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Analysis of blowoff dynamics from flames with stratified fueling
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Proceedings of the
Proceedings of the Combustion Institute 34 (2013) 1491–1498
Combustion Institute www.elsevier.com/locate/proci
Analysis of blowoff dynamics from flames with stratified fueling Kristin M. Kopp-Vaughan, Trevor R. Jensen, Baki M. Cetegen, Michael W. Renfro ⇑ Department of Mechanical Engineering, 191 Auditorium Rd., U-3139, University of Connecticut, Storrs, CT 06269-3139, USA Available online 30 June 2012
Abstract In some compact combustors with bluff body flame stabilization, fuel injection may be too closely coupled to permit uniform mixing. This stratification in the fuel profile can be asymmetric about the bluff body, and the flame equivalence ratio may differ across the recirculation zone. An experimental study of asymmetric fueling about a bluff body is reported in this paper with a focus on the impact of stratification on flame blowoff. In order to understand the blowoff dynamics of turbulent flames with stratified fueling, high speed chemiluminescence imaging was performed for five levels of fuel stratification through blowoff. Physical probe measurements of the local equivalence ratios were used to characterize the stratification. It was found that for overall fuel lean flames (averaged across the bluff body), fuel stratification increases the flame stability such that the overall equivalence ratio at blowoff is decreased for increased stratification. It was also found that the stronger (richer) shear layer determines the flame dynamics near blowoff. The leaner branch of the flame extinguishes earlier and the richer branch is shown to pilot the overall flame and therefore be responsible for the increase in flame stability at larger gradients. Proper orthogonal decomposition (POD) was applied to the high speed chemiluminescence images of the flames and used to quantitatively track the flame front dynamics through blowoff. All flames were found to exhibit Benard–von Karman vortex shedding just prior to blowoff. The POD time constants demonstrate that a strong fuel gradient decreases the time it takes for the flame to shift from its mean fully burning shape to blowoff and decreases the dwell time of the flame in the recirculation zone following local extinction. These time scales indicate a faster blowoff process with fuel stratification. Ó 2012 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Fuel stratification; Blowoff; Bluff body flames; Proper orthogonal decomposition; Chemiluminescence imaging
1. Introduction Flame holding in high-speed turbulent premixed combustible gas streams can be achieved ⇑ Corresponding author. Fax: +1 (860) 486 5088.
E-mail Renfro).
address:
[email protected]
(M.W.
by recirculating flow behind a bluff body that allows hot products to be continually supplied to the attached reaction layers. While this flow field extends the limits for stable premixed combustion, there is still a lower limit of equivalence ratio or an upper limit of velocity beyond which the flame will blow off. These limits are affected by many parameters and flame blowoff limits have been reported
1540-7489/$ - see front matter Ó 2012 The Combustion Institute. Published by Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.proci.2012.06.074
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extensively in the literature for fully premixed conditions. We report here on the effect of non-uniform fueling upstream of the bluff body on both blowoff limits and associated flame dynamics. Fuel stratification in practical combustors commonly occurs due to incomplete mixing between the bluff body and fuel injector. Lovett et al. [1] discuss the design of “legacy” bluff body stabilized flames in augmentors compared to newer “close-coupled” designs. In close-coupled designs, the fuel injectors are closer to the flame holder, even within the holder itself, to mitigate auto ignition at higher turbine exit temperatures of modern engines. One consequence of close coupling is fuel stratification since there is insufficient time to achieve fully premixed conditions. This can cause a difference in chemical time scales along the flame sheet or across the recirculation zone. Moreover, this stratification may be unsteady due to turbulent fluctuations [1]. This study seeks to examine the blowoff dynamics of bluff body stabilized flames in a combustor where the mixture approaching the flame holder is stratified. 2. Background Flame blowoff has been studied extensively for the case of fully premixed reactants. Williams et al. [2] and Longwell et al. [3] suggested that blowoff occurs when the recirculation zone is unable to transfer sufficient heat for ignition at the bluff body. Zukoski and Marble [4] proposed that the mixing time scale of reactants with products must exceed a critical chemical time in order for ignition to occur. This time scale was related to both the recirculation zone aerodynamics and the mixture chemical time scale via a Damko¨hler number (Da). Later, Ozawa [5] used data from many different studies to compile a purely empirical correlation of flame blowoff for non-stratified conditions. Radhakrishnan et al. [6] also reduced many data sets using scaling based on laminar flame speeds and global velocity. These stability parameters indicate that for fuel lean flames as the equivalence ratio decreases and the velocity increases flame blowoff is more likely, consistent with a Da number scaling. However, these types of global stability correlations do not provide insight into the dynamics of flame blowoff. Lieuwen et al. [7] reported flame dynamics at blowoff for flames without fuel stratification. They showed that as a flame approached blowoff, large scale asymmetric vortices became prevalent consistent with the onset of Benard–von Karman (BVK) vortex shedding. This type of vortex shedding it not seen far from blowoff due to the large density differences between reactants and products and the resulting damping of vorticity. Dynamics of flame blowoff for swirl stabilized flames were separately reported [8].
