- Email: [email protected]
Particle combustion rates for mechanically alloyed Al–Ti and aluminum powders burning in air
Combustion and Flame 145 (2006) 714–722 www.elsevier.com/locate/combustflame
Particle combustion rates for mechanically alloyed Al–Ti and aluminum powders burning in air Yuriy L. Shoshin, Edward L. Dreizin ∗ Department of Mechanical Engineering, New Jersey Institute of Technology, Newark, NJ 07102-1972, USA Received 27 January 2005; received in revised form 1 November 2005; accepted 27 November 2005 Available online 9 March 2006
Abstract Mechanically alloyed aluminum-rich powders of Al–Ti (10, 15, 20, and 25 atom% of Ti) were produced and their combustion was compared to that of aluminum and titanium powders of comparable sizes. A laminar liftedflame aerosol burner developed recently was used in this research. The aerosols were produced and burned in air. Measured flame speeds were higher for the aerosols of Al–Ti mechanical alloys than for the aerosols of pure Al or Ti. The particle combustion rates were evaluated based on the comparison of the measured and calculated profiles of the flame radiation. To calculate radiation profiles a simple model of particle combustion was used, in which both the radiation intensity and particle burn time were expressed as power functions of the initial particle size. For all the powders, the burning particle radiation intensity was observed to be best described by a function proportional to the cube of the initial particle size. For aluminum aerosol, the best match between the experimental and calculated flame radiation profiles was observed for the linear particle combustion law, when the particle combustion time, t, was expressed as a function of the initial particle size, d, as t [s] = 310d [m]. To match the experimental and calculated flame radiation profiles for the Al–Ti mechanical alloys, the combustion times of individual particles could be described by either d 1 or d 2 expressions. The burning time of mechanically alloyed particles increased with the increase of titanium concentration. The overall combustion times for aluminum particles are significantly longer than those for mechanically alloyed particles of Al–Ti of the same size. © 2006 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Aerosol flame; Flame emission; Metal combustion; Mechanical alloying
1. Introduction Metal powders are often used as additives in propellants, explosives, or pyrotechnics because of their high enthalpy of combustion [1,2]. Addition of metal powders to propellants is also known to * Corresponding author. Fax: +1 (973) 642 4282.
E-mail address: [email protected] (E.L. Dreizin).
improve the combustion stability in rocket engines [2,3]. The most common metal additive is aluminum, which is relatively inexpensive, is safe to handle, and has a relatively high volumetric combustion enthalpy. However, the potential of aluminum as a fuel is often underutilized. Aluminum particles ignite at fairly high temperatures and they often melt before ignition. Molten particles agglomerate, forming large aluminum droplets that burn slowly and incompletely. Furthermore, large aluminum and alumina
0010-2180/$ – see front matter © 2006 The Combustion Institute. Published by Elsevier Inc. All rights reserved. doi:10.1016/j.combustflame.2005.11.006
Y.L. Shoshin, E.L. Dreizin / Combustion and Flame 145 (2006) 714–722
droplets produce slug that plugs rocket exhaust nozzles. Recently, aluminum-based mechanical alloys have been suggested as alternative fuel additives [4,5]. It was expected that the combustion enthalpy of mechanical alloys could approach that of pure aluminum, but the ignition temperatures could be reduced and burning rates increased. During mechanical alloying, powders composed of metastable metal– metal solid solutions are formed from the precursor powders of elemental metals, such as Al and additives of Mg, Ti, Zr, etc. It was hypothesized [6] and, recently, experimentally confirmed for the aluminumrich Al–Ti mechanical alloys that the equilibration of metastable phases occurring upon heating can trigger ignition at a temperature significantly lower then the typical Al ignition temperature [7]. Therefore, further analyses of the overall powder burning rates are of interest for these and other aluminum-based mechanical alloys. Recently, a lifted laminar-flame aerosol burner (LLFAB) was developed for experimental characterization of solid fuel aerosols [8–10]. Flames of aerosolized powders of aluminum-based mechanical alloys were surveyed [10] and the highest burning rate was observed for the Al–Ti alloy. This work aims to further characterize laminar flames of Al–Ti mechanical alloy powders aerosolized in air. The specific objective of this work is to obtain a phenomenological expression for the particle combustion time as a function of the particle size, similar to the d 2 law or, more generally, the power law commonly used to describe combustion of liquid fuel droplets [11] and metal particles [12,13]. Such an expression is useful for modeling combustion in complex systems, for example, a solid rocket motor chamber, in which specific fuel particles are used. It was also interesting to compare the particle combustion times for the Al–Ti mechanical alloys with those for pure aluminum powders. The processing of the experimental data produced using LLFAB was developed in Ref. [9] to determine whether the particle combustion could be described using a simple power law and if yes, what was the combustion constant and which exponent should be used. This processing was based on a detailed analysis of the measured vertical radiation profile of a lifted laminar flame of aerosolized fuel particles. The analysis takes into account the powder size distribution, the flame speed, and the characteristic ignition temperature of the material. Despite a number of simplifying assumptions, this approach was found to be quite successful in the characterization of burn rates of aerosolized metal particles [9]. This approach is implemented here to characterize combustion of mechanically alloyed Al–Ti powders and similar-size aluminum powders.
715
2. Materials Four different Al–Ti mechanical alloy compositions, with titanium concentrations of 10, 15, 20, and 25 atom%, were produced and examined. The powders were produced in an 8000D series shaker mill by SPEX CertiPrep using zirconia vials and balls. Aluminum powder (Alfa Aesar, 99.8%, −40 + 325 mesh) and titanium powder (Alfa Aesar, 99%, −325 mesh) were used as starting materials. A process control agent (stearic acid, 2 mass%) was used to minimize formation of agglomerates. The total powder load in one run was 5 g and the ball-to-powder mass ratio was 10. Powders were mechanically alloyed for 15 h. The synthesis details are described elsewhere [14]. Particle morphology was characterized using scanning electron microscopy (SEM). Fig. 1 shows a typical image of the produced Al–Ti mechanically alloyed powder. The particles have irregular shapes and a fairly wide range of sizes. The metal powders used in the combustion experiments in addition to the mechanical alloys were 10–14 µm nominal size, 98% pure spherical aluminum; 17–30 µm nominal size, 99% pure spherical aluminum sieved through a 400-mesh sieve (38 µm opening size); and −325 mesh, 99% pure titanium. All powders were supplied by Alfa Aesar. The particle size distributions were measured using a Beckman Coulter LS 230 analyzer. The instrument determines particle size distribution based on the measured angular pattern of Fraunhofer diffraction of a laser beam [15]. For nonspherical particles, the diffraction angles depend on how the particles are oriented with regard to the incident laser beam at the moment of measurement. The effect of particle orientation results in a systematic error of the mea-
Fig. 1. SEM image of Al0.9 Ti0.1 mechanical alloy particles.
716
Y.L. Shoshin, E.L. Dreizin / Combustion and Flame 145 (2006) 714–722
No correction is needed for spherical powders, e.g., the spherical Al powders used in these experiments. The measured size distributions and the size distributions corrected for nonspherical powders are shown in Figs. 2 and 3. These corrected size distributions were used in analyses of the vertical radiation profiles of the flames with respective powders, as discussed in Ref. [9] and below.
