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Heat transfer effects in nano-aluminum combustion at high temperatures
Combustion and Flame xxx (2013) xxx–xxx
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Combustion and Flame j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / c o m b u s t fl a m e
Heat transfer effects in nano-aluminum combustion at high temperatures David Allen ⇑, Herman Krier, Nick Glumac Mechanical Science and Engineering Department, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
a r t i c l e
i n f o
Article history: Received 13 May 2013 Received in revised form 11 July 2013 Accepted 11 July 2013 Available online xxxx Keywords: Nano-aluminum combustion Heat transfer Shock tube
a b s t r a c t Recent measurements of nano-aluminum combustion in which burning time and peak particle temperature are measured simultaneously have suggested that heat transfer models currently used for burning nanoparticles may significantly overestimate heat losses during combustion. By applying conventional non-continuum heat transfer correlations to burning nano-aluminum particles, the observed peak temperatures, which greatly exceed the ambient temperature, should only be observable if the burning time were very short, of the order of 1 ls, whereas the observed burning time is two orders of magnitude larger. These observations can be reconciled if the energy accommodation coefficient for these conditions is of the order of 0.005, which is the value suggested by Altman, instead of approximately unity, which is the common assumption. Experimental data obtained in the heterogeneous shock tube under a wide array of conditions are compared with basic heat transfer models, and the agreement of both peak temperature values and emission intensity traces for low energy accommodation coefficients supports the hypothesis of Altman and co-workers. Ó 2013 The Combustion Institute. Published by Elsevier Inc. All rights reserved.
1. Introduction Nano-aluminum combustion is an active area of research due to the potential to improve performance in propellants and explosives [1,2]. The mechanism of nano-aluminum combustion remains poorly understood. For larger particles burning in the diffusion limit, a fair understanding of the ignition and combustion characteristics has been demonstrated [3] such that predictive simulations are possible. However, for particle sizes approaching the micron scale under most conditions, many of the trends observed in large particle combustion no longer apply. Burning rates begin to deviate from a d2 law, with exponents curiously observed to be less than unity [4–6]. The pressure dependence of the burning rate becomes significant [7], and there is evidence that the relative oxidation efficiencies of CO2 and H2O change [4]. Peak combustion temperatures begin to decrease, and ignition temperatures are also markedly lower [8]. For nano-scale Al, a significant ambient temperature dependence on the burning rate emerges [9]. Several modeling efforts on n-Al combustion have occurred [8,10,11] and some observations have been reconciled. However, a robust model capable of simulating combustion kinetics over a wide range of conditions has not yet been achieved. A common assumption in particle combustion is that as particle size decreases, particle combustion transitions from a gas-phase diffusion ⇑ Corresponding author. E-mail address: [email protected] (D. Allen).
limit to a mode of combustion limited by surface reaction or solidstate diffusion. In this classic latter limit, there is no gas-phase combustion, and species concentration and thermal gradients approach zero. Due to rapid heat transfer of small particles, the particle temperature does not significantly exceed that of the ambient gas. Indeed for some conditions, e.g., n-Al burning in CO2, negligible temperature overshoots were observed in previous work. However, under other conditions with more efficient oxidizers at higher pressures, significant rises in particle temperature were measured [9]. For nano-scale particles in most environments, Knudsen number effects on heat transfer cannot be neglected since Kn .001–1. These effects are considered in laser induced incandescence (LII) experiments to determine particle size distributions of nano-particles in flows [12] and must also be considered when determining the transient thermal profile of a combusting nanoaluminum particle. However, use of non-continuum heat transfer expressions requires estimation of the energy accommodation coefficient (EAC). For LII experiments involving carbon particles, values of 0.4 have been measured [13], and thus it is common to use similar values (or even a value of 1) for other materials under similar conditions. However, theoretical and experimental work performed by Altman suggests that at high particle and gas temperatures, certain metal and metal oxide nano-particles have very small energy accommodation coefficients [14,15]. Radiation consequently becomes a more significant pathway for heat transfer in the low accommodation coefficient regime. The experimental work
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by Altman et al. was performed using laser irradiation to heat up nanoparticles generated in a flame. The energy accommodation coefficient was found to be near 0.005 which agreed nicely with their theoretical upper limit [14]. Nano-aluminum particle combustion may potentially experience a similar thermal isolation effect in many applications. With such low accommodation coefficients the heat transfer from the particle via collision with gas molecules becomes inefficient, leading to particle temperatures much higher than those expected using EAC 1. In this work we perform experiments on nano-aluminum combustion to monitor the particle temperature, burn rate, and emission spectra. High particle temperatures and longer burn times are expected for a transition to the free molecular regime accompanied by a low energy accommodation coefficient. For ultrafine particles, classical theory predicts that rapid heat transfer results in combustion temperatures that