Nair et al. [9] conducted experimental studies of perfectly premixed flames as they approached blowoff. They qualitatively described the general flame dynamics throughout the blowoff process. They state that as flame nears blowoff it begins to transition into a BVK type vortex shedding mode. This mode was later quantified by taking a Fourier transform of flame motion at specific points along a tracked flame front [10]. When the flame front movement produced a frequency with a Strouhal number (St) in the BVK range (St 0.24), the flame exhibited the BVK vortex shedding mode. Flame holes were observed throughout the shear layers and these holes appeared more frequently as blowoff was approached. It was clearly shown that vortex shedding was suppressed for stable flames far from blowoff and that near-blowoff conditions were correlated with high levels of vortex shedding but these results were limited to the case of fully premixed reactants. Fuel stratification is often seen in bluff body flame studies by the intentional piloting of a flame to help it anchor. This type of stratification is known to increase the lean blowoff stability limit. Fetting et al. [11] showed that creating intentionally fuel rich zones in the separation layer behind a cylinder could extend the lean blowoff limit of the flame. They also discovered that for fuel rich flames, stability could be increased by injecting oxygen into the recirculation zone. In experiments by Seffrin et al. [12] fuel was stratified with several different geometries. They showed differences in the flame behavior when increased stratification was provided, but they did not examine flame blowoff dynamics. The fuel stratification was symmetric about the flame holder for all cases and the flames were stabilized with an axisymmetric pilot. The current study investigates flames without piloting. In an experimental study by Pasquier et al. [13], fuel was stratified throughout the combustor such that there were pockets of richer and leaner fuel/air mixtures and flame speeds were measured. They found that the flame speed was highly dependent on the local stratification. The speed of lean flames was increased when it resided near richer flames and decreased when it was nearer to leaner flames. Anselmo-Filho et al. [14] suggest that heat from richer parts of the flame serve to pilot weaker parts of the flame. These studies were not conducted near blowoff and only characterize the heat release and flame speed for stable conditions. Chaudhuri et al. [15,16], using both a small axisymmetric burner and the same experimental facility used in the present work, expanded on the flame dynamics near blowoff that were reported in [10]. Local velocities and strain rates along the flame were measured. Just before blowoff there was a brief period of time when the flame retracted and resided in the recirculation zone
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behind the bluff body [16]. The time scale for this residual flame phenomenon was not quantified but it was shown that burning in the recirculation zone was sometimes sufficient to relight the flame in the shear layers and re-establish it. In the current study, measurements are extended to cases of fuel stratification that are non-symmetric about the bluff body as may occur in practical combustors. 3. Specific objectives The primary goal of this work is to study the stability and dynamics of bluff body flames as they approach blowoff for flames with varying degrees of fuel stratification. The static stability limits in terms of equivalence ratios at blowoff are reported and discussed. This work seeks to expand on the flame dynamics described by Shanbougue et al. [10] and Chaudhuri et al. [15,16] to include flames that are stratified non-symmetrically about the bluff body. The presented work includes quantitative analysis of flame dynamics using high speed chemiluminescence imaging. Proper orthogonal decomposition (POD) is used for image analysis. The POD time constants are used to quantitatively examine the flame blowoff processes and the time scales associated with blowoff dynamics. A discussion of the physical interpretation of the POD modes and their associated time constants is included. 4. Experimental set up A combustion rig developed for studying turbulent partially premixed bluff body stabilized flames was used as schematically shown in Fig. 1 and described in [17]. For these studies, room temperature air was provided with Re = 12,000, where the Reynolds number is based on the bluff body height, H = 9.53 mm, and room-temperature air properties. The incoming turbulence intensity was measured to be approximately 10% [18]. Propane (Airgas Instrument Grade, 99.8%) is provided through three fuel injectors, as shown in Fig. 1, which were separately metered. The fuel injectors are close to the bluff body (60 mm upstream) so that the injected fuel is not well mixed by the time it approaches the triangular shaped bluff body in the test section. The test section is 38.1 mm high and 76.2 mm wide with optical access on three sides, as shown in Fig. 1. The exhaust includes water injection and perforated plates to cool the exhaust gases and damp any acoustics and is then open to the atmosphere [17]. The test section pressure is approximately 1 atm. For this study, four different levels of fuel stratification were employed by varying propane flow
Fig. 1. (top) Schematic of combustion rig and experimental set up: L, lense; F, filter; PMT, photo-multiplier tube. (bottom) Fuel injectors used for stratification.
to each injector. The amount of fuel from each fuel injector is determined by setting a global equivalence ratio (/), based on the total propane flow and total airflow through the rig, and a non-dimensional fuel gradient (G = H d//dx), based on the differences in propane flow rates through each injector. For the equivalence ratio gradient, d//dx, x is the coordinate perpendicular to the flow direction as shown in Fig. 2. We have verified that there are negligible fuel gradients in the span-wise direction of the bluff body as measured in [18]; thus the experiment is statistically two-dimensional. Four different gradients were used in this study: G = 0.25, G = 0.5, G = 0.75, and G = 1 in addition to the case of uniform fueling across the bluff body (G = 0). G = 0.5, for example, corresponds to a difference in equivalence ratio of 0.5 over a distance of one bluff body height. For cases where G P 0.5, no propane was provided to the top fuel injector. After the flame was lit the overall equivalence ratio was lowered slowly in each injector while maintaining the same gradient. When the flame could no longer be stabilized by the bluff body, the flame blew off. The equivalence ratio at which blowoff occurred was recorded. Equivalence ratios were measured using a gas sampling probe. A MEXA 584-L continuous gas analyzer was used to measure the propane and oxygen concentra-
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could affect flame stability. The PMT was fitted with a 432 nm bandpass filter centered on CH* chemiluminescence and a 200 mm objective lens was used to focus on the flame. Only CH* chemiluminescence was collected for consistency with camera collection. The PMT was used to post trigger the camera. Once the intensity from the PMT dropped below a threshold value, the camera was triggered and the last four seconds of data obtained by the camera was saved. 5. Chemiluminescence data analysis
Fig. 2. Equivalence ratios at blowoff versus distance in the direction x, used for defining the equivalence ratio gradient.