3. Flame speed and radiation profile measurements
Fig. 2. Size distributions for Al 10–14 and Al 400 powders measured by Beckman Coulter LS 230 size analyzer.
Fig. 3. Size distributions for Al–Ti mechanically alloyed powders measured by Beckman Coulter LS 230 size analyzer and corrected to account for nonspherical shape of particles.
sured size distributions. A correction procedure suggested to account for this error [9] was used here. This correction uses particles’ shape factors found from processing the powder SEM images. As a result of processing, the range of particle sizes inferred from the laser diffraction measurements is compressed to the range between the minimum and maximum Ferets diameters measured from the particle images.
The aerosol flames were produced using LLFAB as described in detail elsewhere [8–10]. The burner uses electrostatic fluidization of a conductive powder in a plate capacitor to produce a narrow (∼1-mmdiameter), vertically rising, laminar aerosol jet. The jet issues from a small orifice in the top electrode of the capacitor. Air is used as a carrier gas. The jet velocity at the nozzle is on the order of 1 m/s. A slower shroud co-flow of air is produced around the jet to improve its stability. The aerosol jet is decelerated because of viscous forces, so the local aerosol speed decreases at longer distances from the nozzle. The jet is ignited in a region where the aerosol particles are nearly stopped and the laminar flame propagates downward. The flame position stabilizes at a location where the flame speed becomes equal to the local aerosol jet velocity (with the opposite sign). It was experimentally observed that when the flame is ignited, the aerosol jet velocity below the flame front [8,10] does not change noticeably, compared to that in a cold jet. Therefore, the flame speed could be determined as the speed of the unignited aerosol jet at the location where the flame stabilizes. A Dantec Flowlite one-dimensional laser Doppler velocimetry (LDV) setup based on a 632.8-nm wavelength He–Ne laser was used to measure the aerosol jet speed. The LDV optical head was focused on the aerosol jet at a specific distance above the nozzle. The aerosol was ignited and the air flowrate was adjusted to move the front of the lifted flame (the bottom edge of the flame) to the location where the LDV head was focused. Once the flame was stabilized at that location, the flame was quenched and the aerosol jet velocity was measured. In one measurement, velocities of 2000 particles were determined. Several measurements were carried out for each powder. For each measurement, a histogram of the particle velocities was produced and the average jet velocity was found. Examples of the velocity distributions for different aerosols measured at a distance of 20 mm above the nozzle are shown in Fig. 4. The particle velocity distributions are quite narrow, indicating that the particles follow the gas nearly uniformly. This ob-
Y.L. Shoshin, E.L. Dreizin / Combustion and Flame 145 (2006) 714–722
717
Fig. 4. Histograms of the particle velocities for Al0.90 Ti0.10 and Al0.85 Ti0.15 alloy aerosols measured at the location of the flame front.
Fig. 6. A typical image of an aluminum aerosol flame used for measurements of the vertical radiation profile. Nominal particle size 10–14 µm. Exposure time 1/60 s.
Fig. 5. Laminar aerosol flame speeds measured for different powders.
EZ30P camcorder equipped with a close-up lens and neutral density filters. To produce time-averaged images of the flame, a relatively long exposure time (1/60 s) was selected. Fig. 6 shows a sample flame image for the aerosol of spherical aluminum particles with nominal diameters of 10–14 µm. The vertical flame radiation profiles were measured along the vertical centerlines of the flame images using Tracker software [16]. In preliminary analyses, it was found that the profiles determined from the blue, green, and red color-separated images, as well as from the grayscale image, practically coincided with one another after normalization by the maximum image intensity. Therefore, the gray-scale images were consistently used to measure the flame radiation profiles.
servation is in agreement with the results of Ref. [10], where only the initial particle velocity distributions at distances from 0 to 10–15 mm from the nozzle were found to be affected by the slip for larger particles and by the initial particle acceleration from the electric field within the capacitor. To ensure uniform particle velocities, in these experiments the flames lifted 20 mm above the nozzle were used consistently. The flame speeds measured for pure Al, Ti, and Al–Ti mechanical alloy powders are shown in Fig. 5. The flame speeds are nearly the same for both types of aluminum and for the titanium powder. At the same time, the flame speeds are consistently higher for the synthesized powders of Al–Ti mechanical alloys. To determine the vertical flame radiation profiles, the flames were videorecorded using a Panasonic AG-
4. Interpretation of the flame radiation profiles A simplified model interpreting the radiation profiles of the lifted laminar flames produced by LLFAB in terms of individual particle combustion laws was described in detail elsewhere [9]. For completeness, the model is briefly reviewed below. The burning particles are considered to move with a constant velocity equal to the measured flame speed. This assumption is justified in Ref. [9] based on experimental observation of particle streaks within the flame. The gas temperature is assumed to increase linearly from the room temperature to the flame temperature in the flame preheat zone. This length of the preheat zone is assumed to be equal to α/v, where v is the flame
718
Y.L. Shoshin, E.L. Dreizin / Combustion and Flame 145 (2006) 714–722
speed and α is the thermal diffusivity of air. The particles are convectively heated within the preheat zone. The heat transfer equation uses particle Ferets diameter and because of the small slip effect, the Nusselt number is assumed to be equal to 2. Therefore, the effect of particle shape on the rate of heat transfer is neglected. The air thermal diffusivity is considered at a temperature equal to the average temperature in the preheat zone. For aluminum particles, the density and heat capacity are obtained from the literature: ρAl = 2700 kg/m3 , CpAl = 900 J/(kg K) [17]. The density and heat capacity of the Al–Ti mechanical alloys are estimated as average values for the respective mechanical mixtures. For these estimates, the literature values for the titanium density and heat capacity are used: ρTi = 4507 kg/m3 , heat capacity CpTi = 523 J/(kg K) [17]. Ignition is assumed to occur when the particles attain a threshold temperature specified for each material. Generally, the ignition temperatures depend on the heating rate, which is close to 106 K/s for these experiments. The ignition kinetics necessary to identify an appropriate threshold temperature for each material was determined in separate experiments [7,18]. In those experiments, the ignition temperatures were measured for powders thinly coated on an electrically heated filament. The ignition temperature was determined as a function of heating rate for each mechanical alloy and aluminum powder used in these combustion experiments. The experimental heating rates varied from 10 to 104 K/s and the ignition temperatures expected at 106 K/s were estimated by extrapolating the experimental trends. Estimated ignition threshold temperatures used in this work for the Al–Ti mechanical alloys and for pure Al particles are summarized in Table 1. Particle radiation during combustion was assumed to be constant, corresponding to quasi-steady burning. The radiation intensity, I , was assumed to be a simple function of the particle initial diameter, d: I = Ln d n , where L is a constant and the exponent n could be either 1, 2, or 3. Different combustion models (e.g., [9,10,19,20]) imply different exponents for the radiation power law. While detailed analysis of the specific models is outside the scope of this paper, the mathematical processing of the data allows one to change the exponent n to determine which model better describes the experimental data. The selection of the constant L depends on the sensitivity of the optical sensor and is therefore insignificant. Finally, the particle combustion time is also determined by the particle initial size using a simple power law, t = Km d m , where K is a combustion constant and the exponent m could be equal to 1 (kinetic regime of particle reaction) or 2 (diffusion regime). An intermediate value of m = 1.5 is also considered,
and similarly to exponent n in the “radiation power law,” the exponent m is used as an adjustable parameter to achieve the best fit with the experimental data. The constant Km is used as another adjustable parameter optimized for each specific value of m. The optical thickness of the laminar lifted aerosol flame was found to be small [9,10] and therefore the total flame radiation intensity is assumed to be proportional to the sum of radiation intensities of all the particles burning simultaneously. The experimental particle size distribution is used to determine the ignition delays and combustion times for particles of different sizes sorted within a fixed number of “size bins.” For each particle size bin, the vertical coordinate corresponding to the particle ignition was found from the respective particle heat transfer analysis. The vertical coordinate corresponding to the particle extinction was determined using a power combustion law. The total flame height is described by a onedimensional mesh with 200 equidistant nodal points. For each node, particles of which bin sizes are burning, and which ones did not ignite, or were already extinguished, was determined. Taking into account the fraction of particles in each bin size inferred by the experimental particle size distribution, the total radiation intensity of all the simultaneously burning particles is computed for each node. Thus, the vertical flame radiation profile is calculated. These calculated profiles are normalized and compared with the experimental radiation profiles. The best match was attempted separately for each combination of radiation and combustion law powers, n and m, by the selection of appropriate coefficients Ln and Km . The quality of the achieved match for each case was evaluated using normalized sum of squares error (NSSE), N 2 j =1 (Ij,exp − Ij,calc ) , NSSE = N where I is the normalized radiation intensity and N is the number of experimental data points for which the radiation intensity was quantified along the vertical coordinate (in both experiment processing and calculation).
