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Dynamic behavior of a freely-propagating turbulent premixed flame under global stretch rate oscillations
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Proceedings of the
Proceedings of the Combustion Institute 32 (2009) 1795–1802
Combustion Institute www.elsevier.com/locate/proci
Dynamic behavior of a freely-propagating turbulent premixed flame under global stretch-rate oscillations Shigeru Tachibana a,*, Junpei Yamashita b, Laurent Zimmer c, Kazuo Suzuki d, A. Koichi Hayashi b a
Aerospace Research and Development Directorate, Japan Aerospace Exploration Agency, 7-44-1 Jindaiji-Higashi, Chofu, Tokyo 182-8522, Japan b Department of Mechanical Engineering, Aoyama Gakuin University, 5-10-1 Fuchinobe, Sagamihara, Kanagawa 229-8558, Japan c EM2C laboratory, UPR 288 CNRS-Ecole Centrale Paris, Grande voie des vignes 92295 Chaˆtenay-Malabry, France d Aviation Program Group, Japan Aerospace Exploration Agency, 7-44-1 Jindaiji-Higashi, Chofu, Tokyo 182-8522, Japan
Abstract Dynamic features of a freely propagating turbulent premixed flame under global stretch rate oscillations were investigated by utilizing a jet-type low-swirl burner equipped with a high-speed valve on the swirl jet line. The bulk flow velocity, equivalence ratio and the nominal mean swirl number were 5 m/s, 0.80 and 1.23, respectively. Seven velocity forcing amplitudes, from 0.09 to 0.55, were examined with a single forcing frequency of 50 Hz. Three kinds of optical measurements, OH-PLIF, OH* chemiluminescence and PIV, were conducted. All the data were measured or post-processed in a phase-locked manner to obtain phase-resolved information. The global transverse stretch rate showed in-phase oscillations centering around 60 (1/s). The oscillation amplitude of the stretch rate grew with the increment of the forcing amplitude. The turbulent flame structure in the core flow region varied largely in axial direction in response to the flowfield oscillations. The flame brush thickness and the flame surface area oscillated with a phase shift to the stretch rate oscillations. These two properties showed a maximum and minimum values in the increasing and decreasing stretch periods, respectively, for all the forcing amplitudes. Despite large variations in flame brush thickness at different phase angles, the normalized profiles collapse onto a consistent curve. This suggests that the self-similarity sustains in this dynamic flame. The global OH* fluctuation response (i.e. response of global heat-release rate fluctuation) showed a linear dependency to the forcing velocity oscillation amplitudes. The flame surface area fluctuation response showed a linear tendency as well with a slope similar to that of the global OH* fluctuation. This indicated that the flame surface area variations play a critical role in the global flame response. Ó 2009 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Flame dynamics; Flame response; Low-swirl burner; Turbulent premixed flame; Stretch rate
*
Corresponding author. Fax: +81 422 40 3440. E-mail address: [email protected] Tachibana).
(S.
1540-7489/$ - see front matter Ó 2009 The Combustion Institute. Published by Elsevier Inc. All rights reserved. doi:10.1016/j.proci.2008.06.206
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1. Introduction The turbulent premixed flame stabilized by the low-swirl burner (LSB) has been an active subject for investigating detailed structure of turbulent premixed flames for more than a decade. The flame is a close approximation of a freely propagating planar turbulent premixed flame in the core flow region, which is considered the most fundamental configuration. Therefore, essential characteristics of turbulent premixed flames, like turbulent flame propagation speed, can be investigated [1–3]. In these works, swirl numbers were adjusted so that the flame brush is locally perpendicular to the incoming reactant flow. Our focus in this study is to investigate how the flame behaves when cyclic perturbations are imparted to the swirl flow. The LSB generates a divergent flow by the centrifugal forces due to the weak swirl component of the flow. A lifted flame is stabilized in the manner of freely propagating premixed flame at a balancing position between the reactant flow speed and the flame propagation speed. Cyclic oscillations of the swirl flow result in cyclic motions of the divergent flow field. The divergent flow can be characterized by the global stretch rate as shown in previous literatures (e.g. Ref.[4]). Therefore, the unsteady flow field in this study can be characterized by the global stretch rate oscillations. There are a few studies in the literatures on the dynamic feature of premixed flames under global stretch rate oscillations. Among them are an early investigation of unsteady laminar diffusion and premixed counter flow flames [5], numerical studies of a laminar flame response in oscillating counter flow [6,7] and an experimental study of the response of a laminar wall stagnating premixed flame under stagnation plate oscillations [8]. To the best of our knowledge, there has yet to be a study of global stretch oscillation on turbulent premixed flames. One may conduct such an experiment utilizing wall-stagnating flow or counter flow configurations. However, there are several factors, like the effects of heat loss from the wall and pressure gradient in the flow field that should be dealt with carefully. The LSB flame is free from these constraints and is more suitable to investigate the effect of unsteady stretch rate on turbulent flame structure. This kind of experiments will add insights into the dynamic feature of turbulent premixed flame. For instance, it is shown that turbulent flame brush thickness is strongly modified by the dynamic variations of global stretch rate. Turbulent flame brush thickness is an important characteristic scale that describes the region where reaction is taking place and has been reported in many previous works. Key features like self-similarity and spatial development of this scale were widely examined in the review of Lipatnikov and
Chomiak [9]. Dynamic features of the flame thickness were included in two previous works [10,11] on flame response to normal acoustic excitation. In these works, the self-similarity was implicitly indicated by the fact that a fitting equation utilizing the thickness worked well. But beyond these works, this feature has not been widely reported. It is interesting to look at if the self-similarity is sustained in the present dynamic flame as well. Another aspect is the response of the flame to inlet velocity oscillations. The flame response function and its phenomenological background have been studied with acoustically forced oscillating flames in previous works [12,13]. It was reported that nonlinear heat-release responses were observed at high velocity oscillation amplitudes for a high-swirl [12] and a bluff body [13] flames. The nonlinearity was considered to be due to a kinematic distortion process of the flame front. The flame stabilization mechanism of the LSB flame is clearly different from those of the high-swirl and the bluff-body flames. For instance, the LSB flame is expected to be less affected by separated vortices from solid boundaries, like a bluff body or a corner step. Investigating how the LSB flame responds to forced oscillations will add an insight into the flame response study. The objective of this work is to characterize the effect of unsteady global stretch rate on the turbulent flame. Three kinds of optical measurements, OH-PLIF, OH* chemiluminescence and PIV, were conducted. All the data were measured or postprocessed in a phase-locked manner to obtain phase-resolved mean profiles of the flame structure and the flow field. The responses of the fluctuations of the global OH* intensity and the flame surface area in the core flow region to the inlet velocity oscillations were addressed as well. 2. Experimental arrangements 2.1. Experimental system and conditions Figure 1 shows the configuration of the lowswirl burner. The design is similar to the 5 cm-
Fig. 1. Configuration of the jet type low-swirl burner. Vertical view of the burner (left) and horizontal view of the swirl generator (right).
