- Email: [email protected]
Burning velocity measurements of microgravity spherical sooting premixed flames using rainbow Schlieren deflectometry
Combustion and Flame 140 (2005) 93–102 www.elsevier.com/locate/jnlabr/cnf
Burning velocity measurements of microgravity spherical sooting premixed flames using rainbow S CHLIEREN deflectometry Alfonso F. Ibarreta a,∗ , Chih-Jen Sung a , Taro Hirasawa b , Hai Wang c a Department of Mechanical and Aerospace Engineering, Case Western Reserve University, Cleveland, OH 44106, USA b Department of Mechanical Engineering, Chubu University, Kasugai, Aichi 487-8501, Japan c Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, CA 90089, USA
Received 5 October 2004; received in revised form 14 October 2004; accepted 14 October 2004 Available online 26 November 2004
Abstract The determination of the sooting flame speed of an ethylene/air mixture was explored using two quasi-onedimensional flame configurations: a counterflow configuration in normal gravity and a spherical flame in microgravity. The widely used counterflow configuration was demonstrated to be unsuitable for burning velocity measurements of sooting flames. In the second configuration, a burner-supported, spherical flame was generated by discharging a reactant mixture from a porous spherical burner into a quiescent ambience in microgravity. The purely curved spherical flame allows the measurement of sooting flame speeds without the complications of hydrodynamic straining and heat loss to the burner. A compact rainbow S CHLIEREN deflectometry (RSD) system was developed and utilized to characterize the flame radius and temperature field. This optical technique was able to provide data even under heavily sooting conditions and allowed us to measure the sooting flame speed with reasonable accuracy. The flame speed of an ethylene/air mixture with an equivalence ratio equal to 3.5 was determined. The adiabatic flame speed value predicted by gas-phase reactions, without soot chemistry, was twice the experimental value. Clearly this difference points to the strong influence of soot chemistry and radiation on sooting flame propagation. 2004 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Diagnostics laminar; Laminar experiments; Premixed; Soot
1. Introduction One of the most active endeavors in combustion research has been the determination of the onedimensional laminar flame speed. As a fundamental property of premixed combustion, the laminar * Corresponding author. Fax: +1-216-368-6445.
E-mail address: [email protected] (A.F. Ibarreta).
flame speed has had a notable impact in the development of fuel combustion chemistry. Previous studies, however, have focused solely on nonsooting flames. The determination of sooting flame speeds remains completely undocumented because of limitations of known experimental approaches for such measurements, and difficulties associated with the conceptual definition of “adiabaticity.” There was also little incentive to determine sooting flame speeds, because
0010-2180/$ – see front matter 2004 The Combustion Institute. Published by Elsevier Inc. All rights reserved. doi:10.1016/j.combustflame.2004.10.007
94
A.F. Ibarreta et al. / Combustion and Flame 140 (2005) 93–102
of our inability to account for the detailed kinetics of soot formation in premixed flames. The recent progress in soot chemistry and modeling [1–6] has drastically changed the aforementioned situation. With the growth of our capability to model soot formation, it is now possible to question whether the soot chemistry should be viewed as an integral part of flame chemistry. Indeed, notable advances have been made to model the structure and properties of sooting non-premixed flames [3–5] by considering detailed reaction kinetics, soot chemistry, and mass/heat transport. Progress in soot chemistry modeling of freely propagating premixed flames, however, has been hampered by the lack of suitable experimental techniques/configurations to test the validity of the models. To this end, we note that the sooting flame speed embeds several important and strongly coupled properties of fuel pyrolysis and oxidation, including the sooting tendency of the fuel, fuel consumption, heat release rates, and heat dissipation through radiation. It would be possible to gauge the accuracy and effectiveness of soot and radiation models by simply comparing the resulting burning velocities, over a range of equivalence ratios, with those observed in properly conducted experiments. Therefore, the primary goal of this work is to study the feasibility of measuring the propagation velocity of sooting premixed flames in the absence of conductive heat loss. Two different geometries, namely the counterflow (or stagnation) flame configuration and the spherically symmetric burner-generated flame, were explored. Many techniques have previously been utilized to obtain burning velocities under normal gravity conditions. Among them, the counterflow and stagnation flame configurations have been widely used to obtain burning velocities for nonsooting fuel/air mixtures [7–11]. In the case of the counterflow configuration, two steady identical planar flames are stabilized on each side of the stagnation plane, and the effects of stretch on the burning velocity are later subtracted using well-established methodologies. While the counterflow flame will be used in the present study as a proven method to measure unstretched burning velocities, we will demonstrate in due course that there exist intrinsic limitations in applying this configuration to soot-forming flames. In contrast, burner-generated cylindrical or spherical premixed flames hold the potential to eliminate both conductive heat loss and flow straining, and hence are better suited for sooting flame studies. The feasibility of generating purely curved symmetric flames was first illustrated by Eng et al. [12] in nonsooting cylindrical flames in microgravity. In the present work, we explore this conceptual development further, and demonstrate that it is indeed possible to measure laminar sooting flame speeds in micro-
gravity using this flame configuration. Ethylene/air mixtures were first studied because of the fundamental and practical importance of this fuel. In the following, we will first present the results of counterflow sooting premixed flames, demonstrating that the counterflow configuration is not suited for measuring flame speeds under sooting conditions due to two-dimensional effects intrinsic to this configuration. Next, the spherically symmetric flame geometry will be explored, and the specifications of current microgravity experiments will be detailed. The setup of rainbow S CHLIEREN deflectometry (RSD), methodology for the data reduction, and its associated uncertainties will be discussed. This is followed by results and discussion.
2. Counterflow flame experiments The two-dimensional flow field of an opposedjet flame was measured using digital particle image velocimetry (DPIV). The counterflow twin-flame apparatus used in this work consisted of two nitrogenshrouded, convergent nozzle burners of 10.5-mm exit diameter and 12.0-mm separation distance. The specific details of the DPIV setup and the burner system have been documented elsewhere [11]. Fig. 1 shows axial and radial velocity profiles from a typical DPIV measurement performed for a stretched ethylene/air flame of φ = 2.2. The axial velocity (Fig. 1a) reaches a minimum just ahead of the flame. This minimum axial velocity is customarily used as the reference speed (Su,ref ), and the corresponding axial location is labeled as the reference point. The flame stretch rate (K) is equal to two times the gradient of radial velocity with respect to the radial distance at that reference point, as shown in Fig. 1b. In the past, flame stretch was often determined from the axial velocity profile. This stretch rate can be ambiguous because of nonlinear variation of axial velocity with respect to the axial distance. The use of the radial velocity component has the advantage that this velocity profile is quite linear as a function of the radial distance as seen in Fig. 1b. Fig. 2 plots the measured Su,ref against K for atmospheric ethylene/air flames at φ = 2.2. The laminar flame speed, Suo , is determined by linearly extrapolating the reference speed to K = 0 s−1 . We also include the direct photographs and schematics for flames of two representative stretch rates. Clearly the appearance of the soot layer is highly dependent on the stretch rate and equivalence ratio. For φ < 1.92 no visible soot layer could be observed, whereas for φ > 1.92 the flame/soot structure varied significantly with stretch rate. For small K, a soot layer was sandwiched between twin blue flames. With increasing K,
A.F. Ibarreta et al. / Combustion and Flame 140 (2005) 93–102
95
Fig. 3. Variations of the reference speed and visual appearance of counterflow ethylene/air flames (φ = 2.4), as a function of stretch rate. The figure also demonstrates that extrapolation to zero stretch is inadequate for the present sooting counterflow flames.
Fig. 1. DPIV measurement of a φ = 2.2 ethylene/air counterflow flame. (a) Axial velocity profile and (b) radial velocity profile at the reference point.
