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Laser imaging of conditional velocities in premixed propane-air flames by simulataneous OH PLIF and PIV
Twenty-Seventh Symposium (International) on Combustion/The Combustion Institute, 1998/pp. 751–758
LASER IMAGING OF CONDITIONAL VELOCITIES IN PREMIXED PROPANE-AIR FLAMES BY SIMULTANEOUS OH PLIF AND PIV PETER A. M. KALT, JONATHAN H. FRANK and ROBERT W. BILGER Department of Mechanical and Mechatronic Engineering The University of Sydney N.S.W. 2006, Australia
;
¯ , of the reaction progress variable, c, is experimentally characterized by The turbulent scalar flux, qu9c9 means of laser-imaging diagnostics. Two-dimensional measurements of the instantaneous velocity and hydroxyl concentration fields are obtained simultaneously by particle image velocimetry (PIV) and qualitative planar laser-induced fluorescence (PLIF), respectively. The combination of these two diagnostic techniques allows the determination of mean conditional velocities. The mean reactant and product velocities are used to infer the turbulent flux of reaction progress variable in turbulent premixed propane/air flames. Four flames having different ratios of root mean square (rms) velocity, u8, to laminar flame speed, SL, are considered. A transition from countergradient to gradient turbulent diffusion is found as u8/SL increases. Such a transition has been predicted by direct numerical simulations (DNSs) but has only been observed in one previous experimental study of turbulent premixed methane/air flames. This work contributes to the experimental evidence of this transition from countergradient to gradient turbulent diffusion and addresses issues related to variations in Lewis number. The results indicate that there is little effect of Lewis number on the transition. It is important to understand this phenomenon so that it may be infcorporated into models of turbulent premixed combustion.
Introduction Laser diagnostics are nonintrusive techniques capable of resolving combustion phenomena normally difficult to observe. This study is a continuation of our earlier work [1,2] to determine the behavior of ; , through the coupling the turbulent scalar flux, qu9c9 ¯ of two laser-imaging methods. The scalar flux is an unclosed term in the turbulent transport equation for the Favre-averaged progress variable, c˜ [3]: q¯
;
]c˜ ˜ • ¹c˜ 4 x ` q¯ U ˙¯ c ` ¹ • [qD¹c 1 q¯ u9c9] ]t
(1)
The turbulent flux term characterizes the structure of the turbulent flame brush [4], and accurately de; has become an imscribing the behavior of qu9c9 ¯ portant research goal [5]. The Bray-Moss-Libby (BML) model for turbulent premixed flames [6–8] qualifies the behavior of the turbulent flux in a gradient or counter-gradient sense in terms of conditional mean velocities, u¯p and u¯r. According to the BML formalism, the turbulent flux of c˜ is given as
;
q¯ u9c9 4 q¯ c˜(1 1 c˜)(u¯p 1 u¯ r)
;
(2)
where positive values of qu9c9 ¯ correspond to
counter-gradient diffusion and negative values correspond to gradient diffusion. ; is inferred from conditional A value for qu9c9 ¯ mean velocities measured using a laser-imaging system developed at the University of Sydney [1,2]. Simultaneous two-dimensional measurements of the instantaneous velocity and hydroxyl (OH) fields are obtained by particle image velocimetry (PIV) and qualitative planar laser-induced fluorescence (PLIF), respectively. The instantaneous OH fluorescence image is used to demarcate regions of product and reactant within the turbulent flame brush. An ensemble of PIV images are conditionally evaluated to determine mean product, u¯p, and reactant, u¯r, velocities. Studies using direct numerical simulations (DNSs) at low [9,10] and high [11] turbulence intensities have found counter-gradient diffusion for low relative turbulence, u8/SL 4 1, and gradient diffusion at high relative turbulence, u8/SL 4 10. Here u8 is the turbulent rms velocity and SL is the laminar flame speed. These findings are confirmed in the previous experimental study of methane-air flames [1,2]: A transition from strong counter-gradient diffusion through to gradient diffusion is observed as u8/SL is increased from 2 to 9.
751
752
PREMIXED TURBULENT COMBUSTION
Fig. 1. Experimental apparatus for simultaneous PIV and OH PLIF measurements in turbulent premixed flames.
The mechanisms that cause this transition are not well understood. Swaminathan et al. [12] show that the characteristics of the turbulent flux are directly related to the instantaneous flame-front structure. Some insight may be gained from velocities near the instantaneous flame front. The present experimental technique is capable of evaluating velocity vectors based on position relative to the instantaneous flame front. By considering only vectors adjacent to the instantaneous flame front, so-called mean strip-conditioned velocities can be determined. A comparison between the strip- and zone-conditioned mean velocities indicates how the velocity fields at the flame front and the bulk fluid differ. This study applies the laser-imaging system to turbulent premixed flames of propane and air for which the Lewis number of the deficient reactant, propane, is much greater than unity. For methane-air flames studied, the Lewis number is close to unity. By examining propane-air flames and comparing with methane-air flame data [1,2], the effect of nonunity Lewis numbers on the observed behavior of scalar flux is found.
Experimental Method The experimental setup is subsequently described briefly with a more complete description reported in Frank et al. [1,2]. A premixed propane-air flame is stabilized on a 36mm-diameter axisymmetric piloted Bunsen-style burner. The stoichiometry of the fuel-air mixture is varied while the mean exit velocity is maintained at approximately 4.9 m/s. Turbulence is generated by a perforated grid, located upstream of the burner exit.