5. Results and discussion The flame radiation profiles calculated using individual particle radiation power laws with n = 1 and n = 2 deviated significantly from the experimental profiles for any particle combustion laws and for all the aerosol flames studied. The only case where reasonable agreement between the calculated and experimental flame radiation profiles could be obtained was for the cubic radiation power law: I = L3 d 3 . The
Y.L. Shoshin, E.L. Dreizin / Combustion and Flame 145 (2006) 714–722
719
Table 1 Ignition temperatures of Al and Al–Ti mechanical alloys particles used to process the aerosol flame radiation profiles Power used
Al 10–14, Al 400
Al0.90 Ti0.10
Al0.85 Ti0.15
Al0.80 Ti0.20
Al0.75 Ti0.25
Ignition temperature (heating rate 106 K/s)
2150 K
1326 K
1342 K
1301 K
1242 K
Fig. 7. Measured and calculated laminar flame radiation profiles for aluminum aerosol flames.
same result was reported in Ref. [9] for aluminum and magnesium aerosol flames. Therefore, in optically thin metal aerosol flames the radiation is generated volumetrically. The radiation law corresponding to n = 3 was used consistently below. The experimental and calculated flame radiation profiles for different powders are presented in Figs. 7– 9. The respective values of NSSE are summarized in Table 2. The values of constants Km corresponding to the best match achieved for each value of m are shown in Table 3. For both aluminum powders used in combustion experiments (cf. Fig. 8), the best match between the calculated and measured flame radiation profiles was achieved for the particle combustion law t = K1 d, based on the values of NSSE shown in Table 2. This result, once again, is in agreement with our earlier measurements for aluminum powder [9]. It is also remarkable that for m = 1, the values of the constant K1 corresponding to the best match for both aluminum powders are the same, as shown in Table 3. At the same time, for m = 1.5 and 2, the discrepancy between the values of the respective constants K1.5 and K2 are significant. Therefore, both the lowest value of NSSE and the consistent coefficients K1 for both aluminum powders support the conclusion that the
particle combustion law is linear for aluminum particles burning in an aerosol. This appearance of the kinetic regime could be interpreted by assuming that the individual aluminum particle flames are likely to be overlapped in the aerosol. Therefore, the concentration of oxidizer is relatively uniform within the flame, while it is likely limited by the bulk diffusion rate from the surrounding air to the burning group of particles. Thus, the effect of the individual particle size on its combustion rate is weaker than for single particles. It is also likely that the value of K1 found to match the experimental data depends on the overall dimension of the burning group of particles (in this case, around 2 mm). For the Al–Ti mechanical alloys, a relatively good match between the experimental and calculated flame radiation profiles could be produced with any value of the exponent in the combustion power law. Therefore, the results of the processing could not be used to conclusively identify the specific exponent appropriate for describing combustion of such mechanical alloys. Generally, judging from the appearance of the experimental and calculated profiles shown in Figs. 8 and 9, the d 2 combustion law produced a somewhat better match between the measured and calculated flame radiation profiles. However, the minimum normalized
720
Y.L. Shoshin, E.L. Dreizin / Combustion and Flame 145 (2006) 714–722
Fig. 8. Measured and calculated radiation profiles for aerosol fames of Al90 Ti10 and Al85 Ti15 mechanical alloys.
Fig. 9. Measured and calculated radiation profiles for aerosol fames of Al80 Ti20 and Al75 Ti25 mechanical alloys.
sums of squares errors were observed for the d 1.5 and d 1 expressions for the Al0.85 Ti0.15 and Al0.80 Ti0.20 compositions, respectively. At the same time, the normalized sum of squares errors for the d 2 law was also reasonably small. Comparison of the combustion constants for the alloys with different concentrations of Ti could be made for any of the tested combustion law expressions based on the results presented in Table 3. A consistent increase of the constant Km is observed for the alloys with increased concentration of Al. This generally implies that longer combustion times are expected for the particles with higher
titanium concentrations. Note that the ignition temperatures were determined to be lower for the alloys with higher titanium concentrations (see Table 1 and Ref. [7]), implying a shorter ignition delay. Therefore, shorter ignition delays but longer burn times are generally expected for the Al–Ti mechanical alloys with increased concentrations of Ti. It is also apparent from Table 3 that for all the combustion laws considered, the combustion constants for any of the Al–Ti mechanical alloy powders are significantly smaller then those for pure Al powders. Therefore, Al–Ti mechanical alloy particles
Y.L. Shoshin, E.L. Dreizin / Combustion and Flame 145 (2006) 714–722
721
Table 2 Normalized sum of square error (NSSE) for the comparison of the experimental and calculated flame radiation profiles Combustion law
Powder Al 10–14
Al 400
Al0.90 Ti0.10
Al0.85 Ti0.15
Al0.80 Ti0.20
Al0.75 Ti0.25
t = K1 d t = K1.5 d 1.5 t = K2 d 2
3.35 × 10−3 9.22 × 10−3 1.48 × 10−2
4.44 × 10−3 6.91 × 10−3 8.97 × 10−3
2.63 × 10−3 1.77 × 10−3 3.40 × 10−4
1.46 × 10−3 1.16 × 10−3 2.41 × 10−3
9.01 × 10−4 1.68 × 10−3 2.96 × 10−3
5.12×10−3 4.85×10−3 4.66×10−4
Table 3 Constants for different tested combustion power laws for which the minimum NSSE was achieved while comparing the experimental and measured flame radiation profiles Combustion law constant
Powder Al 10–14
Al 400
Al0.90 Ti0.10
Al0.85 Ti0.15
Al0.80 Ti0.20
Al0.75 Ti0.25
K 1 , s m−1 K 1.5 , s m−1.5 K 2 , s m−2
310 6.5 × 104 1.3 × 107
310 4.5 × 104 7 × 106
135 1.45 × 104 1.57 × 106
130 1.5 × 104 2 × 106
165 1.8 × 104 2.4 × 106
195 2.1 × 104 2.75 × 106
Fig. 10. Comparison of combustion times for single aluminum particles [21], aluminum particles burning in an aerosol flame, and aerosols of Al–Ti mechanical alloys.
