Energy Fuels 2009, 23, 4395–4403 Published on Web 07/29/2009
: DOI:10.1021/ef900555u
Formation of Sootshell and Attendant Effects on Droplet Burning Rate and Radiative Heat Transfer in Microgravity Ethanol Droplet Flames Seul-Hyun Park* Department of Mechanical Engineering and Mechanics, Drexel University, Philadelphia, Pennsylvania 19104
Mun Young Choi Department of Mechanical Engineering, University of Connecticut, Storrs, Connecticut 06269-3139 Received May 29, 2009. Revised Manuscript Received July 6, 2009
Microgravity ethanol droplet combustion experiments were performed at the NASA 2.2 s droptower in Cleveland, OH to investigate the formation of sootshell and its attendant influences on the burning behavior and radiative heat transfer. Measurements include the burning rate, soot standoff ratio, soot volume fraction, soot temperature, and radiative heat losses. These experiments demonstrated strong influence of inert gas substitution (that caused changes in the thermophysical properties and temperature) between nitrogen and argon. The experimentally measured soot standoff ratio (SSR) for the argon inert experiment was ∼1.4, whereas the value for the nitrogen inert experiment was ∼2.5. The SSR was also calculated using balance among Stefan, thermophoretic, and diffusiophoretic fluxes. This analysis represents the first quantitative study in which diffusiophoretic transport was considered using experimentally determined gas-phase temperature distributions for the analysis of sootshell formation. The computed values of the SSR are in excellent agreement with the experimental measurements. The location of sootshell influences the radiative heat transfer from the flame to the droplet and to the surrounding environment and can modify the burning rate.
oxide (NOx). However, aldehydes (such as acetaldehyde, C2H4O) emissions are higher with ethanol content in the fuel blend3,4 due to lower oxidation rates.2,4 Therefore, selective emission control for ethanol combustion is an area of research that requires further examination. In an effort to advance the understanding of the burning and emission characteristics of ethanol fuel, microgravity droplet combustion experiments have been pursued since the mid-1970s.6-10 Microgravity environments provides an ideal configuration for advancing the understanding of the combustion characteristics of liquid fuel combustion due to its simplified flame dimension that provides a tractable geometry for computational modeling and experimental diagnostics. For example, in this configuration, diffusive, convective, and thermophoretic transport occurs only in the radial direction, so it allows flexibility in investigating transport characteristics of heat and species. Microgravity droplet combustion also affords the unique opportunity to vary the residence time (defined as the transport time of the fuel vapor from the droplet surface to the flame front) over a wide range of conditions by varying the droplet diameter, pressure, oxygen concentration, and inert variation.
1. Introduction Ethanol is a promising alternative energy source for the transportation sector since it is competitive in price with conventional liquid hydrocarbon fuels and is renewable.1 Also, ethanol has an advantage that it can be easily distributed using the current infrastructures for transportation without additional investments.2 The first use of ethanol as a motor fuel can be traced back more than 180 years ago when Samuel Morey designed the first internal combustion engine that used ethanol.3 With the advent of increasing fuel prices, many countries including the United States have promoted the use of ethanol through the Alternative Motor Fuels Act of 1988 (AMFA) and the Energy Policy Act of 1992 (EPACT). These policies have encouraged auto manufacturers to develop and market flexible fuel vehicles (FFV) that operate on blends of ethanol up to 85%. Recent studies4,5 indicate that ethanol addition (as fuel additives) to gasoline and diesel fuels can significantly reduce pollutant emissions such as particulates (i.e., soot), carbon monoxide (CO), unburned hydrocarbon (UHC), and nitrogen *To whom correspondence should be addressed. E-mail: seulpark@ nist.gov. Telephone: þ1-975-301-3908. Fax: þ1-975-301-4052. Current address: Building and Fire Research Laboratory (BFRL) National Institute of Standards and Technology (NIST) Gaithersburg, MD 20899-8662. (1) Demirbas, A. Prog. Energy Combust. Sci. 2007, 33 (1), 1–18. (2) Agarwal, A. K. Prog. Energy Combust. Sci. 2007, 33 (3), 233–271. (3) Jacobson, M. Z. Environ. Sci. Technol. 2007, 41 (11), 4150–4157. (4) Poulopoulos, S. G.; Samaras, D. P.; Philippopoulos, C. Atmos. Environ. 2001, 35 (26), 4399–4406. (5) Hsieh, W. D.; Chen, R. H.; Wu, T. L.; Lin, T. H. Atmos. Environ. 2002, 36 (3), 403–410. r 2009 American Chemical Society
(6) Kumagai, S.; Sakai, T.; Okajima, S. 1971 Proc. Combust. Inst. 13, 779-785. (7) Lee, K. O.; Manzello, S. L.; Choi, M. Y. 1998 Combust. Sci. Technol. 132, 139-156. (8) Nayagam, V.; Haggard, J. B.; Colantonio, R.; Marchese, A. J.; Zhang, B. L.; Williams, F. A.; Dryer, F. L. 1998 AIAA J. 26, 1369-1378. (9) Yozgatligil, A.; Park, S. H.; Choi, M. Y.; Kazakov, A.; Dryer, F. L. 2004 Combust. Sci. Technol. 176, 1-15. (10) Park, S. H.; Choi, S. C.; Choi, M. Y.; Yozgatligil, A. Combust. Sci. Technol. 2008, 180 (4), 631–651.
