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Determination of magnetic field effects on a jet diffusion flame in a microgravity environment
Twenty-Seventh Symposium (International) on Combustion/The Combustion Institute, 1998/pp. 2573–2578
DETERMINATION OF MAGNETIC FIELD EFFECTS ON A JET DIFFUSION FLAME IN A MICROGRAVITY ENVIRONMENT OSAMU FUJITA,1 KENICHI ITO,1 TOMOYUKI CHIDA,1 SHINOBU NAGAI1 and YASUHIRO TAKESHITA2 1Division of Mechanical Science Hokkaido University Sapporo, 060-8628, Japan 2Japan Space Utilization Promotion Center Shinjuku-ku Tokyo, 169, Japan
The effect of magnetic fields on a laminar jet diffusion flame has been investigated by using a microgravity environment. The magnetic field was changed from fairly low (around 0 mT) to strong (around 215 mT) intensities. The effect of oxygen concentration was also investigated. The buoyancy caused by gravity is dominant for diffusion flames under normal gravity, so the microgravity environment was used to allow an observation of the effect of the magnetic field on combustion, especially for weak magnetic fields. A steady flame could be sustained with a field intensity larger than a critical value that depends on the O2 concentration. The critical value was determined experimentally and evaluated with a nondimensional number corresponding to the Grashof number used for gravitational fields. The changes in combustion characteristics, that is, flame shape, length, brightness, and color, were evaluated as a function of the magnetic-field intensity. The flame length decreased with increases in the magnetic-field strength, and the color of the flame shifted from red to yellow, indicating a temperature increase with increases in magneticfield strength. By evaluating the changes in the flame color with chromaticity treatment, it was concluded that the effect of the magnetic field is dominated by F [O2], where F is the magnetic force acting on the combustion, a function of field strength, and [O2] is the surrounding oxygen concentration.
Introduction Substances placed in a magnetic-field gradient are subject to a magnetic force in proportion to their magnetic susceptibility. The magnitude of the force, F, in a one-dimensional magnetic-field gradient is expressed as [1]: F 4 l0xH(dH/dx)
(1)
where l0 is the vacuum magnetic permeability, v is the magnetic susceptibility, H is the magnetic-field strength (4 B/l0, B being the intensity of the magnetic field), and (dH/dx) is the magnetic field gradient. When the substance has paramagnetic properties (v . 0), the direction of the magnetic force is toward the higher intensity field, while with diamagnetic substances (v , 0), the force is toward the opposite direction. In gas components present in a combustion field, O2 has the largest magnetic susceptibility (1.54 2 1017 emu/mL), whereas other possible components have diamagnetic characteristics with magnetic susceptibilities lesser by 2 orders of magnitude than that of oxygen. For example, the magnetic susceptibility of N2, CO2, H2O, and propane are 10.54 2 1019, 10.11 2 1019, 10.58 2 1019, and 11.8 2 1019 in emu/mL, respectively. Therefore, a gas containing more O2, such as air, tends to move toward the stronger magnetic-field
direction, and a gas with less O2, such as fuel or combustion gas, tends to move toward the weaker magnetic field. Based on this principle, it may be possible to utilize a magnetic field to control the flow field of the combustion region to improve combustion characteristics. There is less research on magnetic-field effects on combustion [2,3] than on electric-field effects [4]. Recently, Wakayama [3] showed that the magnetic field enforces the combustion of diffusion flames, caused by the principle previously explained. However, since the magnetic force acting on a combustion field is much smaller than that of gravitational buoyancy and combustion phenomena are mainly dominated by gravitationally induced flows, it is difficult to observe the effect of magnetic force alone. Wakayama [5] and the authors here have tried to observe flames with and without magnetic fields in a microgravity environment achieved by a drop shaft. There it was shown that the shape and luminosity of the flame in microgravity dramatically changed when a magnetic field was imposed. With a magnetic field, the flame was sustained steadily with high luminosity, whereas without a magnetic field, it could not be sustained steadily in microgravity. However, this research only examined cases with and without magnetic fields and compared the results. To understand the effect of magnetic fields more systematically, it
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Fig. 1. Relative position of tubular burner and magnetic poles (left) and distribution of magnetic-field intensities along the vertical centerline.
is necessary to observe flames under various magnetic-field intensities from fairly weak to stronger magnetic fields. When evaluating changes in combustion characteristics as a function of magneticfield intensity, the use of microgravity is especially helpful with weaker magnetic fields. In the present work, diffusion flames with magnetic fields of various intensities have been observed. The changes in combustion characteristics, flame shape, length, brightness, and color were evaluated as a function of the field intensity. As the diffusion flame had very low fuel injection velocity that could not generate a sufficient fluid flow in the surrounding air, flames could not be kept steady without the magnetic field. Flames become steady at intensities higher than a certain magnetic-field intensity. According to the results, the effect of magnetic fields over a wide range of field intensities are discussed.