have shorter burn times in aerosol flames than Al particles of the same size. The interpretation of this result is not straightforward. Both Al and mechanically alloyed Al–Ti powders burn primarily in the vapor phase, while the particle temperatures are typically at their saturation point. It is likely that Al and Ti evaporate at substantially different rates and that a significant portion of Ti oxidizes heterogeneously. It is reasonable to expect that the presence of Ti reduces the saturation temperature of the molten alloy particles compared to that of pure Al, and thus leads to an accelerated rate of Al evaporation. On the other hand, greater concentrations of Ti can lead to a more heterogeneous and thus a somewhat slower reaction. Previously, combustion of single aluminum particles has been described using a d 2 combustion law
and results of multiple experiments were reviewed and processed accordingly in Ref. [21]. The results of that review are represented by two thin solid lines shown in Fig. 10 corresponding to the maximum and the minimum combustion constants that should be considered to fit multiple single-particle combustion time measurements by the d 2 law. Combustion times obtained in the present study for particles burning in aerosol for both pure Al and Al–Ti mechanical alloy aerosols are also shown. The shown trends correspond to the d 1 combustion law for Al and the somewhat arbitrarily chosen d 2 law for the Al–Ti mechanical alloys. The presented trends show that the combustion rates observed in this work for Al–Ti mechanical alloy particles are higher than or comparable to the highest combustion rates determined in experiments
722
Y.L. Shoshin, E.L. Dreizin / Combustion and Flame 145 (2006) 714–722
with single Al particles. It is also clear that for the specific range of particle sizes studied in this work, the combustion times for Al–Ti alloys are shorter then those of Al.
6. Conclusions Speeds of lifted laminar aerosol flames were measured for powders of aluminum, titanium, and Al– Ti mechanical alloys containing 10, 15, 20, and 25 atom% of Ti burning in air. The measurements showed that the flame speeds are higher for the aerosols of Al–Ti mechanical alloys than for the aerosols of pure Al or Ti with similar particle sizes. The vertical flame radiation profiles for the Al and Al–Ti mechanical alloys were measured. These profiles were also calculated using a simplified model of particle combustion in which both the radiation intensity and particle burning time were expressed as power functions of the initial particle size, d. For all the powders, the burning particle radiation intensity, I , was observed to be best described by a cube law, i.e., I = Const d 3 . For aluminum, the best match between the experimental and calculated flame radiation profiles was observed for the linear particle combustion law, when the particle combustion time, t, was expressed as a function of the initial particle size as t [s] = 310d [m]. To match the experimental and calculated flame radiation profiles for the Al–Ti mechanical alloys the combustion times of individual particles could be described by either d 1 or d 2 expressions. For any of the selected description, the combustion constant describing the burning time of mechanical alloy particles decreased with the increase of titanium concentration, implying longer combustion times. The overall combustion times for aluminum particles are significantly longer compared to those for the same size particles of Al–Ti mechanical alloys.
Acknowledgments This work was supported in part by the Office of Naval Research, Grant N00014-00-1-0446, the NSWC Crane Division, Award N00164-02-C4702, the Defense Threat Reduction Agency, Award
DAAE30-1-9-0080, and TACOM-ARDEC, Award DAAE30-03-D-1015. References [1] C.N. Divekar, S.N. Asthana, H. Singh, J. Propuls. Power 19 (4) (2003) 614–622. [2] E.W. Price, in: K.K. Kuo, M. Summerfield (Eds.), Fundamentals of Solid Propellant Combustion, in: AIAA Progress Series, vol. 90, AIAA, 1984, p. 891. [3] M. Summerfield, H. Krier, Problems of Hydrodynamics, SIAM, Philadelphia, PA, 1969, pp. 703–717. [4] Y. Shoshin, R. Mudryy, E. Dreizin, Combust. Flame 128 (2002) 259–269. [5] M. Schoenitz, E.L. Dreizin, E. Shtessel, J. Propuls. Power 19 (3) (2003) 405–412. [6] E.L. Dreizin, Prog. Energy Combust. Sci. 26 (1) (2000) 57–78. [7] Y.L. Shoshin, M.A. Trunov, X. Zhu, M. Schoenitz, E.L. Dreizin, Combust. Flame 144 (4) (2006), in press. [8] Y. Shoshin, E. Dreizin, Aerosol Sci. Technol. 36 (2002) 953–962. [9] Y. Shoshin, E. Dreizin, Combust. Flame 133 (2003) 275–287. [10] Y. Shoshin, E. Dreizin, AIAA J. 42 (2004) 1416–1426. [11] I. Glassman, Combustion, third ed., Academic Press, New York, 1996, 631 p. [12] M.W. Beckstead, B.R. Newbold, C.A. Waroquet, in: 37th JANNAF Combustion Meeting, CPIA Publ. 701, vol. 1, 2000, pp. 485–504. [13] J. Servaites, H. Krier, J.C. Melcher, R.L. Burton, Combust. Flame 125 (2001) 729–1073. [14] M. Schoenitz, X. Zhu, E.L. Dreizin, J. Metastable Nanocryst. Mat. 20–21 (2004) 455–461. [15] M. Born, E. Wolf, Principles of Optics, seventh (expanded) ed., Cambridge Univ. Press, Cambridge, 1999. [16] “Tracker 3.0,” Computer software by R. Klimek, T. Wright, NASA Lewis Research Center, 1998. [17] D.R. Lide (Ed.), CRC Handbook of Chemistry and Physics, 80th ed., CRC Press, New York, 1999/2000. [18] S. Mohan, M.A. Trunov, E.L. Dreizin, in: The 2003 Technical Meeting of the Eastern States Section of the Combustion Institute, University Park, PA, 2003, pp. 329–332. [19] Y. Shoshin, I. Altman, in: K.K. Kuo, L.T. De Luca (Eds.), Combustion of Energetic Materials, Begell House, New York, NY, 2002, p. 1030. [20] T.A. Brzustowski, I. Glassman, in: H.G. Wolfhard, I. Glassman, L. Green (Eds.), Heterogeneous Combustion, Academic Press, New York, 1964, pp. 75–116. [21] R.P. Wilson, F.A. Williams, Proc. Combust. Inst. 13 (1971) 833–845.