S. Tachibana et al. / Proceedings of the Combustion Institute 32 (2009) 1795–1802
jet LSB appeared in the work of Cheng et al. [14]. The burner is composed of a circular pipe nozzle with a 53 mm diameter, a swirl generator and a perforated plate. A divergent flow is produced by the weak swirl generator and a lifted flame is stabilized in the manner of freely propagating premixed flame. Methane and air are well mixed by a static mixer before entering the burner. Swirl number, S, for the jet-LSB is given by the following expression [15]: S¼
pR2 Q2j cos a 4pR2j ðQm þ Qj Þ2
:
ð1Þ
Here, a is the inclined angle of the air jets, R and Rj are the radii of the circular pipe nozzle and the secondary air jet orifice, respectively. Qm and Qj are the mass flow rate of the mixture and the swirl jets, respectively. The schematic of the experimental system is shown in Fig. 2. In this study, the swirl air flow rate was modulated in a cyclic manner by implementing a high-speed valve (the MOOG D633 DDV) in the secondary air line at the location just before the line was separated into four branches which were connected with the four tangential jets. The cyclic swirl oscillations produce an oscillatory divergent flow. The valve was controlled by the voltage signal which was generated by a signal generator. Sinusoidal signal was used as the command signal. With a single frequency of 50 Hz, the amplitude of the sinusoidal signal was varied to produce different magnitudes of the swirl oscillations. The bulk flow velocity was 5 m/s. Equivalence ratio of the methane-air mixture was 0.80. The nominal mean swirl number, which can be defined by the steady secondary air flow rate before the plenum chamber, was 1.23. All these flow conditions were fixed throughout this study. The relative velocity oscillation amplitude, which is defined as the ratio of the zero-to-peak amplitude of the phase-locked mean axial velocity, V0 , to the mean value of the phase-locked mean velocity, V , at the location of x = 0 mm and
Fig. 2. Schematic of the experimental setup. The LSB is equipped with the DDV valve in the secondary air line to impart cyclic perturbations on the swirl jet flow. The valve command signal is the reference signal for the phase-locked treatments.
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y = 10 mm, was used as the parameter which expresses oscillation magnitude. All the zero-topeak values p in this paper were calculated by multiplying 2 by the standard deviation values of the phase-resolved data. Seven velocity oscillation amplitudes, V 0 =V ¼ 0:09, 0.24, 0.27, 0.36, 0.44, 0.51 and 0.55, were examined in this study. 2.2. Measurement system and data processing A phase-locked OH-PLIF measurement, a time-resolved OH* chemiluminescence measurement and a high-speed PIV measurement were conducted. For the OH-PLIF excitation, a dye laser (Spectron Laser Systems, 4000G with Rhodamine 590) pumped by an Nd:YAG laser (Spectron Laser Systems, SL 825G-400 mJ) was used. The wavelength of the laser beam after the KDP doubling crystal was 283.636 nm with the pulse energy of 10 mJ. This wavelength pumps the Q1 (8) transition of the A2R+ X2P (1,0) band. An ICCD camera (Princeton Instruments, PI-MAX) with the UV-Nikkor lens and a set of optical filters (Schott UG-5 and WG-305) was used for capturing the OH-PLIF images. The resolution was 256 512 pixels with the field of view of 32.7 65.5 mm2. The ICCD gate width was 10 ns. Phase-locked measurement was carried out for 16 phase angles from 0 to 337.5° with a step of 22.5°. The valve control signal was used as the reference signal. Zero-degree angle was defined as the zero-crossing point with a positive slope. For each phase angle, 500 images were captured. The acquired PLIF images were post-processed to obtain the statistical feature of the flame structure like mean progress variable, c(x, y), and mean flame surface density, r(x, y). The post-processing procedures for calculating c(x,y) and r(x, y) were similar to those of ref. [13]. Window size for the flame surface density calculation was 9 9 pixels (about 1.15 1.15 mm2). The time-resolved global OH* chemiluminescence measurement was conducted with a similar way to refs. [12,13] by utilizing a photo-multiplier system (Fig. 2). The light collecting lens gathered spontaneous light emission from the global flame. The voltage signal from the photo-multiplier was recorded with a sampling frequency of 51.2 kHz. Simultaneously, the valve command signal was recorded on another channel and used as the reference signal for the phase-locked analysis. The number of data points was 1,015,808, which are corresponding to 992 cycles for the frequency of 50 Hz. The acquired data were post-processed to derive the phase-locked mean intensity profiles of the global OH*. The simultaneously obtained valve command signal was used for tagging the phase-angle information on the OH* data. The tagged data were sorted according to the phaseresolved bins. The sorted data were averaged in each bin. The phase resolution of a bin was 0.7°.
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The time-resolved PIV measurement was carried out to acquire phase-resolved velocity field. The PIV system was composed of a continuouswave Nd:YAG laser (KANOMAX, CW532-5W) with laser sheet optics and a high-speed camera (Photron, FASTCAM-APX RS). The resolution was 512 512 pixels with the field of view of 60 60 mm2. The camera was operated at a sampling frequency of 5000 Hz with an exposure time of 100 lsec. The valve command and the camera exposure timing signals were simultaneously recorded for the phase-locked post-processing as in the case of the OH* measurement. In one sequence, 5099 images, which are corresponding to almost 50 cycles, were recorded. Vector calculation was done by the DaVis 7.2 software of LaVision. The cross-correlation method with a multi-pass iteration mode (from 64 64 to 16 16 pixels) was applied. Only a validation with the peak ratio factor of 1.3 was implemented and no filter was used. The phase resolution was 11.25*. The number of data in each bin was about 150. 3. Results and discussion 3.1. The unsteady velocity field The mean velocity fields at two phases are shown in Fig. 3 to illustrate typical flow fields corresponding to a low (Fig. 3a) and a high (Fig. 3b) stretch rates during an oscillation cycle for V 0 =V ¼ 0:44. The contour map indicates the velocity magnitude in axial direction with streamtraces to show the mean flow patterns. The low and high stretch rates can be recognized by the narrower and wider flow discharge angles. This trend is quantitatively identified in Fig. 4 by the phase-locked mean global stretch rates at three velocity forcing amplitudes. The global stretch rate, sj, is defined by the gradient of transverse velocity in transverse direction, i.e., j dU/dx.