only minimally exceed the ambient temperature, even when common Knudsen number correlations are used for Nusselt number calculation [12]. Prediction of the particle temperature requires specification of the reaction rate (i.e., heat release rate) in addition to the heat transfer coefficient. In this research the experimental data on burning time and temperature are supported by a simple model of nano-aluminum combustion that employs as few limiting assumptions as possible, focusing only on the energy balance leading to particle temperature rise. Multiple heat transfer models are considered to determine the predicted transient particle temperature and to see if the nano-aluminum particle experiences thermal isolation from the surrounding gas. 2. Experimental set-up The nano-aluminum particles were investigated using a heterogeneous shock tube described in detail in a previous publication [16]. The shock tube is capable of producing controlled high temperature and high pressure environments with various gas compositions. Temperatures greater than 4000 K and pressures above 30 atm are achievable behind the reflected shock with test times near 2 ms. Low temperatures were used for this study to test nano-aluminum combustion which has been shown to ignite at temperatures below 2000 K [9]. The combustion of the nanoaluminum particles was monitored behind the reflected shock in
order to achieve the high pressures desired. The pressure was varied between 3.5–20 atm to determine the effect of the oxidizer concentration on the particle temperature and burn time. The shock tube has an 8.4 m driven section and an 8.9 cm internal diameter. A converging dual diaphragm system separates the high pressure helium gas from the oxidizing environment. The driver to driven pressure ratio is controlled to produce the desired shock strength. The velocity of the shock is measured using four piezoelectric pressure transducers at different axial locations. The ambient temperature and pressure of the gases trailing the incident and reflected shock are calculated with the Gordon-McBride equilibrium code [17] using the known initial driven pressure, composition, and measured shock velocity. The test time of the shock tube can also be found from the pressure transducer traces and is typically near 2 ms. A schematic of the shock tube operation with radial injection and the end section with fiber optic view ports is shown in Fig. 1. This end section allows for photodiode access at multiple axial locations. The end wall has a sapphire view port for further optical access. The fiber optic section is described in further detail in a previous publication [9]. Each test was run with three photodiodes monitoring different axial locations centered at the location of aluminum particle stagnation behind the reflected shock. A nano-aluminum particle has a very small Stokes number, and therefore the particle accelerates quickly behind the incident shock and stagnates within a few microseconds behind the reflected shock. For this reason particle motion behind the reflected shock is neglected. Particles are injected radially into the test gas prior to diaphragm rupture using a pneumatically driven piston. The particles become entrained in the gas flow behind the incident shock and are swept towards the end-wall until the reflected shock stagnates them and they combust. Four particle classes were chosen to vary particle diameter while measuring burn time, temperature, and emission spectra. A Hitachi S-4700 high resolution scanning electron microscope (SEM) was used to accurately characterize the particle size distribution of each sample. Over 100 particle diameter measurements were made from each sample in order to obtain a distribution. Table 1 shows the number average and mass average particle diameters of each nominal sample powder. The SkySpring 18 nm particles were not characterized because the resolution required
Fig. 1. Schematic of shock tube test section with fiber optic access.
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D. Allen et al. / Combustion and Flame xxx (2013) xxx–xxx
full-width-half-maximum (FWHM). The spectra were time integrated over the entire combustion event; a mechanical shutter was used to avoid emission from particles after the test time of the shock tube. The shutter was fully closed 1.2 ms after the incident shock reflected off of the endwall. This ensured that all of the thermal emission during the nanoparticle heat up and cool down was captured, but any luminosity from events occurring after the test time was rejected. The spectrometer was intensity calibrated using a tungsten calibration lamp with a filament temperature of 3200 K. Pyrometry was performed using a custom-built 3-color pyrometer. A trifurcated fiber bundle imaged the light from the test section through a narrow slit. The trifurcated cable split the light collected from the test into three separate branches. Each branch passed through a collimator, interference filter, and to a photomultiplier. The interference filters each had a 10 nm FWHM bandpass centered at 705, 826, and 905 nm. The shorter wavelengths were measured using Hamamatsu R928 photomultipliers; the 905 nm light was measured using a R636-10 photomultiplier with an infrared-sensitive GaAs photocathode. The outputs of the photomultipliers were amplified using a Stanford Research Systems Quad preamplifier unit with a 300 MHz bandwidth. The time response of the pyrometry system is sub-microsecond. The system was calibrated using a tungsten calibration lamp. Noise level is typically 10–20% of the signal and the measurement uncertainty has previously been estimated to be 150 K for micron sized particles [18]. Photometric burning time measurements were made using photodiodes coupled to different axial locations using the fiber optics in the end section shown in Fig. 1. Three ThorLabs PDA36A amplified photodiodes were used to capture the luminosity from each experiment. The emission was unfiltered because the spectroscopic measurements indicated no molecular emission. The time resolution of the photodiodes is sub-microsecond.