Particle combustion rates for mechanically alloyed Al–Ti and aluminum powders burning in air Yuriy L. Shoshin, Edward L. Dreizin ∗ Department of Mechanical Engineering, New Jersey Institute of Technology, Newark, NJ 07102-1972, USA Received 27 January 2005; received in revised form 1 November 2005; accepted 27 November 2005 Available online 9 March 2006
Abstract Mechanically alloyed aluminum-rich powders of Al–Ti (10, 15, 20, and 25 atom% of Ti) were produced and their combustion was compared to that of aluminum and titanium powders of comparable sizes. A laminar liftedflame aerosol burner developed recently was used in this research. The aerosols were produced and burned in air. Measured flame speeds were higher for the aerosols of Al–Ti mechanical alloys than for the aerosols of pure Al or Ti. The particle combustion rates were evaluated based on the comparison of the measured and calculated profiles of the flame radiation. To calculate radiation profiles a simple model of particle combustion was used, in which both the radiation intensity and particle burn time were expressed as power functions of the initial particle size. For all the powders, the burning particle radiation intensity was observed to be best described by a function proportional to the cube of the initial particle size. For aluminum aerosol, the best match between the experimental and calculated flame radiation profiles was observed for the linear particle combustion law, when the particle combustion time, t, was expressed as a function of the initial particle size, d, as t [s] = 310d [m]. To match the experimental and calculated flame radiation profiles for the Al–Ti mechanical alloys, the combustion times of individual particles could be described by either d 1 or d 2 expressions. The burning time of mechanically alloyed particles increased with the increase of titanium concentration. The overall combustion times for aluminum particles are significantly longer than those for mechanically alloyed particles of Al–Ti of the same size. © 2006 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Aerosol flame; Flame emission; Metal combustion; Mechanical alloying
1. Introduction Metal powders are often used as additives in propellants, explosives, or pyrotechnics because of their high enthalpy of combustion [1,2]. Addition of metal powders to propellants is also known to * Corresponding author. Fax: +1 (973) 642 4282.
E-mail address: [email protected] (E.L. Dreizin).
improve the combustion stability in rocket engines [2,3]. The most common metal additive is aluminum, which is relatively inexpensive, is safe to handle, and has a relatively high volumetric combustion enthalpy. However, the potential of aluminum as a fuel is often underutilized. Aluminum particles ignite at fairly high temperatures and they often melt before ignition. Molten particles agglomerate, forming large aluminum droplets that burn slowly and incompletely. Furthermore, large aluminum and alumina
0010-2180/$ – see front matter © 2006 The Combustion Institute. Published by Elsevier Inc. All rights reserved. doi:10.1016/j.combustflame.2005.11.006
Y.L. Shoshin, E.L. Dreizin / Combustion and Flame 145 (2006) 714–722
droplets produce slug that plugs rocket exhaust nozzles. Recently, aluminum-based mechanical alloys have been suggested as alternative fuel additives [4,5]. It was expected that the combustion enthalpy of mechanical alloys could approach that of pure aluminum, but the ignition temperatures could be reduced and burning rates increased. During mechanical alloying, powders composed of metastable metal– metal solid solutions are formed from the precursor powders of elemental metals, such as Al and additives of Mg, Ti, Zr, etc. It was hypothesized [6] and, recently, experimentally confirmed for the aluminumrich Al–Ti mechanical alloys that the equilibration of metastable phases occurring upon heating can trigger ignition at a temperature significantly lower then the typical Al ignition temperature [7]. Therefore, further analyses of the overall powder burning rates are of interest for these and other aluminum-based mechanical alloys. Recently, a lifted laminar-flame aerosol burner (LLFAB) was developed for experimental characterization of solid fuel aerosols [8–10]. Flames of aerosolized powders of aluminum-based mechanical alloys were surveyed [10] and the highest burning rate was observed for the Al–Ti alloy. This work aims to further characterize laminar flames of Al–Ti mechanical alloy powders aerosolized in air. The specific objective of this work is to obtain a phenomenological expression for the particle combustion time as a function of the particle size, similar to the d 2 law or, more generally, the power law commonly used to describe combustion of liquid fuel droplets [11] and metal particles [12,13]. Such an expression is useful for modeling combustion in complex systems, for example, a solid rocket motor chamber, in which specific fuel particles are used. It was also interesting to compare the particle combustion times for the Al–Ti mechanical alloys with those for pure aluminum powders. The processing of the experimental data produced using LLFAB was developed in Ref. [9] to determine whether the particle combustion could be described using a simple power law and if yes, what was the combustion constant and which exponent should be used. This processing was based on a detailed analysis of the measured vertical radiation profile of a lifted laminar flame of aerosolized fuel particles. The analysis takes into account the powder size distribution, the flame speed, and the characteristic ignition temperature of the material. Despite a number of simplifying assumptions, this approach was found to be quite successful in the characterization of burn rates of aerosolized metal particles [9]. This approach is implemented here to characterize combustion of mechanically alloyed Al–Ti powders and similar-size aluminum powders.
715
2. Materials Four different Al–Ti mechanical alloy compositions, with titanium concentrations of 10, 15, 20, and 25 atom%, were produced and examined. The powders were produced in an 8000D series shaker mill by SPEX CertiPrep using zirconia vials and balls. Aluminum powder (Alfa Aesar, 99.8%, −40 + 325 mesh) and titanium powder (Alfa Aesar, 99%, −325 mesh) were used as starting materials. A process control agent (stearic acid, 2 mass%) was used to minimize formation of agglomerates. The total powder load in one run was 5 g and the ball-to-powder mass ratio was 10. Powders were mechanically alloyed for 15 h. The synthesis details are described elsewhere [14]. Particle morphology was characterized using scanning electron microscopy (SEM). Fig. 1 shows a typical image of the produced Al–Ti mechanically alloyed powder. The particles have irregular shapes and a fairly wide range of sizes. The metal powders used in the combustion experiments in addition to the mechanical alloys were 10–14 µm nominal size, 98% pure spherical aluminum; 17–30 µm nominal size, 99% pure spherical aluminum sieved through a 400-mesh sieve (38 µm opening size); and −325 mesh, 99% pure titanium. All powders were supplied by Alfa Aesar. The particle size distributions were measured using a Beckman Coulter LS 230 analyzer. The instrument determines particle size distribution based on the measured angular pattern of Fraunhofer diffraction of a laser beam [15]. For nonspherical particles, the diffraction angles depend on how the particles are oriented with regard to the incident laser beam at the moment of measurement. The effect of particle orientation results in a systematic error of the mea-
Fig. 1. SEM image of Al0.9 Ti0.1 mechanical alloy particles.
716
Y.L. Shoshin, E.L. Dreizin / Combustion and Flame 145 (2006) 714–722
No correction is needed for spherical powders, e.g., the spherical Al powders used in these experiments. The measured size distributions and the size distributions corrected for nonspherical powders are shown in Figs. 2 and 3. These corrected size distributions were used in analyses of the vertical radiation profiles of the flames with respective powders, as discussed in Ref. [9] and below.