Fig. 2. Variations of the reference speed and visual appearance of counterflow ethylene/air flames (φ = 2.2), as a function of stretch rate. The figure also shows how the reference speed is extrapolated to zero stretch to obtain the unstretched burning velocity.
the separation distance between twin flames became smaller. Eventually, for K > 165 s−1 the centers of the two flamelets merged into one, while the soot layer was visible as a ring surrounding it. At a sufficiently large equivalence ratio (φ = 2.4), the variations of the flame/soot structure became more
intricate as seen in Fig. 3. For all stretch rates investigated the twin flames merged completely, including the edge. No flame existed for K > 225 s−1 due to blow-off extinction. For relatively large stretch rates (155 < K < 225 s−1 ), a blue, flat, and merged flamelet was observed. With K reduced to 130– 155 s−1 , the merged flamelet was partially sooting as evidenced by an orange luminous zone at the flame edge. A further decrease in the stretch rate led to a shrinkage and, eventually, the disappearance of the blue flame portion. For K < 130 s−1 , the entire luminous zone is orange with the flame thickened and curved due to buoyancy. These flames were also unstable, as manifested by the large scatter in the data for K ∼ 100 s−1 . There existed a critical stretch rate below which the flame cannot be stabilized, possibly due to excessive flame/soot radiation [13–15] coupled with the effect of buoyancy and heat loss to the nozzle. The above observations clearly indicate that the stretch-rate variation causes fundamental changes in the soot and flame chemistry. For this reason, the approach of extrapolating the reference velocity to zero stretch is invalid for sooting flames. Thus, we conclude that the counterflow configuration is not suited for measuring flame speeds under sooting conditions.
3. Microgravity spherical flame geometry In this section we discuss an alternate, spherically symmetric, burner-generated flame. This geometry offers several advantages. The quasi-1D nature of this geometry means that (theoretically) the local
96
A.F. Ibarreta et al. / Combustion and Flame 140 (2005) 93–102
properties depend only on the radial location, avoiding any complicated flame/soot structural variations. Unlike the planar burner-stabilized case, the divergent nature of the flow provides an additional stabilization mechanism, in that as the flow rate is increased, the flame recedes from the burner and conductive heat loss is reduced to a negligible level. This allows the spherical flame to be stabilized over a wide range of flow rates. These flames are not aerodynamically strained because they are stationary and the flow direction is always normal to the flame surface. Lastly, the soot radiative heat loss can be explicitly defined in the spherical/cylindrical geometry, if the flame is steady and the soot number density and size distribution can be predicted. Thus an “adiabatic” flame (without conductive heat loss) may be defined by considering flame/soot radiation as an intrinsic property of the unburned mixture. Stationary spherically symmetric flames were established under microgravity conditions and studied using the nonintrusive RSD optical method. It is important to note that the use of microgravity is necessary, since under 1g the buoyancy-driven flow would distort the flame symmetry. The experiments were conducted in the 2.2-second Drop Tower Facility at NASA Glenn Research Center. Both spherical and cylindrical burners of different sizes and porosities were initially tested for optimal flame symmetry. This paper will focus on results obtained using a spherical porous brass burner of 0.92 cm diameter with a nominal pore size of 8 µm because the resulting flame shape is satisfactory over a wide range of experimental conditions. The fuel/air mixture was fed into the burner through a tube of 0.15 cm diameter, attached to the bottom of the burner sphere. The mass-flow rate was controlled by sonic nozzles with an accuracy in φ better than 2%. R-type thermocouples were used to record the temperature history of the combustion chamber, burner surface, and gas products downstream of the flame. To facilitate ignition, the combustion chamber was filled with a mixture composed of 10% (by volume) oxygen in nitrogen. The ambient oxygen concentration was kept as low as possible while still supporting ignition. The presence of ambient oxygen led to a weak non-premixed flame surrounding the premixed flame. This non-premixed flame rapidly moved outward in microgravity and its influence diminished during the drop. Two ignition methods were tested: ignition in 1g immediately before the drop and ignition during the microgravity drop; both yielded similar results. Fig. 4 shows the images of flame chemiluminescence of the 1g (left panel) and microgravity (right panel) ethylene/air flames (φ = 3.5). The 1g flame exhibits the characteristic buoyant tear-shaped flame.
Fig. 4. Comparison of sample 1g (left panel) and microgravity (right panel) flames generated with the present spherical porous burner. The microgravity flame is formed using a fuel-rich ethylene/air mixture (φ = 3.5) burning in a 10% oxygen/90% nitrogen atmosphere. The burner mass-flow rate is 0.050 g/s.
The inner premixed flame, located between the burner and the non-premixed flame, is barely discernible. For the microgravity flame, the outer non-premixed flame has moved far beyond the field of view. Both the flame and sooting layer are identifiable. The soot luminosity is relatively low in this case because of the reduced flame temperature at such rich conditions (soot luminosity can overpower chemiluminescence at lower values of rich φ). The microgravity flame will never be perfectly spherical because of the presence of the reactant feed tube and possible imperfections of the burner. The resulting chemiluminescence images and RSD temperature contours, however, indicate that the stand-off distance remains fairly constant around the burner surface. This provides some assurance that the flame is locally spherically symmetric. Unlike non-premixed flames, premixed flames can readily adjust to changes in the flow conditions. Even for a flame with a propagation velocity as low as 4 cm/s, the characteristic flame time is less than 50 ms. For this reason the use of the 2.2-s drop tower facility is deemed adequate. Our experiments also confirmed that the flame reached a steady state during the very early stage of the drop. 3.1. Determination of burning velocity Stationary, burner-generated cylindrical and spherical premixed flames were previously studied using asymptotics with one-step reaction and constant properties by Eng et al. [12] and Qian et al. [16]. These purely curved flames can be stabilized by either heat loss or flow divergence, depending on the flame standoff distance. For small standoff distances, there exists substantial conductive heat loss to the burner surface. When the standoff distance is sufficiently large, the amount of heat loss to the burner surface becomes insignificant and flow divergence is the dominant
A.F. Ibarreta et al. / Combustion and Flame 140 (2005) 93–102
mechanism of flame stabilization. As a result, the ratio of the burner mass-flow rate to the resulting flame surface area was shown to increase with increasing injection rate. This ratio should eventually approach a constant value, equal to the unstretched burning flux [12,16]. To determine the mass flux into the reaction zone it is necessary to determine the radial location of the reaction zone rf . If the mass-flow rate through the burner surface, m ˙ s , is known, the burning flux of a spherical flame surface is given by f =m ˙ s / 4π rf2 . With negligible heat loss to the burner, the fundamental laminar burning flux is f o = f = ρu Suo , where ρu is the mass density of unburned mixture. From the above equations, we can define the fundamental unstretched laminar burning velocity as Suo = m ˙ s / 4πρu rf2 . Therefore, the determination of the flame speed requires only the radial position of the flame, rf , to be determined at a given mass-flow rate m ˙ s. The above expression is valid for an ideal spherically symmetric flame. The blockage by the tube that feeds the reactant mixture naturally must be accounted for in the data analysis. We estimated from visual observation that the blockage covers a solid cone of 35◦ in half-angle or 9% of the total burner surface. The equation for the burning flux was corrected accordingly. It is possible to ascertain the exact percentage of blockage by measuring the flow velocity distribution as a function of burner angle. This measurement was not made here because we estimated that the uncertainty in the percentage of blockage would lead to an uncertainty in the measured flame speed velocity well within 10%. 3.2. Determining flame radius using RSD In this study, the accuracy of the RSD optical technique [17–19] in determining the radial location of the reaction zone was explored. RSD visualization was chosen over other methods because of its simplicity and its ability to provide quantitative information under sooting conditions (to be demonstrated in due course). The technique and its advantages have been discussed elsewhere [20] in the context of nonsooting methane flames. Briefly, RSD can be used to obtain the entire temperature field of a symmetric flowfield from a single image. This technique measures the angular deflection of light as it passes through the test section. While the local deflection is caused by refraction due to gradients of the gas index of refraction, the total deflection is an integral of the local deflections along the beam path, and must be deconvoluted
97
Fig. 5. Schematic of optical system showing both the RSD and the chemiluminescence imaging systems.