Experimental Facility In the experiments, an electromagnet was used to generate the various magnetic-field intensities. Figure 1 shows the position of the tested flame relative to the magnet’s poles. The interval between the N and S poles is 40 mm. The flame is held above a tubular burner of 6 mm inner and 8 mm outer diameters. The fuel was propane with a flow rate of 1.2 mL/s. The position of the burner rim is slightly (3 mm) higher than the center of the magnetic poles. The right part of Fig. 1 shows the typical magneticfield intensity distribution in millitesla along the vertical centerline. As the magnetic poles are circular, the magnetic field has a radially axisymmetric distribution, and the field intensity has its maximum value at the center of the poles. The field strength gradually decreases above the burner, and above 15-mm height, the gradient of the magnetic-field intensity
Fig. 2. Relationship between maximum intensity of magnetic field and the supplied electric current to the electromagnet.
becomes constant. In the present research, the maximum intensity of the magnetic field at the center is used as the representative value of the magneticfield strength. The maximum field strength can be varied by electric current sent to the magnet as shown in Fig. 2, and the field-intensity distribution is similar to that shown in Fig. 1 when the maximum magnetic-field intensity increases. In the experiments, the electromagnet and burner are set in an air-tight chamber to control the surrounding O2 concentration. The combustion phenomena are recorded by a charge-coupled device (CCD) camera (Sony CCD-TR705) through the window of the combustion chamber. Ignition is effected by an electric spark after the microgravity period has started. The microgravity experiments were performed at Japan Microgravity Center (JAMIC), which provides high-quality microgravity environments around 1015 g0 (g0 is the gravity at sea level) for 10 s.
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Fig. 3. Direct photos taken under various magnetic-field intensities in microgravity. t (time after microgravity starts) 4 8 s, O2 4 21%, fuel flow rate 4 1.2 mL/s. Steady flame is visible at 85.9 mT or lager values.
Because of limited access to the microgravity rig, each point plotted in the figures of this paper correspond to one experimental run. A few experiments were repeated for selected conditions; however, it was confirmed that the reproducibility of the flame, such as flame height or flame color, was quite high difficult to differentiate and it was between the experiments. Results and Discussion Observation of Direct Flame Picture The changes in the flame shape versus magneticfield strength were observed as shown in Fig. 3. These pictures were taken 8 s after the start of the capsule drop. The fuel flow rate is 1.2 mL/s (mean velocity is 2.4 cm/s), and the surrounding environment is air. The magnetic-field intensity denoted below each picture shows the maximum field strength. Without any magnetic field, flame luminosity decreased, and the flame diameter increased with time under microgravity. The flame finally became invisible and may have reached extinction. When the magnetic field is increased somewhat, a steady flame could be maintained throughout the microgravity. A field strength of 85.9 mT maintained a steady flame, while the 71.6-mT field did not. This indicates that there is a critical magnetic-field strength above which steady flames can be maintained. The critical strength may depend on a steady convective flow, and the appearance of the steady convective flow may be determined by the ratio between the viscous force and convective force caused by the magnetic field. When the viscous force is much larger than the convective force, there is limited convection, and the combustion phenomena become dominated by diffusion, which results in unsteadiness. Once the convective force becomes larger, the steady flame can be maintained.