Fig. 4. Phase-locked mean global stretch rates at y = 10 mm for three forcing amplitudes. Flow conditions are same with those of Fig. 3. Symbols: Square: V 0 =V ¼ 0:55, Delta: V 0 =V ¼ 0:44, Right triangle: V 0 =V ¼ 0:27. Curves are the 6th order polynomial fittings.
The gradient was deduced by applying a linear-fitting approximation to the transverse velocity data, which has 23 data points, in the range of 10 mm < x < 10 mm at an axial position of y = 10 mm. The stretch rates clearly show inphase oscillations centering around j 60(1/s). The oscillation amplitude of the stretch rate grows with the increment of the forcing amplitude. Except for the amplitude values, those profiles have a similar distribution with a small phase shifts. The distributions deviate slightly from sinusoidal functions. The wave forms at the minimum positions are sharper compared to the more rounded forms at the maximums. We consider that to be a feature of this specific system for generating stretch oscillations by the secondary tangential jet oscillations. Phase-resolved profiles of the unsteady velocity in axial direction at the location of x = 0 mm, y = 10 mm are shown in Fig. 5. The oscillation amplitude of the axial velocity grows with the increment of the forcing amplitude as can be seen for the stretch rate in Fig. 4. As
Fig. 3. Phase-locked mean velocity fields at two phase angles, (a) low stretched case (h = 45°) and (b) high stretched case (h = 225°). Grayscale contour indicates the axial velocity magnitude. Bulk velocity = 5 m/s, equivalence ratio=0.80, forcing frequency = 50 Hz, V 0 =V ¼ 0:44.
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Fig. 5. Phase-locked mean axial velocity at x = 0 mm,y = 10 mm for three forcing amplitudes. Flow conditions are same with those of Fig. 3. Symbols: Square: V 0 =V ¼ 0:55, Delta: V 0 =V ¼ 0:44, Right triangle: V 0 =V ¼ 0:27. Curves are the 6th order polynomial fittings.
described in Section 2.1, the zero-to-peak amplitude relative to the mean value of each profile is used for the representative value indicating the velocity oscillation amplitude. 3.2. Unsteady behavior of the flame structure In this section, the unsteady behavior of the turbulent flame structures is discussed with the post-processed data of OH-PLIF measurement. Only the core flow region, which is bounded by x = ± 14 mm, was chosen as the field of interest to avoid dealing with the gas dilution effect and the shear flow effect which exist in the outer swirl region. Figure 6 shows four sets of two-dimensional (2-D) distributions of the phase-locked mean progress variable and the mean flame surface density for V 0 =V ¼ 0:44. Considering the symmetric feature of the distributions, only the right-hand sides of the core region are displayed here. For convenience, the x-axis of mean progress variable distribution was inverted and shown on the left-hand side. The corresponding distribution of mean flame surface density is shown on the right-hand side. It can be seen that the flame structure varies largely in axial direction in response to the flow-field oscillations. For instance, flame brush thickness at the phase angle of 135° (Fig. 6b, left) is about 1.5 times larger than that of 315° (Fig. 6d, left). At h = 315°, flame fronts are confined to a relatively narrower horizontal band along the c = 0.50 contour (Fig. 6d, right), while those of h = 135° are distributed in a wider thickness (Fig. 6b, right). The flame liftoff height shows variations also. In the four phase angles, the flame position at h = 45 and 225 show the highest and lowest values, respectively. The thickness of c(x, y) and r(x, y) for h = 45 and 225° are in-between those of h = 135 and 315°. To see the phase-relations between the unsteady flame structure and the velocity field,
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the flame brush thickness, the flame lift-off height and the global stretch rate are plotted against the phase angle in Fig. 7. Averaging the 2-D mean progress variable distribution in horizontal direction over the core region gives a 1-D distribution of mean progress variable, c1D(y), in axial direction. The flame brush thickness, d, and the flame lift-off height were defined as the distance between c1D = 0.10 and 0.90 and the axial position of c1D = 0.50, respectively. The global stretch rate shown in this figure was conditioned on the c1D = 0.01 position which can be considered as the leading edge of the flame front. In each phase-locked mean velocity field data, an axial position closest to the c1D = 0.01 position was chosen to calculate the transverse stretch rate. In Fig. 7, it can be seen that the flame brush thickness and the lift-off height oscillate with phase shifts to the forced stretch rate oscillations. The flame lift-off height shows an inverted trend against the stretch rate. This makes sense since the stretch rate is a direct measure of the decay rate of axial velocity in axial direction and the flame balancing position is controlled by the decaying velocity profile. On the other hand, the flame brush thickness shows a different trend. The thickness oscillates with a phase shift to the stretch rate oscillations. It shows a peak and a valley in the periods where the stretch rate has a positive and negative slopes, respectively. For instance, at h = 135 and 315°, the stretch rates themselves are almost the same, but the corresponding flame brush thicknesses are very different. The thickness of h = 135° has a value almost 1.5 times larger than that of h = 315°. The positive/negative sign of the gradient in time evolution of the stretch rate seems to have a dominant effect on the dynamic behavior of the flame thickness. It is interesting to note that the self-similarity of the mean progress variable profiles reported in refs.[9–11] is observed in this dynamic flame as well. Figure 8 shows the mean progress variable profiles normalized by the flame brush thickness at different phase angles. Despite large variations in flame brush thickness at different phase angles, the normalized profiles collapse onto a consistent curve. Revolving the 2-D flame surface density distribution around y-axis provides an estimate of the total flame surface area in the core volume. The relative flame surface area, R/R0, is shown in Fig. 9. The area of a circle with a radius of the core region (14 mm) is used as the reference value and denoted as R. One can see that the profile of the relative flame surface area is very similar to that of the flame brush thickness. This implies that the change of the flame surface area is due to the change of flame brush thickness or, in other words, large scale flame wrinkles, and not due to the change of fine scale wrinkles.
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Fig. 6. Mean progress variable and mean flame surface density distributions for phase angles of (a) 45, (b) 135, (c) 225 and (d) 315 degrees. Left and right in each figure show the mean progress variable (x-axis inverted) and the mean flame surface density, respectively. Flow conditions are same with those of Fig. 3.