The layout of the burner and fuel delivery system used in this study are the same as those used by Frank et al. [1,2]. Zone-conditioned mean velocities of both reactants and products are determined experimentally. Particle image velocimetry measures a two-dimensional velocity field within a premixed turbulent flame and is simultaneously coupled with PLIF of the OH radical. Regions of product and reactant are demarcated by the contours of the OH radical concentration. These zone-conditioned mean product and reactant velocities, u¯p and u¯r, are measured in propane-air flames for relative turbulence ranging from u8/SL ' 2.4 → 8.5. The relative turbulence is manipulated in two ways: first, by altering the upstream position of the turbulence generating grid (to vary the rms fluctuations of the flow velocity, u8). Second, by altering the stoichiometry of the propane-air mixture (to vary the laminar flame speed, SL). Figure 1 shows the layout of the optical setup. An ultraviolet-sensitive intensifier coupled to a Photometrics Star-1 CCD camera is used to image OH PLIF. A Photometrics Star-1 CCD camera is used to capture the instantaneous Mie-scattering particle images used for PIV. Images returned from the Star1 CCDs are 576 pixels wide by 384 pixels high. The magnification of the PIV camera (M ' 3.3) is greater than that of the PLIF camera. The region imaged by the PIV camera is a subset of the region imaged by the PLIF camera. The PIV images covered an area 4.5 mm wide by 2.8 mm high. The flame brush thickness varies with the stoichiometry of the propane-air mixture and is typically 10–15 mm wide at the imaging location. In order to image a larger cross section of the turbulent
LASER IMAGING OF CONDITIONAL VELOCITIES TABLE 1 Turbulent premixed propane-air flame parameters (u8 and SL are given in ms11) Flame
u8/SL
f
s
u8
SL
A B C D
2.4 2.7 5.0 8.5
1.0 0.7 0.7 0.6
6.68 5.47 5.47 4.83
0.97 0.62 1.15 1.13
0.40 0.23 0.23 0.13
flame brush, data sets from adjacent regions are collected for each flame configuration. The positions of the data sets are fixed relative to the burner. The center of the combined imaging region for the twin adjacent data sets is 16 mm off the burner axis and 28 mm downstream of the burner exit. Illumination for the PIV Mie scattering is provided by a double-pulsed Nd:YAG laser and harmonic generator producing two 532-nm wavelength laser pulses. The interval between successive PIV pulses is 25 ls. The camera shutter remains open for this period, and both Mie-scattering images of the particles are collected in one exposure. Autocorrelation PIV calculations can resolve a vector field showing fluid velocities, provided there is no flow reversal. For the burner used in this study, the flow is streaming at all locations. Triggered between the two PIV laser sheet pulses is a 283-nm wavelength pulse from a Nd:YAG pumped dye laser. This laser sheet is spatially coincident with the PIV laser sheets and excites the fluorescence of the OH radical in a region encompassing the PIV imaging region. Cropping provides an image of OH fluorescence corresponding to the imaging region resolved by PIV. Each data set consists of between 200 and 240 image pairs. The OH fluorescence image is normalized to account for energy density variations in the exciting laser sheet. The normalized OH fluorescence image is used to locate the instantaneous flame front using the sharp gradient in the OH signal. A threshold value is assigned to distinguish between reactant and product zones. A threshold value is selected for each image as the average OH signal value occurring at the points where OH signal gradients are maximum. A binary mask image is created from the OH fluorescence image, indicating only burned and unburned zones. The border between the two zones indicates the instantaneous flame front location. Using this mask to conditionally resolve burned and unburned regions of the PIV particle image produces two velocity vector fields, one each for the burned and unburned regions of the PIV image. The PIV image is broken into 0.9 by 0.9 mm, overlapping subregions with a 50% offset. The final vector fields are 8 vectors by 5 vectors. The mask
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images produced from an entire dataset are ensemble averaged to provide the Reynolds mean progress variable, c¯ [14]. This quantity indicates position through the flame brush, where c¯ 4 0 is the unburned state and c¯ 4 1 is the fully reacted state. Values of c¯, for 0 , c¯ , 1, correspond to locations within the turbulent flame brush that may exist as either burned or unburned. The burned velocity fields produced by conditionally evaluating the PIV images are averaged to provide the zone-conditioned mean product velocity field, u¯p. The zone-conditioned mean reactant velocity field, u¯r, is similarly determined. Each vector in these velocity fields corresponds to a fixed position in the turbulent flame brush and hence to a value of c¯. Later, the same PIV image is processed again. The binary mask is modified to evaluate areas of the PIV image that are within 0.9 mm of the instantaneous flame front only. Only vectors immediately adjacent to the instantaneous flame front are resolved. The particle image outside the strip area is not evaluated. These burned and unburned velocity fields are ensemble averaged to provide strip-conditioned mean velocities of the products and reactants, u¯p,strip and u¯r,strip, respectively. Results and Discussion Table 1 shows the flame parameters for the various premixed propane-air flames that have been investigated. The turbulence ratio u8/SL ranges from 2.4 to 8.5. The laminar flame speed SL is a function of the equivalence ratio of the propane-air mixture. Values of SL are taken from the experimental data of Vagelopoulos et al. [15]. The heat release parameter, s, is obtained from one-dimensional laminar flame calculations and describes the volumetric expansion of gases across the flame front normalized by the upstream value. The root mean square of the velocity fluctuations, u8, is a measure of the turbulence of the flow and is directly affected by the upstream distance to the turbulence-generating grid. The values cited in Table 1 for u8 are calculated from the axial component of the unburned velocities resolved by PIV. Only the dataset closest to the burner axis is used to calculate u8 because c¯ is lower in this region and unburned fluid velocities more commonly occur. Flames B and C have the same stoichiometry but different turbulence intensity due to different locations of the turbulence-generating grid. In flames A, C, and D, the turbulence-generating grid is at the same distance upstream of the burner exit with the equivalence ratio of the fuel-air mixture being varied. The variation in u8 is due to the change in location of the flame brush. Zone-Conditioned Mean Velocities The plots of the radial zone-conditioned velocities for each flame configuration in Table 1 are presented
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PREMIXED TURBULENT COMBUSTION
Fig. 2. Radial conditional mean velocities for flame A.
Fig. 3. Radial conditional mean velocities for flame B.
Fig. 4. Radial conditional mean velocities for flame C.
