotropy of turbulence. The transverse Taylor microscale, kg, was calculated from the energy spectrum of the turbulence to the calculate the turbulence Reynolds number, Rk. 3. Results and discussion 3.1. OH-PLIF images of flames for different size burners and the effect of pressure and temperature Figures 2A and B show the OH-PLIF image of methane/air turbulent premixed flames of / = 0.9 for the O.D.60 burner at atmospheric
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Fig. 2. OH-PLIF images for different burner sizes and effect of pressure and mixture temperature (/ = 0.9): (A) O.D.60 burner: 0.1 MPa, 300 K, u 0 = 0.92 m/s, Rk = 89.2; (B) O.D.20 burner: 0.5 MPa, 573 K, u 0 = 0.67 m/s, Rk = 60.3.
pressure and room temperature, and that for the O.D.20 burner at 0.5 MPa and a mixture temperature of 573 K. Compared to the images using the O.D.20 burner as shown in our previous paper (Fig. 1A in [6]), the flame front is very corrugated, and many broken unburned gas islands are seen. However, the tip of the flame wrinkling is not as sharp as that of the image shown for the case at high pressure in Fig. 2B. Turbulence Reynolds numbers Rk, of the condition in Fig. 2A is 89.2, and that of the condition in Fig. 2B is 60.3, meaning that the approaching flow of mixture has a distinct inertial subrange in the turbulence spectrum [7]. By using the O.D.60 burner, it was confirmed that the range of the turbulence Reynolds number can be extended, and that discussion of the flame characteristics based on Rk is possible over a wide range of pressures and temperatures. 3.2. Turbulent burning velocity measurement at high-pressure and high-temperature Figure 3 the shows the Borghi diagram of turbulent flame structure refined by Peters [16], in which all data in these experiments are plotted. Regardless of pressure, temperature, and burner size, the flame structure is in the flamelet regime, though several data at high u 0 /SL are in thin reaction zones. The progress variable c is defined when local temperature was used as cðx; yÞ ¼ ½T ðx; yÞ T u =½T b T u ;
ð2Þ
where T is the temperature, subscripts u and b are the unburned and burned sides, respectively, and x and y are the coordinates in two-dimensional images. Strictly speaking, c varies gradually in
Fig. 3. Borghi diagram modified by Peters [16] in which all data of this experiment are plotted. d, Ka, Kad, and Re are laminar flame thicknesses represented by a/SL, where a is the thermal diffusivity of unburned mixture, turbulent Karlovitz number, second Karlovitz number, and turbulence Reynolds number based on integral scale of turbulence, respectively.
the direction normal to the local flame front. However, if the scale of the flame thickness is very thin compared with the global scale of the flames, it is reasonable to consider that the instantaneous flame front is sufficiently thin to assume that c is a step function, i.e., c = 0 on the unburned side and c = 1 on the burned side, especially at high pressure. Because the OH radical concentration quickly increases at the flame front for a premixed flame, the binarized images of OH-PLIF can be used for the instantaneous boundary between c = 0 and c = 1. Thus, in this study, the mean progress variable was defined in the two-dimensional space as hci ¼
N X
cn ðx; yÞ=N;
ð3Þ
n¼1
where N is the number of images. Figures. 4A and B show Æcæ contours and mean flame cones calculated using fifty images of OHPLIF in total for the O.D.60 burner at 0.1 MPa and 300 K, and those for the O.D.20 burner at 0.5 MPa and 573 K. As the number of images is limited due to the huge size of image data for the fine resolution ICCD camera, the Æcæ contour is not yet smooth. However, the tip angle of each Æcæ contour can be determined and, by using the mean velocity at the nozzle outlet, the turbulent burning velocity, ST, depending on Æcæ can be calculated. In this figure, images of the mean flame cone are also shown. The procedure to determine the mean flame cone and ST is the same as that used in a previous study [3] for the images of the laser tomography for small seeding particles. The following equation was used: S T ¼ U sinðh=2Þ;
ð4Þ
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Fig. 5. Effect of the methods to measure turbulent burning velocity: 0.1 MPa, 300 K, O.D.60 burner.