Fig. 7. Comparison of the phase-resolved profiles of the flame brush thickness, the flame lift-off height and the global stretch rate. Flow conditions are same with those of Fig. 3. Symbols: Square: Flame brush thickness, Delta: Flame lift-off height, Gradient: Global stretch rate conditioned on c1D = 0.01. Curves are the 6th order polynomial fittings.
To see if the observed dynamic features of d and R/R0 in Figs. 7–9 are unique for all the oscillation amplitudes or not, phase relations among the stretch rate and these two properties were investigated. The phase angles of maximum and
Fig. 8. Mean progress variable profiles normalized by the flame brush thicknesses for eight different phase angles. Flow conditions are same with those of Fig. 3.
minimum of the three properties are shown in Fig. 10. These angles were retrieved from the 6th order polynomial fitting curves of the data to remove spurious trends in the profiles. The maximum positions of d and R/R0 stay around 135° and are in-between the phase angles of the minimum and maximum stretch rates for all oscillation amplitudes (Fig. 10a). On the other hand, the minimum positions of the two properties
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Fig. 9. Phase-resolved profile of the relative flame surface area. The flame brush thickness profile is shown for comparison. Flow conditions are same with those of Fig. 3.
Fig. 11. Responses of the fluctuations of the relative flame surface area in the core region and the global OH* intensity. Flow conditions are same with those of Fig. 3. Lines are linear fittings of the data.
locate in the other side of the two boundaries of the stretch rate (Fig. 10b). Thus, it is confirmed that the flame brush thickness and the flame surface area have a maximum and minimum values in the increasing and decreasing stretch periods, respectively, for all the oscillation amplitudes. The mechanism of this dynamic feature is not clear at this point and is a good subject for future works. For instance, one may examine an instability analysis of disturbances under dynamic stretch oscillations in a divergent flow or address turbulence intensity and scale in each phase angle to clarify the controlling factors of the flame brush thickness evolution. Finally, the amplitude responses of the fluctuations of the global OH* intensity and the flame surface area are shown in Fig. 11. Unlike the response curves reported in previous works [12,13] which showed nonlinear features at high oscillation amplitudes, this flame shows a linear tendency. One reason may be due to the relatively narrower range of the velocity forcing amplitudes. One cannot conclude that the
dynamic flame in this study has no nonlinear response unless the responses for higher oscillation amplitudes are investigated. In Fig. 11, it can be seen also that the flame surface area fluctuation response shows a linear tendency with a slope similar to that of the OH* fluctuation response. This indicates that the flame surface area variations play a critical role in the global flame response. To investigate what happens when the forcing frequency is changed is another interesting topic for our future work. In very lower frequencies, it is expected that the flame responds in a quasi-steady manner as can be seen in the low Strouhal number cases of Hirasawa et al. [8]. On the other hand, in higher frequencies, like the order of 10,000 Hz, the time period of one cycle becomes relevant to the chemical characteristic time and the flame response amplitude will saturate at a level as reported by Sung and Law [7]. The frequency of 50 Hz addressed in this study was in-between the two domains and the flame showed the unique unsteady behavior.
Fig. 10. Phase relationship among the phase angles corresponding to maximum and minimum of the global stretch rate, the flame brush thickness and the flame surface area for seven velocity amplitude conditions. Flow conditions are same with those of Fig. 3.
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4. Conclusions
Acknowledgment
Dynamic features of a freely propagating turbulent premixed flame under global stretch rate oscillations were investigated. The turbulent flame structure in the core flow region varied largely in axial direction in response to the flow-field oscillations. The flame brush thickness oscillated with a phase shift to the stretch rate oscillations. The relative flame surface area that is an indicator of the local reaction rate showed a similar trend. It was found that the flame brush thickness and the flame surface area had a maximum and minimum values in the increasing and decreasing stretch periods, respectively, for all the oscillation amplitudes. Despite the fact that the flame brush thickness showed such a large variation, the mean progress variable profiles normalized by the flame brush thicknesses for different phase angles collapse onto a consistent curve. This suggests that the self-similarity of the mean progress variable profile sustains in this dynamic flame. The global OH* fluctuation response (i.e. response of global heat-release rate fluctuation) to the inlet velocity oscillations showed a linear feature in the velocity oscillation amplitude range between V 0 =V ¼ 0:09 and 0.55. The flame surface area fluctuation response showed a linear tendency with a slope similar to that of the global OH* fluctuation response. This indicated that the flame surface area variations play a critical role in the global flame response. All these issues should be studied further to characterize the response characteristics in a broad range of oscillation amplitudes and frequencies and to clarify the underlying mechanisms.
The authors acknowledge Dr. Robert K. Cheng of Lawrence Berkeley National Laboratory for very useful discussion. References [1] B. Be´dat, R.K. Cheng, Combust. Flame 100 (1995) 485–494. [2] T. Plessing, C. Kortschik, N. Peters, M.S. Mansour, R.K. Cheng, Proc. Combust. Inst. 28 (2000) 359– 366. [3] I.G. Shepherd, R.K. Cheng, Combust. Flame 127 (2001) 2066–2075. [4] L.W. Kostiuk, K.N.C. Bray, R.K. Cheng, Combust. Flame 92 (1993) 377–395. [5] T. Saitoh, Y. Otsuka, Combust. Sci. Technol. 12 (1976) 135–146. [6] G. Stahl, J. Warnatz, Comust. Flame 85 (1991) 285– 299. [7] C.J. Sung, C.K. Law, Combust. Flame 123 (2000) 375–388. [8] T. Hirasawa, T. Ueda, A. Matsuo, M. Mizomoto, Combust. Flame 121 (2000) 312–322. [9] A.N. Lipatnikov, J. Chomiak, Prog. Energ. Combust. Sci. 28 (2002) 1–74. [10] C.J. Lawn, T.C. Williams, R.W. Schefer, Proc. Combust. Inst. 30 (2005) 1749–1756. [11] V.R. Savarianandam, C.J. Lawn, Proc. Combust. Inst. 31 (2007) 1419–1426. [12] B.D. Bellows, M.K. Bobba, A. Forte, J.M. Seitzman, T. Lieuwen, Proc. Combust. Inst. 31 (2007) 3181–3188. [13] R. Balachandran, B.O. Ayoola, C.F. Kaminski, A.P. Dowling, E. Mastorakos, Combust. Flame 143 (2005) 37–55. [14] R.K. Cheng, D.T. Yegian, M.M. Miyasato, et al., Proc. Combust. Inst. 28 (2000) 1305–1313. [15] M.R. Johnson, R.K. Cheng, In: Proc. of the 19th ICDERS in Hakone, Japan, 2003.