to obtain the radial distribution of index of refraction. The spatial resolution of the RSD data depends only on the image pixel size and the spot size of the light source. This technique is also ideal for accurately determining the location of the flame surface, since it is sensitive to large temperature gradients. In addition, RSD can provide information about the flame thickness and temperature distribution [20]. Because of the restrictions imposed by the microgravity drop tower facility, a compact and lightweight system was developed. The optical setup was similar to that of Ref. [21] and is shown in Fig. 5. The light source was a 100-W halogen lamp located on board the rig and its output was guided to a proper location using a 600-µm-diameter fiber optic cable. A 50-µm-wide vertical slit was positioned at the end of the fiber and served as a “point” source. The limited space available restricted the focal length of the focusing lens to 75 cm. Fig. 6 shows the time evolution of a sample microgravity drop (φ = 3.5 and m ˙ s = 0.050 g/s) as seen using both direct imaging (top) and RSD imaging (bottom). The figure demonstrates the ability to image the flame using RSD even for sooting conditions. The RSD images of Fig. 6 also show how the premixed flame zone rapidly stabilizes (within 0.5–0.8 s of the drop). The RSD technique maps the index of refraction relative to a reference value. Currently the system is only sensitive to horizontal changes of the index of refraction, and thus is accurate only near the equator of the spherical flame. In order to obtain quantitative information, the raw RSD images were first converted from RGB to hue values. The hue distribution of a typical µg flame is shown in Fig. 7. Large changes in hue correspond to large horizontal gradients in the index of refraction. The hue was converted to ray deflection values using the rainbow filter calibration curve [18]. The horizontal deflection profiles were further reduced by an Abel inversion, which provided the index of refraction distribution. In order to convert the index of refraction field to a temperature profile, it is first necessary to provide
98
A.F. Ibarreta et al. / Combustion and Flame 140 (2005) 93–102
Fig. 6. Sample time sequence of a µg drop (φ = 3.5 and m ˙ s = 0.050 g/s) using direct imaging (top) and RSD imaging (bottom). Time t = 0 corresponds to the release of the drop package. Ignition occurred at 0.5 s before the drop (t = −0.5 s). The retractable igniter is seen in the first frame of the RSD video. The minor asymmetry on the left side of the RSD image is caused by the intrusion of the thermocouple at the left side of the flame.
Fig. 7. Hue contours for the φ = 3.5 ethylene/air flame at 0.045 g/s mass-flow rate. The minor asymmetry on the left side of the RSD image is caused by the intrusion of the thermocouple on the left.
Fig. 8. Indices of refraction versus temperature. The unburned and burned gas mixtures are those of an ethylene/air flame (φ = 3.5).
a correlation function. The local index of refraction depends mostly on the gas density (and therefore temperature), and to a lesser extent, on the gas composition. For lean methane/air flames, one may assume that the index of refraction is a function of temperature only because the local composition of the gas mixture can be approximated to be that of air [19,20]. For fuel-rich flames and heavy fuel molecules, with refractive indices very different from nitrogen, this assumption is invalid. Fig. 8 plots the indices of refraction as a function of temperature for burned and unburned gas mixtures of an ethylene/air flame (φ = 3.5). The burned gas composition was estimated by an equilibrium calculation. For comparison, the index of refraction of air is also included in the plot. The large variation of the index values clearly indicates it is necessary to account for products and intermediates in the correlation function. In this work, the species concentration profiles were computed using PREMIX [22] and an ethylene reaction model of Ref. [23]. The local refractivities were then calculated using the computed gas density and species concentrations and the database of
Ref. [24]. The resulting index of refraction is plotted in Fig. 8. As expected, the PREMIX calculated index value is close to that of unburned gas at 300 K and approaches that of the equilibrium assumption at high temperatures. The data plotted in Fig. 8 also indicate that the choice of correlation can cause discrepancies in temperature of up to 200 K (comparing equilibrium composition versus PREMIX calculation in the hightemperature region). Ideally, the RSD method requires that the entire density field, from the center to surrounding ambient conditions, be imaged. Because the optics were limited to a 3-inch diameter and the outer mixing layer of the spherical flame rapidly expanded outward, it was not possible to capture the entire temperature field. The data had to be analyzed in a manner such that the ray deflection due to the outer mixing layer was first subtracted out of the total deflection. To do this, the deflection (δy) profile beyond the premixed flame region was fitted with an exponential function, δy = Ar exp(Br), where A and B are fitted coefficients. This functional form was justified on the basis of a numerical study of a spherical flame burning in an
A.F. Ibarreta et al. / Combustion and Flame 140 (2005) 93–102
Fig. 9. Plots of (a) ray deflection profiles before and after subtraction (see text) and (b) resulting temperature field.
atmosphere of room temperature. The resulting function was then subtracted from the entire deflection profile as seen in Fig. 9a. Fig. 9b shows the corresponding temperature profile. Clearly the information regarding the temperature variation in the outer mixing layer is lost and the derived temperature values are constant downstream of the premixed flame. The accuracy of the temperature field through the premixed flame region, however, is still retained. In addition, the RSD method requires a reference temperature to anchor the results. If the lowest temperature point is used as the anchor point, the resulting high-temperature region may become wildly inaccurate [20]. Here we instead chose the maximum gas temperature calculated with the PREMIX code, considering gas-phase reactions only. The use of this reference temperature value led to an accurate prediction of the temperature near the burner surface. Alternatively, we could also use the calculated equilibrium burned-gas temperature. For ethylene/air mixture with φ = 3.5 the maximum temperature from the PREMIX calculation is 1527 K, whereas considering carbon formation we calculated the equilibrium flame temperature to be 1413 K. The measured flame radius, on the other hand, was not sensitive to the choice of maximum flame temperature. We found that the difference in the flame radii was well within the experimental uncertainty even if the peak temperature was reduced by 300 K. The choice of maximum flame temperature, therefore, does not play a major role in deducing the flame speed. The radial location of the reaction zone was determined by the isotherm with temperature of Tmax (1 − 1/Ze). The assumption was made on the basis of an asymptotic analysis [25], which demonstrated that, for a large value of Zeldovich number, Ze, most of the heat release takes place in a region where the local temperature is no less than Tmax by O(1/Ze). Flame structure calculations showed that Ze of rich ethylene/air flames varies almost linearly with the equiva-
99
Fig. 10. Comparison of (a) direct chemiluminescence image and (b) resulting temperature contours obtained using RSD (φ = 3.5 and m ˙ s = 0.050 g/s). Solid lines illustrate how the radial temperature profiles are obtained.
Fig. 11. Sample temperature profiles (symbols) obtained using RSD at varying mass-flow rates. The solid rectangle represents the burner surface. The solid line corresponds to the predicted temperature profile obtained using PREMIX.
lence ratio. Extrapolation to φ = 3.5 gave Ze ≈ 6.2. Therefore, the reaction zone was defined as the location where the temperature is 0.84Tmax . Typically the RSD data at 80 different heights were processed to produce the 2D temperature map, as shown in Fig. 10b. The RSD temperature contours of the φ = 3.5 flame are compared to the direct image shown in Fig. 10a. The mean radial temperature profile was obtained by averaging the 2D data along a family of radial lines with angles ranging from −10 to 10◦ , as depicted in Fig. 10b. It was estimated that the uncertainty in the resulting flame radial location is ±0.3 mm, based on a previous RSD study [20] and the scatter in flame radius at different angles.
4. Results and discussion In this paper, we focus our discussion on data obtained for the φ = 3.5 ethylene/air flames. Fig. 11 shows the temperature profiles measured for flames with 0.025 < m ˙ s < 0.065 g/s. As expected, the standoff distance increased with an increase in m ˙ s.
100
A.F. Ibarreta et al. / Combustion and Flame 140 (2005) 93–102
Fig. 12. Plot of spherical flame radius versus mass-flow rate of reactants. The solid line indicates the expected result for a laminar burning velocity of 3.86 cm/s, assuming there is no conductive heat loss to the burner. The symbols indicate the microgravity data at φ = 3.5.
Fig. 13. Experimentally determined burning flux versus burner mass-flow rate, showing how, for the φ = 3.5 case, the burning flux tends to a constant value. This is the fundamental laminar burning flux.