Fig. 5. Radial conditional mean velocities for flame D.
in Figs. 2–5. For the radial direction, a steady progression in the behavior of the zone-conditioned mean velocities is clearly evident. In the case of flame A (u8/SL 4 2.4), the mean radial velocity of the products is higher than that of the reactants by an average of 1.5 m/s (Fig. 2). Equation 2 gives a ¯ ; in the radial direction, and positive value of qu9c9 the flame A case corresponds to strong counter-gradient diffusion. In flame B (u8/SL 4 2.7), mean radial product velocities are on average 0.4 m/s higher than the mean radial velocity of the reactants (Fig. 3). This also indicates counter-gradient diffusion, although weaker than that observed in the flame A case. In flame C (u8/SL 4 5.0), the radial components of the product and reactant mean velocities are similar throughout the flame brush. Here the ¯ ; is close to zero according radial component of qu9c9 to equation 2, which indicates no turbulent scalar flux in this direction. Finally, in flame D (u8/SL 4 8.5), gradient behavior is observed. In this case, the mean product velocity is lower than the mean reactant velocity in the radial direction. The value of qu9c9 ¯ ; calculated from equation 2 is negative, indicating gradient flux of c˜ in the radial direction. In these high heat release flames, a transition in the behavior of the radial component of the turbulent scalar flux, from strongly counter-gradient to gradient, is observed over the range of u8/SL from 2.4 → 8.5. The axial components of the mean reactant and product velocities also demonstrate this behavior; however, the transition to gradient diffusion occurs earlier and becomes more strongly gradient as u8/SL increases. It should be pointed out that in these flames, contours of c¯ are roughly parallel to the burner axis, and the radial velocity components are approximately normal to the turbulent flame brush. Strip-Conditioned Mean Velocities Figures 6 through 9 show the radial strip-conditioned velocities for the various flame configurations
LASER IMAGING OF CONDITIONAL VELOCITIES
Fig. 6. Strip- and zone-conditioned mean radial velocities for flame A.
Fig. 7. Strip- and zone-conditioned mean radial velocities for flame B.
given in Table 1. The solid lines in these figures are the curve fits to the zone-conditioned mean velocities presented in Figs. 2–5. The strip-conditioned velocities, being a subset of the zone-conditioned velocities, have a smaller sample size and exhibit higher scatter compared to the zone-conditioned data. This is particularly noticeable for strip-averaged burned velocities in positions of low c¯. This results from the fact that burned velocities are less probable in regions of the turbulent flame brush where c¯ is low. Similarly, the scatter of unburned velocities increases in areas of high c¯. The width of the strip used to evaluate the strip-conditioned velocities is of a similar dimension as the flame front thickness. The strip-conditioned mean velocities, though noisy, give a useful qualitative measurement of the behavior of velocities at the flame front. Stripconditioned mean velocities reveal differences in the
755
Fig. 8. Strip- and zone-conditioned mean radial velocities for flame C.
Fig. 9. Strip- and zone-conditioned mean radial velocities for flame D.
average behavior of the fluid at the flame front compared to the mean velocity of the bulk fluid at the same location. In flame A (u8/SL 4 2.4), shown in Fig. 6, the product velocities close to the flame front are slightly lower than those in the bulk fluid, indicating that the acceleration of hot products extends beyond the narrow strip used for conditioning the strip data. In this flame, reactant velocities close to the flame front are the same as those observed in the bulk fluid. In flames B (u8/SL 4 2.7), C (u8/SL 4 5.0), and D (u8/ SL 4 8.5), the reactant velocities at the flame front are less than the reactant velocities in the bulk fluid. Toward the outer edge of the turbulent flame brush (i.e., c¯ → 1), the sampling rate of reactants drops off, because it becomes less likely for the flame to be
756
PREMIXED TURBULENT COMBUSTION
heat release (u8/SL 4 10, s 4 3), and exhibited gradient diffusion. One interpretation of these results is that such flames preferentially consume those pockets of unburned gas that are moving the slowest. Turbulent Scalar Flux The axial and radial components of the turbulent ; , can be modeled using equation 2 ¯ scalar flux, qu9c9 and the experimentally determined values for the conditional mean velocities. Values of c˜ are found using the definition of the Favre mean, c˜ 4 qc/q¯ , and the thin reaction zone assumption employed in the derivation of equation 2 to give c˜ 4
c¯ 1 ` s(1 1 c¯)
(3)
Figure 10 shows the radial and axial components ; . The transition ¯ of the calculated scalar flux, qu9c9 from counter-gradient to gradient behavior is seen in both the axial and radial directions. Comparing the data of this study to the data of Frank et al. [1,2] in premixed methane-air flames reveals that the behavior of the turbulent flux is not strongly dependent on Lewis number. The trend radially in both the methane-air and propane-air flames is for the scalar flux to have strong countergradient diffusion at low turbulence levels (u8/SL , 4). At moderate turbulence (4 < u8/SL < 5), there is almost no scalar flux in the radial direction. At higher turbulence ratios, u8/SL, the mixing of the gases dominates the acceleration of products caused by heat release and results in increasingly gradient behavior. Interestingly, in both methane-air (Le ' 1) and propane-air (Le k 1) flames, the trend of ; is the same at similar values of u8/SL. qu9c9 ¯ Fig. 10. (a) Radial and (b) axial turbulent scalar flux of flames A–D.