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: DOI:10.1021/ef900555u
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Figure 1. Schematic of the experimental apparatus.
formation of sootshell on the droplet burning and radiative heat transfer by modifying the location and temperature of the sootshell, soot volume fraction, and the flame temperature.
Early microgravity experiments on ethanol droplet combustion indicated minimal sooting tendency and therefore supported the observations of significant reductions in particulate emissions reported in previous ethanol-fired engine studies. However, more recent experiments performed under high oxygen concentrations and ambient pressures indicated that ethanol droplet flames in microgravity conditions can display significant sooting behavior.9-11,15 The wide variation in sooting behavior that can be imposed on ethanol droplet combustion was one of the reasons that it was selected as a test fuel for future space-platform studies on the sooting behavior of droplet flames.11 There are several suggested mechanisms through which sooting can affect the burning behavior of microgravity droplet flames. The droplet burning rate can be modified through changes in the thermophysical properties of the soot-laden gas, including the thermal conductivity and the specific heat.11,12 The attendant radiative emission from the soot and gas-phase products can also reduce the flame temperature, leading to a reduction in the burning rate7,13 and causing extinction that is promoted by radiative heat losses.8 The primary objective of this study is to investigate the formation of sootshell in microgravity droplet flames on radiative heat transfer and the droplet burning rate. In this study, the judicious selection of inert gas substitution (Ar vs N2) enabled quantitative analyses on the influences of the
2. Experimental Descriptions Experiments were performed in the 2.2 s microgravity droptower at the NASA Glenn Research Center at Lewis Field. Figure 1 displays the schematic diagram of the experimental drop apparatus. The drop apparatus consists of a 12 L combustion chamber with five optical access windows, diode laser, beam expander and collimator, high resolution CCD cameras, and electro-mechanical components (batteries, stepper motors, motion controllers etc.). This apparatus enables the measurements of various parameters including the soot volume fraction, flame temperature, flame radiative emission, sootshell and flame dynamics, and droplet burning rate of the isolated droplet flame in microgravity condition. More details on these experimental apparatuses can be obtained from other references.9-11,15 Previous isolated droplet combustion experiments9,15 indicated that sooting in ethanol droplet flames was only observed when higher ambient pressure was combined with higher flame temperature afforded by increased oxygen concentrations. The ethanol droplet combustion experiments were therefore conducted at the elevated oxygen concentration of 30% and pressure of 0.24 MPa in order to produce distinct sootshells. In addition, the parameter adjustments were made through inert substitutions (Ar vs N2) which lead to drastic changes in the residence time and temperature. The droplet was formed using aids of two horizontally opposed hypodermic needles with the diameter of 0.25 mm onto a 15 μm SiC fiber, which was used to tether the formed droplet and to prevent it from moving out of the field of view. The droplet formed on the fiber was then ignited in microgravity by
(11) Park, S. H. Investigation of sooting behavior and soot nanostructures of ethanol droplet flames in microgravity; Ph.D. Thesis, Drexel University: Philadelphia, PA., 2007. (12) Choi, M. Y.; Dryer, F. L.; Haggard, J. B.Jr. Proc. Combust. Inst. 1990, 23, 1597–1604. (13) Jackson, G. S.; Avedisian, C. T. Proc. R. Soc.: Math. Phys. Sci. (1990-1995) 1994, 446 (1927), 255–276. (14) Manzello, S. L.; Choi, M. Y.; Kazakov, A.; Dryer, F. L.; Dobashi, R.; Hirano, T. Proc. Combust. Inst. 2000, 28, 1079–1086.
(15) Yozgatligil, A.; Park, S. H.; Choi, M. Y.; Kazakov, A.; Dryer, F. L. Proc. Combust. Inst. 2007, 31, 2165–2173.