Fig. 4. Æcæ contours and mean flame cones calculated using fifty OH-PLIF images (/ = 0.9): (A) O.D.60 burner: 0.1 MPa, 300 K, u 0 = 0.92 m/s, Rk = 89.2; (B) O.D.20 burner: 0.5 MPa, 573 K, u 0 = 0.67 m/s, Rk = 60.3.
where U and h are the mean flow rate at the nozzle outlet and tip angle of the Æcæ contours, respectively. We can see that the contour of Æcæ = 0.5 corresponds well to the mean flame cone using OH-PILF images, except for the region around the flame tip. The difference between Æcæ = 0.5 contour and the mean flame cone is caused by the difference in dealing with the tip region in the calculation code. However, because the angle method in this study does not use this tip region to measure the turbulent burning velocity, we can say that the burning velocities measured using the mean flame cone and the angle method correspond very well to those measured for the Æcæ = 0.5 contour. It is seen that the cone angles determined by Æcæ = 0.1 and the Æcæ = 0.05 contours are larger than those by Æcæ = 0.5, meaning that the turbulent burning velocities determined at Æcæ = 0.1 and Æcæ = 0.05 are larger than that at Æcæ = 0.5. As is seen in Figs. 4A and B, the contour of Æcæ = 0.1 is located at almost the same place as that of Æcæ = 0.05. In fact, the difference in the cone angle between Æcæ = 0.1 and Æcæ = 0.05 contours was less than several percentage points when the data scattering is considered, and thus the difference in turbulent burning velocity is very small. Therefore, we decided to use Æcæ = 0.1 contours for the measurement of turbulent burning velocity based on the angle method using Eq. (4). However, in some cases of small flame height, especially for the O.D.60 burner experiment, the cone angle of the Æcæ = 0.1 contour was not clearly
detected. In this case, the approximation of Æcæ = 0.1 contour to a polynomial curve whose order is higher than second was performed assuming axisymmetry of the contours, and then the total flame area was determined. Figure 5 shows the effects of methods to measure the turbulent burning velocity, i.e., the angle method and area method, indicating that the difference is sufficiently small. Thus, both methods were used depending on the Æcæ = 0.1 contour images. In this figure, we can see that, even at atmospheric pressure (0.1 MPa), high u 0 /SL over 3.0 could be attained. In our previous experiment using the O.D.20 burner at ordinary pressure, the maximum u 0 /SL was 1.5 as shown in Fig. 6 of [3,5], indicating the effectiveness of using the large-scale burner for the turbulent flame experiments at atmospheric pressure. Figure 6 shows the variations of ST/SL with u 0 / SL and the effects of pressure and mixture temper-
Fig. 6. Variations of turbulent burning velocity, ST, with turbulence intensity, u 0 , normalized by laminar burning velocity, SL, and effects of pressure and mixture temperature.
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ature up to 1.0 MPa and 573 K. We can see that the effect of pressure is significant even for a preheated mixture and that when ST and u 0 are normalized by SL at the mixture temperature, the variation of ST/SL with u 0 /SL is identical at each pressure, meaning that the pressure is the predominant parameter. This figure also implies a significant effect of the laminar burning velocity on the flame characteristics of turbulent combustion at high pressure and high temperature. 3.3. Correlation of turbulent burning velocity at high pressure and high temperature From Fig. 6, it is seen that the variation of ST/SL with u 0 /SL is not linear. This ÔbendingÕ tendency in the higher u 0 /SL region has been known and is interpreted as being the effect of such factors as flame stretch in highly turbulent flows [17]. In the case of turbulent premixed flames in the flamelet regime, turbulent burning velocity is determined by the total area of the flame front, meaning that the scale of flame front wrinkling is one of the predominant parameters of the flame area. Especially when the fractal characteristics of the instantaneous turbulent flame front are considered, the smallest scale of flame wrinkling corresponds to the inner-cutoff scale and is one of the three predominant parameters, i.e., inner-cutoff scale, outercutoff scale, and fractal dimension. In our previous research, it was found that, at high-pressure, the fractal inner-cutoff, ei, and average length scale of the vortex tube diameter in turbulent flows, lv, defined as lv = 12gk (where gk is the Kolmogorov scale) based on DNS [18], decreased with Rk, regardless of pressure and mixture temperature. The magnitude of ei was close to lv when lv was larger than the characteristic instability scale and corresponded to the maximum growth rate of Darrieus–Landau flame instability combined with the diffusive-thermal effects, li [7,19]. When Rk increased further and lv became smaller than li, ei became almost constant, while, at atmospheric pressure, the abovementioned relationship between lv, li, and ei was not clear because of the limited range of Rk, i.e., experimental limitation due to the small burner. In this study, using the O.D.60 burner, the range of Rk could be extended, and thus the comparison of ei, lv, and li was successful. Figure 7A shows the variations. We can clearly see the decrease in ei with Rk and that ei becomes almost constant when lv becomes smaller than li, indicating that the scale relation of ei, lv , and li for Rk variation exists even at atmospheric pressure. In Fig. 7B, the variation of ST/SL with Rk is also shown. It is interesting to see that the bending region of ST/SL corresponds well to the region of Rk where ei becomes almost constant. This characteristic was also seen at high pressure and
Fig. 7. Variation of the relation between ST/SL and characteristic length scales of turbulent premixed flame at 0.1 MPa and 300 K: (A) characteristic length scales; (B) turbulent burning velocity.