Table 1 Summary of average particle diameters. Particle type
Number average diameter (nm)
Mass average diameter (nm)
SkySpring 18 nm SkySpring 50 nm NovaCentrix 80 nm NovaCentrix 110 nm
– 73.2 83.4 100
– 80.9 90.1 110
to characterize these particles accurately was not achievable. Any distribution obtained would have been biased towards the larger particles which were readily resolved while the smaller particles below 18 nm would not have been accounted for. The highest resolution images achieved qualitatively showed the SkySpring 18 nm particle distribution to be significantly smaller than the other sample distributions even though an accurate average could not be quantified. Each sample had a large distribution of particle sizes. Figure 2(a)–(c) shows the histograms of the three characterized samples and Fig. 2(d) shows a corresponding SEM image for the NovaCentrix 80 nm particles. All particles imaged were found to be highly spherical. Nano-aluminum has previously been shown to form both weak and strong agglomerates dependent on the manufacturing process. The images show the particles acquired have weak agglomeration and very little particle necking. The particles acquired from NovaCentrix are specified to be 80–90% aluminum and the oxide-coating thickness is 1.5–2.5 nm. Both samples acquired from SkySpring Nanomaterials are 99.9% pure on a trace metals basis. Emission spectra were collected using an Ocean Optics spectrometer with a 10 lm inlet slit and a 200–550 nm range. The spectral resolution of the spectrometer was approximately 1 nm
(a) Particle size distribution for the SkySpring Nanomaterials 50 nm particles
(c) Particle size distribution for the NovaCentrix 110 nm particles
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(b) Particle size distribution for the NovaCentrix 80 nm particles
(d) Sample Scanning Electron Microscopy (SEM) image of the NovaCentrix 80 nm particles
Fig. 2. Particle characterization.
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3. Experimental results In a previous study [9],we reported nano-aluminum burning times and temperatures for a single class of particles (80 nm) in O2 and CO2. In that study, one of the results was that the degree of temperature overshoot (Tparticle Tambient) depended on oxidizer and pressure. For this study, we have expanded the dataset to include different sized particles while focusing on accurate measurements of burning time and temperature. For temperature, our measurement accuracy and precision are significantly improved by using the results of our recent study on the emissive properties of alumina at elevated temperatures [19]. Since we do not repeat the exact conditions of the previous report, we do not compare results, but the general trends in burning time and temperature overshoot are consistent with the initial study. Current and previous measurements have shown weak or no molecular aluminum monoxide (AlO) emission at pressures below 32 atm for nano-aluminum combustion [9]. Each spectra showed only thermal radiation and no significant gas phase emission, indicating that the primary combustion mechanism involves surface reactions as hypothesized. If gaseous aluminum were present, atomic aluminum lines would likely be seen at 394.4 and 396.1 nm, and banded aluminum monoxide (AlO) emission from the B-X transition would likely be seen in the range from 460–530 nm. It is possible that the gas phase species are present but are not at high enough temperatures to cause detectable spontaneous emission. However, measurements by Lynch et al. showed no aluminum or aluminum monoxide absorption below 1500 K which further suggests that gas phases are not present in significant amounts [20]. The lack of gas phase emission is consistent with a reaction model in which surface processes limit the combustion rate. The average burning times can be seen in Table 2 using the 10%90% area method to calculate the burn time. In order to calculate the 10%-90% area burn time the background intensity in the post combustion environment due to heated particles was subtracted off following the method described in a previous publication [9]. In short, a linear rise is fit from initial noise level to the background intensity level. The rise is assumed to occur from the onset of luminosity to the point of peak intensity where it then remains constant. There is some deviation from the average due to the large particle distribution and also due to the inherent uncertainty in determining the background intensity levels. More important, however, is that the luminosity traces show that as the average particle diameter increases, the photodiode trace becomes wider and the time it takes to reach peak intensity becomes longer. The burning time of the particles spans from 50–200 ls consistently for all samples. The values for the burn time seen in Table 2 compare favorably with those seen previously by Bazyn et al. in similar conditions and are shorter than those seen in micron sized aluminum at higher temperature. Bazyn found burn times near 170 ls for 80 nm aluminum particles in 20% O2 and 80% N2 at higher pressures [9]. It is important to consider the interpretation of the luminosity traces. The emission spectrum showed no evidence of molecular emission, and therefore, the luminosity profiles being shown cannot be directly correlated to the presence of aluminum monoxide,
Table 2 Summary of particle burning time in air calculated using the 10–90% area burn time method of calculation.