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formed near the flame then migrate to an equilibrium position where those influences are counter-balanced, producing a distinct sootshell. For thermophoretic transport,24,25 gas molecules colliding with the side of the soot particles facing the flame front possess greater kinetic energy than gas molecules that collide on the side of the soot particles facing the droplet surface. This is due to the temperature variations from the flame front to the droplet surface. Therefore, gas molecules (on the flame front side) with higher kinetic energy compared to the gas molecules (on the droplet surface side) with lower kinetic energy will impart a greater net force on the soot particles, thereby transporting the soot particles from the higher temperature region to the lower temperature region. There are also other phoretic mechanisms that can affect the transport of particles, namely photophoresis and diffusiophoresis. For example, photophoresis is particle motion induced by a temperature gradient within the solid-phase (in this case, temperature gradients within the soot particles) due to nonuniform absorption of radiant energy by the soot particle.26 In this mechanism, the side of the soot particles that is facing the flame front experiences higher rates of irradiation from the flame front compared to the side of the soot particles facing the droplet. The other side of the soot particles, facing the droplet surface, will also experience irradiation from the opposite side of the flame but the lower view factor of this irradiation will cause the temperature gradient within the particle with higher temperature on the flame front side compared to the droplet surface side. Compared to thermophoresis, photophoretic transport was found to be a much less important mechanism in the transport of soot particles.28 It was found that typical photophoretic velocities represented approximately 1% of the typical magnitude of thermophoretic velocities and that photophoretic velocities decreased as the sootshell migrated toward the droplet. This may be related due to the fact that as the sootshell resided closer to the droplet surface (away from the flame front), the view factor difference for the side facing the flame front and the side facing the droplet surface decreases. Diffusiophoresis is a mechanism through which particle transport is caused by the differences in gas-phase species concentrations. The influence of diffusiophoresis, which can affect the balance of forces acting upon soot particles, has not been included in previous analysis of sootshell formation.15,28,29 The difference in the gas-phase species gradients within the diffusion flame causes the difference in the number of molecular collisions, resulting in the imbalance in the net force imparted on the soot particles. Because the gas-phase fuel concentration distribution ranges from near unity at the droplet surface to negligible values near the flame front, diffusiophoretic transport will drive the particles toward the flame front and away from the droplet surface.
using two Kanthal hotwire igniters. Igniters were heated for 0.3 s with a peak current of 10 Amps and then deactivated and retracted promptly from the view angle of a radiometer to minimize the thermal effects of the glowing igniters on the flame radiative emission measurements. The radiometer used was calibrated using a blackbody source before experiments. The full-field light extinction technique was applied to measure the soot volume fraction, fv, and monitor the formation of sootshell. More details on the full-field light extinction apparatus and measurement process can be obtained from previous studies.16,17 To measure the droplet burning rate, the digitized images of the laser backlit droplet were analyzed to distinguish the droplet from the background using appropriate graylevel thresholds. The burning rates were then obtained from a linear fit to the evolution of the square of the droplet diameter with time after the transient heat-up period. Flame diameters were determined by measuring the spatial extent of the maximum luminosity region of the SiC fiber used to tether the droplet. The luminosity of the SiC fiber was imaged using a high-resolution black/white CCD camera equipped with a 700 nm interference filter with a full width at half maximum (FWHM) of 25 nm. In this study, the gas-phase temperature was measured using a thin filament pyrometry (TFP) technique, which is described in detail in several investigations on laminar jet diffusion flames in normal gravity18-20 and droplet diffusion flames in microgravity.10,15 The 15 μm SiC fiber (the same fiber used to tether the droplet) was selected as filament because its emissivity, 0.8 is weakly dependent upon the variations in temperature18 and the magnitude to conductive heat losses along the fiber is negligible due to the narrow cross-sectional area.21 The calibration of the TFP signal for temperature measurement employed techniques developed and validated for laminar flames by previous researchers. Ravikrishna and Laurendeau19 and Bundy et al.20 calibrated their TFP signals from laminar methane/air diffusion flames with temperature predictions from detailed numerical models. Following this approach, the temperatures of the microgravity droplet flame were calibrated using the spherically symmetric, transient, numerical model inclusive of detailed gas-phase kinetics predictions for ethanol droplet flames developed by Dryer and coworkers.22
3. Formation of Sootshell in Micrograivty Formation of a sootshell in microgravity droplet flames was first reported by Shaw and co-workers.23 In microgravity droplet flames, soot particles form in the fuel-rich region where fuel pyrolysis reactions involve high-activation energy pyrolysis processes and thus maximum soot yield will likely occur near the flame.15 Soot particles formed within the droplet flame are acted upon by viscous drag (which is mainly caused by Stefan flow) and phoretic processes (which is defined as localization of driving forces near a particle suspended in a fluid) with thermophoresis (which is a mechanism through which the particle transport is caused by the temperature gradient in the surrounding gas phase) being the most dominant. With the progression of time, soot particles (16) Dasch, C. J. Appl. Opt. 1992, 31 (8), 1146–1152. (17) Lee, K. O.; Choi, M. Y. Microgravity Sci. Technol. 1997, 10 (2), 86–94. (18) Vilimpoc, V.; Goss, L. P.; Sarka, B. Opt. Lett. 1988, 13 (2), 93–95. (19) Ravikrishna, R. V.; Laurendeau, N. M. Combust. Flame 2000, 122 (4), 474–482. (20) Bundy, M.; Hamins, A.; Lee, K. Y. Combust. Flame 2003, 133 (3), 299–310. (21) Maun, J. D.; Sunderland, P. B.; Urban, D. L. Appl. Opt. 2007, 46 (4), 483–488. (22) Kazakov, A.; Conley, J.; Dryer, F. L. Combust. Flame 2003, 134 (4), 301–314. (23) Shaw, B. D.; Dryer, F. L.; Williams, F. A.; Haggard, J. B. Acta Astronautica 1988, 17 (11-12), 1195–1202.