tions just upstream of the bluff body with a 2 mm diameter probe. Measurements were taken at equally spaced locations between the top and bottom of the test section. An equivalence ratio, based on molecular volume, at each point was calculated. When flame blowoff was reached the equivalence ratio about the bluff body was found for each gradient case. The fuel profile just upstream of the bluff body at blowoff is shown in Fig. 2 and is discussed further with the results. During the blowoff process, a high speed Photron SA5 monochromatic camera with a 50 mm f/ 1.9 objective lens was used to image the visual chemiluminescence from the flame. The front of the lens was fitted with a 2 close up filter (Hoya) so that the flame would fill the width of the CMOS chip. The filter is not UV transmissive, therefore no OH* chemiluminescence was detected. The camera was set to record at 6000 frames per second. This speed was the fastest speed where flame near blowoff can still be recorded by the camera. A few images for the G = 0.5 gradient case as the flame approaches blowoff are presented in Fig. 3. Each image is normalized by the highest intensity pixel in the image. Far from blowoff both the top and bottom shear layer are seen to be strongly burning. As blowoff approaches the weaker flame branch begins to retract into the recirculation zone sporadically. The flame also begins to show large vortex structures in the stronger flame branch (as observed in Fig. 3). Finally the stronger branch breaks and the flame resides for a short time in the recirculation zone. A quantitative analysis of this process is discussed subsequently. While the camera was recording, a photomultiplier tube (PMT) and a differential pressure transducer simultaneously recorded integrated chemiluminescence intensity and pressure. The pressure sensor was mounted directly above the bluff body to assure no acoustic oscillations occurred in the test section, as these oscillations
In order to quantitatively study the dynamics of these stratified flames during blowoff, POD was implemented on the chemiluminescence images. POD is a statistical method that reduces a set of original data into a set of Eigen bases that contain all of the spatial information and constants that contain all of the temporal information. While several studies have focused on qualitatively examining the POD mode shapes (e.g., [19–23]), this study examines the time constants for quantitative results on blowoff dynamics. This work used the snapshot method of POD [19], represented by ODti ¼
M X atj wji
ð1Þ
j¼1
where ODti is selected snapshots of original data, i is the pixel number, t is the time step, j is the mode number or principal component index, M is the total number of modes, atj are time constants, and wji are the basis functions (commonly referred to as POD modes). Here the bases are found from the eigen vectors of the covariance of the original data matrix. The time constants are found by projecting the original data onto the bases. A detailed description of POD can be found in [19]. We have previously used this POD algorithm on periodic flames with expected modes shapes [24]. In the method of snapshots, the original data to find the bases must not be highly correlated [19]. Kostka et al. [23] used the first minimum of mutual information (MMI) in order to find a sufficient time step between successive images to be selected as snapshots. The concept of mutual information, Z, and using its first minimum is most often seen in image tracking [25] and can be defined by ZðDtÞ ¼
M X M X P kl ðDtÞlnP kl ðDtÞ k¼1 l¼1 M X 2 P k lnP k
ð2Þ
k¼‘
where P kl is the probability that ODti was in a bin I at time t and in bin j at time t + Dt, P k is the probability that ODti was in bin k. The bin denotes a
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Fig. 3. Flame images of G = 0.5 flame through blowoff. The steps shown indicate time prior to blowoff. Each image is separately normalized between the maximum and minimum chemiluminescence signals. The average equivalence ratio at blowoff is / = 0.48.
particular range of pixel intensity counts. Sprott [25] shows that the size of the bin for the probability calculation is not critical. This method was used here and all stratified cases were found to have a minimum in Z corresponding to a time step Dt = 0.67 ms. Thus, POD was conducted on every 4th image collected at 6 kHz from all gradient cases in a single analysis. This provided a single set of bases that represented all of the gradients studied and provides a benefit of direct quantitative comparison between the constants associated with each mode for all of the gradient cases. It is important to note that while only every 4th image was used to find the bases, every image in the original data set was subsequently used to find the time constants, so these constants completely describe the time dependence of each mode for all flame images.
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rately fueled pilot flame from the wake of the bluff body was used. Unlike the study by Fetting et al. [11], the flame pilots itself due to stratification across the recirculation zone in the present case. To characterize the blowoff equivalence ratio, an average value was determined from the measured equivalence ratios from +10 mm to 10 mm (+H to H) since the regions closest to the wall were not fueled [16,17]. For the case of no stratification (G = 0) the mean equivalence ratio about the bluff body at blowoff was 0.63 ± 0.05. This is in agreement with blowoff limits for uniform fueling from [5]. As the fuel gradient increases, the average equivalence ratio at blowoff was found to decrease and reach its lowest value at G = 1 when the overall equivalence ratio is 0.41 ± 0.02. Each blowoff experiment was repeated at least 15 times and the error reported here includes the scatter of these measurements and the error associated with the propane concentration measurement. This decrease in mean equivalence ratio with increasing mixture gradient is expected to be a result of the higher equivalence ratio in the richer flame branch. A richer flame branch can act as a stronger pilot for the leaner flame. This suggests that it is the strength of the stronger flame branch that governs the stability of the flame and therefore the flame dynamics in this shear layer is important to understanding flame blowoff in these cases. It is helpful to directly compare the flame POD results between different fuel gradients. If POD were applied separately to two distinct flame cases, the physical interpretation of the modes may be difficult to correlate. However, because MMI showed that all gradients required the same time step (Dt) to form the reduced data set for POD mode calculation, all of the gradients could be analyzed together. Figure 4 shows a select set of bases from all gradient cases. Only 6 modes are shown but additional modes were also evaluated. The analyzed modes accounted for 90% of the energy in the chemiluminescence images and comprise most of the large scale features of the flow as higher order modes only represent the smaller features in the data. As expected, the first mode represents the mean asymmetric flame shape. In this case, the
6. Results and discussion Figure 2 shows the equivalence ratio profiles at blowoff for each of the five stratification levels. For the G P 0.5 cases, the equivalence ratio of the leaner flame branch at blowoff were below the expected flammability limit for propane at atmospheric conditions of approximately 0.5 [26]. This suggests that the stronger branch of the stratified flame (lower shear layer) serves as a pilot to keep the weaker (upper) branch lit, as was suggested by Fetting et al. [11], where a sepa-
Fig. 4. The first six mode shapes from POD from all flames studied.