temperature. Although the mechanism of the ÔbendingÕ related to the smallest scale of flame wrinkling is not clear at present, when fractal characteristics of turbulent flame front are considered, a convincing explanation of this feature is that the limit of the smallest scale of flame wrinkling causes a certain limit of area increase when the Rk or u 0 /SL becomes very high. In our previous paper, an experimentally obtained general correlation of ST/SL as an equation of power law for (P/P0) (u 0 /SL), where P0 is atmospheric pressure, 0.1 MPa, was proposed [5]. In this study, a similar correlation was examined for ST/SL determined at Æcæ = 0.1 contours. Fig. 8A shows all the data at high pressure and high temperature obtained in this experiment using the parameter, (P/P0) (u 0 /SL), on a log scale. The linear correlation of ST/SL, except for smaller (P/P0) (u 0 /SL) data at each pressure and temperature, is seen. The existence of these data regions of non-linear variation on a log scale was also seen in the previous study using laser tomography and mean flame cone. Figure 8B shows that the correlation of the data before bending was removed in the region of smaller Rk. The distinct linear correlation between ST/SL and (P/P0) (u 0 /SL) is seen regardless of
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tics, laminar burning velocity, and thermal properties of the mixture including Lewis number. Thus, the correlation can be used not only for actual combustors operated at high pressure and high temperature but also for verification of turbulent combustion models including the pressure and temperature effects. Also, it will be useful for further investigation of combustion induced oscillation mechanism of premixed-type gas-turbine combustors. 4. Conclusions Measurement of turbulent burning velocities for a methane/air mixture in a high-pressure, high-temperature environment was performed using Bunsen-type burner stabilized flames and OH-PLIF in a high-pressure chamber with the pressure and mixture temperature being maintained at constant levels. The pressure range was 0.1–1.0 MPa, and the mixture temperature was 300 and 573 K. The following results were obtained:
Fig. 8. General correlation of turbulent burning velocity at high pressure and high temperature: (A) all data of this experiment; (B) the correlation in the region where smaller Rk before ÔbendingÕ was removed, i.e., in the region where the smallest scale of flame wrinkling is almost constant. The equation with coefficient of 2.9 is from previous study [6].
pressure and mixture temperature and the correlation shown in Fig. 8B is written as S T= S L ¼ 5:04 ½ðP =P 0 Þðu0 =S L Þ0:38 :
ð5Þ
In Fig. 8B, the correlation obtained in the previous study is also shown, indicating that the difference in the coefficient 5.04 (it was 2.9 in the previous study [5]) is seen due to the increase in the thickness of the flame zones downstream, while the exponent 0.38 is the same as that in the previous study in which the mechanism is interpreted to be based on the intrinsic instability of the flame front at high pressure. Therefore, the effect of pressure on ST/SL is essentially described by a power law for (P/P0) (u 0 /SL) even at high temperature, and the exponent is close to 0.4, regardless of Æcæ contours to determine ST. Based on examination of the relation between turbulent energy spectrum, smallest scale of flame wrinkling, flame instability scale, and bending characteristics of ST/SL, we can say that Eq. (5) can be well applied in the region of 12gk < li, which is determined from turbulence characteris-
1. By using a large-scale burner (O.D.60), the maximum turbulence Reynolds number based on the Taylor microscale, Rk, of more than 100 could be attained even at atmospheric pressure, and comparison with experimental results under high-pressure conditions could be performed based on Rk and u 0 /SL. 2. ST/SL measured based on Æcæ contours was affected by the pressure as well as that based on mean flame cones, as previously reported [3]. At each pressure, variations of ST/SL with u 0 /SL were identical regardless of mixture temperature when the laminar burning velocity, SL, was correctly estimated. 3. The scale relation between the averaged vortex tube diameter of turbulence, the smallest scale flame wrinkling scale measured as a fractal inner-cutoff, and the characteristic flame instability scale was confirmed even at atmospheric pressure using a large-scale burner (O.D.60). 4. A bending tendency of the ST/SL curves with increasing u 0 /SL was seen, regardless of pressure and temperature. Moreover, the Rk region of the bending corresponded to the region where the smallest scale of flame wrinkling approaches the characteristic flame instability scale and becomes almost constant, indicating that the total flame area and the scale of flame wrinkling play important roles in the determination of turbulent burning velocity, even at high pressure and high temperature. 5. A power law of ST/SL with (P/P0) (u 0 /SL) was confirmed for ST based on Æcæ = 0.1 contours, and the exponent was close to 0.4. This indicates agreement with the power law seen in the previous measurement using the mean
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flame cone, and the significant effects of pressure on turbulent burning velocity for a high temperature mixture.