(24) Friedlander, S. K.; Smoke, Dust, and Haze: Fundamentals of Aerosol Behavior; Wiley: New York, 1977; p xvii, 317. (25) Gomez, A.; Rosner, D. E. Combust. Sci. Technol. 1993, 89 (5-6), 335–362. (26) Karasev, V. V.; Ivanova, N. A.; Sadykova, A. R.; Kukhareva, N.; Baklanov, A. M.; Onischuk, A. A.; Kovalev, F. D.; Beresnev, S. A. J. Aerosol Sci. 2004, 35 (3), 363–381. (27) Manzello, S. L.; Yozgatligil, A.; Choi, M. Y. Int. J. Heat Mass Transfer 2004, 47 (24), 5381–5385. (28) Jackson, G. S.; Avedisian, C. T.; Yang, J. C. Int. J. Heat Mass Transfer 1992, 35 (8), 2017–2033. (29) Choi, M. Y.; Dryer, F. Y.; Green, G. J.; Sangiovanni, J. J. AIAA 1993, 1993–0823.
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where Fg is the gas-phase density, Ur is the radial velocity, VS is the Stefan velocity, and VF is the fuel mass diffusion velocity. Ur was determined by calculating the sum of VS and VF that are defined as:10,28 KFl rd VS ¼ ð2Þ 8Fg r2
29
Jackson and Avedisian and Choi et al. experimentally measured the location of sootshell for the n-heptane droplet combustion in air at atmospheric pressure. They also compared the measured the locations of sootshell to the predicted values (defined as an equilibrium position where the Stefan and thermophoretic fluxes are counter-balanced). In both studies, the transient gas-phase temperature distributions were calculated using numerical models for the spherically symmetric n-heptane combustion to predict the Stefan and thermophoretic fluxes. However, the numerical models did not include explicit soot formation mechanisms, thus the influence of the sooting/radiation behavior on the temperature distribution and the burning rate were not analyzed quantitatively. As a result, the predicted locations of sootshell were much larger than the measured values in both experiments. In recent experiments performed by Yozgatligil et al.,15 the experimentally measured gas-phase temperature distributions and flame sizes (determined by a thin filament pyrometry technique) were used to provide more accurate predictions of the location of the sootshell, resulting in favorable comparisons with experiments. Recently, Ben-Dor et al.30 performed a numerical analysis on the motion of soot particles in spherically symmetric n-heptane droplet flames. Their numerical model included radiative heat losses (from the soot particles), variable transport properties of reactants, and transient droplet surface temperature. The calculations of sootshell location were performed with and without the influences of diffusiophoretic flux and were compared with the experimental results performed by Jackson and Avedisian.28 The results indicate that the influences of diffusiophoretic flux must be included for accurate analysis of the transport mechanisms affecting soot partilces formed in spherically symmetric droplet combustion. However soot formation was not evaluated using explicit soot formation chemistry in their numerical model. Instead, the concentration of soot was directly incorporated into the model from the previous n-heptane droplet combustion experiments7 to predict the motion of soot particles. As a result, calculated burning rates and flame temperatures were not in good agreement with experimental results6 and numerical results31 with detailed soot formation chemistry and radiation models. More recently, Shaw and Dakka32 numerically investigated the influence of fuel pyrolysis on the formation of sootshell. They showed that the onset of abrupt fuel pyrolysis led to the increases in the local temperature gradient and thus changes in the location of sootshell. As part of this investigation, the location of sootshell in this study was defined as the equilibrium position where the influences of Stefan and diffusiophoretic fluxes (which transport the soot particles toward the flame front and away from the droplet surface) and the counteracting influences of thermophoretic flux (which transport the soot particles away from the flame front and toward the droplet surface) are counter-balanced. The influences of Stefan and diffusiophoretic fluxes are calculated by evaluating the Stefan and fuel mass diffusion velocities:10,28 Fg Ur ¼ Fg ðVS þVF Þ ð1Þ
VF ¼ -DAB
lnð1 -YFS Þð1 -YFS Þrd r2
ð3Þ
where K is the measured average droplet burning rate, Fl is the liquid-phase density, DAB is the mass diffusion coefficient of fuel in the gas phase, and YFS is the fuel mass fraction at the droplet surface. The influences of themophoretic flux are calculated using the following description:15,24 -3μ dT dr Fg Vt ¼ ð4Þ 4ð1 þ πR=8ÞT where Vt is the thermophoretic velocity, μ is the viscosity, dT/dr is the temperature gradient of the gas-phase, T is the gas temperature, and R is the thermal accommodation factor (assigned a value of 0.9). The temperature gradients were calculated based upon the gas temperature distributions (that were experimentally determined by using the TFP technique). 