3. Flame speed and radiation profile measurements
Fig. 2. Size distributions for Al 10–14 and Al 400 powders measured by Beckman Coulter LS 230 size analyzer.
Fig. 3. Size distributions for Al–Ti mechanically alloyed powders measured by Beckman Coulter LS 230 size analyzer and corrected to account for nonspherical shape of particles.
sured size distributions. A correction procedure suggested to account for this error [9] was used here. This correction uses particles’ shape factors found from processing the powder SEM images. As a result of processing, the range of particle sizes inferred from the laser diffraction measurements is compressed to the range between the minimum and maximum Ferets diameters measured from the particle images.
The aerosol flames were produced using LLFAB as described in detail elsewhere [8–10]. The burner uses electrostatic fluidization of a conductive powder in a plate capacitor to produce a narrow (∼1-mmdiameter), vertically rising, laminar aerosol jet. The jet issues from a small orifice in the top electrode of the capacitor. Air is used as a carrier gas. The jet velocity at the nozzle is on the order of 1 m/s. A slower shroud co-flow of air is produced around the jet to improve its stability. The aerosol jet is decelerated because of viscous forces, so the local aerosol speed decreases at longer distances from the nozzle. The jet is ignited in a region where the aerosol particles are nearly stopped and the laminar flame propagates downward. The flame position stabilizes at a location where the flame speed becomes equal to the local aerosol jet velocity (with the opposite sign). It was experimentally observed that when the flame is ignited, the aerosol jet velocity below the flame front [8,10] does not change noticeably, compared to that in a cold jet. Therefore, the flame speed could be determined as the speed of the unignited aerosol jet at the location where the flame stabilizes. A Dantec Flowlite one-dimensional laser Doppler velocimetry (LDV) setup based on a 632.8-nm wavelength He–Ne laser was used to measure the aerosol jet speed. The LDV optical head was focused on the aerosol jet at a specific distance above the nozzle. The aerosol was ignited and the air flowrate was adjusted to move the front of the lifted flame (the bottom edge of the flame) to the location where the LDV head was focused. Once the flame was stabilized at that location, the flame was quenched and the aerosol jet velocity was measured. In one measurement, velocities of 2000 particles were determined. Several measurements were carried out for each powder. For each measurement, a histogram of the particle velocities was produced and the average jet velocity was found. Examples of the velocity distributions for different aerosols measured at a distance of 20 mm above the nozzle are shown in Fig. 4. The particle velocity distributions are quite narrow, indicating that the particles follow the gas nearly uniformly. This ob-
Y.L. Shoshin, E.L. Dreizin / Combustion and Flame 145 (2006) 714–722
717
Fig. 4. Histograms of the particle velocities for Al0.90 Ti0.10 and Al0.85 Ti0.15 alloy aerosols measured at the location of the flame front.
Fig. 6. A typical image of an aluminum aerosol flame used for measurements of the vertical radiation profile. Nominal particle size 10–14 µm. Exposure time 1/60 s.
Fig. 5. Laminar aerosol flame speeds measured for different powders.
EZ30P camcorder equipped with a close-up lens and neutral density filters. To produce time-averaged images of the flame, a relatively long exposure time (1/60 s) was selected. Fig. 6 shows a sample flame image for the aerosol of spherical aluminum particles with nominal diameters of 10–14 µm. The vertical flame radiation profiles were measured along the vertical centerlines of the flame images using Tracker software [16]. In preliminary analyses, it was found that the profiles determined from the blue, green, and red color-separated images, as well as from the grayscale image, practically coincided with one another after normalization by the maximum image intensity. Therefore, the gray-scale images were consistently used to measure the flame radiation profiles.
servation is in agreement with the results of Ref. [10], where only the initial particle velocity distributions at distances from 0 to 10–15 mm from the nozzle were found to be affected by the slip for larger particles and by the initial particle acceleration from the electric field within the capacitor. To ensure uniform particle velocities, in these experiments the flames lifted 20 mm above the nozzle were used consistently. The flame speeds measured for pure Al, Ti, and Al–Ti mechanical alloy powders are shown in Fig. 5. The flame speeds are nearly the same for both types of aluminum and for the titanium powder. At the same time, the flame speeds are consistently higher for the synthesized powders of Al–Ti mechanical alloys. To determine the vertical flame radiation profiles, the flames were videorecorded using a Panasonic AG-
4. Interpretation of the flame radiation profiles A simplified model interpreting the radiation profiles of the lifted laminar flames produced by LLFAB in terms of individual particle combustion laws was described in detail elsewhere [9]. For completeness, the model is briefly reviewed below. The burning particles are considered to move with a constant velocity equal to the measured flame speed. This assumption is justified in Ref. [9] based on experimental observation of particle streaks within the flame. The gas temperature is assumed to increase linearly from the room temperature to the flame temperature in the flame preheat zone. This length of the preheat zone is assumed to be equal to α/v, where v is the flame
718
Y.L. Shoshin, E.L. Dreizin / Combustion and Flame 145 (2006) 714–722
speed and α is the thermal diffusivity of air. The particles are convectively heated within the preheat zone. The heat transfer equation uses particle Ferets diameter and because of the small slip effect, the Nusselt number is assumed to be equal to 2. Therefore, the effect of particle shape on the rate of heat transfer is neglected. The air thermal diffusivity is considered at a temperature equal to the average temperature in the preheat zone. For aluminum particles, the density and heat capacity are obtained from the literature: ρAl = 2700 kg/m3 , CpAl = 900 J/(kg K) [17]. The density and heat capacity of the Al–Ti mechanical alloys are estimated as average values for the respective mechanical mixtures. For these estimates, the literature values for the titanium density and heat capacity are used: ρTi = 4507 kg/m3 , heat capacity CpTi = 523 J/(kg K) [17]. Ignition is assumed to occur when the particles attain a threshold temperature specified for each material. Generally, the ignition temperatures depend on the heating rate, which is close to 106 K/s for these experiments. The ignition kinetics necessary to identify an appropriate threshold temperature for each material was determined in separate experiments [7,18]. In those experiments, the ignition temperatures were measured for powders thinly coated on an electrically heated filament. The ignition temperature was determined as a function of heating rate for each mechanical alloy and aluminum powder used in these combustion experiments. The experimental heating rates varied from 10 to 104 K/s and the ignition temperatures expected at 106 K/s were estimated by extrapolating the experimental trends. Estimated ignition threshold temperatures used in this work for the Al–Ti mechanical alloys and for pure Al particles are summarized in Table 1. Particle radiation during combustion was assumed to be constant, corresponding to quasi-steady burning. The radiation intensity, I , was assumed to be a simple function of the particle initial diameter, d: I = Ln d n , where L is a constant and the exponent n could be either 1, 2, or 3. Different combustion models (e.g., [9,10,19,20]) imply different exponents for the radiation power law. While detailed analysis of the specific models is outside the scope of this paper, the mathematical processing of the data allows one to change the exponent n to determine which model better describes the experimental data. The selection of the constant L depends on the sensitivity of the optical sensor and is therefore insignificant. Finally, the particle combustion time is also determined by the particle initial size using a simple power law, t = Km d m , where K is a combustion constant and the exponent m could be equal to 1 (kinetic regime of particle reaction) or 2 (diffusion regime). An intermediate value of m = 1.5 is also considered,
and similarly to exponent n in the “radiation power law,” the exponent m is used as an adjustable parameter to achieve the best fit with the experimental data. The constant Km is used as another adjustable parameter optimized for each specific value of m. The optical thickness of the laminar lifted aerosol flame was found to be small [9,10] and therefore the total flame radiation intensity is assumed to be proportional to the sum of radiation intensities of all the particles burning simultaneously. The experimental particle size distribution is used to determine the ignition delays and combustion times for particles of different sizes sorted within a fixed number of “size bins.” For each particle size bin, the vertical coordinate corresponding to the particle ignition was found from the respective particle heat transfer analysis. The vertical coordinate corresponding to the particle extinction was determined using a power combustion law. The total flame height is described by a onedimensional mesh with 200 equidistant nodal points. For each node, particles of which bin sizes are burning, and which ones did not ignite, or were already extinguished, was determined. Taking into account the fraction of particles in each bin size inferred by the experimental particle size distribution, the total radiation intensity of all the simultaneously burning particles is computed for each node. Thus, the vertical flame radiation profile is calculated. These calculated profiles are normalized and compared with the experimental radiation profiles. The best match was attempted separately for each combination of radiation and combustion law powers, n and m, by the selection of appropriate coefficients Ln and Km . The quality of the achieved match for each case was evaluated using normalized sum of squares error (NSSE), N 2 j =1 (Ij,exp − Ij,calc ) , NSSE = N where I is the normalized radiation intensity and N is the number of experimental data points for which the radiation intensity was quantified along the vertical coordinate (in both experiment processing and calculation).