Proceedings of the
Proceedings of the Combustion Institute 32 (2009) 1795–1802
Combustion Institute www.elsevier.com/locate/proci
Dynamic behavior of a freely-propagating turbulent premixed flame under global stretch-rate oscillations Shigeru Tachibana a,*, Junpei Yamashita b, Laurent Zimmer c, Kazuo Suzuki d, A. Koichi Hayashi b a
Aerospace Research and Development Directorate, Japan Aerospace Exploration Agency, 7-44-1 Jindaiji-Higashi, Chofu, Tokyo 182-8522, Japan b Department of Mechanical Engineering, Aoyama Gakuin University, 5-10-1 Fuchinobe, Sagamihara, Kanagawa 229-8558, Japan c EM2C laboratory, UPR 288 CNRS-Ecole Centrale Paris, Grande voie des vignes 92295 Chaˆtenay-Malabry, France d Aviation Program Group, Japan Aerospace Exploration Agency, 7-44-1 Jindaiji-Higashi, Chofu, Tokyo 182-8522, Japan
Abstract Dynamic features of a freely propagating turbulent premixed flame under global stretch rate oscillations were investigated by utilizing a jet-type low-swirl burner equipped with a high-speed valve on the swirl jet line. The bulk flow velocity, equivalence ratio and the nominal mean swirl number were 5 m/s, 0.80 and 1.23, respectively. Seven velocity forcing amplitudes, from 0.09 to 0.55, were examined with a single forcing frequency of 50 Hz. Three kinds of optical measurements, OH-PLIF, OH* chemiluminescence and PIV, were conducted. All the data were measured or post-processed in a phase-locked manner to obtain phase-resolved information. The global transverse stretch rate showed in-phase oscillations centering around 60 (1/s). The oscillation amplitude of the stretch rate grew with the increment of the forcing amplitude. The turbulent flame structure in the core flow region varied largely in axial direction in response to the flowfield oscillations. The flame brush thickness and the flame surface area oscillated with a phase shift to the stretch rate oscillations. These two properties showed a maximum and minimum values in the increasing and decreasing stretch periods, respectively, for all the forcing amplitudes. Despite large variations in flame brush thickness at different phase angles, the normalized profiles collapse onto a consistent curve. This suggests that the self-similarity sustains in this dynamic flame. The global OH* fluctuation response (i.e. response of global heat-release rate fluctuation) showed a linear dependency to the forcing velocity oscillation amplitudes. The flame surface area fluctuation response showed a linear tendency as well with a slope similar to that of the global OH* fluctuation. This indicated that the flame surface area variations play a critical role in the global flame response. Ó 2009 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Flame dynamics; Flame response; Low-swirl burner; Turbulent premixed flame; Stretch rate
*
Corresponding author. Fax: +81 422 40 3440. E-mail address: [email protected] Tachibana).
(S.
1540-7489/$ - see front matter Ó 2009 The Combustion Institute. Published by Elsevier Inc. All rights reserved. doi:10.1016/j.proci.2008.06.206
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1. Introduction The turbulent premixed flame stabilized by the low-swirl burner (LSB) has been an active subject for investigating detailed structure of turbulent premixed flames for more than a decade. The flame is a close approximation of a freely propagating planar turbulent premixed flame in the core flow region, which is considered the most fundamental configuration. Therefore, essential characteristics of turbulent premixed flames, like turbulent flame propagation speed, can be investigated [1–3]. In these works, swirl numbers were adjusted so that the flame brush is locally perpendicular to the incoming reactant flow. Our focus in this study is to investigate how the flame behaves when cyclic perturbations are imparted to the swirl flow. The LSB generates a divergent flow by the centrifugal forces due to the weak swirl component of the flow. A lifted flame is stabilized in the manner of freely propagating premixed flame at a balancing position between the reactant flow speed and the flame propagation speed. Cyclic oscillations of the swirl flow result in cyclic motions of the divergent flow field. The divergent flow can be characterized by the global stretch rate as shown in previous literatures (e.g. Ref.[4]). Therefore, the unsteady flow field in this study can be characterized by the global stretch rate oscillations. There are a few studies in the literatures on the dynamic feature of premixed flames under global stretch rate oscillations. Among them are an early investigation of unsteady laminar diffusion and premixed counter flow flames [5], numerical studies of a laminar flame response in oscillating counter flow [6,7] and an experimental study of the response of a laminar wall stagnating premixed flame under stagnation plate oscillations [8]. To the best of our knowledge, there has yet to be a study of global stretch oscillation on turbulent premixed flames. One may conduct such an experiment utilizing wall-stagnating flow or counter flow configurations. However, there are several factors, like the effects of heat loss from the wall and pressure gradient in the flow field that should be dealt with carefully. The LSB flame is free from these constraints and is more suitable to investigate the effect of unsteady stretch rate on turbulent flame structure. This kind of experiments will add insights into the dynamic feature of turbulent premixed flame. For instance, it is shown that turbulent flame brush thickness is strongly modified by the dynamic variations of global stretch rate. Turbulent flame brush thickness is an important characteristic scale that describes the region where reaction is taking place and has been reported in many previous works. Key features like self-similarity and spatial development of this scale were widely examined in the review of Lipatnikov and
Chomiak [9]. Dynamic features of the flame thickness were included in two previous works [10,11] on flame response to normal acoustic excitation. In these works, the self-similarity was implicitly indicated by the fact that a fitting equation utilizing the thickness worked well. But beyond these works, this feature has not been widely reported. It is interesting to look at if the self-similarity is sustained in the present dynamic flame as well. Another aspect is the response of the flame to inlet velocity oscillations. The flame response function and its phenomenological background have been studied with acoustically forced oscillating flames in previous works [12,13]. It was reported that nonlinear heat-release responses were observed at high velocity oscillation amplitudes for a high-swirl [12] and a bluff body [13] flames. The nonlinearity was considered to be due to a kinematic distortion process of the flame front. The flame stabilization mechanism of the LSB flame is clearly different from those of the high-swirl and the bluff-body flames. For instance, the LSB flame is expected to be less affected by separated vortices from solid boundaries, like a bluff body or a corner step. Investigating how the LSB flame responds to forced oscillations will add an insight into the flame response study. The objective of this work is to characterize the effect of unsteady global stretch rate on the turbulent flame. Three kinds of optical measurements, OH-PLIF, OH* chemiluminescence and PIV, were conducted. All the data were measured or postprocessed in a phase-locked manner to obtain phase-resolved mean profiles of the flame structure and the flow field. The responses of the fluctuations of the global OH* intensity and the flame surface area in the core flow region to the inlet velocity oscillations were addressed as well. 2. Experimental arrangements 2.1. Experimental system and conditions Figure 1 shows the configuration of the lowswirl burner. The design is similar to the 5 cm-
Fig. 1. Configuration of the jet type low-swirl burner. Vertical view of the burner (left) and horizontal view of the swirl generator (right).