4. Results and Discussion 4.1. Influences of Inert Substitutions on Sootshell Formation. Figure 2 displays the laser-backlit images of 1.9 mm ethanol droplets burning in 30% O2 in Ar and N2 at 0.24 MPa with respect to time (after ignition). As shown in the figure, soot particles formed migrate to an equilibrium position with the progression of time, producing a distinct sootshell. The location of sootshell was determined from the time-varying soot volume fraction distributions plotted in Figures 3a-b. The results indicate the soot standoff ratios (SSR; defined as the sootshell radius divided by the instantaneous droplet radius) as well as the soot volume fraction, fv, are very sensitive to the changes in the inert. The measured soot standoff ratio is 1.4 for the Ar inert experiment and 2.5 for the N2 inert experiment, respectively, which is a significant difference. In addition, the maximum soot volume fraction measured for the Ar inert experiment of 25 ppm is 43% higher than the value of 14.3 ppm measured for the N2 inert experiment. The differences in the maximum soot volume fraction with inert substitutions are attributed to the variations in transport characteristics of heat, species and attendant flame temperatures, and residence time for soot formation and growth.10,11 In previous studies performed using microgravity droplet flames,10,15 it was found that inert substitutions can significantly affect the burning rate (which affects Stefan flux), fuel mass diffusion (which affects diffusiophoretic flux), and flame radius and temperature (which affect thermophoretic flux). Therefore, variations in the phoretic forces acting upon soot particles are expected to produce changes in the location of sootshell. To accurately analyze the influence of inert substitutions on the location of sootshell, Stefan, diffusiophoretic, and thermophoretic fluxes were calculated for the 1.9 mm ethanol droplets burning in 30% O2 in Ar and N2 at 0.24 MPa. Figure 4 displays the calculated viscous drag (induced by Stefan flux only and Stefan flux plus diffusiophoretic flux) as a function of nondimensionalized radii (the ratio of radial location, r to the
(30) Ben-Dor, G.; Elperin, T.; Krasovitov, B. Proc. R. Soc. London Ser. A: Math. Phys. Eng. Sci. 2003, 459 (2031), 677–703. (31) Marchese, A. J.; Dryer, F. L.; Nayagam, V. Combust. Flame 1999, 432–459. (32) Shaw, B. D.; Dakka, S. M. Combust. Sci. Technol. 2005, 177 (10), 1939–1959.
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Figure 2. Light extinction images of sootshell formed in the 1.9 mm ethanol droplet burning in 30% O2 in Ar and N2 at 0.24 MPa. (a) Ar inert experiment. (b) N2 inert experiment.
Figure 4. Viscous drag acting on soot particles produced from 1.9 mm ethanol droplets burning in 30% O2 in Ar and N2 at 0.24 MPa. Table 1. Summary of Parameters Used and Computed/Measured Droplet Burning Rates computed measured T [K] λg [W/m 3 K] cpg [J/kg 3 K] Fl [kg/m3] K [mm2/s] K [mm2/s] Ar 1584 N2 1490
0.134 0.128
3651 3583
706 706
0.61 0.60
0.56 0.57
Figure 5 displays the calculated thermophoretic flux as a function of nondimensionalized radii for 1.9 mm ethanol droplets burning in environments of 30% O2 in Ar and N2 at 0.24 MPa. As shown in eq 4, the gas-phase temperature gradient and viscosity are the most critical parameters for the evaluation of thermophoretic flux. The Ar inert experiment produces higher magnitudes of thermophoretic flux due to the higher flame temperature (see Figure 6) and higher values in viscosity. On the other hand, the N2 inert experiment produces lower magnitudes of thermophoretic flux due to the lower flame temperature and the lower values of viscosity. Calculating the net flux (which consists of Stefan, thermophoretic, and diffusiophoretic fluxes) enables the determination of the equilibrium position for the sootshell. Figures 7a-b display the calculated net flux plotted versus nondimensionalized radii for the 1.9 mm ethanol droplets burning in 30% O2 in Ar and N2 at 0.24 MPa environments. The position where the net flux is equal to zero defines the location of sootshell. As shown in the figure, two separate locations exist where the net flux is equal to zero. The first position is the location of the stable
Figure 3. Temporal soot volume fraction distributions for 1.9 mm ethanol droplet burning in 30% O2 in Ar and N2 at 0.24 MPa.
instantaneous droplet radius, ri). Stefan fluxes for the Ar and N2 inert experiments are very similar in magnitude due to similarities in the droplet burning rate (See Table 1). As shown in the figure, the influence of Stefan flux on viscous drag is more dominant compared to that of diffusiophoretic flux. However, the results also demonstrate that the diffusiophoretic flux is an important mechanism required for accurate calculation of soot agglomerate transport. It is found that the diffusiophoretic flux is responsible for approximately 20% of net viscous drag acting on soot particles and thus cannot be ignored. 4399
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Figure 5. Thermophoretic flux for 1.9 mm ethanol droplet burning in 30% O2 in Ar and N2 at 0.24 MPa.