as has previously been done. When monitoring molecular emission such as AlO the assumption is that the luminosity trace corresponds to the presence of AlO, which indicates combustion because AlO is a key intermediate species in the gas phase combustion process. However, in this case the luminosity is due to thermal radiation evidenced by the emission spectra. Therefore, we are correlating burn time to particle temperature which is a different assumption than that made when monitoring emission filtered around an aluminum monoxide band as is normally the case for micron sized particles [4]. The three color pyrometry measurements indicated a rise in particle temperature above the ambient gas temperature. Multiple tests were performed for each particle size at 1500 K and 20 atm in 20% O2–80% N2. Table 3 shows the peak temperature calculated at the location of peak intensity tabulated for each particle class. The average temperature remains relatively constant for all particle sizes. The average peak temperature is between 3200–3500 K for all cases. Bazyn et al. [9] similarly found peak temperatures for nano-aluminum combustion near 2500 K for 8.5 atm pressures and 3500 K for 32 atm pressures. The values of the peak temperatures at 20 atm found in these tests range between the values found by Bazyn. These temperatures are near the boiling temperature of aluminum which varies from 3040 K at 4 atm to 3600 K at 32 atm. In a surface-process limited combustion mechanism the peak temperature increases with pressure since the reaction rate (heat release rate) is proportional to the number density of oxidizer in the vicinity of the particle. A low pressure test performed at 3.5 atm gave a peak temperature of 2375 K, which is again consistent with the trend predicted by the surface-process limited combustion model. The high peak temperatures and relatively long burn times observed in this work and previously by Bazyn [9] suggest that heat transfer from the particles must be relatively slow compared to that suggested by common models. In the continuum limit (Nu 2), the nano-aluminum particle would need to fully combust in less than 0.5 ls in order for the particle to reach 3200 K in the ambient conditions of the experiment. Using a non-continuum expression valid for the transition regime (Nu = 0.3/Kn), the burning time is only extended to 1.5 ls. The data suggest this is not the case. A more detailed heat transfer analysis is presented in the next section.
4. Model description A nano-aluminum combustion model was developed to further investigate the heat transfer of the particles. The model is an energy balance of the particle that assumes a surface-process limited combustion mechanism and heat transfer through conduction to the ambient gas and radiation to the walls of the shock tube at 300 K. Figure 3 depicts facets of the combustion model. The reaction surface is the initial surface area of the particle and does not change because diffusion of oxidizer and fuel are assumed to occur much faster than the limiting surface process (i.e., surface diffusion or chemical reaction).
Table 3 Summary of peak temperature of combusting nano-aluminum particles in air.