This is similar to using the Gr number to determine if natural convection occurs in a closed chamber. The Gr number is expressed as Gr 4 g b (Tf 1 T0) d 3/m 2 (2) where g is the gravity level at ground level, b the coefficient of thermal volumetric expansion, Tf the flame temperature, T0 the surrounding temperature, d a representative dimension, and m the kinetic viscosity. In a box with a heated vertical wall face, natural convection occurs when the Gr number is larger than 102–103 (which strongly depends on the boundary conditions, assuming the Prandtl number is unity) [6,7]. Analogous to the gravitational field, the criterion to maintain a steady flame with magnetic field is given by the nondimensional number, Grm, having a physical meaning similar to the Gr number in gravitational fields. The Grm value is determined by Grm 4 l0 (vf 1 vo) H (dH/dx) d 3/qm 2 (3) where vf is the mean magnetic susceptibility of the combustion gas and v0 the susceptibility of the surrounding atmosphere. Thus, l0 (vf 1 v0) H (dH/dx) d 3 shows a buoyancy-like force caused by differences between the magnetic forces acting on the combustion gas and surrounding air. According to the observation in Fig. 3, this takes place between 71.6 and 85.9 mT, and the critical value may be around 80 mT. The value of Grm at 80 mT is around 400 assuming a flame width d of 15 mm, and vf is negligible relative to the value of v0. The intensity of the magnetic field and the gradient necessary to calculate Grm are 64 mT and 16 mT/cm, respectively, which are 80% of the maximum intensity. Considering the differences in the boundary condition from Ref. [6], this Grm appears reasonable as the criterion for steady convective flow. It may be concluded that a flame under microgravity will be sustained by a magnetic field with Grm larger than 102–103 like the Grashof number for the gravitational force.
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the field-induced flow is larger with the higher O2 concentration due to the larger value of (vf 1 v0) in equation 3, which also has a significant effect on the decrease in flame length. As seen in Fig. 4, steady flames can be sustained at lower field intensities, which implies that the Grm increases with increases in O2 concentration at the same field intensity. Though the data at zero intensity are plotted in Fig. 4, it is an unsteady value as the flame at O2 4 50% without magnetic field kept expanding during the whole microgravity time, 10 s. All other data in Fig. 4 are the flame length of a steadily burning flame.
Fig. 4. Changes in flame length as a function of magnetic-field intensity.
Fig. 5. Changes in flame brightness as a function of time after start of microgravity. O2 4 21%.
In magnetic fields larger than the critical field intensity, the flame becomes brighter with increasing field intensity, as seen in Fig. 3. It is also noted that the tip of the flame tends to close with increase in the field intensity. These phenomena must be caused by the increased forced convective flow induced by the magnetic effect. Flame length as a function of magnetic-field intensity has also been measured as shown in Fig. 4. Here the data are established at two different oxygen concentrations. The flame length decreased with increases in the field intensity for both oxygen concentrations, while the flame length with the higher oxygen concentration is everywhere shorter than that of the lower oxygen concentration. The magnetic-field–induced flow increases with increases in field intensity and causes increases in the fresh air supply to the bottom of the flame, resulting in shorter flame length. When the oxygen concentration increases, the concentration gradient increases, increasing the oxygen diffusion rate, and this is also a factor in shortening the flame length. It is important to note that
Observation of Magnetic-Field Effects Based on the Light Emission of the Flame To evaluate the effect of magnetic fields on diffusion flames in microgravity, the light emission from the flame was observed. Figure 5 shows the changes in brightness of flames under various magnetic-field intensities as a function of time after the capsule drop. At higher magnetic fields, the brightness reached a constant value immediately after the start of microgravity. Lower magnetic fields take longer times to reach steady brightness. For example, the flame brightness at 85.9 mT reduces for around 2 s after the capsule drops, and then the flame recovers to a steady brightness, while with 71.6 mT, the brightness reached zero around 1.5 s after microgravity started and then did not recover. According to the figure, the brightness reaches a steady value at 8 s for all cases, and in the following, the data at 8 s after the start of capsule drop are normally used. Assuming that the light emission from the soot particles, which mainly dominate the luminosity of the diffusion flame, has the same characteristics as the thermal radiation from a blackbody, the brightness and color of the flame should be determined from the principles of blackbody thermal radiation, Planck’s law, to give the spectrum as a function of wavelength for a given temperature. Thus, the flame brightness decreases and flame color shifts toward red (longer wavelength) with decreases in flame temperature. In the present paper, the degree of red, the r coordinate determined as R/(R ` G ` B), has been introduced for the qualitative evaluation of flame-temperature changes at various magnetic-field intensities. The value of R, G, and B are the absolute values given by a CCD camera corresponding to red, green, and blue colors, respectively. Generally, the degree of flame color, the chromaticity coordinate (r, g, b), is determined as (R, G, B)/ (R ` G ` B). Also, it is known that there is only one blackbody temperature correlated with a flame color expressed by a chromaticity coordinate [7–9]. One of the most useful characteristics is that the r coordinate increases monotonically with decreases in flame temperature.