Conclusions unburned in this region. The reactant velocities become highly scattered. The trend for reactant velocities at the flame front to be lower than in the bulk fluid is not observable for c¯ . 0.8. The discrepancy between reactant velocities in the strip and zone averages becomes more prominent as u8/SL increases (Figs. 7–9). Finally, as shown in Fig. 9, the reactant velocities resolved at the flame front are substantially lower than the bulk reactant velocities indicated in the figure by a thick gray line. This finding is consistent with trends found in DNS studies. Mantel and Bilger [13] show that the velocity of reactants just on the unburned side of the instantaneous flame front is lower than the mean velocity of reactants at the same point in the flame brush. This DNS data base was of a highly turbulent flame with moderate
Conditional mean velocity fields in turbulent premixed propane-air flames have been determined using the laser-imaging techniques of PLIF and PIV. These techniques provide information on relative OH concentration and a two-dimensional velocity field, respectively. In processing, velocity information is conditionally evaluated as either product or reactant using the hydroxyl fluorescence field to demarcate the burned and unburned regions of the flame at each instant. Four flames are considered, each having a different value of u8/SL. The conditional mean velocities, u¯p and u¯r, are used to infer ;. A ¯ the behavior of the turbulent scalar flux, qu9c9 transition from counter-gradient to gradient diffusion is observed in these flames as u8/SL increases. This study finds similar qualitative trends as those in the methane-air flames examined by Frank et al. on
LASER IMAGING OF CONDITIONAL VELOCITIES
the same burner. Further, the observed trends occur at similar values of u8/SL as was found in methaneair flames. This paper contributes to the available experimental evidence of a transition to gradient diffusion in highly turbulent flames and is the first experimental evidence of this trend in nonunity Lewis number flames. There appears to be no significant effect of Lewis number on this transition. The technique presented also provides information on velocities close to the flame front, when evaluated conditional on being adjacent (within 0.9 mm) to the instantaneous flame front. Comparison between the zone- and strip-conditioned velocities indicates a change in the manner by which turbulent flames propagate as u8/SL increases. These results corroborate observations made by Mantel and Bilger [13] based on the results of DNS. It remains unclear as to the exact mechanism causing these changes. Further experimental and DNS investigations are necessary to understand if or how the phenomena of flame front structure and turbulent scalar flux are related. Applying this successful technique to turbulent premixed flames with an externally applied pressure gradient has been planned, as considered by Veynante and Poinsot [16], in order to observe the effect of pressure gradient on the behavior of scalar flux. Acknowledgments This work is supported by the Australian Research Council. The authors wish to thank Dr. Frank O’Young and Mr. Giles S. Quinlan for assistance in the laboratory during the process of data collection and setup.
REFERENCES 1. Frank, J. H., Kalt, P. A. M., and Bilger, R. W., Combust. Flame 116:220–232 (1999).
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2. Frank, J. H., Kalt, P. A. M., and Bilger, R. W., in First Australian Conference on Laser Diagnostics and Fluid Mechanics in Combustion, University of Sydney, 1996, pp. 71–76. 3. Bilger, R. W., in Turbulence and Molecular Processes in Combustion, Elsevier Science Publishers, New York, 1993, pp. 267–285. 4. Mantel, T., Borghi, R., and Picart, A., in Ninth Symposium on Turbulent Shear Flows, Kyoto, Japan, 1993, vol. 3, pp. 28-1–28-6. 5. Bray, K. N. C., in Twenty-Sixth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1996, pp. 267–285. 6. Bray, K. N. C., Libby, P. A., Masuya, G., and Moss, J. B., Combust. Sci. Technol. 25:127–140 (1981). 7. Bray, K. N. C., Libby, P. A., and Moss, J. B., Combust. Flame 61:87–102 (1985). 8. Bray, K. N. C. and Libby, P. A., in Turbulent Reacting Flows, Academic Press, London, 1994, pp. 115–151. 9. Zhang, S. and Rutland, C. J., Combust. Flame 102:447–461 (1995). 10. Rutland, C. J. and Cant, R. S., in Proceedings of the Summer Program, Center for Turbulence Research. Stanford, 1994, pp. 75–94. 11. Veynante, D., Trouve´, A., Bray, K. N. C., and Mantel, T., J. Fluid Mech. 332:263–293 (1997). 12. Swaminathan, N., Bilger, R. W., and Ruetsch, G. R., Combust. Sci. Technol. 128:73 (1997). 13. Mantel, T. and Bilger, R. W., Combust. Sci. Technol. 110–111:393–417 (1995). 14. Chew, T. C., Britter, R. E., and Bray, K. N. C., Combust. Flame 75:165–174 (1989). 15. Vagelopoulos, C. M., Egolfopoulos, F. N., and Law, C. K., in Twenty-Fifth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1994, pp. 1341–1347. 16. Veynante, D. and Poinsot, T., in Annual Research Briefs, Center for Turbulence Research, Stanford, 1995, pp. 273–300.
COMMENTS Larry Kostiuk, University of Alberta, Canada. The only concern I have with the results is that the conditional velocities in both the axial and radial directions were reduced as the flow crossed the flame. When one adds in the fact that the density of the gases is also reduced, this seems to suggest that a large amount of mass is lost as one crosses the flame. Please provide an explanation. Author’s Reply. For the highest relative turbulence flame case, flame D, both the radial and axial components of the conditional mean product velocities are lower that those of the reactants. As pointed out, this suggests a loss of mass across the flame brush. The explanation for this apparent mass loss lies in the fact that velocities are resolved in a two-dimensional imaging plane intersecting the flame
brush. However, the Bunsen-flame brush examined is not a two-dimensional structure, rather an axisymmetric three-dimensional structure. Examination of the mass flux through constant radius surfaces for the flame D case shows the expected conservation of mass. Caution should be exercised in the consideration of mass flux based on only two components of a nonplanar burner geometry. Also, it can be noted that the conditional product velocities at c˜ 4 1 are higher than the conditional reactant velocities at c˜ 4 0. ● Thomas F. Drouillard II, Colorado School of Mines, USA. How did you determine the PIV interrogation cell
758
PREMIXED TURBULENT COMBUSTION
size (128 2 128)? Many criteria need to be satisfied. A 64 2 64 cell had insufficient particle count due to low seed particle density. Author’s Reply. The PIV interrogation cell size is the resolution of the final PIV vector field. Ideally, the interrogation cell size would be as small as feasible. A 64 2 64 pixel cell did not contain an adequate number of resolved
particle pairs for optimum PIV, particularly in the burned regions of the instantaneous Mie-scattering image where there is an associated drop in gas and particle densities. The vector produced from each PIV interrogation cell using the subpixel controid method, as used in this paper, may be considered as the volume-average velocity over the region. Therefore, the condition mean velocity statistics are not expected to be grossly affected by the size of the PIV interrogation cell.