Particle type
Burning time (ls)
Deviation (ls)
Particle type
Peak temperature (K)
Deviation (K)
SkySpring 18 nm SkySpring 50 nm NovaCentrix 80 nm NovaCentrix 110 nm
74.5 119.5 129.2 134.3
20.5 6.4 9.6 6.7
SkySpring 18 nm SkySpring 50 nm NovaCentrix 80 nm NovaCentrix 110 nm
3301 3274 3169 3472
251 338 482 252
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The influx of heat to the particle is assumed to be due to the chemical reaction between the oxygen and aluminum following Eq. (1), which releases 1.85(1018) joules of energy for each collision of oxygen molecule resulting in reaction with the aluminum surface. The rate of reaction is calculated using the number density of oxygen at the particle surface (Eq. (2)), thermal velocity (Eq. (3)), the collision frequency (Eq. (4)), and a sticking probability / which is a variable parameter in the model. The velocity distribution in Eq. (3) assumes a maxwellian distribution. This assumption ignores the chemical reaction occurring at the surface of the aluminum particle which consumes the oxidizer molecules; however, it will be shown that the model predicts very small sticking coefficients (0.001), and in the limit of small sticking coefficients the velocity distribution approaches that of a maxwellian distribution, and the assumption is considered valid. The sticking probability represents the percentage of collisions that react and has a value between zero and one. A sticking probability of zero represents no reaction, and a sticking probability of one indicates each collision results in chemical reaction. The sticking probability is assumed to remain constant during the combustion of the aluminum particle. Eqs. (2)–(6) represent the calculation for the heat due to the reaction. An effective area is used for the influx of heat to model the reduction in the amount of aluminum surface area at the reaction surface during combustion. The effective area is determined by calculating the surface area of the remaining mass of aluminum at each time step as if it were a sphere. The assumption is that the reaction occurs at the outer surface of the particle, but as the particle burns the amount of reactive area decreases as a function of time following Eq. (5). A variable reaction area is chosen to account for changes in reactivity as the aluminum is depleted. As reaction occurs and oxide builds up on the surface, this barrier most likely impedes the oxidizer from reaching fresh metal. This effect can be simulated in our simplistic model by reducing either sticking probability (/) and/or reaction area (A) as a function of reaction extent. We, somewhat arbitrarily, choose the latter approach. The effect of including a time varying / or A alters the predicted transient temperature profile. Assuming the sticking probability or reactive surface area decreases with time results in the particle attaining an initial peak temperature followed by a temperature decay, which is similar to what was seen in experiment. If the product / A is constant, then the particle temperature rises and remains at the peak temperature until particle burnout. The value of the peak temperature is unaffected by this treatment, as the peak temperature occurs at the beginning of particle combustion when the reactive surface area is nearly equal to the outer particle surface area. The burn time is increased by less than 15% using the decreasing reactive area, and therefore this assumption does not significantly affect the conclusions.
Fig. 3. Depiction of the surface process nano-aluminum combustion and heat transfer model.
2 Al þ 3=2 O2 ! Al2 O3 þ 1:85 ð1018 Þ NO2 ¼
J Collision O2
X O2 P T a kb
1=2 8 kb T a c¼ mO2 p c f ¼ NO2 4 2=3 6 mal Aeff ¼
qal p
Ein ¼ Aeff fq/
ð1Þ ð2Þ ð3Þ ð4Þ ð5Þ ð6Þ
The conduction of heat to the surrounding gas is the key effect of interest in the present study. As previously mentioned, Altman predicts a decrease in the accommodation coefficient at high temperatures. Altman puts an upper limit on the accommodation coefficient aE following Eq. (7), where h is the Debye temperature of the solid. For the conditions in this study Eq. (7) puts the upper limit of the accommodation coefficient at approximately 0.006. The heat transfer to the surroundings through conduction in the free molecular regime is calculated following Eq. (8). Eq. (9) shows the corresponding heat transfer equation assuming continuum mechanics, where k is the thermal conductivity of the gas, Nu is the Nusselt number, and d is the particle diameter. The radiation to the walls follows the Stefan–Boltzmann law using Eq. (10) with an emissivity of 0.1 for alumina [19]. The temperature of the particle changes as shown in Eq. (11).
1 h2 2 CRv þ 1 T g T s aE P c c þ 1 ðT p T a Þ Esur ðtÞ ¼ 8 Ta c 1 k Esur ðtÞ ¼ Nu ðT p T a Þ A d
aE <
Erad ðtÞ ¼
r T 4p T 4w A
Ein Esur Erad DTðtÞ ¼ mparticle cp
ð7Þ ð8Þ ð9Þ ð10Þ ð11Þ
5. Discussion The model has two unknown parameters which must be fit to experimental data. These parameters are the sticking probability, /, and the energy accommodation coefficient, aE. The two independent unknowns are fit by comparing the predicted dependent variables of model peak temperature and burning time to the values obtained in the shock tube experiments. Figure 4(a) and (b) show the model predictions graphically for an 80 nm particle. The burn time calculated in the model is independent of the heat transfer of the particle with the assumptions provided, and is plotted in black on the log scale. The particle is considered fully burned in the model once 90% of the original mass is reacted. A sticking probability of zero represents no reaction and therefore the burn time asymptotes towards infinity at this value. The particle temperature increases with increasing sticking probability as expected because a larger percentage of the collisions result in exothermic heat release. Seven potential temperature profiles are plotted for comparison, each using a different accommodation coefficient or heat transfer assumption. Five accommodation coefficients, a correlation for the Nusselt number deduced from laser induced incandescence on nano-particles [12], and a Nusselt number of 2 are considered. For a given sticking probability the burning time and
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(a) Model results for an 80 nm particle comparing burn time and peak temperature at ambient conditions of 1500 K and 20 atm in air for sticking probabilities between 0-0.5
(b) Model results for an 80 nm particle comparing burn time and peak temperature at ambient conditions of 1500 K and 20 atm in air for sticking probabilities between 0-0.01 Fig. 4. Comparison of burn time and peak temperature using various heat transfer models.