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mean shape from all the flames was asymmetric because there were four non-symmetrically fueled cases and only one uniform case. Mode 2 when added to mode 1 represents the symmetric case and is more important for smaller values of G. Mode 3 has contributions to chemiluminescence intensity in the recirculation zone and a negative contribution on the bottom shear layer. This mode, when added to mode 1, represents the process of flame burning in the recirculation zone observed in perfectly premixed and small gradient blowoff events [15,16]. This physical interpretation for mode 3 is subsequently used to quantify the time scale for recirculation zone burning. Modes 4–6 show large coherent vortex structures. Modes 4 and 6 form a pair where the vortex structure is shifted slightly in space. As the constants associated with these two modes oscillate with a fixed phase shift, these modes can represent a vortex convecting down the shear layer. Therefore, by studying the time constants associated with these modes, the frequency content of the vortex street can be determined and the relative importance of the vortex shedding can be calculated. To permit this calculation is it necessary to define which modes represent BVK vortices as opposed to other physical processes such as recirculation zone burning. For BVK vortex shedding over the bluff body a St = 0.24 is expected, as in previous studies [10], which for the flow rate in these experiments corresponds to f = 650 Hz. An FFT was taken from the time constants associated with each mode. Typical examples of the spectra for some modes are shown in Fig. 5. The frequency content associated with modes 4 and higher shows a distinct peak at 650 Hz consistent with BVK vortex shedding. Modes 1, 2, and 3, which represent the steady flame and recirculation zone burning, do not display this oscillation frequency. This method of characterizing BVK vortex shedding is distinct from previous work [10] where a few distinct points along the flame front were evaluated. In this case, time constants represent the entire mode in space and therefore the entire flame front. To further examine the dynamics of these stratified flames near blowoff, each of the constants is normalized in the form of the mode energy. The mode energy is defined as the variance of the mode at an instant in time normalized by the variance of the original data at the same instant and represents the relative contribution of that mode to the instantaneous chemiluminescence signal. Figure 6 shows the energies associated with a few modes for a sample set of fuel gradients. The energy associated with fifth mode was shown to be part of the energy responsible for BVK vortex shedding. The average value of the fifth mode energy is low far from blowoff and increases as blowoff is approached for all cases. This can be seen in Fig. 6 suggesting that that
Fig. 5. The frequency content of selected modes associated with G = 0.75. Modes 4–10 have similar frequency content to mode 5.
Fig. 6. The energy contributions from (top) G = 0.25 and (bottom) G = 1 cases. The black dotted lines denote time scales.
BVK vortex shedding is stronger close to blowoff than it is far from blowoff. Due to the fact that several modes (modes 4–10) are needed to fully describe the vortex shedding it is difficult to assign
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a time scale to this increase in vortex shedding behavior. The energy associated with the first mode decreases to zero as blowoff is approached. Recall that first mode is approximately the average shape for a strongly burning flame. Far from blowoff, most of the energy is contained in the first mode. When the energy of the first mode decreases below 70% of that for a strongly burning flame, the flame always blows off. This 70% value was used as a threshold to determine when the flame has begun to blowoff as shown in Fig. 6. With increased stratification, the flame blowoff process occurs more rapidly. Figure 7 shows these time scales more clearly. For increasing fuel gradient a decrease in the final blowoff time, and the recirculation zone burn time are seen. The final blowoff time is defined by the time when the first mode decreases to 70% of its value far from blowoff. This value was determined as it was the highest percentage that this mode attained that never recovered to its average. Any system developed to track flame dynamics at blowoff should be conditioned to react to the shortest time scale of important dynamics as quantified by these POD results. The time scale for recirculation zone burning can similarly be quantified through POD analysis. For fully burning flames far from blowoff, mode 3
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has a negative time constant for all cases. This means that the contribution of the recirculation zone to the overall chemiluminescence intensity is subtracted. This is balanced by a small positive contribution in mode 1 so that far from blowoff there is little chemiluminescence in the recirculation zone (see Fig. 3). As blowoff approaches, however, the constants associated with mode 3 become positive representing chemiluminescence emission from the recirculation zone. When the energy associated with mode 3 is greater than that of mode 1, the flame is said to have recirculation zone burning and no strong shear layer burning. This cross over between mode 3 and mode 1 can be observed in Fig. 6. The time between this crossover and final blowoff is shown in Fig. 7. For greater fuel gradients, the recirculation zone burn dwell time is reduced. Occasionally the flame will recede into the recirculation zone and then reignite in the shear layers. This occurrence was previously documented for this combustor [16]; however, all reported cases of shear layer re-ignition for flames are for small fuel gradients or uniform fueling. This POD analysis has shown that the dwell time of the flame in the recirculation zone for these small gradient flames is on a longer time scale. This may allow enough time for the flame to reignite. In the larger fuel gradient cases, however, the dwell time is so short that the shear layers do not have a chance to reignite and the recirculation zone burn is imminently followed by flame blowoff. 7. Conclusions
Fig. 7. The times associated with (top) the recirculation zone burn and (bottom) the final blowoff.
The blowoff dynamics of bluff body stabilized flames with various degrees of fuel stratification were examined with high-speed chemiluminescence imaging. It was shown that an increase in stratification decreases the average equivalence ratio about the bluff body at blowoff. Thus, it is suggested that the richer shear layer flame is effective in piloting the weaker flame branch. While the overall average stability margin is increased with more stratification, it is mostly the stronger flame branch that controls flame blowoff. To explore the dynamics of the blowoff process POD was applied to the chemiluminescence images. The POD bases were found from a combined analysis of all gradient cases so that the time constants could be readily compared. The frequency content of the time constants associated with each mode were also studied and this permitted separation of the modes into those associated with vortex shedding versus modes associate with other blowoff phenomena. In these cases, the frequency content associated with modes 4 and higher, as defined in Fig. 5, had a frequency peak corresponding to St = 0.24. Figure 6 showed that as blowoff was approached the energy associated with the BVK
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vortex modes increased suggesting stronger BVK vortex shedding near blowoff. A time scale associated with the final blowoff process was defined based on the departure of the dominant mode (mode 1) from its value far from blowoff. This result showed a decrease in the final blowoff time scale with increased fuel stratification. Likewise, a time scale associated with the burning of reactants in the recirculation zone was determined from the energy associated with mode 3, as shown in Fig. 6. During recirculation zone burning this mode becomes dominant over mode 1 and a dwell time can be defined. A stronger fuel gradient resulted in a smaller dwell time for the recirculation zone burn just prior to blowoff. This explains the observation that reignition of the shear layers after local extinction has been reported for small gradients and uniform fueling cases, but is not observed for large fuel gradients.
Acknowledgement This work was supported by the National Science Foundation (CBET# 0967474) and the Center of Excellence at UConn funded by UTC Pratt & Whitney.