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jet LSB appeared in the work of Cheng et al. [14]. The burner is composed of a circular pipe nozzle with a 53 mm diameter, a swirl generator and a perforated plate. A divergent flow is produced by the weak swirl generator and a lifted flame is stabilized in the manner of freely propagating premixed flame. Methane and air are well mixed by a static mixer before entering the burner. Swirl number, S, for the jet-LSB is given by the following expression [15]: S¼
pR2 Q2j cos a 4pR2j ðQm þ Qj Þ2
:
ð1Þ
Here, a is the inclined angle of the air jets, R and Rj are the radii of the circular pipe nozzle and the secondary air jet orifice, respectively. Qm and Qj are the mass flow rate of the mixture and the swirl jets, respectively. The schematic of the experimental system is shown in Fig. 2. In this study, the swirl air flow rate was modulated in a cyclic manner by implementing a high-speed valve (the MOOG D633 DDV) in the secondary air line at the location just before the line was separated into four branches which were connected with the four tangential jets. The cyclic swirl oscillations produce an oscillatory divergent flow. The valve was controlled by the voltage signal which was generated by a signal generator. Sinusoidal signal was used as the command signal. With a single frequency of 50 Hz, the amplitude of the sinusoidal signal was varied to produce different magnitudes of the swirl oscillations. The bulk flow velocity was 5 m/s. Equivalence ratio of the methane-air mixture was 0.80. The nominal mean swirl number, which can be defined by the steady secondary air flow rate before the plenum chamber, was 1.23. All these flow conditions were fixed throughout this study. The relative velocity oscillation amplitude, which is defined as the ratio of the zero-to-peak amplitude of the phase-locked mean axial velocity, V0 , to the mean value of the phase-locked mean velocity, V , at the location of x = 0 mm and
Fig. 2. Schematic of the experimental setup. The LSB is equipped with the DDV valve in the secondary air line to impart cyclic perturbations on the swirl jet flow. The valve command signal is the reference signal for the phase-locked treatments.
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y = 10 mm, was used as the parameter which expresses oscillation magnitude. All the zero-topeak values p in this paper were calculated by multiplying 2 by the standard deviation values of the phase-resolved data. Seven velocity oscillation amplitudes, V 0 =V ¼ 0:09, 0.24, 0.27, 0.36, 0.44, 0.51 and 0.55, were examined in this study. 2.2. Measurement system and data processing A phase-locked OH-PLIF measurement, a time-resolved OH* chemiluminescence measurement and a high-speed PIV measurement were conducted. For the OH-PLIF excitation, a dye laser (Spectron Laser Systems, 4000G with Rhodamine 590) pumped by an Nd:YAG laser (Spectron Laser Systems, SL 825G-400 mJ) was used. The wavelength of the laser beam after the KDP doubling crystal was 283.636 nm with the pulse energy of 10 mJ. This wavelength pumps the Q1 (8) transition of the A2R+ X2P (1,0) band. An ICCD camera (Princeton Instruments, PI-MAX) with the UV-Nikkor lens and a set of optical filters (Schott UG-5 and WG-305) was used for capturing the OH-PLIF images. The resolution was 256 512 pixels with the field of view of 32.7 65.5 mm2. The ICCD gate width was 10 ns. Phase-locked measurement was carried out for 16 phase angles from 0 to 337.5° with a step of 22.5°. The valve control signal was used as the reference signal. Zero-degree angle was defined as the zero-crossing point with a positive slope. For each phase angle, 500 images were captured. The acquired PLIF images were post-processed to obtain the statistical feature of the flame structure like mean progress variable, c(x, y), and mean flame surface density, r(x, y). The post-processing procedures for calculating c(x,y) and r(x, y) were similar to those of ref. [13]. Window size for the flame surface density calculation was 9 9 pixels (about 1.15 1.15 mm2). The time-resolved global OH* chemiluminescence measurement was conducted with a similar way to refs. [12,13] by utilizing a photo-multiplier system (Fig. 2). The light collecting lens gathered spontaneous light emission from the global flame. The voltage signal from the photo-multiplier was recorded with a sampling frequency of 51.2 kHz. Simultaneously, the valve command signal was recorded on another channel and used as the reference signal for the phase-locked analysis. The number of data points was 1,015,808, which are corresponding to 992 cycles for the frequency of 50 Hz. The acquired data were post-processed to derive the phase-locked mean intensity profiles of the global OH*. The simultaneously obtained valve command signal was used for tagging the phase-angle information on the OH* data. The tagged data were sorted according to the phaseresolved bins. The sorted data were averaged in each bin. The phase resolution of a bin was 0.7°.
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The time-resolved PIV measurement was carried out to acquire phase-resolved velocity field. The PIV system was composed of a continuouswave Nd:YAG laser (KANOMAX, CW532-5W) with laser sheet optics and a high-speed camera (Photron, FASTCAM-APX RS). The resolution was 512 512 pixels with the field of view of 60 60 mm2. The camera was operated at a sampling frequency of 5000 Hz with an exposure time of 100 lsec. The valve command and the camera exposure timing signals were simultaneously recorded for the phase-locked post-processing as in the case of the OH* measurement. In one sequence, 5099 images, which are corresponding to almost 50 cycles, were recorded. Vector calculation was done by the DaVis 7.2 software of LaVision. The cross-correlation method with a multi-pass iteration mode (from 64 64 to 16 16 pixels) was applied. Only a validation with the peak ratio factor of 1.3 was implemented and no filter was used. The phase resolution was 11.25*. The number of data in each bin was about 150. 3. Results and discussion 3.1. The unsteady velocity field The mean velocity fields at two phases are shown in Fig. 3 to illustrate typical flow fields corresponding to a low (Fig. 3a) and a high (Fig. 3b) stretch rates during an oscillation cycle for V 0 =V ¼ 0:44. The contour map indicates the velocity magnitude in axial direction with streamtraces to show the mean flow patterns. The low and high stretch rates can be recognized by the narrower and wider flow discharge angles. This trend is quantitatively identified in Fig. 4 by the phase-locked mean global stretch rates at three velocity forcing amplitudes. The global stretch rate, sj, is defined by the gradient of transverse velocity in transverse direction, i.e., j dU/dx.