Acknowledgments The authors are grateful to Prof. T. Niioka and for helpful discussions. We also acknowledge the assistance of Mr. S. Hasegawa for help in designing the apparatus. This research was supported by the Grant-in-Aid for Scientific Research of the Ministry of Education, Culture, Sports, Science and Technology, Japan.
References [1] F.A. Williams, Combustion Theory, second ed., Addison-Wesley, Redwood City, CA, 1985, p. 411. [2] D. Bradley, A.K.C. Lau, M. Lawes, Philos. Trans. R. Soc. London Ser. A 338 (1992) 359–387. [3] H. Kobayashi, T. Tamura, K. Maruta, T. Niioka, F.A. Williams, Proc. Combust. Inst. 26 (1996) 389–396. [4] H. Kobayashi, T. Nakashima, T. Tamura, K. Maruta, T. Niioka, Combust. Flame 108 (1997) 104–117. [5] H. Kobayashi, Y. Kawabata, K. Maruta, Proc. Combust. Inst. 27 (1998) 941–948. [6] H. Kobayashi, H. Kawazoe, Proc. Combust. Inst. 28 (2000) 375–382. [7] H. Kobayashi, T. Kawahata, K. Seyama, T. Fujimori, J.-S. Kim, Proc. Combust. Inst. 29 (2002) 1793–1800.
[8] A.N. Lipatnikov, J. Chomiak, Prog. Energy Combust. Sci. 28 (2002) 1–74. [9] M. Metghalchi, J.C. Keck, Combust. Flame 38 (1980) 143–157. [10] R.J. Kee, J.F. Grcar, M.D. Smooke, J.A. Miller, Report No. SAND89-8009, Sandia National Laboratories, 1993. [11] R.J. Kee, F.M. Rupley, J.A. Miller, Report No. SAND85-8240, Sandia National Laboratories, 1991. [12] C.T. Bowman, R.K. Hanson, D.F. Davidson, W.C. Gardiner Jr., V. Lissianski, G.P. Smith, D.M. Golden, M. Frenklach, H. Wang, M. Goldenberg, GRI-Mech 2.11, Gas Research Institute, 1995. Available from:
Comment Ralph Aldredge, UC Davis, USA. What mechanism do you attribute to bending of the ST/SL versus u 0 /SL curve, with increasing u 0 /SL? Do you find that this mechanism is more important for large pressure-conditions than for atmospheric? Reply. From the point of view of fractal characteristics of the turbulent flame front, the bending of the u 0 /SL is related to the phenomenon that the smallest scale of flame wrinkle, i.e., the fractal inner cutoff, becomes constant because total flame area is determined by inner cutoff scale, outer cutoff scale, and fractal
dimension. Fractal dimension is almost constant at high turbulent Reynolds number, so that we need more data especially on the fractal outer cutoff of the flame wrinkles in order to confirm it. The mechanism of the bending is identical even at atmospheric pressure. However, at high pressure, the range of turbulence Reynolds number based on the Taylor microscale is wide and the actual high-pressure combustors tends to be operated at higher turbulent Reynolds number after bending, meaning that the prediction of ST/SL may be easier than the case at atmospheric pressure.