For small mass-flow rates, the temperature profiles exhibited a discernible nonzero gradient near the burner, indicating measurable conductive heat loss to the burner surface. In addition, the thermocouplemeasured burner temperature at the end of the 2.2-s drop decreased with increasing standoff distance from 60 to 40 ◦ C. The temperature profiles shown in Fig. 11 are also compared to the PREMIX solution (solid line) using the reaction model of Ref. [23]. The flame thickness is herein defined as the distance between the points corresponding to a change in temperature from 10 to 90% of the entire temperature span. The obtained flame thickness of the φ = 3.5 ethylene/air flame averaged about 2.6 mm for the larger flow rates; which is much larger than the 1.52 mm found using PREMIX, indicating that without considering the soot chemistry and radiation, the gas-phase chemistry calculation does not properly model the laminar sooting flame propagation. Fig. 12 shows that, as expected, the flame radius rf generally increases with an increase in the massflow rate. At small flow rates, and thus small standoff distances, the flame radius levels off because of heat loss to the burner. Fig. 13 shows that the measured burning flux f increases with an increase in the burner mass-flow rate, m ˙ s , and approaches a constant value at large m ˙ s . This limiting value was estimated by averaging the measurements for m ˙ s 0.05 g/s; resulting in an upper limit of 0.044 kg/m2 s, shown as the horizontal dashed line in Fig. 13. The normalized mass-flow rate, defined as m ˙ s /(4π R 2 f o ), is also indicated in Fig. 13, where R is the burner radius. The leveling off occurs at a normalized burner flow rate of 4, after which the burning flux is nearly independent of injection rate. This occurs when heat loss to
the burner becomes negligible, and the constant value is therefore the fundamental burning flux f o . The results are in qualitative agreement with the analytical spherical flame model of Qian et al. [16], where the heat loss for a 1-cm-diameter burner becomes negligible for a normalized flow rate > 2.5. The difference in values of critical normalized flow rate is perhaps due to the larger thickness of our flame and the onestep chemistry used in the analysis of Ref. [16]. Having obtained the value of f o = 0.044 kg/m2 s, we calculated Suo to be 3.86 cm/s (±0.25 cm/s) for φ = 3.5. Using this flame speed value, we plot in Fig. 12 the expected dependence of flame radius on the mass-flow rate for a spherical flame surface (solid line). It is seen that the experimental data obtained for the large flow rates agree well with this dependence. Again, the deviation observed at low flow rates is attributable to heat loss to the burner. Fig. 14 shows the nonsooting flame speeds obtained using the counterflow technique [8,11], the sooting flame speed measured using the current spherical flame (φ = 3.5), and the numerical prediction obtained using PREMIX. The nonsooting counterflow flame data compare well with the PREMIX calculation, but no data are available for φ > 1.9. As expected, the experimental burning velocity for the sooting flame case (φ = 3.5) is notably smaller than the computed value. The PREMIX calculated burning velocity at φ = 3.5 is 8.02 cm/s, compared with the experimentally obtained 3.86 cm/s. The PREMIX calculations were performed for an adiabatic flame and do not account for radiative heat loss or downstream heat loss to the surrounding cold gas. Radiation from CH4 , H2 O, CO, and CO2 resulted in a decrease in the maximum flame temperature by 10– 15 K, which can hardly explain the discrepancy be-
A.F. Ibarreta et al. / Combustion and Flame 140 (2005) 93–102
101
to be 3.86 cm/s. A comparison with numerical results shows that gas-phase reactions alone cannot explain the measured flame speed and suggests that the measured flame speed value imbeds the influence of soot chemistry and radiation on sooting flame propagation. Further microgravity experiments extended to other rich equivalence ratios and varying levels of nitrogen dilution are warranted. Acknowledgments
Fig. 14. Experimental (symbols) and computed (lines) laminar flame speeds of atmospheric ethylene/air mixtures. The open and filled circles are previous counterflow results of [8] and [11], respectively. The open square is the present microgravity result.
tween the experimental and computed flame speeds. Note that the chemical reaction model employed does not account for soot formation. Since soot formation can have both a direct influence on the flame chemistry and an indirect influence due to radiative heat loss, it is clear that the burning velocity of a sooting flame cannot be properly modeled without considering soot chemistry and radiation. 5. Conclusions In this work, we have demonstrated that the laminar sooting flame speed can be adequately determined using a spherical premixed flame stabilized under microgravity. The work was motivated by the observation that the widely used counterflow flame technique is unsuitable for the study of the burning velocity of a sooting flame. For the spherical flame technique, flame speed determination was accomplished by measuring the radius of the steady, spherical flame as a function of the mass-flow rate of the unburned mixture. At low flow rates, the obtained burning flux is diminished due to conductive heat loss to the burner. As the burner flow rate is increased, conductive heat loss becomes negligible, and the obtained burning flux approaches its fundamental unstretched value. The determination of the flame location and temperature profile was accomplished by the use of the rainbow S CHLIEREN deflectometry technique. RSD was shown to be a simple and yet powerful method to obtain useful temperature information, especially for spherically symmetric sooting flames in microgravity. The proposed flame configuration, along with the diagnostic technique proposed herein, allow, for the first time, the determination of the laminar sooting flame speed. For the ethylene/air mixture with the equivalence ratio of 3.5, the laminar flame speed was found
This work was supported by the NASA Microgravity Combustion Program with Dr. Merrill King as contract monitor. We also thank Mr. Paul Greenberg and Dr. Fletcher Miller of NASA Glenn Research Center, as well as Prof. Ajay Agrawal at the University of Oklahoma, for many fruitful discussions on the topic of RSD. References [1] M. Frenklach, H. Wang, Proc. Combust. Inst. 23 (1991) 1559–1566. [2] H. Bockhorn (Ed.), Soot Formation in Combustion— Mechanisms and Models, Springer-Verlag, Berlin, 1994, p. 165. [3] H. Wang, D.X. Du, C.J. Sung, C.K. Law, Proc. Combust. Inst. 26 (1996) 2359–2368. [4] R.J. Hall, M.D. Smooke, M.B. Colket, in: R.F. Sawyer, F.L. Dryer (Eds.), Physical and Chemical Aspects of Combustion, in: A Tribute to Irvin Glassman Combustion Science and Technology Book Series, Gordon & Breach, Amsterdam, 1997. [5] M.D. Smooke, C.S. McEnally, L.D. Pfefferle, R.J. Hall, M.B. Colket, Combust. Flame 117 (1999) 117–139. [6] H. Richter, J.B. Howard, Prog. Energy Combust. Sci. 26 (2000) 565–608. [7] D.L. Zhu, F.N. Egolfopoulos, C.K. Law, Proc. Combust. Inst. 22 (1988) 1537–1545. [8] F.N. Egolfopoulos, D.L. Zhu, C.K. Law, Proc. Combust. Inst. 23 (1990) 471–478. [9] C.M. Vagelopoulos, F.N. Egolfopoulos, C.K. Law, Proc. Combust. Inst. 25 (1994) 1341–1347. [10] F.N. Egolfopoulos, H. Zhang, Z. Zhang, Combust. Flame 109 (1997) 237–252. [11] T. Hirasawa, C.J. Sung, A. Joshi, Z. Yang, H. Wang, C.K. Law, Proc. Combust. Inst. 29 (2002) 1427–1434. [12] J.A. Eng, D.L. Zhu, C.K. Law, Proc. Combust. Inst. 25 (1994) 1711–1718. [13] J.A. Platt, J.S. T’ien, Eastern Section Technical Meeting, The Combustion Institute, Orlando, FL, 1990, Paper No. 31. [14] K. Maruta, M. Yoshida, Y. Ju, T. Niioka, Proc. Combust. Inst. 26 (1996) 1283–1289. [15] C.J. Sung, C.K. Law, Proc. Combust. Inst. 26 (1996) 865–873. [16] J. Qian, J.K. Bechtold, C.K. Law, Combust. Flame 110 (1997) 78–91. [17] W.L. Howes, Appl. Opt. 23 (14) (1984) 2449–2459.
102
A.F. Ibarreta et al. / Combustion and Flame 140 (2005) 93–102
[18] P.S. Greenberg, R.B. Klimek, D.R. Buchele, Appl. Opt. 34 (19) (1995) 3810–3822. [19] X. Xiao, I.K. Puri, A.K. Agrawal, Appl. Opt. 41 (10) (2002) 1922–1928. [20] A.F. Ibarreta, C.J. Sung, Joint Meeting of the US Sections, The Combustion Institute, Chicago, 2003, Paper No. P14. [21] K.N. Al-ammar, A.K. Agrawal, S.R. Gollahalli, Proc. Combust. Inst. 28 (2000) 1997–2004. [22] R.J. Kee, J.F. Grcar, M.D. Smooke, J.A. Miller, A Fortran Programming Tool for Modeling Steady Lami-
nar One-Dimensional Premixed Flames, Sandia Report SAND85-8240, Sandia National Laboratories, Livermore, 1985. [23] H. Wang, A. Laskin, A Comprehensive, Kinetic Model of Ethylene and Acetylene Oxidation at High Temperatures, 2000, available at: http://ignis.usc.edu/ c2_download.html. [24] W.C. Gardiner, Y. Hidaka, T. Tanzawa, Combust. Flame 40 (1981) 213–219. [25] F.A. Williams, Combustion Theory, second ed., Addison–Wesley, Reading, MA, 1985, p. 154.