MICROGRAVITY DIFFUSION FLAMES IN MAGNETIC FIELD
Fig. 6. Changes in the r coordinate (redness of the flame) as a function of magnetic-field intensity (t 4 8s).
Fig. 7. Change in the r coordinate as a function of oxygen concentration (t 4 8s).
Fig. 8. Changes in r coordinate as a function of F[O2]. Almost all data obtained in this research are on the same curve.
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Although it is possible to use brightness to evaluate the flame temperature, the brightness taken by the CCD camera is affected by many factors such as sensitivity of the CCD element, transparency of the lenses, optical thickness of the flame, as well as setting of the iris (or F stop) of the camera. On the other hand, as the chromaticity coordinate, such as the r coordinate, is the value normalized by total light emission intensity, it is useful to evaluate the flame temperature even when flame size or other uncertain factors change the total incident light to the CCD element. In the experiments, the white balance of the camera was fixed at a standard condition where sunlight was recorded as white. The change in the r coordinate of the flame in microgravity as a function of magnetic-field intensity was investigated as shown in Fig. 6. The value of r decreases with increase in magnetic-field intensity for both O2 concentrations. This shows that the correlated flame temperature increases with increases in magnetic field. The dependence of r on the field intensity becomes smaller with increases in the field strength. It is also clear that the higher oxygen concentration results in lower r values, showing higher temperatures with higher O2 concentrations. Figure 7 shows the changes in r versus oxygen concentration. The r value decreased with increases in O2 concentration for all magnetic-field intensities. The dependence of r on O2 concentration is stronger for lower magnetic fields. According to the foregoing discussion, both the magnetic field and O2 concentration have strong effects on the r value or soot temperature. As a trial to unify the effects of oxygen concentration and magnetic-field strength, a new parameter, F[O2], was introduced. Because F, the force acting on the surrounding atmosphere, is basically determined by equation 1 substituted by v0 to v, it is a function of [O2] as well as of the magnetic-field intensity because the v0 is proportional to the O2 concentration. Thus, the value of F[O2] is approximately proportional to the square of the O2 concentration. Figure 8 shows the change in r values as a function of F[O2] for the microgravity data in this report. All plots are almost on the same curve irrespective of the oxygen concentration. This result implies that the flame temperature is determined by the value of F[O2]. The physical meaning of F[O2] is the product of the strength of the magnetically induced convection and the O2 concentration. Thus, F[O2] indicates the transported oxygen by the magnetically induced flow toward the combustion region that replaces the combustion products in the flame zone. As the flame in microgravity is short of oxygen, the increase in oxygen supply to the flame region increases its flame temperature. However, when the supply of air becomes large, the effect of the increase in oxygen becomes smaller than with poor O2 supply. This explanation corresponds to the fact that the change in r
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is quite large at low F[O2], whereas the change becomes smaller at larger F[O2] values in Fig. 8. Conclusions 1. The effect of the magnetic field on a diffusion flame was investigated in a microgravity environment. There is a critical magnetic-field intensity beyond which the flame is sustained. The criteria for the critical magnetic-field intensities can be roughly estimated by the nondimensional Grm number introduced in the report. 2. Flame length was strongly affected by the field intensity and O2 concentration. The effect of those parameters are more evident when the added magnetic-field intensity is relatively low. 3. Combustion characteristics under the effect of magnetic field have been evaluated based on the change in r, the degree of redness of the flame color. The value of r decreased with increases in the magnetic-field strength and O2 concentration. The change in r becomes smaller with increases in magnetic-field strength. 4. The factor F[O2] indicating the amount of O2 supply to the combustion region by the magnetic force was able to universally estimate the changes in r values, correlating to the flame temperature. This implies that this factor dominates the combustion characteristics under the effect of magnetic fields in microgravity.
Acknowledgments This work was performed under the management of the Japan Space Utilization Promotion Center (JSUP) as a part of the R&D project of the Basic Technologies to Control Combustion supported by the New Energy and Industrial Technology Development Organization (NEDO).