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Proceedings of the
Proceedings of the Combustion Institute 34 (2013) 1491–1498
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Analysis of blowoff dynamics from flames with stratified fueling Kristin M. Kopp-Vaughan, Trevor R. Jensen, Baki M. Cetegen, Michael W. Renfro ⇑ Department of Mechanical Engineering, 191 Auditorium Rd., U-3139, University of Connecticut, Storrs, CT 06269-3139, USA Available online 30 June 2012
Abstract In some compact combustors with bluff body flame stabilization, fuel injection may be too closely coupled to permit uniform mixing. This stratification in the fuel profile can be asymmetric about the bluff body, and the flame equivalence ratio may differ across the recirculation zone. An experimental study of asymmetric fueling about a bluff body is reported in this paper with a focus on the impact of stratification on flame blowoff. In order to understand the blowoff dynamics of turbulent flames with stratified fueling, high speed chemiluminescence imaging was performed for five levels of fuel stratification through blowoff. Physical probe measurements of the local equivalence ratios were used to characterize the stratification. It was found that for overall fuel lean flames (averaged across the bluff body), fuel stratification increases the flame stability such that the overall equivalence ratio at blowoff is decreased for increased stratification. It was also found that the stronger (richer) shear layer determines the flame dynamics near blowoff. The leaner branch of the flame extinguishes earlier and the richer branch is shown to pilot the overall flame and therefore be responsible for the increase in flame stability at larger gradients. Proper orthogonal decomposition (POD) was applied to the high speed chemiluminescence images of the flames and used to quantitatively track the flame front dynamics through blowoff. All flames were found to exhibit Benard–von Karman vortex shedding just prior to blowoff. The POD time constants demonstrate that a strong fuel gradient decreases the time it takes for the flame to shift from its mean fully burning shape to blowoff and decreases the dwell time of the flame in the recirculation zone following local extinction. These time scales indicate a faster blowoff process with fuel stratification. Ó 2012 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Fuel stratification; Blowoff; Bluff body flames; Proper orthogonal decomposition; Chemiluminescence imaging
1. Introduction Flame holding in high-speed turbulent premixed combustible gas streams can be achieved ⇑ Corresponding author. Fax: +1 (860) 486 5088.
E-mail Renfro).
address:
[email protected]
(M.W.
by recirculating flow behind a bluff body that allows hot products to be continually supplied to the attached reaction layers. While this flow field extends the limits for stable premixed combustion, there is still a lower limit of equivalence ratio or an upper limit of velocity beyond which the flame will blow off. These limits are affected by many parameters and flame blowoff limits have been reported
1540-7489/$ - see front matter Ó 2012 The Combustion Institute. Published by Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.proci.2012.06.074
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extensively in the literature for fully premixed conditions. We report here on the effect of non-uniform fueling upstream of the bluff body on both blowoff limits and associated flame dynamics. Fuel stratification in practical combustors commonly occurs due to incomplete mixing between the bluff body and fuel injector. Lovett et al. [1] discuss the design of “legacy” bluff body stabilized flames in augmentors compared to newer “close-coupled” designs. In close-coupled designs, the fuel injectors are closer to the flame holder, even within the holder itself, to mitigate auto ignition at higher turbine exit temperatures of modern engines. One consequence of close coupling is fuel stratification since there is insufficient time to achieve fully premixed conditions. This can cause a difference in chemical time scales along the flame sheet or across the recirculation zone. Moreover, this stratification may be unsteady due to turbulent fluctuations [1]. This study seeks to examine the blowoff dynamics of bluff body stabilized flames in a combustor where the mixture approaching the flame holder is stratified. 2. Background Flame blowoff has been studied extensively for the case of fully premixed reactants. Williams et al. [2] and Longwell et al. [3] suggested that blowoff occurs when the recirculation zone is unable to transfer sufficient heat for ignition at the bluff body. Zukoski and Marble [4] proposed that the mixing time scale of reactants with products must exceed a critical chemical time in order for ignition to occur. This time scale was related to both the recirculation zone aerodynamics and the mixture chemical time scale via a Damko¨hler number (Da). Later, Ozawa [5] used data from many different studies to compile a purely empirical correlation of flame blowoff for non-stratified conditions. Radhakrishnan et al. [6] also reduced many data sets using scaling based on laminar flame speeds and global velocity. These stability parameters indicate that for fuel lean flames as the equivalence ratio decreases and the velocity increases flame blowoff is more likely, consistent with a Da number scaling. However, these types of global stability correlations do not provide insight into the dynamics of flame blowoff. Lieuwen et al. [7] reported flame dynamics at blowoff for flames without fuel stratification. They showed that as a flame approached blowoff, large scale asymmetric vortices became prevalent consistent with the onset of Benard–von Karman (BVK) vortex shedding. This type of vortex shedding it not seen far from blowoff due to the large density differences between reactants and products and the resulting damping of vorticity. Dynamics of flame blowoff for swirl stabilized flames were separately reported [8].