Burning velocity measurements of microgravity spherical sooting premixed flames using rainbow S CHLIEREN deflectometry Alfonso F. Ibarreta a,∗ , Chih-Jen Sung a , Taro Hirasawa b , Hai Wang c a Department of Mechanical and Aerospace Engineering, Case Western Reserve University, Cleveland, OH 44106, USA b Department of Mechanical Engineering, Chubu University, Kasugai, Aichi 487-8501, Japan c Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, CA 90089, USA
Received 5 October 2004; received in revised form 14 October 2004; accepted 14 October 2004 Available online 26 November 2004
Abstract The determination of the sooting flame speed of an ethylene/air mixture was explored using two quasi-onedimensional flame configurations: a counterflow configuration in normal gravity and a spherical flame in microgravity. The widely used counterflow configuration was demonstrated to be unsuitable for burning velocity measurements of sooting flames. In the second configuration, a burner-supported, spherical flame was generated by discharging a reactant mixture from a porous spherical burner into a quiescent ambience in microgravity. The purely curved spherical flame allows the measurement of sooting flame speeds without the complications of hydrodynamic straining and heat loss to the burner. A compact rainbow S CHLIEREN deflectometry (RSD) system was developed and utilized to characterize the flame radius and temperature field. This optical technique was able to provide data even under heavily sooting conditions and allowed us to measure the sooting flame speed with reasonable accuracy. The flame speed of an ethylene/air mixture with an equivalence ratio equal to 3.5 was determined. The adiabatic flame speed value predicted by gas-phase reactions, without soot chemistry, was twice the experimental value. Clearly this difference points to the strong influence of soot chemistry and radiation on sooting flame propagation. 2004 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Diagnostics laminar; Laminar experiments; Premixed; Soot
1. Introduction One of the most active endeavors in combustion research has been the determination of the onedimensional laminar flame speed. As a fundamental property of premixed combustion, the laminar * Corresponding author. Fax: +1-216-368-6445.
E-mail address: [email protected] (A.F. Ibarreta).
flame speed has had a notable impact in the development of fuel combustion chemistry. Previous studies, however, have focused solely on nonsooting flames. The determination of sooting flame speeds remains completely undocumented because of limitations of known experimental approaches for such measurements, and difficulties associated with the conceptual definition of “adiabaticity.” There was also little incentive to determine sooting flame speeds, because
0010-2180/$ – see front matter 2004 The Combustion Institute. Published by Elsevier Inc. All rights reserved. doi:10.1016/j.combustflame.2004.10.007
94
A.F. Ibarreta et al. / Combustion and Flame 140 (2005) 93–102
of our inability to account for the detailed kinetics of soot formation in premixed flames. The recent progress in soot chemistry and modeling [1–6] has drastically changed the aforementioned situation. With the growth of our capability to model soot formation, it is now possible to question whether the soot chemistry should be viewed as an integral part of flame chemistry. Indeed, notable advances have been made to model the structure and properties of sooting non-premixed flames [3–5] by considering detailed reaction kinetics, soot chemistry, and mass/heat transport. Progress in soot chemistry modeling of freely propagating premixed flames, however, has been hampered by the lack of suitable experimental techniques/configurations to test the validity of the models. To this end, we note that the sooting flame speed embeds several important and strongly coupled properties of fuel pyrolysis and oxidation, including the sooting tendency of the fuel, fuel consumption, heat release rates, and heat dissipation through radiation. It would be possible to gauge the accuracy and effectiveness of soot and radiation models by simply comparing the resulting burning velocities, over a range of equivalence ratios, with those observed in properly conducted experiments. Therefore, the primary goal of this work is to study the feasibility of measuring the propagation velocity of sooting premixed flames in the absence of conductive heat loss. Two different geometries, namely the counterflow (or stagnation) flame configuration and the spherically symmetric burner-generated flame, were explored. Many techniques have previously been utilized to obtain burning velocities under normal gravity conditions. Among them, the counterflow and stagnation flame configurations have been widely used to obtain burning velocities for nonsooting fuel/air mixtures [7–11]. In the case of the counterflow configuration, two steady identical planar flames are stabilized on each side of the stagnation plane, and the effects of stretch on the burning velocity are later subtracted using well-established methodologies. While the counterflow flame will be used in the present study as a proven method to measure unstretched burning velocities, we will demonstrate in due course that there exist intrinsic limitations in applying this configuration to soot-forming flames. In contrast, burner-generated cylindrical or spherical premixed flames hold the potential to eliminate both conductive heat loss and flow straining, and hence are better suited for sooting flame studies. The feasibility of generating purely curved symmetric flames was first illustrated by Eng et al. [12] in nonsooting cylindrical flames in microgravity. In the present work, we explore this conceptual development further, and demonstrate that it is indeed possible to measure laminar sooting flame speeds in micro-
gravity using this flame configuration. Ethylene/air mixtures were first studied because of the fundamental and practical importance of this fuel. In the following, we will first present the results of counterflow sooting premixed flames, demonstrating that the counterflow configuration is not suited for measuring flame speeds under sooting conditions due to two-dimensional effects intrinsic to this configuration. Next, the spherically symmetric flame geometry will be explored, and the specifications of current microgravity experiments will be detailed. The setup of rainbow S CHLIEREN deflectometry (RSD), methodology for the data reduction, and its associated uncertainties will be discussed. This is followed by results and discussion.
2. Counterflow flame experiments The two-dimensional flow field of an opposedjet flame was measured using digital particle image velocimetry (DPIV). The counterflow twin-flame apparatus used in this work consisted of two nitrogenshrouded, convergent nozzle burners of 10.5-mm exit diameter and 12.0-mm separation distance. The specific details of the DPIV setup and the burner system have been documented elsewhere [11]. Fig. 1 shows axial and radial velocity profiles from a typical DPIV measurement performed for a stretched ethylene/air flame of φ = 2.2. The axial velocity (Fig. 1a) reaches a minimum just ahead of the flame. This minimum axial velocity is customarily used as the reference speed (Su,ref ), and the corresponding axial location is labeled as the reference point. The flame stretch rate (K) is equal to two times the gradient of radial velocity with respect to the radial distance at that reference point, as shown in Fig. 1b. In the past, flame stretch was often determined from the axial velocity profile. This stretch rate can be ambiguous because of nonlinear variation of axial velocity with respect to the axial distance. The use of the radial velocity component has the advantage that this velocity profile is quite linear as a function of the radial distance as seen in Fig. 1b. Fig. 2 plots the measured Su,ref against K for atmospheric ethylene/air flames at φ = 2.2. The laminar flame speed, Suo , is determined by linearly extrapolating the reference speed to K = 0 s−1 . We also include the direct photographs and schematics for flames of two representative stretch rates. Clearly the appearance of the soot layer is highly dependent on the stretch rate and equivalence ratio. For φ < 1.92 no visible soot layer could be observed, whereas for φ > 1.92 the flame/soot structure varied significantly with stretch rate. For small K, a soot layer was sandwiched between twin blue flames. With increasing K,
A.F. Ibarreta et al. / Combustion and Flame 140 (2005) 93–102
95
Fig. 3. Variations of the reference speed and visual appearance of counterflow ethylene/air flames (φ = 2.4), as a function of stretch rate. The figure also demonstrates that extrapolation to zero stretch is inadequate for the present sooting counterflow flames.
Fig. 1. DPIV measurement of a φ = 2.2 ethylene/air counterflow flame. (a) Axial velocity profile and (b) radial velocity profile at the reference point.