REFERENCES 1. Pauiling, L., Wood, R. E., and Sturdivant, J. H., J. Am. Chem. Soc. 68:795–798 (1946). 2. Faraday, M., Philos. Mag. (Supplement 3), 31:401–421 (1847). 3. Wakayama, N. I., Combust. Flame 93:207–214 (1993). 4. Lawton, J. and Weinberg, F. L., in Electrical Aspects of Combustion, Clarendon, Oxford, 1969, chaps. 1–8. 5. Wakayama, N. I., et al., Combust. Flame 107:187–192 (1996). 6. Churchill, S. W. and Chu, H. H. S., Heat Exchanger Design Handbook, Hemisphere, 1983. 7. Churchill, S. W. and Chu, H. H. S., Int. J. Heat Mass Transfer 18:1323–1335 (1975). 8. Mori, L., Sugiyama, H., and Kambe, N., Acta Chromatica 1(3):93–102 (1964). 9. JIS (Japan Industrial Standard) Z8725, “Methods for Determining Distribution Temperature and Colour Temperature or Correlated Colour Temperature of Light Source” (in Japanese), 1987, pp. 6–11.
DETERMINATION OF MAGNETIC FIELD EFFECTS ON A JET DIFFUSION FLAME IN A MICROGRAVITY ENVIRONMENT OSAMU FUJITA,1 KENICHI ITO,1 TOMOYUKI CHIDA,1 SHINOBU NAGAI1 and YASUHIRO TAKESHITA2 1Division of Mechanical Science Hokkaido University Sapporo, 060-8628, Japan 2Japan Space Utilization Promotion Center Shinjuku-ku Tokyo, 169, Japan
The effect of magnetic fields on a laminar jet diffusion flame has been investigated by using a microgravity environment. The magnetic field was changed from fairly low (around 0 mT) to strong (around 215 mT) intensities. The effect of oxygen concentration was also investigated. The buoyancy caused by gravity is dominant for diffusion flames under normal gravity, so the microgravity environment was used to allow an observation of the effect of the magnetic field on combustion, especially for weak magnetic fields. A steady flame could be sustained with a field intensity larger than a critical value that depends on the O2 concentration. The critical value was determined experimentally and evaluated with a nondimensional number corresponding to the Grashof number used for gravitational fields. The changes in combustion characteristics, that is, flame shape, length, brightness, and color, were evaluated as a function of the magnetic-field intensity. The flame length decreased with increases in the magnetic-field strength, and the color of the flame shifted from red to yellow, indicating a temperature increase with increases in magneticfield strength. By evaluating the changes in the flame color with chromaticity treatment, it was concluded that the effect of the magnetic field is dominated by F [O2], where F is the magnetic force acting on the combustion, a function of field strength, and [O2] is the surrounding oxygen concentration.
Introduction Substances placed in a magnetic-field gradient are subject to a magnetic force in proportion to their magnetic susceptibility. The magnitude of the force, F, in a one-dimensional magnetic-field gradient is expressed as [1]: F 4 l0xH(dH/dx)
(1)
where l0 is the vacuum magnetic permeability, v is the magnetic susceptibility, H is the magnetic-field strength (4 B/l0, B being the intensity of the magnetic field), and (dH/dx) is the magnetic field gradient. When the substance has paramagnetic properties (v . 0), the direction of the magnetic force is toward the higher intensity field, while with diamagnetic substances (v , 0), the force is toward the opposite direction. In gas components present in a combustion field, O2 has the largest magnetic susceptibility (1.54 2 1017 emu/mL), whereas other possible components have diamagnetic characteristics with magnetic susceptibilities lesser by 2 orders of magnitude than that of oxygen. For example, the magnetic susceptibility of N2, CO2, H2O, and propane are 10.54 2 1019, 10.11 2 1019, 10.58 2 1019, and 11.8 2 1019 in emu/mL, respectively. Therefore, a gas containing more O2, such as air, tends to move toward the stronger magnetic-field
direction, and a gas with less O2, such as fuel or combustion gas, tends to move toward the weaker magnetic field. Based on this principle, it may be possible to utilize a magnetic field to control the flow field of the combustion region to improve combustion characteristics. There is less research on magnetic-field effects on combustion [2,3] than on electric-field effects [4]. Recently, Wakayama [3] showed that the magnetic field enforces the combustion of diffusion flames, caused by the principle previously explained. However, since the magnetic force acting on a combustion field is much smaller than that of gravitational buoyancy and combustion phenomena are mainly dominated by gravitationally induced flows, it is difficult to observe the effect of magnetic force alone. Wakayama [5] and the authors here have tried to observe flames with and without magnetic fields in a microgravity environment achieved by a drop shaft. There it was shown that the shape and luminosity of the flame in microgravity dramatically changed when a magnetic field was imposed. With a magnetic field, the flame was sustained steadily with high luminosity, whereas without a magnetic field, it could not be sustained steadily in microgravity. However, this research only examined cases with and without magnetic fields and compared the results. To understand the effect of magnetic fields more systematically, it
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Fig. 1. Relative position of tubular burner and magnetic poles (left) and distribution of magnetic-field intensities along the vertical centerline.