LASER IMAGING OF CONDITIONAL VELOCITIES IN PREMIXED PROPANE-AIR FLAMES BY SIMULTANEOUS OH PLIF AND PIV PETER A. M. KALT, JONATHAN H. FRANK and ROBERT W. BILGER Department of Mechanical and Mechatronic Engineering The University of Sydney N.S.W. 2006, Australia
;
¯ , of the reaction progress variable, c, is experimentally characterized by The turbulent scalar flux, qu9c9 means of laser-imaging diagnostics. Two-dimensional measurements of the instantaneous velocity and hydroxyl concentration fields are obtained simultaneously by particle image velocimetry (PIV) and qualitative planar laser-induced fluorescence (PLIF), respectively. The combination of these two diagnostic techniques allows the determination of mean conditional velocities. The mean reactant and product velocities are used to infer the turbulent flux of reaction progress variable in turbulent premixed propane/air flames. Four flames having different ratios of root mean square (rms) velocity, u8, to laminar flame speed, SL, are considered. A transition from countergradient to gradient turbulent diffusion is found as u8/SL increases. Such a transition has been predicted by direct numerical simulations (DNSs) but has only been observed in one previous experimental study of turbulent premixed methane/air flames. This work contributes to the experimental evidence of this transition from countergradient to gradient turbulent diffusion and addresses issues related to variations in Lewis number. The results indicate that there is little effect of Lewis number on the transition. It is important to understand this phenomenon so that it may be infcorporated into models of turbulent premixed combustion.
Introduction Laser diagnostics are nonintrusive techniques capable of resolving combustion phenomena normally difficult to observe. This study is a continuation of our earlier work [1,2] to determine the behavior of ; , through the coupling the turbulent scalar flux, qu9c9 ¯ of two laser-imaging methods. The scalar flux is an unclosed term in the turbulent transport equation for the Favre-averaged progress variable, c˜ [3]: q¯
;
]c˜ ˜ • ¹c˜ 4 x ` q¯ U ˙¯ c ` ¹ • [qD¹c 1 q¯ u9c9] ]t
(1)
The turbulent flux term characterizes the structure of the turbulent flame brush [4], and accurately de; has become an imscribing the behavior of qu9c9 ¯ portant research goal [5]. The Bray-Moss-Libby (BML) model for turbulent premixed flames [6–8] qualifies the behavior of the turbulent flux in a gradient or counter-gradient sense in terms of conditional mean velocities, u¯p and u¯r. According to the BML formalism, the turbulent flux of c˜ is given as
;
q¯ u9c9 4 q¯ c˜(1 1 c˜)(u¯p 1 u¯ r)
;
(2)
where positive values of qu9c9 ¯ correspond to
counter-gradient diffusion and negative values correspond to gradient diffusion. ; is inferred from conditional A value for qu9c9 ¯ mean velocities measured using a laser-imaging system developed at the University of Sydney [1,2]. Simultaneous two-dimensional measurements of the instantaneous velocity and hydroxyl (OH) fields are obtained by particle image velocimetry (PIV) and qualitative planar laser-induced fluorescence (PLIF), respectively. The instantaneous OH fluorescence image is used to demarcate regions of product and reactant within the turbulent flame brush. An ensemble of PIV images are conditionally evaluated to determine mean product, u¯p, and reactant, u¯r, velocities. Studies using direct numerical simulations (DNSs) at low [9,10] and high [11] turbulence intensities have found counter-gradient diffusion for low relative turbulence, u8/SL 4 1, and gradient diffusion at high relative turbulence, u8/SL 4 10. Here u8 is the turbulent rms velocity and SL is the laminar flame speed. These findings are confirmed in the previous experimental study of methane-air flames [1,2]: A transition from strong counter-gradient diffusion through to gradient diffusion is observed as u8/SL is increased from 2 to 9.
751
752
PREMIXED TURBULENT COMBUSTION
Fig. 1. Experimental apparatus for simultaneous PIV and OH PLIF measurements in turbulent premixed flames.
The mechanisms that cause this transition are not well understood. Swaminathan et al. [12] show that the characteristics of the turbulent flux are directly related to the instantaneous flame-front structure. Some insight may be gained from velocities near the instantaneous flame front. The present experimental technique is capable of evaluating velocity vectors based on position relative to the instantaneous flame front. By considering only vectors adjacent to the instantaneous flame front, so-called mean strip-conditioned velocities can be determined. A comparison between the strip- and zone-conditioned mean velocities indicates how the velocity fields at the flame front and the bulk fluid differ. This study applies the laser-imaging system to turbulent premixed flames of propane and air for which the Lewis number of the deficient reactant, propane, is much greater than unity. For methane-air flames studied, the Lewis number is close to unity. By examining propane-air flames and comparing with methane-air flame data [1,2], the effect of nonunity Lewis numbers on the observed behavior of scalar flux is found.
Experimental Method The experimental setup is subsequently described briefly with a more complete description reported in Frank et al. [1,2]. A premixed propane-air flame is stabilized on a 36mm-diameter axisymmetric piloted Bunsen-style burner. The stoichiometry of the fuel-air mixture is varied while the mean exit velocity is maintained at approximately 4.9 m/s. Turbulence is generated by a perforated grid, located upstream of the burner exit.