Figure 7. Net fluxes acting on soot particles produced from 1.9 mm ethanol droplet burning in 30% O2 in Ar and N2 at 0.24 MPa.
of 1.1 for the Ar inert experiments and 2.1 for the N2 inert experiment, respectively. 4.2. Influences of the Formation of Sootshell on Droplet Burning Rate. For nonsooting droplet flames, the droplet burning rate, K can be simply estimated using the classical d2 law: 8λg K ¼ lnð1þBÞ ð5Þ Fl cpg
Figure 6. Measured gas-phase temperature distributions plotted versus nondimensionalized radii for 1.9 mm initial diameter ethanol droplets burning in 30% O2 in Ar and N2 at 0.24 MPa. (a) Calculated net flux vs nondimensionalized radii. (b) Enlarged view of subset area in Figure 7a.
equilibrium (denoted as location No. 1), whereas the second position is the location of the unstable equilibrium (denoted as location No. 2). The existence of two equilibrium positions was first discussed by Jackson and Avedisian.28 In the first equilibrium location, soot particles on either side of that location will be transported toward the equilibrium location. For example, if soot particles are formed at location A, the influence of thermophoretic flux, which has a larger magnitude than the combined Stefan and diffusiophoretic fluxes, will transport the particles toward equilibrium location No. 1. If particles are found in location B, the higher combined magnitudes of the Stefan and diffusiophoretic fluxes compared to the thermophoretic flux will transport the particles toward the equilibrium location No. 1. For the unstable equilibrium location No. 2, soot particles on either side of this location will be transported away from the equilibrium location. The calculated sootshell standoff ratio for Ar and N2 inert experiments are 1.2 and 2.3, respectively. These values are in excellent agreement with the experimentally measured values of 1.4 and 2.5, respectively. It is important to note that the removal of the influence of diffusiophoretic flux resulted in the sootshell standoff ratio
where B is the heat transfer number and λg and cpg are the thermal conductivity and heat capacity of gas, respectively. The appropriate thermophysical properties of λg and cpg can be empirically obtained using the following relationships:33 cpg ¼ cpF ðTÞ
ð6Þ
λg ¼ 0:4λF ðTÞ þ 0:6λO ðTÞ
ð7Þ
T ¼
Ts þTad 2
ð8Þ
where subscripts F and O represent fuel and oxidizer, respectively. Ts is the boiling temperature of liquid fuel, and Tad is the adiabatic flame temperature. All thermophysical properties used and computed burning rates are summarized in Table 1. The close correspondence in the value of the thermophysical properties for Ar and N2 results in similar values of the calculated burning rate (the value of K is 0.61 mm2/s for Ar and 0.60 mm2/s for N2). (33) Law, C. K.; Williams, F. A. Combust. Flame 1972, 19, 293–405.
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The measured burning rate for the Ar and N2 experiments are also displayed in Table 1. As in the calculated values of the burning rate, the measured K values show only small variation with inert substitution. The K value for Ar is 0.57 mm2/s, whereas for N2 the K value is 0.56 mm2/s. The difference between the calculated and the measured values of the burning rate may be related to the fact that the d2-law does not account for soot formation and attendant radiation, which can reduce the burning rate. A number of experimental investigations7,10,11,13 have demonstrated that the presence of the sootshell in the droplet flames can reduce the droplet burning rate. In these studies, the reductions in the droplet burning rate was attributed to the modification of the thermophysical properties of sootladen gas,12,13 radiative heat losses to the surroundings,7,14 and reduction in the effective heat of combustion since the soot particles collected within the sootshell is not oxidized. On the basis of these observations, the higher value of the soot concentration for the Ar experiment is expected to cause a more significant reduction in the burning rate compared to the N2 experiments. But, the similarities in the burning rate measurements indicate that other counter-balancing mechanisms must be explored to explain this phenomenon. Microgravity experiments7 performed for n-heptane as a function of initial droplet diameter revealed variation in the maximum soot volume fraction, fvmax and attendant reduction in the droplet burning rate. For example, the burning rate varied from 0.77 to 0.55 mm2/s when the fvmax varied from 38 to 65 ppm. In those experiments in which the initial diameter was varied for n-heptane, the flame standoff ratios and the soot standoff ratios were nearly constant. The invariance in the SSR and the FSR also ensured that the flame temperature was different from the temperature in the vicinity of the sootshell. The calculation of the radiative heat loss fraction using the soot volume fraction measurements varied inversely with the initial droplet diameter, thus leading to the relationship between radiative heat loss fraction and the droplet burning rate. As demonstrated in Figures 3a-b, the SSR for Ar is significantly smaller than the SSR for N2, which will counter-balance the higher value of the soot concentration for the Ar experiments compared to the N2 experiments. This effect (as will be discussed in the next section) will contribute to the radiative heat losses from the flame and thus on the droplet burning rate. 4.3. Influences of the Formation of Sootshell on Radiative Heat Loss. In previous studies of sootshell formation,8,10 it was reported that the presence of the sootshell in microgravity droplet flames produced greater contributions to radiative heat loss compared to gaseous products such as H2O and CO2. Since soot volume fraction is maximized in the central location of the sootshell, the influence of radiative heat loss caused by soot emission will be likely to be confined to a narrow zone.31 Furthermore, the variation of the soot concentration and the location of the sootshell (as shown in Figures 3a-b) as a function of time cause a time-dependent variation of the radiative heat transfer. To elucidate the influence of the sootshell formed in microgravity droplet flames on radiative heat losses, radiative emissions from the flame were measured using a broadband radiometer that was placed 12.5 cm from the center of the droplet. The spectral response of the radiometer is rated from 1 to 20 μm, thereby capturing the majority of the near-infrared and infrared radiation emitted from soot particles and radiating gases such as CO2 and H2O. Figure 8
Figure 8. Measured radiative emission power for 1.9 mm initial diameter ethanol droplets burning in 30% O2 in Ar and N2 at 0.24 MPa.