is necessary to observe flames under various magnetic-field intensities from fairly weak to stronger magnetic fields. When evaluating changes in combustion characteristics as a function of magneticfield intensity, the use of microgravity is especially helpful with weaker magnetic fields. In the present work, diffusion flames with magnetic fields of various intensities have been observed. The changes in combustion characteristics, flame shape, length, brightness, and color were evaluated as a function of the field intensity. As the diffusion flame had very low fuel injection velocity that could not generate a sufficient fluid flow in the surrounding air, flames could not be kept steady without the magnetic field. Flames become steady at intensities higher than a certain magnetic-field intensity. According to the results, the effect of magnetic fields over a wide range of field intensities are discussed.
Experimental Facility In the experiments, an electromagnet was used to generate the various magnetic-field intensities. Figure 1 shows the position of the tested flame relative to the magnet’s poles. The interval between the N and S poles is 40 mm. The flame is held above a tubular burner of 6 mm inner and 8 mm outer diameters. The fuel was propane with a flow rate of 1.2 mL/s. The position of the burner rim is slightly (3 mm) higher than the center of the magnetic poles. The right part of Fig. 1 shows the typical magneticfield intensity distribution in millitesla along the vertical centerline. As the magnetic poles are circular, the magnetic field has a radially axisymmetric distribution, and the field intensity has its maximum value at the center of the poles. The field strength gradually decreases above the burner, and above 15-mm height, the gradient of the magnetic-field intensity
Fig. 2. Relationship between maximum intensity of magnetic field and the supplied electric current to the electromagnet.
becomes constant. In the present research, the maximum intensity of the magnetic field at the center is used as the representative value of the magneticfield strength. The maximum field strength can be varied by electric current sent to the magnet as shown in Fig. 2, and the field-intensity distribution is similar to that shown in Fig. 1 when the maximum magnetic-field intensity increases. In the experiments, the electromagnet and burner are set in an air-tight chamber to control the surrounding O2 concentration. The combustion phenomena are recorded by a charge-coupled device (CCD) camera (Sony CCD-TR705) through the window of the combustion chamber. Ignition is effected by an electric spark after the microgravity period has started. The microgravity experiments were performed at Japan Microgravity Center (JAMIC), which provides high-quality microgravity environments around 1015 g0 (g0 is the gravity at sea level) for 10 s.
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Fig. 3. Direct photos taken under various magnetic-field intensities in microgravity. t (time after microgravity starts) 4 8 s, O2 4 21%, fuel flow rate 4 1.2 mL/s. Steady flame is visible at 85.9 mT or lager values.
Because of limited access to the microgravity rig, each point plotted in the figures of this paper correspond to one experimental run. A few experiments were repeated for selected conditions; however, it was confirmed that the reproducibility of the flame, such as flame height or flame color, was quite high difficult to differentiate and it was between the experiments. Results and Discussion Observation of Direct Flame Picture The changes in the flame shape versus magneticfield strength were observed as shown in Fig. 3. These pictures were taken 8 s after the start of the capsule drop. The fuel flow rate is 1.2 mL/s (mean velocity is 2.4 cm/s), and the surrounding environment is air. The magnetic-field intensity denoted below each picture shows the maximum field strength. Without any magnetic field, flame luminosity decreased, and the flame diameter increased with time under microgravity. The flame finally became invisible and may have reached extinction. When the magnetic field is increased somewhat, a steady flame could be maintained throughout the microgravity. A field strength of 85.9 mT maintained a steady flame, while the 71.6-mT field did not. This indicates that there is a critical magnetic-field strength above which steady flames can be maintained. The critical strength may depend on a steady convective flow, and the appearance of the steady convective flow may be determined by the ratio between the viscous force and convective force caused by the magnetic field. When the viscous force is much larger than the convective force, there is limited convection, and the combustion phenomena become dominated by diffusion, which results in unsteadiness. Once the convective force becomes larger, the steady flame can be maintained.