5. Results and discussion The flame radiation profiles calculated using individual particle radiation power laws with n = 1 and n = 2 deviated significantly from the experimental profiles for any particle combustion laws and for all the aerosol flames studied. The only case where reasonable agreement between the calculated and experimental flame radiation profiles could be obtained was for the cubic radiation power law: I = L3 d 3 . The
Y.L. Shoshin, E.L. Dreizin / Combustion and Flame 145 (2006) 714–722
719
Table 1 Ignition temperatures of Al and Al–Ti mechanical alloys particles used to process the aerosol flame radiation profiles Power used
Al 10–14, Al 400
Al0.90 Ti0.10
Al0.85 Ti0.15
Al0.80 Ti0.20
Al0.75 Ti0.25
Ignition temperature (heating rate 106 K/s)
2150 K
1326 K
1342 K
1301 K
1242 K
Fig. 7. Measured and calculated laminar flame radiation profiles for aluminum aerosol flames.
same result was reported in Ref. [9] for aluminum and magnesium aerosol flames. Therefore, in optically thin metal aerosol flames the radiation is generated volumetrically. The radiation law corresponding to n = 3 was used consistently below. The experimental and calculated flame radiation profiles for different powders are presented in Figs. 7– 9. The respective values of NSSE are summarized in Table 2. The values of constants Km corresponding to the best match achieved for each value of m are shown in Table 3. For both aluminum powders used in combustion experiments (cf. Fig. 8), the best match between the calculated and measured flame radiation profiles was achieved for the particle combustion law t = K1 d, based on the values of NSSE shown in Table 2. This result, once again, is in agreement with our earlier measurements for aluminum powder [9]. It is also remarkable that for m = 1, the values of the constant K1 corresponding to the best match for both aluminum powders are the same, as shown in Table 3. At the same time, for m = 1.5 and 2, the discrepancy between the values of the respective constants K1.5 and K2 are significant. Therefore, both the lowest value of NSSE and the consistent coefficients K1 for both aluminum powders support the conclusion that the
particle combustion law is linear for aluminum particles burning in an aerosol. This appearance of the kinetic regime could be interpreted by assuming that the individual aluminum particle flames are likely to be overlapped in the aerosol. Therefore, the concentration of oxidizer is relatively uniform within the flame, while it is likely limited by the bulk diffusion rate from the surrounding air to the burning group of particles. Thus, the effect of the individual particle size on its combustion rate is weaker than for single particles. It is also likely that the value of K1 found to match the experimental data depends on the overall dimension of the burning group of particles (in this case, around 2 mm). For the Al–Ti mechanical alloys, a relatively good match between the experimental and calculated flame radiation profiles could be produced with any value of the exponent in the combustion power law. Therefore, the results of the processing could not be used to conclusively identify the specific exponent appropriate for describing combustion of such mechanical alloys. Generally, judging from the appearance of the experimental and calculated profiles shown in Figs. 8 and 9, the d 2 combustion law produced a somewhat better match between the measured and calculated flame radiation profiles. However, the minimum normalized
720
Y.L. Shoshin, E.L. Dreizin / Combustion and Flame 145 (2006) 714–722
Fig. 8. Measured and calculated radiation profiles for aerosol fames of Al90 Ti10 and Al85 Ti15 mechanical alloys.
Fig. 9. Measured and calculated radiation profiles for aerosol fames of Al80 Ti20 and Al75 Ti25 mechanical alloys.
sums of squares errors were observed for the d 1.5 and d 1 expressions for the Al0.85 Ti0.15 and Al0.80 Ti0.20 compositions, respectively. At the same time, the normalized sum of squares errors for the d 2 law was also reasonably small. Comparison of the combustion constants for the alloys with different concentrations of Ti could be made for any of the tested combustion law expressions based on the results presented in Table 3. A consistent increase of the constant Km is observed for the alloys with increased concentration of Al. This generally implies that longer combustion times are expected for the particles with higher
titanium concentrations. Note that the ignition temperatures were determined to be lower for the alloys with higher titanium concentrations (see Table 1 and Ref. [7]), implying a shorter ignition delay. Therefore, shorter ignition delays but longer burn times are generally expected for the Al–Ti mechanical alloys with increased concentrations of Ti. It is also apparent from Table 3 that for all the combustion laws considered, the combustion constants for any of the Al–Ti mechanical alloy powders are significantly smaller then those for pure Al powders. Therefore, Al–Ti mechanical alloy particles
Y.L. Shoshin, E.L. Dreizin / Combustion and Flame 145 (2006) 714–722
721
Table 2 Normalized sum of square error (NSSE) for the comparison of the experimental and calculated flame radiation profiles Combustion law
Powder Al 10–14
Al 400
Al0.90 Ti0.10
Al0.85 Ti0.15
Al0.80 Ti0.20
Al0.75 Ti0.25
t = K1 d t = K1.5 d 1.5 t = K2 d 2
3.35 × 10−3 9.22 × 10−3 1.48 × 10−2
4.44 × 10−3 6.91 × 10−3 8.97 × 10−3
2.63 × 10−3 1.77 × 10−3 3.40 × 10−4
1.46 × 10−3 1.16 × 10−3 2.41 × 10−3
9.01 × 10−4 1.68 × 10−3 2.96 × 10−3
5.12×10−3 4.85×10−3 4.66×10−4
Table 3 Constants for different tested combustion power laws for which the minimum NSSE was achieved while comparing the experimental and measured flame radiation profiles Combustion law constant
Powder Al 10–14
Al 400
Al0.90 Ti0.10
Al0.85 Ti0.15
Al0.80 Ti0.20
Al0.75 Ti0.25
K 1 , s m−1 K 1.5 , s m−1.5 K 2 , s m−2
310 6.5 × 104 1.3 × 107
310 4.5 × 104 7 × 106
135 1.45 × 104 1.57 × 106
130 1.5 × 104 2 × 106
165 1.8 × 104 2.4 × 106
195 2.1 × 104 2.75 × 106
Fig. 10. Comparison of combustion times for single aluminum particles [21], aluminum particles burning in an aerosol flame, and aerosols of Al–Ti mechanical alloys.