Figure 9. Measured flame standoff ratios and flame temperatures for 1.9 mm initial diameter ethanol droplets burning in 30% O2 in Ar and N2 at 0.24 MPa.
displays the measured instantaneous radiative emission power, Qm, for each of inert experiment as a function of time. It is observed that the instantaneous radiative emission power rapidly increases and approaches qusai-steady values for each of inert experiment. Previous microgravity droplet combustion experiments7,10 revealed that the radiative heat losses caused by the flame emission were strongly dependent on the concentration of soot, the volume of the participating medium (which is proportional to the flame volume), and flame temperature. Note that these parameters significantly vary with inert substitutions (Ar versus N2) in this study. As shown in Figures 3a-b, the maximum soot volume fraction for the Ar experiment (25 ppm) is much higher compared to the N2 inert experiment (14.3 ppm). The flame temperature is also strongly influenced by inert substitution (varying from 2275 K for Ar to 2013 K for N2 as shown in Figure 6), whereas the flame standoff ratios (FSR; defined as the luminous flame radius divided by the instantaneous droplet radius) is weakly dependent (with FSR of ∼4.0 for Ar and ∼3.9 for N2 as shown in Figure 9). Considering the fact that the Ar inert experiment produces higher concentration of soot and flame temperatures compared to the N2 inert experiment for a similar corresponding flame volume, it is expected that the radiative heat losses for the Ar inert 4401
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Figure 11. Normalized radiative heat loss distributions for 1.9 mm ethanol droplets burning in 30% O2 in Ar and N2 at 0.24 MPa.
Figure 10. Calculated radiative emission power emitted from gaseous products of combustion.
product, CO2 and H2O are calculated based on the stoichiometric combustion of ethanol in 30% O2 in Ar and N2, respectively. The calculation for mole fractions was performed using a chemical equilibrium code for measured flame temperatures at the atmospheric pressure of 0.24 MPa. Figure 10 displays the calculated radiative emission power using eq 9 for ethanol droplet flames produced for the Ar and N2 inert experiments. Similar to the variations in the FSR, the calculated radiative emission increases rapidly and approaches quasi-steady values despite gradual reductions in the flame temperature (that can directly lead to the reduction in Qc,gas). This phenomenon is mainly attributed to the variations in the flame standoff ratio. Rapid increases in the FSR (that cause a significant increase in the flame volumes) at the early stage of burning result in the increase in radiative heat losses from gaseous products, overwhelming the influence of flame temperature reductions as a function of time. As the FSR approaches quasi-steady values, the variations in the radiative emission power become minimal, maintaining a constant value (approximately 1.6 W for the Ar inert experiment and 1.3 W for the N2 inert experiment, respectively). These results indicate that the difference in the measured flame radiative emission power between Ar and N2 inert experiments (See Figure 8) may be due to the emission from radiating gaseous products. To quantitatively investigate the radiative heat losses caused by sootshell emissions, the contribution of sootshell emissions to the total radiative heat loss (which is determined as (Qm - Qc,gas)/Qm) is plotted against time for the Ar and N2 experiments in Figure 11. It clearly demonstrates that sootshell emissions are responsible for majority of the radiative heat losses (up to 83% of the total flame radiative heat losses) but that radiative emission from the gaseous products cannot be ignored. For each of inert experiments, the radiative heat losses caused by sootshell emissions at the earliest stage of burning are the highest due to the smaller radiating flame volume and then gradually decrease with the growth of the flame volume. The radiative heat losses caused by sootshell emissions are strongly affected by the various factors including the thickness of sootshell layer (which can alter the effective volume of the participating medium) and the sootshell temperature
experiment will be significantly higher compared to the N2 inert experiment. Surprisingly, the measurements indicate that there are no dramatic differences in the radiative emission power for droplet flames produced for the two inert cases with Ar experiments producing Qm of ∼3.6 W and N2 experiments producing Qm of ∼3.3 W. The measured radiative emission power combines the component produced by the soot and gaseous products and intermediates. To ascertain the radiative heat losses caused by soot and gaseous radiative emission, analysis was performed to decouple soot and gaseous emission. To this end, an optically thin radiation model34,35 was employed to consider the radiative emission from gaseous products of combustion. It was also assumed that H2O and CO2 are only radiating gaseous species. Under these conditions, the radiative emissions for spherically symmetric droplet flames are attributed to the radiating volume of gaseous products of combustion confined between the flame and the droplet surface. Therefore, the radiative emission power for radiating products of combustion can be formulated as:34 " # 16 rf 3 3 Qc;gas ¼ πσKp r -1 Tf4 ð9Þ 3 ri where σ is the Stefan-Boltzmann constant, Kp is the average Planck mean absorption coefficient, ri is the instantaneous droplet radius, rf is the flame radius, and Tf is the flame temperature. In this study, the Kp was evaluated using the following relationships:35 Kp ¼ P ½XCO2 kp, CO2 ðTf ÞþXH2 O kp, H2 O ðTf Þ kp ¼
X πIbj Rj j
σTf4
ð10Þ ð11Þ
where P is the ambient pressure; XCO2 and XH2O are the mole fraction for CO2 and H2O, respectively, Ibj is the average blackbody intensity for band j; and Rj is the integrated intensity of band j. The mole fraction of combustion (34) Colantonio, R. O.; Nayagam, V. In Radiative Heat Loss Measurements during Microgravity Droplet Combustion, Technical Meeting of the Central States Section of the Combustion Institute, 1997; pp 125-129. (35) Tien, C. L. Thermal radiation properties of gases. In Advances in Heat Transfer; Irvine, T. F. H., J. P., Ed.; Academic Press: New York, 1968; Vol 5, pp 254-324.