particle temperature considering one of the seven heat transfer models satisfy the energy balance of the system. It is evident that an accommodation coefficient between 0.001– 0.005 is necessary in order to achieve burn times greater than 100 ls and peak temperatures of 3300 K as indicated by the highlighted section of Fig. 4(b). The dashed box indicates the experimentally determined possible peak temperatures for sticking probabilities that give burning times also in the experimentally observed range. The best fit values for the accommodation coefficient and sticking probability are 0.0035 and 0.0009 respectively. The values obtained for the accommodation coefficient here match extremely well with the value of 0.005 found experimentally by Altman in previous work. These results clearly suggest that the nano-aluminum particles are experiencing thermal isolation from the ambient gas due to low energy accommodation coefficients. Further comparison of the simple model with the experiment can be made by comparing the luminosity trace to the relative model-predicted thermal radiation intensity (i.e., T4). Figure 5(a)–(d) shows the predicted luminosity compared to photodiode traces from the experiment at 1500 K and 20 atm in air. For these traces the best fit accommodation coefficient of 0.0035 and sticking probability of 0.0009 were chosen. The comparison between model and experiment is quite good. The model predicts the peak temperature for each particle size to be approximately 3400 which is below the 3450 K boiling
temperature of aluminum at 20 atm within uncertainty. It is likely that as the particle heats up some of the aluminum is volatilized and reacts at the surface of the particle limiting the peak temperature of the system to the boiling temperature of the aluminum at the given pressure. The peak temperature does not change significantly in the model with particle size because all modes of heat transfer scale similarly. The heat loss scales with d2 and the heat due to chemical reaction scales with the effective area, but the peak temperature occurs near the start of the particle reaction when the effective area is very near the initial area of the particle. The transient temperature profiles change with particle size due to the effective area approximation as seen in Fig. 5(a)–(d). The model prediction that the peak temperature remains constant independent of the particle diameter agrees with the experimental data shown in Table 3 within experimental uncertainty. The comparison extends to lower pressures as well. The model predicts a peak temperature of 2600 K at a pressure of 3.5 atm using the accommodation coefficient (0.0035) and sticking probability (0.0009) as those used to fit the data at 20 atm. Pyrometry measurements found the temperature to be 2375 K at 3.5 atm. The model slightly over predicts the temperature, but the accommodation coefficient used was fit to a system with the peak particle temperature of 3100 K and an ambient gas temperature of 1500 K. In the case of lower pressure, the peak temperature is lower and following Eq. (6), a lower particle temperature implies a higher accommodation coefficient. Scaling the accommodation coefficient by this difference in expected temperature brings it to a value of approximately 0.0047. Using this value further drops the predicted temperature to 2500 K which is within the experimental value of 2375 ± 150 K. Clearly the accommodation coefficient may vary as the particle temperature changes during the combustion event, but here it is assumed constant. The possible effect of particle agglomeration on the results and conclusions is worthy of consideration. If nanoparticles agglomerate rapidly or are not efficiently de-agglomerated, then large agglomerates may still readily ignite at low temperatures but will coalesce and burn as larger particles. If agglomerates contain enough primary particles, the coalesced particulate may be large enough to burn in the diffusion limit, with correspondingly high temperatures. In our arrangement, breakup of agglomerates is strongly promoted during injection and by the shock waves. During injection, the dispersed aerosolized particles are entrained in a jet of gas, then sent through an array of fine meshes that have been shown to effectively produce a well-dispersed cloud [21]. Petersen used a much milder form of injection [22] and directly measured particle sizes in the resulting cloud, finding little agglomeration of aluminum nanoparticles within the first minute after injection. Furthermore, it has been shown that the strong shear forces of the shock waves are effective at breaking weak agglomeration in nano-particles [23–25]. Thus, the experimental evidence to date suggests clouds formed in the shock tube are, at the least, resistant to the formation of agglomerates. Post shock agglomeration should also be relatively slow. Calculations considering an evenly dispersed thin cloud of particles behind the incident and reflected shock using the Smoluchowski monodisperse model, which ignores electrostatic forces, suggest that each particle will conservatively collide with less than two other nano-particles during the test time. In order for a nanoparticle to increase in size from 100 nm to 500 nm, it would require an agglomerate consisting of approximately 125 primary particles assuming spherical geometry. Heat transfer analysis of a 500 nm particle using the non-continuum heat transfer approximation still shows that the agglomerate particle must combust in less than 15 ls in order to reach 3000 K, still well below what is seen in
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(a) Model radiation for SkySpring 18 nm particles at 1500 K and 20 atm in air compared to experimental data
(c) Model radiation for NovaCentrix 80 nm particles at 1500 K and 20 atm in air compared to experimental data
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(b) Model radiation for SkySpring 50 nm particles at 1500 K and 20 atm in air compared to experimental data
(d) Model radiation for NovaCentrix 110 nm particles at 1500 K and 20 atm in air compared to experimental data
Fig. 5. Comparison of model radiation and experimental luminosity measurements for each particle class.