Nair et al. [9] conducted experimental studies of perfectly premixed flames as they approached blowoff. They qualitatively described the general flame dynamics throughout the blowoff process. They state that as flame nears blowoff it begins to transition into a BVK type vortex shedding mode. This mode was later quantified by taking a Fourier transform of flame motion at specific points along a tracked flame front [10]. When the flame front movement produced a frequency with a Strouhal number (St) in the BVK range (St 0.24), the flame exhibited the BVK vortex shedding mode. Flame holes were observed throughout the shear layers and these holes appeared more frequently as blowoff was approached. It was clearly shown that vortex shedding was suppressed for stable flames far from blowoff and that near-blowoff conditions were correlated with high levels of vortex shedding but these results were limited to the case of fully premixed reactants. Fuel stratification is often seen in bluff body flame studies by the intentional piloting of a flame to help it anchor. This type of stratification is known to increase the lean blowoff stability limit. Fetting et al. [11] showed that creating intentionally fuel rich zones in the separation layer behind a cylinder could extend the lean blowoff limit of the flame. They also discovered that for fuel rich flames, stability could be increased by injecting oxygen into the recirculation zone. In experiments by Seffrin et al. [12] fuel was stratified with several different geometries. They showed differences in the flame behavior when increased stratification was provided, but they did not examine flame blowoff dynamics. The fuel stratification was symmetric about the flame holder for all cases and the flames were stabilized with an axisymmetric pilot. The current study investigates flames without piloting. In an experimental study by Pasquier et al. [13], fuel was stratified throughout the combustor such that there were pockets of richer and leaner fuel/air mixtures and flame speeds were measured. They found that the flame speed was highly dependent on the local stratification. The speed of lean flames was increased when it resided near richer flames and decreased when it was nearer to leaner flames. Anselmo-Filho et al. [14] suggest that heat from richer parts of the flame serve to pilot weaker parts of the flame. These studies were not conducted near blowoff and only characterize the heat release and flame speed for stable conditions. Chaudhuri et al. [15,16], using both a small axisymmetric burner and the same experimental facility used in the present work, expanded on the flame dynamics near blowoff that were reported in [10]. Local velocities and strain rates along the flame were measured. Just before blowoff there was a brief period of time when the flame retracted and resided in the recirculation zone
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behind the bluff body [16]. The time scale for this residual flame phenomenon was not quantified but it was shown that burning in the recirculation zone was sometimes sufficient to relight the flame in the shear layers and re-establish it. In the current study, measurements are extended to cases of fuel stratification that are non-symmetric about the bluff body as may occur in practical combustors. 3. Specific objectives The primary goal of this work is to study the stability and dynamics of bluff body flames as they approach blowoff for flames with varying degrees of fuel stratification. The static stability limits in terms of equivalence ratios at blowoff are reported and discussed. This work seeks to expand on the flame dynamics described by Shanbougue et al. [10] and Chaudhuri et al. [15,16] to include flames that are stratified non-symmetrically about the bluff body. The presented work includes quantitative analysis of flame dynamics using high speed chemiluminescence imaging. Proper orthogonal decomposition (POD) is used for image analysis. The POD time constants are used to quantitatively examine the flame blowoff processes and the time scales associated with blowoff dynamics. A discussion of the physical interpretation of the POD modes and their associated time constants is included. 4. Experimental set up A combustion rig developed for studying turbulent partially premixed bluff body stabilized flames was used as schematically shown in Fig. 1 and described in [17]. For these studies, room temperature air was provided with Re = 12,000, where the Reynolds number is based on the bluff body height, H = 9.53 mm, and room-temperature air properties. The incoming turbulence intensity was measured to be approximately 10% [18]. Propane (Airgas Instrument Grade, 99.8%) is provided through three fuel injectors, as shown in Fig. 1, which were separately metered. The fuel injectors are close to the bluff body (60 mm upstream) so that the injected fuel is not well mixed by the time it approaches the triangular shaped bluff body in the test section. The test section is 38.1 mm high and 76.2 mm wide with optical access on three sides, as shown in Fig. 1. The exhaust includes water injection and perforated plates to cool the exhaust gases and damp any acoustics and is then open to the atmosphere [17]. The test section pressure is approximately 1 atm. For this study, four different levels of fuel stratification were employed by varying propane flow
Fig. 1. (top) Schematic of combustion rig and experimental set up: L, lense; F, filter; PMT, photo-multiplier tube. (bottom) Fuel injectors used for stratification.
to each injector. The amount of fuel from each fuel injector is determined by setting a global equivalence ratio (/), based on the total propane flow and total airflow through the rig, and a non-dimensional fuel gradient (G = H d//dx), based on the differences in propane flow rates through each injector. For the equivalence ratio gradient, d//dx, x is the coordinate perpendicular to the flow direction as shown in Fig. 2. We have verified that there are negligible fuel gradients in the span-wise direction of the bluff body as measured in [18]; thus the experiment is statistically two-dimensional. Four different gradients were used in this study: G = 0.25, G = 0.5, G = 0.75, and G = 1 in addition to the case of uniform fueling across the bluff body (G = 0). G = 0.5, for example, corresponds to a difference in equivalence ratio of 0.5 over a distance of one bluff body height. For cases where G P 0.5, no propane was provided to the top fuel injector. After the flame was lit the overall equivalence ratio was lowered slowly in each injector while maintaining the same gradient. When the flame could no longer be stabilized by the bluff body, the flame blew off. The equivalence ratio at which blowoff occurred was recorded. Equivalence ratios were measured using a gas sampling probe. A MEXA 584-L continuous gas analyzer was used to measure the propane and oxygen concentra-
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could affect flame stability. The PMT was fitted with a 432 nm bandpass filter centered on CH* chemiluminescence and a 200 mm objective lens was used to focus on the flame. Only CH* chemiluminescence was collected for consistency with camera collection. The PMT was used to post trigger the camera. Once the intensity from the PMT dropped below a threshold value, the camera was triggered and the last four seconds of data obtained by the camera was saved. 5. Chemiluminescence data analysis
Fig. 2. Equivalence ratios at blowoff versus distance in the direction x, used for defining the equivalence ratio gradient.