The layout of the burner and fuel delivery system used in this study are the same as those used by Frank et al. [1,2]. Zone-conditioned mean velocities of both reactants and products are determined experimentally. Particle image velocimetry measures a two-dimensional velocity field within a premixed turbulent flame and is simultaneously coupled with PLIF of the OH radical. Regions of product and reactant are demarcated by the contours of the OH radical concentration. These zone-conditioned mean product and reactant velocities, u¯p and u¯r, are measured in propane-air flames for relative turbulence ranging from u8/SL ' 2.4 → 8.5. The relative turbulence is manipulated in two ways: first, by altering the upstream position of the turbulence generating grid (to vary the rms fluctuations of the flow velocity, u8). Second, by altering the stoichiometry of the propane-air mixture (to vary the laminar flame speed, SL). Figure 1 shows the layout of the optical setup. An ultraviolet-sensitive intensifier coupled to a Photometrics Star-1 CCD camera is used to image OH PLIF. A Photometrics Star-1 CCD camera is used to capture the instantaneous Mie-scattering particle images used for PIV. Images returned from the Star1 CCDs are 576 pixels wide by 384 pixels high. The magnification of the PIV camera (M ' 3.3) is greater than that of the PLIF camera. The region imaged by the PIV camera is a subset of the region imaged by the PLIF camera. The PIV images covered an area 4.5 mm wide by 2.8 mm high. The flame brush thickness varies with the stoichiometry of the propane-air mixture and is typically 10–15 mm wide at the imaging location. In order to image a larger cross section of the turbulent
LASER IMAGING OF CONDITIONAL VELOCITIES TABLE 1 Turbulent premixed propane-air flame parameters (u8 and SL are given in ms11) Flame
u8/SL
f
s
u8
SL
A B C D
2.4 2.7 5.0 8.5
1.0 0.7 0.7 0.6
6.68 5.47 5.47 4.83
0.97 0.62 1.15 1.13
0.40 0.23 0.23 0.13
flame brush, data sets from adjacent regions are collected for each flame configuration. The positions of the data sets are fixed relative to the burner. The center of the combined imaging region for the twin adjacent data sets is 16 mm off the burner axis and 28 mm downstream of the burner exit. Illumination for the PIV Mie scattering is provided by a double-pulsed Nd:YAG laser and harmonic generator producing two 532-nm wavelength laser pulses. The interval between successive PIV pulses is 25 ls. The camera shutter remains open for this period, and both Mie-scattering images of the particles are collected in one exposure. Autocorrelation PIV calculations can resolve a vector field showing fluid velocities, provided there is no flow reversal. For the burner used in this study, the flow is streaming at all locations. Triggered between the two PIV laser sheet pulses is a 283-nm wavelength pulse from a Nd:YAG pumped dye laser. This laser sheet is spatially coincident with the PIV laser sheets and excites the fluorescence of the OH radical in a region encompassing the PIV imaging region. Cropping provides an image of OH fluorescence corresponding to the imaging region resolved by PIV. Each data set consists of between 200 and 240 image pairs. The OH fluorescence image is normalized to account for energy density variations in the exciting laser sheet. The normalized OH fluorescence image is used to locate the instantaneous flame front using the sharp gradient in the OH signal. A threshold value is assigned to distinguish between reactant and product zones. A threshold value is selected for each image as the average OH signal value occurring at the points where OH signal gradients are maximum. A binary mask image is created from the OH fluorescence image, indicating only burned and unburned zones. The border between the two zones indicates the instantaneous flame front location. Using this mask to conditionally resolve burned and unburned regions of the PIV particle image produces two velocity vector fields, one each for the burned and unburned regions of the PIV image. The PIV image is broken into 0.9 by 0.9 mm, overlapping subregions with a 50% offset. The final vector fields are 8 vectors by 5 vectors. The mask
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images produced from an entire dataset are ensemble averaged to provide the Reynolds mean progress variable, c¯ [14]. This quantity indicates position through the flame brush, where c¯ 4 0 is the unburned state and c¯ 4 1 is the fully reacted state. Values of c¯, for 0 , c¯ , 1, correspond to locations within the turbulent flame brush that may exist as either burned or unburned. The burned velocity fields produced by conditionally evaluating the PIV images are averaged to provide the zone-conditioned mean product velocity field, u¯p. The zone-conditioned mean reactant velocity field, u¯r, is similarly determined. Each vector in these velocity fields corresponds to a fixed position in the turbulent flame brush and hence to a value of c¯. Later, the same PIV image is processed again. The binary mask is modified to evaluate areas of the PIV image that are within 0.9 mm of the instantaneous flame front only. Only vectors immediately adjacent to the instantaneous flame front are resolved. The particle image outside the strip area is not evaluated. These burned and unburned velocity fields are ensemble averaged to provide strip-conditioned mean velocities of the products and reactants, u¯p,strip and u¯r,strip, respectively. Results and Discussion Table 1 shows the flame parameters for the various premixed propane-air flames that have been investigated. The turbulence ratio u8/SL ranges from 2.4 to 8.5. The laminar flame speed SL is a function of the equivalence ratio of the propane-air mixture. Values of SL are taken from the experimental data of Vagelopoulos et al. [15]. The heat release parameter, s, is obtained from one-dimensional laminar flame calculations and describes the volumetric expansion of gases across the flame front normalized by the upstream value. The root mean square of the velocity fluctuations, u8, is a measure of the turbulence of the flow and is directly affected by the upstream distance to the turbulence-generating grid. The values cited in Table 1 for u8 are calculated from the axial component of the unburned velocities resolved by PIV. Only the dataset closest to the burner axis is used to calculate u8 because c¯ is lower in this region and unburned fluid velocities more commonly occur. Flames B and C have the same stoichiometry but different turbulence intensity due to different locations of the turbulence-generating grid. In flames A, C, and D, the turbulence-generating grid is at the same distance upstream of the burner exit with the equivalence ratio of the fuel-air mixture being varied. The variation in u8 is due to the change in location of the flame brush. Zone-Conditioned Mean Velocities The plots of the radial zone-conditioned velocities for each flame configuration in Table 1 are presented
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Fig. 2. Radial conditional mean velocities for flame A.
Fig. 3. Radial conditional mean velocities for flame B.
Fig. 4. Radial conditional mean velocities for flame C.