This is similar to using the Gr number to determine if natural convection occurs in a closed chamber. The Gr number is expressed as Gr 4 g b (Tf 1 T0) d 3/m 2 (2) where g is the gravity level at ground level, b the coefficient of thermal volumetric expansion, Tf the flame temperature, T0 the surrounding temperature, d a representative dimension, and m the kinetic viscosity. In a box with a heated vertical wall face, natural convection occurs when the Gr number is larger than 102–103 (which strongly depends on the boundary conditions, assuming the Prandtl number is unity) [6,7]. Analogous to the gravitational field, the criterion to maintain a steady flame with magnetic field is given by the nondimensional number, Grm, having a physical meaning similar to the Gr number in gravitational fields. The Grm value is determined by Grm 4 l0 (vf 1 vo) H (dH/dx) d 3/qm 2 (3) where vf is the mean magnetic susceptibility of the combustion gas and v0 the susceptibility of the surrounding atmosphere. Thus, l0 (vf 1 v0) H (dH/dx) d 3 shows a buoyancy-like force caused by differences between the magnetic forces acting on the combustion gas and surrounding air. According to the observation in Fig. 3, this takes place between 71.6 and 85.9 mT, and the critical value may be around 80 mT. The value of Grm at 80 mT is around 400 assuming a flame width d of 15 mm, and vf is negligible relative to the value of v0. The intensity of the magnetic field and the gradient necessary to calculate Grm are 64 mT and 16 mT/cm, respectively, which are 80% of the maximum intensity. Considering the differences in the boundary condition from Ref. [6], this Grm appears reasonable as the criterion for steady convective flow. It may be concluded that a flame under microgravity will be sustained by a magnetic field with Grm larger than 102–103 like the Grashof number for the gravitational force.
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the field-induced flow is larger with the higher O2 concentration due to the larger value of (vf 1 v0) in equation 3, which also has a significant effect on the decrease in flame length. As seen in Fig. 4, steady flames can be sustained at lower field intensities, which implies that the Grm increases with increases in O2 concentration at the same field intensity. Though the data at zero intensity are plotted in Fig. 4, it is an unsteady value as the flame at O2 4 50% without magnetic field kept expanding during the whole microgravity time, 10 s. All other data in Fig. 4 are the flame length of a steadily burning flame.
Fig. 4. Changes in flame length as a function of magnetic-field intensity.
Fig. 5. Changes in flame brightness as a function of time after start of microgravity. O2 4 21%.
In magnetic fields larger than the critical field intensity, the flame becomes brighter with increasing field intensity, as seen in Fig. 3. It is also noted that the tip of the flame tends to close with increase in the field intensity. These phenomena must be caused by the increased forced convective flow induced by the magnetic effect. Flame length as a function of magnetic-field intensity has also been measured as shown in Fig. 4. Here the data are established at two different oxygen concentrations. The flame length decreased with increases in the field intensity for both oxygen concentrations, while the flame length with the higher oxygen concentration is everywhere shorter than that of the lower oxygen concentration. The magnetic-field–induced flow increases with increases in field intensity and causes increases in the fresh air supply to the bottom of the flame, resulting in shorter flame length. When the oxygen concentration increases, the concentration gradient increases, increasing the oxygen diffusion rate, and this is also a factor in shortening the flame length. It is important to note that
Observation of Magnetic-Field Effects Based on the Light Emission of the Flame To evaluate the effect of magnetic fields on diffusion flames in microgravity, the light emission from the flame was observed. Figure 5 shows the changes in brightness of flames under various magnetic-field intensities as a function of time after the capsule drop. At higher magnetic fields, the brightness reached a constant value immediately after the start of microgravity. Lower magnetic fields take longer times to reach steady brightness. For example, the flame brightness at 85.9 mT reduces for around 2 s after the capsule drops, and then the flame recovers to a steady brightness, while with 71.6 mT, the brightness reached zero around 1.5 s after microgravity started and then did not recover. According to the figure, the brightness reaches a steady value at 8 s for all cases, and in the following, the data at 8 s after the start of capsule drop are normally used. Assuming that the light emission from the soot particles, which mainly dominate the luminosity of the diffusion flame, has the same characteristics as the thermal radiation from a blackbody, the brightness and color of the flame should be determined from the principles of blackbody thermal radiation, Planck’s law, to give the spectrum as a function of wavelength for a given temperature. Thus, the flame brightness decreases and flame color shifts toward red (longer wavelength) with decreases in flame temperature. In the present paper, the degree of red, the r coordinate determined as R/(R ` G ` B), has been introduced for the qualitative evaluation of flame-temperature changes at various magnetic-field intensities. The value of R, G, and B are the absolute values given by a CCD camera corresponding to red, green, and blue colors, respectively. Generally, the degree of flame color, the chromaticity coordinate (r, g, b), is determined as (R, G, B)/ (R ` G ` B). Also, it is known that there is only one blackbody temperature correlated with a flame color expressed by a chromaticity coordinate [7–9]. One of the most useful characteristics is that the r coordinate increases monotonically with decreases in flame temperature.