tions just upstream of the bluff body with a 2 mm diameter probe. Measurements were taken at equally spaced locations between the top and bottom of the test section. An equivalence ratio, based on molecular volume, at each point was calculated. When flame blowoff was reached the equivalence ratio about the bluff body was found for each gradient case. The fuel profile just upstream of the bluff body at blowoff is shown in Fig. 2 and is discussed further with the results. During the blowoff process, a high speed Photron SA5 monochromatic camera with a 50 mm f/ 1.9 objective lens was used to image the visual chemiluminescence from the flame. The front of the lens was fitted with a 2 close up filter (Hoya) so that the flame would fill the width of the CMOS chip. The filter is not UV transmissive, therefore no OH* chemiluminescence was detected. The camera was set to record at 6000 frames per second. This speed was the fastest speed where flame near blowoff can still be recorded by the camera. A few images for the G = 0.5 gradient case as the flame approaches blowoff are presented in Fig. 3. Each image is normalized by the highest intensity pixel in the image. Far from blowoff both the top and bottom shear layer are seen to be strongly burning. As blowoff approaches the weaker flame branch begins to retract into the recirculation zone sporadically. The flame also begins to show large vortex structures in the stronger flame branch (as observed in Fig. 3). Finally the stronger branch breaks and the flame resides for a short time in the recirculation zone. A quantitative analysis of this process is discussed subsequently. While the camera was recording, a photomultiplier tube (PMT) and a differential pressure transducer simultaneously recorded integrated chemiluminescence intensity and pressure. The pressure sensor was mounted directly above the bluff body to assure no acoustic oscillations occurred in the test section, as these oscillations
In order to quantitatively study the dynamics of these stratified flames during blowoff, POD was implemented on the chemiluminescence images. POD is a statistical method that reduces a set of original data into a set of Eigen bases that contain all of the spatial information and constants that contain all of the temporal information. While several studies have focused on qualitatively examining the POD mode shapes (e.g., [19–23]), this study examines the time constants for quantitative results on blowoff dynamics. This work used the snapshot method of POD [19], represented by ODti ¼
M X atj wji
ð1Þ
j¼1
where ODti is selected snapshots of original data, i is the pixel number, t is the time step, j is the mode number or principal component index, M is the total number of modes, atj are time constants, and wji are the basis functions (commonly referred to as POD modes). Here the bases are found from the eigen vectors of the covariance of the original data matrix. The time constants are found by projecting the original data onto the bases. A detailed description of POD can be found in [19]. We have previously used this POD algorithm on periodic flames with expected modes shapes [24]. In the method of snapshots, the original data to find the bases must not be highly correlated [19]. Kostka et al. [23] used the first minimum of mutual information (MMI) in order to find a sufficient time step between successive images to be selected as snapshots. The concept of mutual information, Z, and using its first minimum is most often seen in image tracking [25] and can be defined by ZðDtÞ ¼
M X M X P kl ðDtÞlnP kl ðDtÞ k¼1 l¼1 M X 2 P k lnP k
ð2Þ
k¼‘
where P kl is the probability that ODti was in a bin I at time t and in bin j at time t + Dt, P k is the probability that ODti was in bin k. The bin denotes a
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Fig. 3. Flame images of G = 0.5 flame through blowoff. The steps shown indicate time prior to blowoff. Each image is separately normalized between the maximum and minimum chemiluminescence signals. The average equivalence ratio at blowoff is / = 0.48.
particular range of pixel intensity counts. Sprott [25] shows that the size of the bin for the probability calculation is not critical. This method was used here and all stratified cases were found to have a minimum in Z corresponding to a time step Dt = 0.67 ms. Thus, POD was conducted on every 4th image collected at 6 kHz from all gradient cases in a single analysis. This provided a single set of bases that represented all of the gradients studied and provides a benefit of direct quantitative comparison between the constants associated with each mode for all of the gradient cases. It is important to note that while only every 4th image was used to find the bases, every image in the original data set was subsequently used to find the time constants, so these constants completely describe the time dependence of each mode for all flame images.
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rately fueled pilot flame from the wake of the bluff body was used. Unlike the study by Fetting et al. [11], the flame pilots itself due to stratification across the recirculation zone in the present case. To characterize the blowoff equivalence ratio, an average value was determined from the measured equivalence ratios from +10 mm to 10 mm (+H to H) since the regions closest to the wall were not fueled [16,17]. For the case of no stratification (G = 0) the mean equivalence ratio about the bluff body at blowoff was 0.63 ± 0.05. This is in agreement with blowoff limits for uniform fueling from [5]. As the fuel gradient increases, the average equivalence ratio at blowoff was found to decrease and reach its lowest value at G = 1 when the overall equivalence ratio is 0.41 ± 0.02. Each blowoff experiment was repeated at least 15 times and the error reported here includes the scatter of these measurements and the error associated with the propane concentration measurement. This decrease in mean equivalence ratio with increasing mixture gradient is expected to be a result of the higher equivalence ratio in the richer flame branch. A richer flame branch can act as a stronger pilot for the leaner flame. This suggests that it is the strength of the stronger flame branch that governs the stability of the flame and therefore the flame dynamics in this shear layer is important to understanding flame blowoff in these cases. It is helpful to directly compare the flame POD results between different fuel gradients. If POD were applied separately to two distinct flame cases, the physical interpretation of the modes may be difficult to correlate. However, because MMI showed that all gradients required the same time step (Dt) to form the reduced data set for POD mode calculation, all of the gradients could be analyzed together. Figure 4 shows a select set of bases from all gradient cases. Only 6 modes are shown but additional modes were also evaluated. The analyzed modes accounted for 90% of the energy in the chemiluminescence images and comprise most of the large scale features of the flow as higher order modes only represent the smaller features in the data. As expected, the first mode represents the mean asymmetric flame shape. In this case, the
6. Results and discussion Figure 2 shows the equivalence ratio profiles at blowoff for each of the five stratification levels. For the G P 0.5 cases, the equivalence ratio of the leaner flame branch at blowoff were below the expected flammability limit for propane at atmospheric conditions of approximately 0.5 [26]. This suggests that the stronger branch of the stratified flame (lower shear layer) serves as a pilot to keep the weaker (upper) branch lit, as was suggested by Fetting et al. [11], where a sepa-
Fig. 4. The first six mode shapes from POD from all flames studied.