Fig. 5. Radial conditional mean velocities for flame D.
in Figs. 2–5. For the radial direction, a steady progression in the behavior of the zone-conditioned mean velocities is clearly evident. In the case of flame A (u8/SL 4 2.4), the mean radial velocity of the products is higher than that of the reactants by an average of 1.5 m/s (Fig. 2). Equation 2 gives a ¯ ; in the radial direction, and positive value of qu9c9 the flame A case corresponds to strong counter-gradient diffusion. In flame B (u8/SL 4 2.7), mean radial product velocities are on average 0.4 m/s higher than the mean radial velocity of the reactants (Fig. 3). This also indicates counter-gradient diffusion, although weaker than that observed in the flame A case. In flame C (u8/SL 4 5.0), the radial components of the product and reactant mean velocities are similar throughout the flame brush. Here the ¯ ; is close to zero according radial component of qu9c9 to equation 2, which indicates no turbulent scalar flux in this direction. Finally, in flame D (u8/SL 4 8.5), gradient behavior is observed. In this case, the mean product velocity is lower than the mean reactant velocity in the radial direction. The value of qu9c9 ¯ ; calculated from equation 2 is negative, indicating gradient flux of c˜ in the radial direction. In these high heat release flames, a transition in the behavior of the radial component of the turbulent scalar flux, from strongly counter-gradient to gradient, is observed over the range of u8/SL from 2.4 → 8.5. The axial components of the mean reactant and product velocities also demonstrate this behavior; however, the transition to gradient diffusion occurs earlier and becomes more strongly gradient as u8/SL increases. It should be pointed out that in these flames, contours of c¯ are roughly parallel to the burner axis, and the radial velocity components are approximately normal to the turbulent flame brush. Strip-Conditioned Mean Velocities Figures 6 through 9 show the radial strip-conditioned velocities for the various flame configurations
LASER IMAGING OF CONDITIONAL VELOCITIES
Fig. 6. Strip- and zone-conditioned mean radial velocities for flame A.
Fig. 7. Strip- and zone-conditioned mean radial velocities for flame B.
given in Table 1. The solid lines in these figures are the curve fits to the zone-conditioned mean velocities presented in Figs. 2–5. The strip-conditioned velocities, being a subset of the zone-conditioned velocities, have a smaller sample size and exhibit higher scatter compared to the zone-conditioned data. This is particularly noticeable for strip-averaged burned velocities in positions of low c¯. This results from the fact that burned velocities are less probable in regions of the turbulent flame brush where c¯ is low. Similarly, the scatter of unburned velocities increases in areas of high c¯. The width of the strip used to evaluate the strip-conditioned velocities is of a similar dimension as the flame front thickness. The strip-conditioned mean velocities, though noisy, give a useful qualitative measurement of the behavior of velocities at the flame front. Stripconditioned mean velocities reveal differences in the
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Fig. 8. Strip- and zone-conditioned mean radial velocities for flame C.
Fig. 9. Strip- and zone-conditioned mean radial velocities for flame D.
average behavior of the fluid at the flame front compared to the mean velocity of the bulk fluid at the same location. In flame A (u8/SL 4 2.4), shown in Fig. 6, the product velocities close to the flame front are slightly lower than those in the bulk fluid, indicating that the acceleration of hot products extends beyond the narrow strip used for conditioning the strip data. In this flame, reactant velocities close to the flame front are the same as those observed in the bulk fluid. In flames B (u8/SL 4 2.7), C (u8/SL 4 5.0), and D (u8/ SL 4 8.5), the reactant velocities at the flame front are less than the reactant velocities in the bulk fluid. Toward the outer edge of the turbulent flame brush (i.e., c¯ → 1), the sampling rate of reactants drops off, because it becomes less likely for the flame to be
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heat release (u8/SL 4 10, s 4 3), and exhibited gradient diffusion. One interpretation of these results is that such flames preferentially consume those pockets of unburned gas that are moving the slowest. Turbulent Scalar Flux The axial and radial components of the turbulent ; , can be modeled using equation 2 ¯ scalar flux, qu9c9 and the experimentally determined values for the conditional mean velocities. Values of c˜ are found using the definition of the Favre mean, c˜ 4 qc/q¯ , and the thin reaction zone assumption employed in the derivation of equation 2 to give c˜ 4
c¯ 1 ` s(1 1 c¯)
(3)
Figure 10 shows the radial and axial components ; . The transition ¯ of the calculated scalar flux, qu9c9 from counter-gradient to gradient behavior is seen in both the axial and radial directions. Comparing the data of this study to the data of Frank et al. [1,2] in premixed methane-air flames reveals that the behavior of the turbulent flux is not strongly dependent on Lewis number. The trend radially in both the methane-air and propane-air flames is for the scalar flux to have strong countergradient diffusion at low turbulence levels (u8/SL , 4). At moderate turbulence (4 < u8/SL < 5), there is almost no scalar flux in the radial direction. At higher turbulence ratios, u8/SL, the mixing of the gases dominates the acceleration of products caused by heat release and results in increasingly gradient behavior. Interestingly, in both methane-air (Le ' 1) and propane-air (Le k 1) flames, the trend of ; is the same at similar values of u8/SL. qu9c9 ¯ Fig. 10. (a) Radial and (b) axial turbulent scalar flux of flames A–D.