experiment. Furthermore, the lack of significant AlO and Al emission during nano-particle combustion at 1500 K also suggests that it is not particles burning in the diffusion limit that is responsible for the measured temperature overshoot [20].
6. Conclusions It has been shown that in order for nano-aluminum particles to achieve the burning time and peak temperatures observed experimentally, the heat transfer from the burning particles must be significantly slower than would be expected assuming energy accommodation coefficient values approaching 1. This effect was theoretically described by Altman and shown to be true in experiments using laser irradiation. In those experiments the energy accommodation coefficient was found to be approximately 0.005. It has been shown here with a simple surface based heat transfer model, that the best fit for the energy accommodation coefficient is 0.0035 which agrees very well both with the experiments performed by Altman and the upper estimate described previously in Eq. (6). It is therefore concluded that at the high ambient temperatures recorded in the shock tube, the particles are experiencing thermal isolation from the surrounding gas. More complex combustion reaction models can be implemented; however, without
accounting for the low energy accommodation coefficient it is not possible to correctly predict the particle temperatures and burning times seen in experiment. This effect has important consequences for modeling of nanoaluminum combustion. In particular, particle temperatures will likely be much higher than current models predict, and radiation effects may be enhanced. It is expected that similar results will arise for other metal condensed phase nano-particles combusting at high temperatures, as suggested by Altman.
Acknowledgments This project was supported by the US Air Force under Contract FA9300-11-M-2004. Additional support was obtained from DTRA under Grant HDTRA1-10-1-0003. The project manager is Dr. Suhithi Peiris. The Scanning Electron Micrographs were taken in the Frederick Seitz Materials Research Laboratory Central Facilities, University of Illinois, which are partially supported by the US Department of Energy under Grant DEFG02-9-ER45439. Special thanks to Ed Dreizin and Michael Zachariah for helpful discussion on the issue of temperature overshoot. Thanks also to Sam Goroshin for providing us with the references on thermal isolation which made this work possible.
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Combustion and Flame j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / c o m b u s t fl a m e
Heat transfer effects in nano-aluminum combustion at high temperatures David Allen ⇑, Herman Krier, Nick Glumac Mechanical Science and Engineering Department, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
a r t i c l e
i n f o
Article history: Received 13 May 2013 Received in revised form 11 July 2013 Accepted 11 July 2013 Available online xxxx Keywords: Nano-aluminum combustion Heat transfer Shock tube
a b s t r a c t Recent measurements of nano-aluminum combustion in which burning time and peak particle temperature are measured simultaneously have suggested that heat transfer models currently used for burning nanoparticles may significantly overestimate heat losses during combustion. By applying conventional non-continuum heat transfer correlations to burning nano-aluminum particles, the observed peak temperatures, which greatly exceed the ambient temperature, should only be observable if the burning time were very short, of the order of 1 ls, whereas the observed burning time is two orders of magnitude larger. These observations can be reconciled if the energy accommodation coefficient for these conditions is of the order of 0.005, which is the value suggested by Altman, instead of approximately unity, which is the common assumption. Experimental data obtained in the heterogeneous shock tube under a wide array of conditions are compared with basic heat transfer models, and the agreement of both peak temperature values and emission intensity traces for low energy accommodation coefficients supports the hypothesis of Altman and co-workers. Ó 2013 The Combustion Institute. Published by Elsevier Inc. All rights reserved.