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mean shape from all the flames was asymmetric because there were four non-symmetrically fueled cases and only one uniform case. Mode 2 when added to mode 1 represents the symmetric case and is more important for smaller values of G. Mode 3 has contributions to chemiluminescence intensity in the recirculation zone and a negative contribution on the bottom shear layer. This mode, when added to mode 1, represents the process of flame burning in the recirculation zone observed in perfectly premixed and small gradient blowoff events [15,16]. This physical interpretation for mode 3 is subsequently used to quantify the time scale for recirculation zone burning. Modes 4–6 show large coherent vortex structures. Modes 4 and 6 form a pair where the vortex structure is shifted slightly in space. As the constants associated with these two modes oscillate with a fixed phase shift, these modes can represent a vortex convecting down the shear layer. Therefore, by studying the time constants associated with these modes, the frequency content of the vortex street can be determined and the relative importance of the vortex shedding can be calculated. To permit this calculation is it necessary to define which modes represent BVK vortices as opposed to other physical processes such as recirculation zone burning. For BVK vortex shedding over the bluff body a St = 0.24 is expected, as in previous studies [10], which for the flow rate in these experiments corresponds to f = 650 Hz. An FFT was taken from the time constants associated with each mode. Typical examples of the spectra for some modes are shown in Fig. 5. The frequency content associated with modes 4 and higher shows a distinct peak at 650 Hz consistent with BVK vortex shedding. Modes 1, 2, and 3, which represent the steady flame and recirculation zone burning, do not display this oscillation frequency. This method of characterizing BVK vortex shedding is distinct from previous work [10] where a few distinct points along the flame front were evaluated. In this case, time constants represent the entire mode in space and therefore the entire flame front. To further examine the dynamics of these stratified flames near blowoff, each of the constants is normalized in the form of the mode energy. The mode energy is defined as the variance of the mode at an instant in time normalized by the variance of the original data at the same instant and represents the relative contribution of that mode to the instantaneous chemiluminescence signal. Figure 6 shows the energies associated with a few modes for a sample set of fuel gradients. The energy associated with fifth mode was shown to be part of the energy responsible for BVK vortex shedding. The average value of the fifth mode energy is low far from blowoff and increases as blowoff is approached for all cases. This can be seen in Fig. 6 suggesting that that
Fig. 5. The frequency content of selected modes associated with G = 0.75. Modes 4–10 have similar frequency content to mode 5.
Fig. 6. The energy contributions from (top) G = 0.25 and (bottom) G = 1 cases. The black dotted lines denote time scales.
BVK vortex shedding is stronger close to blowoff than it is far from blowoff. Due to the fact that several modes (modes 4–10) are needed to fully describe the vortex shedding it is difficult to assign
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a time scale to this increase in vortex shedding behavior. The energy associated with the first mode decreases to zero as blowoff is approached. Recall that first mode is approximately the average shape for a strongly burning flame. Far from blowoff, most of the energy is contained in the first mode. When the energy of the first mode decreases below 70% of that for a strongly burning flame, the flame always blows off. This 70% value was used as a threshold to determine when the flame has begun to blowoff as shown in Fig. 6. With increased stratification, the flame blowoff process occurs more rapidly. Figure 7 shows these time scales more clearly. For increasing fuel gradient a decrease in the final blowoff time, and the recirculation zone burn time are seen. The final blowoff time is defined by the time when the first mode decreases to 70% of its value far from blowoff. This value was determined as it was the highest percentage that this mode attained that never recovered to its average. Any system developed to track flame dynamics at blowoff should be conditioned to react to the shortest time scale of important dynamics as quantified by these POD results. The time scale for recirculation zone burning can similarly be quantified through POD analysis. For fully burning flames far from blowoff, mode 3
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has a negative time constant for all cases. This means that the contribution of the recirculation zone to the overall chemiluminescence intensity is subtracted. This is balanced by a small positive contribution in mode 1 so that far from blowoff there is little chemiluminescence in the recirculation zone (see Fig. 3). As blowoff approaches, however, the constants associated with mode 3 become positive representing chemiluminescence emission from the recirculation zone. When the energy associated with mode 3 is greater than that of mode 1, the flame is said to have recirculation zone burning and no strong shear layer burning. This cross over between mode 3 and mode 1 can be observed in Fig. 6. The time between this crossover and final blowoff is shown in Fig. 7. For greater fuel gradients, the recirculation zone burn dwell time is reduced. Occasionally the flame will recede into the recirculation zone and then reignite in the shear layers. This occurrence was previously documented for this combustor [16]; however, all reported cases of shear layer re-ignition for flames are for small fuel gradients or uniform fueling. This POD analysis has shown that the dwell time of the flame in the recirculation zone for these small gradient flames is on a longer time scale. This may allow enough time for the flame to reignite. In the larger fuel gradient cases, however, the dwell time is so short that the shear layers do not have a chance to reignite and the recirculation zone burn is imminently followed by flame blowoff. 7. Conclusions
Fig. 7. The times associated with (top) the recirculation zone burn and (bottom) the final blowoff.
The blowoff dynamics of bluff body stabilized flames with various degrees of fuel stratification were examined with high-speed chemiluminescence imaging. It was shown that an increase in stratification decreases the average equivalence ratio about the bluff body at blowoff. Thus, it is suggested that the richer shear layer flame is effective in piloting the weaker flame branch. While the overall average stability margin is increased with more stratification, it is mostly the stronger flame branch that controls flame blowoff. To explore the dynamics of the blowoff process POD was applied to the chemiluminescence images. The POD bases were found from a combined analysis of all gradient cases so that the time constants could be readily compared. The frequency content of the time constants associated with each mode were also studied and this permitted separation of the modes into those associated with vortex shedding versus modes associate with other blowoff phenomena. In these cases, the frequency content associated with modes 4 and higher, as defined in Fig. 5, had a frequency peak corresponding to St = 0.24. Figure 6 showed that as blowoff was approached the energy associated with the BVK
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vortex modes increased suggesting stronger BVK vortex shedding near blowoff. A time scale associated with the final blowoff process was defined based on the departure of the dominant mode (mode 1) from its value far from blowoff. This result showed a decrease in the final blowoff time scale with increased fuel stratification. Likewise, a time scale associated with the burning of reactants in the recirculation zone was determined from the energy associated with mode 3, as shown in Fig. 6. During recirculation zone burning this mode becomes dominant over mode 1 and a dwell time can be defined. A stronger fuel gradient resulted in a smaller dwell time for the recirculation zone burn just prior to blowoff. This explains the observation that reignition of the shear layers after local extinction has been reported for small gradients and uniform fueling cases, but is not observed for large fuel gradients.
Acknowledgement This work was supported by the National Science Foundation (CBET# 0967474) and the Center of Excellence at UConn funded by UTC Pratt & Whitney.
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