have shorter burn times in aerosol flames than Al particles of the same size. The interpretation of this result is not straightforward. Both Al and mechanically alloyed Al–Ti powders burn primarily in the vapor phase, while the particle temperatures are typically at their saturation point. It is likely that Al and Ti evaporate at substantially different rates and that a significant portion of Ti oxidizes heterogeneously. It is reasonable to expect that the presence of Ti reduces the saturation temperature of the molten alloy particles compared to that of pure Al, and thus leads to an accelerated rate of Al evaporation. On the other hand, greater concentrations of Ti can lead to a more heterogeneous and thus a somewhat slower reaction. Previously, combustion of single aluminum particles has been described using a d 2 combustion law
and results of multiple experiments were reviewed and processed accordingly in Ref. [21]. The results of that review are represented by two thin solid lines shown in Fig. 10 corresponding to the maximum and the minimum combustion constants that should be considered to fit multiple single-particle combustion time measurements by the d 2 law. Combustion times obtained in the present study for particles burning in aerosol for both pure Al and Al–Ti mechanical alloy aerosols are also shown. The shown trends correspond to the d 1 combustion law for Al and the somewhat arbitrarily chosen d 2 law for the Al–Ti mechanical alloys. The presented trends show that the combustion rates observed in this work for Al–Ti mechanical alloy particles are higher than or comparable to the highest combustion rates determined in experiments
722
Y.L. Shoshin, E.L. Dreizin / Combustion and Flame 145 (2006) 714–722
with single Al particles. It is also clear that for the specific range of particle sizes studied in this work, the combustion times for Al–Ti alloys are shorter then those of Al.
6. Conclusions Speeds of lifted laminar aerosol flames were measured for powders of aluminum, titanium, and Al– Ti mechanical alloys containing 10, 15, 20, and 25 atom% of Ti burning in air. The measurements showed that the flame speeds are higher for the aerosols of Al–Ti mechanical alloys than for the aerosols of pure Al or Ti with similar particle sizes. The vertical flame radiation profiles for the Al and Al–Ti mechanical alloys were measured. These profiles were also calculated using a simplified model of particle combustion in which both the radiation intensity and particle burning time were expressed as power functions of the initial particle size, d. For all the powders, the burning particle radiation intensity, I , was observed to be best described by a cube law, i.e., I = Const d 3 . For aluminum, the best match between the experimental and calculated flame radiation profiles was observed for the linear particle combustion law, when the particle combustion time, t, was expressed as a function of the initial particle size as t [s] = 310d [m]. To match the experimental and calculated flame radiation profiles for the Al–Ti mechanical alloys the combustion times of individual particles could be described by either d 1 or d 2 expressions. For any of the selected description, the combustion constant describing the burning time of mechanical alloy particles decreased with the increase of titanium concentration, implying longer combustion times. The overall combustion times for aluminum particles are significantly longer compared to those for the same size particles of Al–Ti mechanical alloys.
Acknowledgments This work was supported in part by the Office of Naval Research, Grant N00014-00-1-0446, the NSWC Crane Division, Award N00164-02-C4702, the Defense Threat Reduction Agency, Award
DAAE30-1-9-0080, and TACOM-ARDEC, Award DAAE30-03-D-1015. References [1] C.N. Divekar, S.N. Asthana, H. Singh, J. Propuls. Power 19 (4) (2003) 614–622. [2] E.W. Price, in: K.K. Kuo, M. Summerfield (Eds.), Fundamentals of Solid Propellant Combustion, in: AIAA Progress Series, vol. 90, AIAA, 1984, p. 891. [3] M. Summerfield, H. Krier, Problems of Hydrodynamics, SIAM, Philadelphia, PA, 1969, pp. 703–717. [4] Y. Shoshin, R. Mudryy, E. Dreizin, Combust. Flame 128 (2002) 259–269. [5] M. Schoenitz, E.L. Dreizin, E. Shtessel, J. Propuls. Power 19 (3) (2003) 405–412. [6] E.L. Dreizin, Prog. Energy Combust. Sci. 26 (1) (2000) 57–78. [7] Y.L. Shoshin, M.A. Trunov, X. Zhu, M. Schoenitz, E.L. Dreizin, Combust. Flame 144 (4) (2006), in press. [8] Y. Shoshin, E. Dreizin, Aerosol Sci. Technol. 36 (2002) 953–962. [9] Y. Shoshin, E. Dreizin, Combust. Flame 133 (2003) 275–287. [10] Y. Shoshin, E. Dreizin, AIAA J. 42 (2004) 1416–1426. [11] I. Glassman, Combustion, third ed., Academic Press, New York, 1996, 631 p. [12] M.W. Beckstead, B.R. Newbold, C.A. Waroquet, in: 37th JANNAF Combustion Meeting, CPIA Publ. 701, vol. 1, 2000, pp. 485–504. [13] J. Servaites, H. Krier, J.C. Melcher, R.L. Burton, Combust. Flame 125 (2001) 729–1073. [14] M. Schoenitz, X. Zhu, E.L. Dreizin, J. Metastable Nanocryst. Mat. 20–21 (2004) 455–461. [15] M. Born, E. Wolf, Principles of Optics, seventh (expanded) ed., Cambridge Univ. Press, Cambridge, 1999. [16] “Tracker 3.0,” Computer software by R. Klimek, T. Wright, NASA Lewis Research Center, 1998. [17] D.R. Lide (Ed.), CRC Handbook of Chemistry and Physics, 80th ed., CRC Press, New York, 1999/2000. [18] S. Mohan, M.A. Trunov, E.L. Dreizin, in: The 2003 Technical Meeting of the Eastern States Section of the Combustion Institute, University Park, PA, 2003, pp. 329–332. [19] Y. Shoshin, I. Altman, in: K.K. Kuo, L.T. De Luca (Eds.), Combustion of Energetic Materials, Begell House, New York, NY, 2002, p. 1030. [20] T.A. Brzustowski, I. Glassman, in: H.G. Wolfhard, I. Glassman, L. Green (Eds.), Heterogeneous Combustion, Academic Press, New York, 1964, pp. 75–116. [21] R.P. Wilson, F.A. Williams, Proc. Combust. Inst. 13 (1971) 833–845.