Fig. 2. Variations of the reference speed and visual appearance of counterflow ethylene/air flames (φ = 2.2), as a function of stretch rate. The figure also shows how the reference speed is extrapolated to zero stretch to obtain the unstretched burning velocity.
the separation distance between twin flames became smaller. Eventually, for K > 165 s−1 the centers of the two flamelets merged into one, while the soot layer was visible as a ring surrounding it. At a sufficiently large equivalence ratio (φ = 2.4), the variations of the flame/soot structure became more
intricate as seen in Fig. 3. For all stretch rates investigated the twin flames merged completely, including the edge. No flame existed for K > 225 s−1 due to blow-off extinction. For relatively large stretch rates (155 < K < 225 s−1 ), a blue, flat, and merged flamelet was observed. With K reduced to 130– 155 s−1 , the merged flamelet was partially sooting as evidenced by an orange luminous zone at the flame edge. A further decrease in the stretch rate led to a shrinkage and, eventually, the disappearance of the blue flame portion. For K < 130 s−1 , the entire luminous zone is orange with the flame thickened and curved due to buoyancy. These flames were also unstable, as manifested by the large scatter in the data for K ∼ 100 s−1 . There existed a critical stretch rate below which the flame cannot be stabilized, possibly due to excessive flame/soot radiation [13–15] coupled with the effect of buoyancy and heat loss to the nozzle. The above observations clearly indicate that the stretch-rate variation causes fundamental changes in the soot and flame chemistry. For this reason, the approach of extrapolating the reference velocity to zero stretch is invalid for sooting flames. Thus, we conclude that the counterflow configuration is not suited for measuring flame speeds under sooting conditions.
3. Microgravity spherical flame geometry In this section we discuss an alternate, spherically symmetric, burner-generated flame. This geometry offers several advantages. The quasi-1D nature of this geometry means that (theoretically) the local
96
A.F. Ibarreta et al. / Combustion and Flame 140 (2005) 93–102
properties depend only on the radial location, avoiding any complicated flame/soot structural variations. Unlike the planar burner-stabilized case, the divergent nature of the flow provides an additional stabilization mechanism, in that as the flow rate is increased, the flame recedes from the burner and conductive heat loss is reduced to a negligible level. This allows the spherical flame to be stabilized over a wide range of flow rates. These flames are not aerodynamically strained because they are stationary and the flow direction is always normal to the flame surface. Lastly, the soot radiative heat loss can be explicitly defined in the spherical/cylindrical geometry, if the flame is steady and the soot number density and size distribution can be predicted. Thus an “adiabatic” flame (without conductive heat loss) may be defined by considering flame/soot radiation as an intrinsic property of the unburned mixture. Stationary spherically symmetric flames were established under microgravity conditions and studied using the nonintrusive RSD optical method. It is important to note that the use of microgravity is necessary, since under 1g the buoyancy-driven flow would distort the flame symmetry. The experiments were conducted in the 2.2-second Drop Tower Facility at NASA Glenn Research Center. Both spherical and cylindrical burners of different sizes and porosities were initially tested for optimal flame symmetry. This paper will focus on results obtained using a spherical porous brass burner of 0.92 cm diameter with a nominal pore size of 8 µm because the resulting flame shape is satisfactory over a wide range of experimental conditions. The fuel/air mixture was fed into the burner through a tube of 0.15 cm diameter, attached to the bottom of the burner sphere. The mass-flow rate was controlled by sonic nozzles with an accuracy in φ better than 2%. R-type thermocouples were used to record the temperature history of the combustion chamber, burner surface, and gas products downstream of the flame. To facilitate ignition, the combustion chamber was filled with a mixture composed of 10% (by volume) oxygen in nitrogen. The ambient oxygen concentration was kept as low as possible while still supporting ignition. The presence of ambient oxygen led to a weak non-premixed flame surrounding the premixed flame. This non-premixed flame rapidly moved outward in microgravity and its influence diminished during the drop. Two ignition methods were tested: ignition in 1g immediately before the drop and ignition during the microgravity drop; both yielded similar results. Fig. 4 shows the images of flame chemiluminescence of the 1g (left panel) and microgravity (right panel) ethylene/air flames (φ = 3.5). The 1g flame exhibits the characteristic buoyant tear-shaped flame.
Fig. 4. Comparison of sample 1g (left panel) and microgravity (right panel) flames generated with the present spherical porous burner. The microgravity flame is formed using a fuel-rich ethylene/air mixture (φ = 3.5) burning in a 10% oxygen/90% nitrogen atmosphere. The burner mass-flow rate is 0.050 g/s.
The inner premixed flame, located between the burner and the non-premixed flame, is barely discernible. For the microgravity flame, the outer non-premixed flame has moved far beyond the field of view. Both the flame and sooting layer are identifiable. The soot luminosity is relatively low in this case because of the reduced flame temperature at such rich conditions (soot luminosity can overpower chemiluminescence at lower values of rich φ). The microgravity flame will never be perfectly spherical because of the presence of the reactant feed tube and possible imperfections of the burner. The resulting chemiluminescence images and RSD temperature contours, however, indicate that the stand-off distance remains fairly constant around the burner surface. This provides some assurance that the flame is locally spherically symmetric. Unlike non-premixed flames, premixed flames can readily adjust to changes in the flow conditions. Even for a flame with a propagation velocity as low as 4 cm/s, the characteristic flame time is less than 50 ms. For this reason the use of the 2.2-s drop tower facility is deemed adequate. Our experiments also confirmed that the flame reached a steady state during the very early stage of the drop. 3.1. Determination of burning velocity Stationary, burner-generated cylindrical and spherical premixed flames were previously studied using asymptotics with one-step reaction and constant properties by Eng et al. [12] and Qian et al. [16]. These purely curved flames can be stabilized by either heat loss or flow divergence, depending on the flame standoff distance. For small standoff distances, there exists substantial conductive heat loss to the burner surface. When the standoff distance is sufficiently large, the amount of heat loss to the burner surface becomes insignificant and flow divergence is the dominant
A.F. Ibarreta et al. / Combustion and Flame 140 (2005) 93–102
mechanism of flame stabilization. As a result, the ratio of the burner mass-flow rate to the resulting flame surface area was shown to increase with increasing injection rate. This ratio should eventually approach a constant value, equal to the unstretched burning flux [12,16]. To determine the mass flux into the reaction zone it is necessary to determine the radial location of the reaction zone rf . If the mass-flow rate through the burner surface, m ˙ s , is known, the burning flux of a spherical flame surface is given by f =m ˙ s / 4π rf2 . With negligible heat loss to the burner, the fundamental laminar burning flux is f o = f = ρu Suo , where ρu is the mass density of unburned mixture. From the above equations, we can define the fundamental unstretched laminar burning velocity as Suo = m ˙ s / 4πρu rf2 . Therefore, the determination of the flame speed requires only the radial position of the flame, rf , to be determined at a given mass-flow rate m ˙ s. The above expression is valid for an ideal spherically symmetric flame. The blockage by the tube that feeds the reactant mixture naturally must be accounted for in the data analysis. We estimated from visual observation that the blockage covers a solid cone of 35◦ in half-angle or 9% of the total burner surface. The equation for the burning flux was corrected accordingly. It is possible to ascertain the exact percentage of blockage by measuring the flow velocity distribution as a function of burner angle. This measurement was not made here because we estimated that the uncertainty in the percentage of blockage would lead to an uncertainty in the measured flame speed velocity well within 10%. 3.2. Determining flame radius using RSD In this study, the accuracy of the RSD optical technique [17–19] in determining the radial location of the reaction zone was explored. RSD visualization was chosen over other methods because of its simplicity and its ability to provide quantitative information under sooting conditions (to be demonstrated in due course). The technique and its advantages have been discussed elsewhere [20] in the context of nonsooting methane flames. Briefly, RSD can be used to obtain the entire temperature field of a symmetric flowfield from a single image. This technique measures the angular deflection of light as it passes through the test section. While the local deflection is caused by refraction due to gradients of the gas index of refraction, the total deflection is an integral of the local deflections along the beam path, and must be deconvoluted
97
Fig. 5. Schematic of optical system showing both the RSD and the chemiluminescence imaging systems.