Fig. 4. Phase-locked mean global stretch rates at y = 10 mm for three forcing amplitudes. Flow conditions are same with those of Fig. 3. Symbols: Square: V 0 =V ¼ 0:55, Delta: V 0 =V ¼ 0:44, Right triangle: V 0 =V ¼ 0:27. Curves are the 6th order polynomial fittings.
The gradient was deduced by applying a linear-fitting approximation to the transverse velocity data, which has 23 data points, in the range of 10 mm < x < 10 mm at an axial position of y = 10 mm. The stretch rates clearly show inphase oscillations centering around j 60(1/s). The oscillation amplitude of the stretch rate grows with the increment of the forcing amplitude. Except for the amplitude values, those profiles have a similar distribution with a small phase shifts. The distributions deviate slightly from sinusoidal functions. The wave forms at the minimum positions are sharper compared to the more rounded forms at the maximums. We consider that to be a feature of this specific system for generating stretch oscillations by the secondary tangential jet oscillations. Phase-resolved profiles of the unsteady velocity in axial direction at the location of x = 0 mm, y = 10 mm are shown in Fig. 5. The oscillation amplitude of the axial velocity grows with the increment of the forcing amplitude as can be seen for the stretch rate in Fig. 4. As
Fig. 3. Phase-locked mean velocity fields at two phase angles, (a) low stretched case (h = 45°) and (b) high stretched case (h = 225°). Grayscale contour indicates the axial velocity magnitude. Bulk velocity = 5 m/s, equivalence ratio=0.80, forcing frequency = 50 Hz, V 0 =V ¼ 0:44.
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Fig. 5. Phase-locked mean axial velocity at x = 0 mm,y = 10 mm for three forcing amplitudes. Flow conditions are same with those of Fig. 3. Symbols: Square: V 0 =V ¼ 0:55, Delta: V 0 =V ¼ 0:44, Right triangle: V 0 =V ¼ 0:27. Curves are the 6th order polynomial fittings.
described in Section 2.1, the zero-to-peak amplitude relative to the mean value of each profile is used for the representative value indicating the velocity oscillation amplitude. 3.2. Unsteady behavior of the flame structure In this section, the unsteady behavior of the turbulent flame structures is discussed with the post-processed data of OH-PLIF measurement. Only the core flow region, which is bounded by x = ± 14 mm, was chosen as the field of interest to avoid dealing with the gas dilution effect and the shear flow effect which exist in the outer swirl region. Figure 6 shows four sets of two-dimensional (2-D) distributions of the phase-locked mean progress variable and the mean flame surface density for V 0 =V ¼ 0:44. Considering the symmetric feature of the distributions, only the right-hand sides of the core region are displayed here. For convenience, the x-axis of mean progress variable distribution was inverted and shown on the left-hand side. The corresponding distribution of mean flame surface density is shown on the right-hand side. It can be seen that the flame structure varies largely in axial direction in response to the flow-field oscillations. For instance, flame brush thickness at the phase angle of 135° (Fig. 6b, left) is about 1.5 times larger than that of 315° (Fig. 6d, left). At h = 315°, flame fronts are confined to a relatively narrower horizontal band along the c = 0.50 contour (Fig. 6d, right), while those of h = 135° are distributed in a wider thickness (Fig. 6b, right). The flame liftoff height shows variations also. In the four phase angles, the flame position at h = 45 and 225 show the highest and lowest values, respectively. The thickness of c(x, y) and r(x, y) for h = 45 and 225° are in-between those of h = 135 and 315°. To see the phase-relations between the unsteady flame structure and the velocity field,
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the flame brush thickness, the flame lift-off height and the global stretch rate are plotted against the phase angle in Fig. 7. Averaging the 2-D mean progress variable distribution in horizontal direction over the core region gives a 1-D distribution of mean progress variable, c1D(y), in axial direction. The flame brush thickness, d, and the flame lift-off height were defined as the distance between c1D = 0.10 and 0.90 and the axial position of c1D = 0.50, respectively. The global stretch rate shown in this figure was conditioned on the c1D = 0.01 position which can be considered as the leading edge of the flame front. In each phase-locked mean velocity field data, an axial position closest to the c1D = 0.01 position was chosen to calculate the transverse stretch rate. In Fig. 7, it can be seen that the flame brush thickness and the lift-off height oscillate with phase shifts to the forced stretch rate oscillations. The flame lift-off height shows an inverted trend against the stretch rate. This makes sense since the stretch rate is a direct measure of the decay rate of axial velocity in axial direction and the flame balancing position is controlled by the decaying velocity profile. On the other hand, the flame brush thickness shows a different trend. The thickness oscillates with a phase shift to the stretch rate oscillations. It shows a peak and a valley in the periods where the stretch rate has a positive and negative slopes, respectively. For instance, at h = 135 and 315°, the stretch rates themselves are almost the same, but the corresponding flame brush thicknesses are very different. The thickness of h = 135° has a value almost 1.5 times larger than that of h = 315°. The positive/negative sign of the gradient in time evolution of the stretch rate seems to have a dominant effect on the dynamic behavior of the flame thickness. It is interesting to note that the self-similarity of the mean progress variable profiles reported in refs.[9–11] is observed in this dynamic flame as well. Figure 8 shows the mean progress variable profiles normalized by the flame brush thickness at different phase angles. Despite large variations in flame brush thickness at different phase angles, the normalized profiles collapse onto a consistent curve. Revolving the 2-D flame surface density distribution around y-axis provides an estimate of the total flame surface area in the core volume. The relative flame surface area, R/R0, is shown in Fig. 9. The area of a circle with a radius of the core region (14 mm) is used as the reference value and denoted as R. One can see that the profile of the relative flame surface area is very similar to that of the flame brush thickness. This implies that the change of the flame surface area is due to the change of flame brush thickness or, in other words, large scale flame wrinkles, and not due to the change of fine scale wrinkles.
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Fig. 6. Mean progress variable and mean flame surface density distributions for phase angles of (a) 45, (b) 135, (c) 225 and (d) 315 degrees. Left and right in each figure show the mean progress variable (x-axis inverted) and the mean flame surface density, respectively. Flow conditions are same with those of Fig. 3.