(36) Lee, S. C.; Tien, C. L. Proc. Combust. Inst. 1981, 18, 1159–1165.
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as well as the concentration of soot. In the previous study, Lee and Tien demonstrated that soot emission was proportional to the product of the concentration of soot and the path length through an isothermal cloud of soot particles (that is a parameter corresponding to the thickness of sootshell layer in microgravity droplet combustion experiments). In the numerical study of the benzene droplet burning in microgravity,37 it was also found that sootshell emission was increased by a factor of 10 when the thickness of sootshell layer varied from 0.18 to 0.6 mm at a fixed gas-phase temperature (2400 K) and soot concentration (10 ppm). Since the Ar inert experiment produced higher concentrations of soot and thicker sootshell layer compared to the N2 inert experiment in the present study, similar magnitude of radiative heat losses caused by sootshell emissions for each of inert experiments (see Figure 11) cannot be explained solely by the combination of theses parameters (i.e., the concentration of soot and the thickness of sootshell layer). Therefore, the remaining factor that must be investigated is the sootshell temperature. The sootshell formed in the Ar inert experiment resides closer to the droplet surface compared to the N2 inert experiment. Therefore, the gas-phase temperature in the vicinity of the sootshell for the Ar inert experiment will be much lower than for the N2 inert experiment. For example, the gas-phase temperature in the vicinity of the sootshell is found to be approximately 800 K for the Ar inert experiment and approximately 1300 K for the N2 inert experiment (see Figure 6). Since soot particle temperatures can be assumed to be nearly equal to the gas-phase temperature,36 one can conclude that the sootshell temperature in the Ar inert experiment is much lower than in the N2 inert experiment. Despite lower concentrations of soot and flame temperatures for the N2 inert experiment, the closer proximity of the sootshell formed the flame results in a increase in the sootshell temperature and thus increases the radiative heat losses to the surrounding. This concurrent influence for the N2 inert experiment eventually produces
similar magnitude of radiative heat loss compared to the Ar inert experiment. 5. Conclusions The influences of the formation of sootshell on the droplet burning and radiative heat transfer were investigated for ethanol droplet flames in microgravity. The experimental measurements of sootshell location were compared to predicted values using the balance among Stefan, thermophoretic, and diffusiophoretic fluxes. This analysis represents the first study in which diffusiophoretic transport was included in the analysis of sootshell formation. The experimental results demonstrate that the inert gas substitution produces strong influence on the droplet burning behaviors and radiative heat transfer characteristics through the formation of the sootshell. The inert gas substitutions were found to affect the location of sootshell as well as the concentration of soot contained in the sootshell. The Ar inert experiment produced a distinct sootshell that resided closer to the droplet surface and a higher concentration of soot compared to the N2 inert experiment. The sootshell formed within the flame acted as a heat sink through radiative emissions, which can reduce the droplet burning rates and the flame temperatures. Although the N2 inert experiment produced lower flame temperatures and concentrations of soot compared to the Ar inert experiment, the closer proximity of the sootshell near the flame (and thus at higher temperatures, which increases the radiative heat losses) produces similar magnitude of radiative heat loss compared to the Ar inert experiment. These results demonstrate that the variations in the radiative heat loss and attendant changes in the droplet burning rate can not be correlated solely on the basis of the concentration of soot within the sootshell. The location of sootshell strongly influences the sootshell temperature and thus the radiative heat transfer from the sootshell to the surroundings, eventually affecting the flame temperature and the droplet burning rate. Acknowledgment. Support from NASA through Grant NCC3-822 is gratefully acknowledged. S.H.P. would like to acknowledge support from Korea Science and Engineering Foundation (KOSEF) under Grant M06-2003-000-10159-0.
(37) Chang, K. C.; Shieh, J. S. Int. J. Heat Mass Transfer 1995, 38 (2), 2611–2621. (38) Millikan, R. C. J. Opt. Soc. Am. 1961, 51 (6), 698–699.
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