MICROGRAVITY DIFFUSION FLAMES IN MAGNETIC FIELD
Fig. 6. Changes in the r coordinate (redness of the flame) as a function of magnetic-field intensity (t 4 8s).
Fig. 7. Change in the r coordinate as a function of oxygen concentration (t 4 8s).
Fig. 8. Changes in r coordinate as a function of F[O2]. Almost all data obtained in this research are on the same curve.
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Although it is possible to use brightness to evaluate the flame temperature, the brightness taken by the CCD camera is affected by many factors such as sensitivity of the CCD element, transparency of the lenses, optical thickness of the flame, as well as setting of the iris (or F stop) of the camera. On the other hand, as the chromaticity coordinate, such as the r coordinate, is the value normalized by total light emission intensity, it is useful to evaluate the flame temperature even when flame size or other uncertain factors change the total incident light to the CCD element. In the experiments, the white balance of the camera was fixed at a standard condition where sunlight was recorded as white. The change in the r coordinate of the flame in microgravity as a function of magnetic-field intensity was investigated as shown in Fig. 6. The value of r decreases with increase in magnetic-field intensity for both O2 concentrations. This shows that the correlated flame temperature increases with increases in magnetic field. The dependence of r on the field intensity becomes smaller with increases in the field strength. It is also clear that the higher oxygen concentration results in lower r values, showing higher temperatures with higher O2 concentrations. Figure 7 shows the changes in r versus oxygen concentration. The r value decreased with increases in O2 concentration for all magnetic-field intensities. The dependence of r on O2 concentration is stronger for lower magnetic fields. According to the foregoing discussion, both the magnetic field and O2 concentration have strong effects on the r value or soot temperature. As a trial to unify the effects of oxygen concentration and magnetic-field strength, a new parameter, F[O2], was introduced. Because F, the force acting on the surrounding atmosphere, is basically determined by equation 1 substituted by v0 to v, it is a function of [O2] as well as of the magnetic-field intensity because the v0 is proportional to the O2 concentration. Thus, the value of F[O2] is approximately proportional to the square of the O2 concentration. Figure 8 shows the change in r values as a function of F[O2] for the microgravity data in this report. All plots are almost on the same curve irrespective of the oxygen concentration. This result implies that the flame temperature is determined by the value of F[O2]. The physical meaning of F[O2] is the product of the strength of the magnetically induced convection and the O2 concentration. Thus, F[O2] indicates the transported oxygen by the magnetically induced flow toward the combustion region that replaces the combustion products in the flame zone. As the flame in microgravity is short of oxygen, the increase in oxygen supply to the flame region increases its flame temperature. However, when the supply of air becomes large, the effect of the increase in oxygen becomes smaller than with poor O2 supply. This explanation corresponds to the fact that the change in r
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is quite large at low F[O2], whereas the change becomes smaller at larger F[O2] values in Fig. 8. Conclusions 1. The effect of the magnetic field on a diffusion flame was investigated in a microgravity environment. There is a critical magnetic-field intensity beyond which the flame is sustained. The criteria for the critical magnetic-field intensities can be roughly estimated by the nondimensional Grm number introduced in the report. 2. Flame length was strongly affected by the field intensity and O2 concentration. The effect of those parameters are more evident when the added magnetic-field intensity is relatively low. 3. Combustion characteristics under the effect of magnetic field have been evaluated based on the change in r, the degree of redness of the flame color. The value of r decreased with increases in the magnetic-field strength and O2 concentration. The change in r becomes smaller with increases in magnetic-field strength. 4. The factor F[O2] indicating the amount of O2 supply to the combustion region by the magnetic force was able to universally estimate the changes in r values, correlating to the flame temperature. This implies that this factor dominates the combustion characteristics under the effect of magnetic fields in microgravity.
Acknowledgments This work was performed under the management of the Japan Space Utilization Promotion Center (JSUP) as a part of the R&D project of the Basic Technologies to Control Combustion supported by the New Energy and Industrial Technology Development Organization (NEDO).
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