to obtain the radial distribution of index of refraction. The spatial resolution of the RSD data depends only on the image pixel size and the spot size of the light source. This technique is also ideal for accurately determining the location of the flame surface, since it is sensitive to large temperature gradients. In addition, RSD can provide information about the flame thickness and temperature distribution [20]. Because of the restrictions imposed by the microgravity drop tower facility, a compact and lightweight system was developed. The optical setup was similar to that of Ref. [21] and is shown in Fig. 5. The light source was a 100-W halogen lamp located on board the rig and its output was guided to a proper location using a 600-µm-diameter fiber optic cable. A 50-µm-wide vertical slit was positioned at the end of the fiber and served as a “point” source. The limited space available restricted the focal length of the focusing lens to 75 cm. Fig. 6 shows the time evolution of a sample microgravity drop (φ = 3.5 and m ˙ s = 0.050 g/s) as seen using both direct imaging (top) and RSD imaging (bottom). The figure demonstrates the ability to image the flame using RSD even for sooting conditions. The RSD images of Fig. 6 also show how the premixed flame zone rapidly stabilizes (within 0.5–0.8 s of the drop). The RSD technique maps the index of refraction relative to a reference value. Currently the system is only sensitive to horizontal changes of the index of refraction, and thus is accurate only near the equator of the spherical flame. In order to obtain quantitative information, the raw RSD images were first converted from RGB to hue values. The hue distribution of a typical µg flame is shown in Fig. 7. Large changes in hue correspond to large horizontal gradients in the index of refraction. The hue was converted to ray deflection values using the rainbow filter calibration curve [18]. The horizontal deflection profiles were further reduced by an Abel inversion, which provided the index of refraction distribution. In order to convert the index of refraction field to a temperature profile, it is first necessary to provide
98
A.F. Ibarreta et al. / Combustion and Flame 140 (2005) 93–102
Fig. 6. Sample time sequence of a µg drop (φ = 3.5 and m ˙ s = 0.050 g/s) using direct imaging (top) and RSD imaging (bottom). Time t = 0 corresponds to the release of the drop package. Ignition occurred at 0.5 s before the drop (t = −0.5 s). The retractable igniter is seen in the first frame of the RSD video. The minor asymmetry on the left side of the RSD image is caused by the intrusion of the thermocouple at the left side of the flame.
Fig. 7. Hue contours for the φ = 3.5 ethylene/air flame at 0.045 g/s mass-flow rate. The minor asymmetry on the left side of the RSD image is caused by the intrusion of the thermocouple on the left.
Fig. 8. Indices of refraction versus temperature. The unburned and burned gas mixtures are those of an ethylene/air flame (φ = 3.5).
a correlation function. The local index of refraction depends mostly on the gas density (and therefore temperature), and to a lesser extent, on the gas composition. For lean methane/air flames, one may assume that the index of refraction is a function of temperature only because the local composition of the gas mixture can be approximated to be that of air [19,20]. For fuel-rich flames and heavy fuel molecules, with refractive indices very different from nitrogen, this assumption is invalid. Fig. 8 plots the indices of refraction as a function of temperature for burned and unburned gas mixtures of an ethylene/air flame (φ = 3.5). The burned gas composition was estimated by an equilibrium calculation. For comparison, the index of refraction of air is also included in the plot. The large variation of the index values clearly indicates it is necessary to account for products and intermediates in the correlation function. In this work, the species concentration profiles were computed using PREMIX [22] and an ethylene reaction model of Ref. [23]. The local refractivities were then calculated using the computed gas density and species concentrations and the database of
Ref. [24]. The resulting index of refraction is plotted in Fig. 8. As expected, the PREMIX calculated index value is close to that of unburned gas at 300 K and approaches that of the equilibrium assumption at high temperatures. The data plotted in Fig. 8 also indicate that the choice of correlation can cause discrepancies in temperature of up to 200 K (comparing equilibrium composition versus PREMIX calculation in the hightemperature region). Ideally, the RSD method requires that the entire density field, from the center to surrounding ambient conditions, be imaged. Because the optics were limited to a 3-inch diameter and the outer mixing layer of the spherical flame rapidly expanded outward, it was not possible to capture the entire temperature field. The data had to be analyzed in a manner such that the ray deflection due to the outer mixing layer was first subtracted out of the total deflection. To do this, the deflection (δy) profile beyond the premixed flame region was fitted with an exponential function, δy = Ar exp(Br), where A and B are fitted coefficients. This functional form was justified on the basis of a numerical study of a spherical flame burning in an
A.F. Ibarreta et al. / Combustion and Flame 140 (2005) 93–102
Fig. 9. Plots of (a) ray deflection profiles before and after subtraction (see text) and (b) resulting temperature field.
atmosphere of room temperature. The resulting function was then subtracted from the entire deflection profile as seen in Fig. 9a. Fig. 9b shows the corresponding temperature profile. Clearly the information regarding the temperature variation in the outer mixing layer is lost and the derived temperature values are constant downstream of the premixed flame. The accuracy of the temperature field through the premixed flame region, however, is still retained. In addition, the RSD method requires a reference temperature to anchor the results. If the lowest temperature point is used as the anchor point, the resulting high-temperature region may become wildly inaccurate [20]. Here we instead chose the maximum gas temperature calculated with the PREMIX code, considering gas-phase reactions only. The use of this reference temperature value led to an accurate prediction of the temperature near the burner surface. Alternatively, we could also use the calculated equilibrium burned-gas temperature. For ethylene/air mixture with φ = 3.5 the maximum temperature from the PREMIX calculation is 1527 K, whereas considering carbon formation we calculated the equilibrium flame temperature to be 1413 K. The measured flame radius, on the other hand, was not sensitive to the choice of maximum flame temperature. We found that the difference in the flame radii was well within the experimental uncertainty even if the peak temperature was reduced by 300 K. The choice of maximum flame temperature, therefore, does not play a major role in deducing the flame speed. The radial location of the reaction zone was determined by the isotherm with temperature of Tmax (1 − 1/Ze). The assumption was made on the basis of an asymptotic analysis [25], which demonstrated that, for a large value of Zeldovich number, Ze, most of the heat release takes place in a region where the local temperature is no less than Tmax by O(1/Ze). Flame structure calculations showed that Ze of rich ethylene/air flames varies almost linearly with the equiva-
99
Fig. 10. Comparison of (a) direct chemiluminescence image and (b) resulting temperature contours obtained using RSD (φ = 3.5 and m ˙ s = 0.050 g/s). Solid lines illustrate how the radial temperature profiles are obtained.
Fig. 11. Sample temperature profiles (symbols) obtained using RSD at varying mass-flow rates. The solid rectangle represents the burner surface. The solid line corresponds to the predicted temperature profile obtained using PREMIX.
lence ratio. Extrapolation to φ = 3.5 gave Ze ≈ 6.2. Therefore, the reaction zone was defined as the location where the temperature is 0.84Tmax . Typically the RSD data at 80 different heights were processed to produce the 2D temperature map, as shown in Fig. 10b. The RSD temperature contours of the φ = 3.5 flame are compared to the direct image shown in Fig. 10a. The mean radial temperature profile was obtained by averaging the 2D data along a family of radial lines with angles ranging from −10 to 10◦ , as depicted in Fig. 10b. It was estimated that the uncertainty in the resulting flame radial location is ±0.3 mm, based on a previous RSD study [20] and the scatter in flame radius at different angles.
4. Results and discussion In this paper, we focus our discussion on data obtained for the φ = 3.5 ethylene/air flames. Fig. 11 shows the temperature profiles measured for flames with 0.025 < m ˙ s < 0.065 g/s. As expected, the standoff distance increased with an increase in m ˙ s.
100
A.F. Ibarreta et al. / Combustion and Flame 140 (2005) 93–102
Fig. 12. Plot of spherical flame radius versus mass-flow rate of reactants. The solid line indicates the expected result for a laminar burning velocity of 3.86 cm/s, assuming there is no conductive heat loss to the burner. The symbols indicate the microgravity data at φ = 3.5.
Fig. 13. Experimentally determined burning flux versus burner mass-flow rate, showing how, for the φ = 3.5 case, the burning flux tends to a constant value. This is the fundamental laminar burning flux.