Fig. 7. Comparison of the phase-resolved profiles of the flame brush thickness, the flame lift-off height and the global stretch rate. Flow conditions are same with those of Fig. 3. Symbols: Square: Flame brush thickness, Delta: Flame lift-off height, Gradient: Global stretch rate conditioned on c1D = 0.01. Curves are the 6th order polynomial fittings.
To see if the observed dynamic features of d and R/R0 in Figs. 7–9 are unique for all the oscillation amplitudes or not, phase relations among the stretch rate and these two properties were investigated. The phase angles of maximum and
Fig. 8. Mean progress variable profiles normalized by the flame brush thicknesses for eight different phase angles. Flow conditions are same with those of Fig. 3.
minimum of the three properties are shown in Fig. 10. These angles were retrieved from the 6th order polynomial fitting curves of the data to remove spurious trends in the profiles. The maximum positions of d and R/R0 stay around 135° and are in-between the phase angles of the minimum and maximum stretch rates for all oscillation amplitudes (Fig. 10a). On the other hand, the minimum positions of the two properties
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Fig. 9. Phase-resolved profile of the relative flame surface area. The flame brush thickness profile is shown for comparison. Flow conditions are same with those of Fig. 3.
Fig. 11. Responses of the fluctuations of the relative flame surface area in the core region and the global OH* intensity. Flow conditions are same with those of Fig. 3. Lines are linear fittings of the data.
locate in the other side of the two boundaries of the stretch rate (Fig. 10b). Thus, it is confirmed that the flame brush thickness and the flame surface area have a maximum and minimum values in the increasing and decreasing stretch periods, respectively, for all the oscillation amplitudes. The mechanism of this dynamic feature is not clear at this point and is a good subject for future works. For instance, one may examine an instability analysis of disturbances under dynamic stretch oscillations in a divergent flow or address turbulence intensity and scale in each phase angle to clarify the controlling factors of the flame brush thickness evolution. Finally, the amplitude responses of the fluctuations of the global OH* intensity and the flame surface area are shown in Fig. 11. Unlike the response curves reported in previous works [12,13] which showed nonlinear features at high oscillation amplitudes, this flame shows a linear tendency. One reason may be due to the relatively narrower range of the velocity forcing amplitudes. One cannot conclude that the
dynamic flame in this study has no nonlinear response unless the responses for higher oscillation amplitudes are investigated. In Fig. 11, it can be seen also that the flame surface area fluctuation response shows a linear tendency with a slope similar to that of the OH* fluctuation response. This indicates that the flame surface area variations play a critical role in the global flame response. To investigate what happens when the forcing frequency is changed is another interesting topic for our future work. In very lower frequencies, it is expected that the flame responds in a quasi-steady manner as can be seen in the low Strouhal number cases of Hirasawa et al. [8]. On the other hand, in higher frequencies, like the order of 10,000 Hz, the time period of one cycle becomes relevant to the chemical characteristic time and the flame response amplitude will saturate at a level as reported by Sung and Law [7]. The frequency of 50 Hz addressed in this study was in-between the two domains and the flame showed the unique unsteady behavior.
Fig. 10. Phase relationship among the phase angles corresponding to maximum and minimum of the global stretch rate, the flame brush thickness and the flame surface area for seven velocity amplitude conditions. Flow conditions are same with those of Fig. 3.
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4. Conclusions
Acknowledgment
Dynamic features of a freely propagating turbulent premixed flame under global stretch rate oscillations were investigated. The turbulent flame structure in the core flow region varied largely in axial direction in response to the flow-field oscillations. The flame brush thickness oscillated with a phase shift to the stretch rate oscillations. The relative flame surface area that is an indicator of the local reaction rate showed a similar trend. It was found that the flame brush thickness and the flame surface area had a maximum and minimum values in the increasing and decreasing stretch periods, respectively, for all the oscillation amplitudes. Despite the fact that the flame brush thickness showed such a large variation, the mean progress variable profiles normalized by the flame brush thicknesses for different phase angles collapse onto a consistent curve. This suggests that the self-similarity of the mean progress variable profile sustains in this dynamic flame. The global OH* fluctuation response (i.e. response of global heat-release rate fluctuation) to the inlet velocity oscillations showed a linear feature in the velocity oscillation amplitude range between V 0 =V ¼ 0:09 and 0.55. The flame surface area fluctuation response showed a linear tendency with a slope similar to that of the global OH* fluctuation response. This indicated that the flame surface area variations play a critical role in the global flame response. All these issues should be studied further to characterize the response characteristics in a broad range of oscillation amplitudes and frequencies and to clarify the underlying mechanisms.
The authors acknowledge Dr. Robert K. Cheng of Lawrence Berkeley National Laboratory for very useful discussion. References [1] B. Be´dat, R.K. Cheng, Combust. Flame 100 (1995) 485–494. [2] T. Plessing, C. Kortschik, N. Peters, M.S. Mansour, R.K. Cheng, Proc. Combust. Inst. 28 (2000) 359– 366. [3] I.G. Shepherd, R.K. Cheng, Combust. Flame 127 (2001) 2066–2075. [4] L.W. Kostiuk, K.N.C. Bray, R.K. Cheng, Combust. Flame 92 (1993) 377–395. [5] T. Saitoh, Y. Otsuka, Combust. Sci. Technol. 12 (1976) 135–146. [6] G. Stahl, J. Warnatz, Comust. Flame 85 (1991) 285– 299. [7] C.J. Sung, C.K. Law, Combust. Flame 123 (2000) 375–388. [8] T. Hirasawa, T. Ueda, A. Matsuo, M. Mizomoto, Combust. Flame 121 (2000) 312–322. [9] A.N. Lipatnikov, J. Chomiak, Prog. Energ. Combust. Sci. 28 (2002) 1–74. [10] C.J. Lawn, T.C. Williams, R.W. Schefer, Proc. Combust. Inst. 30 (2005) 1749–1756. [11] V.R. Savarianandam, C.J. Lawn, Proc. Combust. Inst. 31 (2007) 1419–1426. [12] B.D. Bellows, M.K. Bobba, A. Forte, J.M. Seitzman, T. Lieuwen, Proc. Combust. Inst. 31 (2007) 3181–3188. [13] R. Balachandran, B.O. Ayoola, C.F. Kaminski, A.P. Dowling, E. Mastorakos, Combust. Flame 143 (2005) 37–55. [14] R.K. Cheng, D.T. Yegian, M.M. Miyasato, et al., Proc. Combust. Inst. 28 (2000) 1305–1313. [15] M.R. Johnson, R.K. Cheng, In: Proc. of the 19th ICDERS in Hakone, Japan, 2003.