Conclusions unburned in this region. The reactant velocities become highly scattered. The trend for reactant velocities at the flame front to be lower than in the bulk fluid is not observable for c¯ . 0.8. The discrepancy between reactant velocities in the strip and zone averages becomes more prominent as u8/SL increases (Figs. 7–9). Finally, as shown in Fig. 9, the reactant velocities resolved at the flame front are substantially lower than the bulk reactant velocities indicated in the figure by a thick gray line. This finding is consistent with trends found in DNS studies. Mantel and Bilger [13] show that the velocity of reactants just on the unburned side of the instantaneous flame front is lower than the mean velocity of reactants at the same point in the flame brush. This DNS data base was of a highly turbulent flame with moderate
Conditional mean velocity fields in turbulent premixed propane-air flames have been determined using the laser-imaging techniques of PLIF and PIV. These techniques provide information on relative OH concentration and a two-dimensional velocity field, respectively. In processing, velocity information is conditionally evaluated as either product or reactant using the hydroxyl fluorescence field to demarcate the burned and unburned regions of the flame at each instant. Four flames are considered, each having a different value of u8/SL. The conditional mean velocities, u¯p and u¯r, are used to infer ;. A ¯ the behavior of the turbulent scalar flux, qu9c9 transition from counter-gradient to gradient diffusion is observed in these flames as u8/SL increases. This study finds similar qualitative trends as those in the methane-air flames examined by Frank et al. on
LASER IMAGING OF CONDITIONAL VELOCITIES
the same burner. Further, the observed trends occur at similar values of u8/SL as was found in methaneair flames. This paper contributes to the available experimental evidence of a transition to gradient diffusion in highly turbulent flames and is the first experimental evidence of this trend in nonunity Lewis number flames. There appears to be no significant effect of Lewis number on this transition. The technique presented also provides information on velocities close to the flame front, when evaluated conditional on being adjacent (within 0.9 mm) to the instantaneous flame front. Comparison between the zone- and strip-conditioned velocities indicates a change in the manner by which turbulent flames propagate as u8/SL increases. These results corroborate observations made by Mantel and Bilger [13] based on the results of DNS. It remains unclear as to the exact mechanism causing these changes. Further experimental and DNS investigations are necessary to understand if or how the phenomena of flame front structure and turbulent scalar flux are related. Applying this successful technique to turbulent premixed flames with an externally applied pressure gradient has been planned, as considered by Veynante and Poinsot [16], in order to observe the effect of pressure gradient on the behavior of scalar flux. Acknowledgments This work is supported by the Australian Research Council. The authors wish to thank Dr. Frank O’Young and Mr. Giles S. Quinlan for assistance in the laboratory during the process of data collection and setup.
REFERENCES 1. Frank, J. H., Kalt, P. A. M., and Bilger, R. W., Combust. Flame 116:220–232 (1999).
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2. Frank, J. H., Kalt, P. A. M., and Bilger, R. W., in First Australian Conference on Laser Diagnostics and Fluid Mechanics in Combustion, University of Sydney, 1996, pp. 71–76. 3. Bilger, R. W., in Turbulence and Molecular Processes in Combustion, Elsevier Science Publishers, New York, 1993, pp. 267–285. 4. Mantel, T., Borghi, R., and Picart, A., in Ninth Symposium on Turbulent Shear Flows, Kyoto, Japan, 1993, vol. 3, pp. 28-1–28-6. 5. Bray, K. N. C., in Twenty-Sixth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1996, pp. 267–285. 6. Bray, K. N. C., Libby, P. A., Masuya, G., and Moss, J. B., Combust. Sci. Technol. 25:127–140 (1981). 7. Bray, K. N. C., Libby, P. A., and Moss, J. B., Combust. Flame 61:87–102 (1985). 8. Bray, K. N. C. and Libby, P. A., in Turbulent Reacting Flows, Academic Press, London, 1994, pp. 115–151. 9. Zhang, S. and Rutland, C. J., Combust. Flame 102:447–461 (1995). 10. Rutland, C. J. and Cant, R. S., in Proceedings of the Summer Program, Center for Turbulence Research. Stanford, 1994, pp. 75–94. 11. Veynante, D., Trouve´, A., Bray, K. N. C., and Mantel, T., J. Fluid Mech. 332:263–293 (1997). 12. Swaminathan, N., Bilger, R. W., and Ruetsch, G. R., Combust. Sci. Technol. 128:73 (1997). 13. Mantel, T. and Bilger, R. W., Combust. Sci. Technol. 110–111:393–417 (1995). 14. Chew, T. C., Britter, R. E., and Bray, K. N. C., Combust. Flame 75:165–174 (1989). 15. Vagelopoulos, C. M., Egolfopoulos, F. N., and Law, C. K., in Twenty-Fifth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1994, pp. 1341–1347. 16. Veynante, D. and Poinsot, T., in Annual Research Briefs, Center for Turbulence Research, Stanford, 1995, pp. 273–300.
COMMENTS Larry Kostiuk, University of Alberta, Canada. The only concern I have with the results is that the conditional velocities in both the axial and radial directions were reduced as the flow crossed the flame. When one adds in the fact that the density of the gases is also reduced, this seems to suggest that a large amount of mass is lost as one crosses the flame. Please provide an explanation. Author’s Reply. For the highest relative turbulence flame case, flame D, both the radial and axial components of the conditional mean product velocities are lower that those of the reactants. As pointed out, this suggests a loss of mass across the flame brush. The explanation for this apparent mass loss lies in the fact that velocities are resolved in a two-dimensional imaging plane intersecting the flame
brush. However, the Bunsen-flame brush examined is not a two-dimensional structure, rather an axisymmetric three-dimensional structure. Examination of the mass flux through constant radius surfaces for the flame D case shows the expected conservation of mass. Caution should be exercised in the consideration of mass flux based on only two components of a nonplanar burner geometry. Also, it can be noted that the conditional product velocities at c˜ 4 1 are higher than the conditional reactant velocities at c˜ 4 0. ● Thomas F. Drouillard II, Colorado School of Mines, USA. How did you determine the PIV interrogation cell
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size (128 2 128)? Many criteria need to be satisfied. A 64 2 64 cell had insufficient particle count due to low seed particle density. Author’s Reply. The PIV interrogation cell size is the resolution of the final PIV vector field. Ideally, the interrogation cell size would be as small as feasible. A 64 2 64 pixel cell did not contain an adequate number of resolved
particle pairs for optimum PIV, particularly in the burned regions of the instantaneous Mie-scattering image where there is an associated drop in gas and particle densities. The vector produced from each PIV interrogation cell using the subpixel controid method, as used in this paper, may be considered as the volume-average velocity over the region. Therefore, the condition mean velocity statistics are not expected to be grossly affected by the size of the PIV interrogation cell.