For small mass-flow rates, the temperature profiles exhibited a discernible nonzero gradient near the burner, indicating measurable conductive heat loss to the burner surface. In addition, the thermocouplemeasured burner temperature at the end of the 2.2-s drop decreased with increasing standoff distance from 60 to 40 ◦ C. The temperature profiles shown in Fig. 11 are also compared to the PREMIX solution (solid line) using the reaction model of Ref. [23]. The flame thickness is herein defined as the distance between the points corresponding to a change in temperature from 10 to 90% of the entire temperature span. The obtained flame thickness of the φ = 3.5 ethylene/air flame averaged about 2.6 mm for the larger flow rates; which is much larger than the 1.52 mm found using PREMIX, indicating that without considering the soot chemistry and radiation, the gas-phase chemistry calculation does not properly model the laminar sooting flame propagation. Fig. 12 shows that, as expected, the flame radius rf generally increases with an increase in the massflow rate. At small flow rates, and thus small standoff distances, the flame radius levels off because of heat loss to the burner. Fig. 13 shows that the measured burning flux f increases with an increase in the burner mass-flow rate, m ˙ s , and approaches a constant value at large m ˙ s . This limiting value was estimated by averaging the measurements for m ˙ s 0.05 g/s; resulting in an upper limit of 0.044 kg/m2 s, shown as the horizontal dashed line in Fig. 13. The normalized mass-flow rate, defined as m ˙ s /(4π R 2 f o ), is also indicated in Fig. 13, where R is the burner radius. The leveling off occurs at a normalized burner flow rate of 4, after which the burning flux is nearly independent of injection rate. This occurs when heat loss to
the burner becomes negligible, and the constant value is therefore the fundamental burning flux f o . The results are in qualitative agreement with the analytical spherical flame model of Qian et al. [16], where the heat loss for a 1-cm-diameter burner becomes negligible for a normalized flow rate > 2.5. The difference in values of critical normalized flow rate is perhaps due to the larger thickness of our flame and the onestep chemistry used in the analysis of Ref. [16]. Having obtained the value of f o = 0.044 kg/m2 s, we calculated Suo to be 3.86 cm/s (±0.25 cm/s) for φ = 3.5. Using this flame speed value, we plot in Fig. 12 the expected dependence of flame radius on the mass-flow rate for a spherical flame surface (solid line). It is seen that the experimental data obtained for the large flow rates agree well with this dependence. Again, the deviation observed at low flow rates is attributable to heat loss to the burner. Fig. 14 shows the nonsooting flame speeds obtained using the counterflow technique [8,11], the sooting flame speed measured using the current spherical flame (φ = 3.5), and the numerical prediction obtained using PREMIX. The nonsooting counterflow flame data compare well with the PREMIX calculation, but no data are available for φ > 1.9. As expected, the experimental burning velocity for the sooting flame case (φ = 3.5) is notably smaller than the computed value. The PREMIX calculated burning velocity at φ = 3.5 is 8.02 cm/s, compared with the experimentally obtained 3.86 cm/s. The PREMIX calculations were performed for an adiabatic flame and do not account for radiative heat loss or downstream heat loss to the surrounding cold gas. Radiation from CH4 , H2 O, CO, and CO2 resulted in a decrease in the maximum flame temperature by 10– 15 K, which can hardly explain the discrepancy be-
A.F. Ibarreta et al. / Combustion and Flame 140 (2005) 93–102
101
to be 3.86 cm/s. A comparison with numerical results shows that gas-phase reactions alone cannot explain the measured flame speed and suggests that the measured flame speed value imbeds the influence of soot chemistry and radiation on sooting flame propagation. Further microgravity experiments extended to other rich equivalence ratios and varying levels of nitrogen dilution are warranted. Acknowledgments
Fig. 14. Experimental (symbols) and computed (lines) laminar flame speeds of atmospheric ethylene/air mixtures. The open and filled circles are previous counterflow results of [8] and [11], respectively. The open square is the present microgravity result.
tween the experimental and computed flame speeds. Note that the chemical reaction model employed does not account for soot formation. Since soot formation can have both a direct influence on the flame chemistry and an indirect influence due to radiative heat loss, it is clear that the burning velocity of a sooting flame cannot be properly modeled without considering soot chemistry and radiation. 5. Conclusions In this work, we have demonstrated that the laminar sooting flame speed can be adequately determined using a spherical premixed flame stabilized under microgravity. The work was motivated by the observation that the widely used counterflow flame technique is unsuitable for the study of the burning velocity of a sooting flame. For the spherical flame technique, flame speed determination was accomplished by measuring the radius of the steady, spherical flame as a function of the mass-flow rate of the unburned mixture. At low flow rates, the obtained burning flux is diminished due to conductive heat loss to the burner. As the burner flow rate is increased, conductive heat loss becomes negligible, and the obtained burning flux approaches its fundamental unstretched value. The determination of the flame location and temperature profile was accomplished by the use of the rainbow S CHLIEREN deflectometry technique. RSD was shown to be a simple and yet powerful method to obtain useful temperature information, especially for spherically symmetric sooting flames in microgravity. The proposed flame configuration, along with the diagnostic technique proposed herein, allow, for the first time, the determination of the laminar sooting flame speed. For the ethylene/air mixture with the equivalence ratio of 3.5, the laminar flame speed was found
This work was supported by the NASA Microgravity Combustion Program with Dr. Merrill King as contract monitor. We also thank Mr. Paul Greenberg and Dr. Fletcher Miller of NASA Glenn Research Center, as well as Prof. Ajay Agrawal at the University of Oklahoma, for many fruitful discussions on the topic of RSD. References [1] M. Frenklach, H. Wang, Proc. Combust. Inst. 23 (1991) 1559–1566. [2] H. Bockhorn (Ed.), Soot Formation in Combustion— Mechanisms and Models, Springer-Verlag, Berlin, 1994, p. 165. [3] H. Wang, D.X. Du, C.J. Sung, C.K. Law, Proc. Combust. Inst. 26 (1996) 2359–2368. [4] R.J. Hall, M.D. Smooke, M.B. Colket, in: R.F. Sawyer, F.L. Dryer (Eds.), Physical and Chemical Aspects of Combustion, in: A Tribute to Irvin Glassman Combustion Science and Technology Book Series, Gordon & Breach, Amsterdam, 1997. [5] M.D. Smooke, C.S. McEnally, L.D. Pfefferle, R.J. Hall, M.B. Colket, Combust. Flame 117 (1999) 117–139. [6] H. Richter, J.B. Howard, Prog. Energy Combust. Sci. 26 (2000) 565–608. [7] D.L. Zhu, F.N. Egolfopoulos, C.K. Law, Proc. Combust. Inst. 22 (1988) 1537–1545. [8] F.N. Egolfopoulos, D.L. Zhu, C.K. Law, Proc. Combust. Inst. 23 (1990) 471–478. [9] C.M. Vagelopoulos, F.N. Egolfopoulos, C.K. Law, Proc. Combust. Inst. 25 (1994) 1341–1347. [10] F.N. Egolfopoulos, H. Zhang, Z. Zhang, Combust. Flame 109 (1997) 237–252. [11] T. Hirasawa, C.J. Sung, A. Joshi, Z. Yang, H. Wang, C.K. Law, Proc. Combust. Inst. 29 (2002) 1427–1434. [12] J.A. Eng, D.L. Zhu, C.K. Law, Proc. Combust. Inst. 25 (1994) 1711–1718. [13] J.A. Platt, J.S. T’ien, Eastern Section Technical Meeting, The Combustion Institute, Orlando, FL, 1990, Paper No. 31. [14] K. Maruta, M. Yoshida, Y. Ju, T. Niioka, Proc. Combust. Inst. 26 (1996) 1283–1289. [15] C.J. Sung, C.K. Law, Proc. Combust. Inst. 26 (1996) 865–873. [16] J. Qian, J.K. Bechtold, C.K. Law, Combust. Flame 110 (1997) 78–91. [17] W.L. Howes, Appl. Opt. 23 (14) (1984) 2449–2459.
102
A.F. Ibarreta et al. / Combustion and Flame 140 (2005) 93–102
[18] P.S. Greenberg, R.B. Klimek, D.R. Buchele, Appl. Opt. 34 (19) (1995) 3810–3822. [19] X. Xiao, I.K. Puri, A.K. Agrawal, Appl. Opt. 41 (10) (2002) 1922–1928. [20] A.F. Ibarreta, C.J. Sung, Joint Meeting of the US Sections, The Combustion Institute, Chicago, 2003, Paper No. P14. [21] K.N. Al-ammar, A.K. Agrawal, S.R. Gollahalli, Proc. Combust. Inst. 28 (2000) 1997–2004. [22] R.J. Kee, J.F. Grcar, M.D. Smooke, J.A. Miller, A Fortran Programming Tool for Modeling Steady Lami-
nar One-Dimensional Premixed Flames, Sandia Report SAND85-8240, Sandia National Laboratories, Livermore, 1985. [23] H. Wang, A. Laskin, A Comprehensive, Kinetic Model of Ethylene and Acetylene Oxidation at High Temperatures, 2000, available at: http://ignis.usc.edu/ c2_download.html. [24] W.C. Gardiner, Y. Hidaka, T. Tanzawa, Combust. Flame 40 (1981) 213–219. [25] F.A. Williams, Combustion Theory, second ed., Addison–Wesley, Reading, MA, 1985, p. 154.