1. Introduction Nano-aluminum combustion is an active area of research due to the potential to improve performance in propellants and explosives [1,2]. The mechanism of nano-aluminum combustion remains poorly understood. For larger particles burning in the diffusion limit, a fair understanding of the ignition and combustion characteristics has been demonstrated [3] such that predictive simulations are possible. However, for particle sizes approaching the micron scale under most conditions, many of the trends observed in large particle combustion no longer apply. Burning rates begin to deviate from a d2 law, with exponents curiously observed to be less than unity [4–6]. The pressure dependence of the burning rate becomes significant [7], and there is evidence that the relative oxidation efficiencies of CO2 and H2O change [4]. Peak combustion temperatures begin to decrease, and ignition temperatures are also markedly lower [8]. For nano-scale Al, a significant ambient temperature dependence on the burning rate emerges [9]. Several modeling efforts on n-Al combustion have occurred [8,10,11] and some observations have been reconciled. However, a robust model capable of simulating combustion kinetics over a wide range of conditions has not yet been achieved. A common assumption in particle combustion is that as particle size decreases, particle combustion transitions from a gas-phase diffusion ⇑ Corresponding author. E-mail address: [email protected] (D. Allen).
limit to a mode of combustion limited by surface reaction or solidstate diffusion. In this classic latter limit, there is no gas-phase combustion, and species concentration and thermal gradients approach zero. Due to rapid heat transfer of small particles, the particle temperature does not significantly exceed that of the ambient gas. Indeed for some conditions, e.g., n-Al burning in CO2, negligible temperature overshoots were observed in previous work. However, under other conditions with more efficient oxidizers at higher pressures, significant rises in particle temperature were measured [9]. For nano-scale particles in most environments, Knudsen number effects on heat transfer cannot be neglected since Kn .001–1. These effects are considered in laser induced incandescence (LII) experiments to determine particle size distributions of nano-particles in flows [12] and must also be considered when determining the transient thermal profile of a combusting nanoaluminum particle. However, use of non-continuum heat transfer expressions requires estimation of the energy accommodation coefficient (EAC). For LII experiments involving carbon particles, values of 0.4 have been measured [13], and thus it is common to use similar values (or even a value of 1) for other materials under similar conditions. However, theoretical and experimental work performed by Altman suggests that at high particle and gas temperatures, certain metal and metal oxide nano-particles have very small energy accommodation coefficients [14,15]. Radiation consequently becomes a more significant pathway for heat transfer in the low accommodation coefficient regime. The experimental work
0010-2180/$ - see front matter Ó 2013 The Combustion Institute. Published by Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.combustflame.2013.07.010
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by Altman et al. was performed using laser irradiation to heat up nanoparticles generated in a flame. The energy accommodation coefficient was found to be near 0.005 which agreed nicely with their theoretical upper limit [14]. Nano-aluminum particle combustion may potentially experience a similar thermal isolation effect in many applications. With such low accommodation coefficients the heat transfer from the particle via collision with gas molecules becomes inefficient, leading to particle temperatures much higher than those expected using EAC 1. In this work we perform experiments on nano-aluminum combustion to monitor the particle temperature, burn rate, and emission spectra. High particle temperatures and longer burn times are expected for a transition to the free molecular regime accompanied by a low energy accommodation coefficient. For ultrafine particles, classical theory predicts that rapid heat transfer results in combustion temperatures that only minimally exceed the ambient temperature, even when common Knudsen number correlations are used for Nusselt number calculation [12]. Prediction of the particle temperature requires specification of the reaction rate (i.e., heat release rate) in addition to the heat transfer coefficient. In this research the experimental data on burning time and temperature are supported by a simple model of nano-aluminum combustion that employs as few limiting assumptions as possible, focusing only on the energy balance leading to particle temperature rise. Multiple heat transfer models are considered to determine the predicted transient particle temperature and to see if the nano-aluminum particle experiences thermal isolation from the surrounding gas. 2. Experimental set-up The nano-aluminum particles were investigated using a heterogeneous shock tube described in detail in a previous publication [16]. The shock tube is capable of producing controlled high temperature and high pressure environments with various gas compositions. Temperatures greater than 4000 K and pressures above 30 atm are achievable behind the reflected shock with test times near 2 ms. Low temperatures were used for this study to test nano-aluminum combustion which has been shown to ignite at temperatures below 2000 K [9]. The combustion of the nanoaluminum particles was monitored behind the reflected shock in
order to achieve the high pressures desired. The pressure was varied between 3.5–20 atm to determine the effect of the oxidizer concentration on the particle temperature and burn time. The shock tube has an 8.4 m driven section and an 8.9 cm internal diameter. A converging dual diaphragm system separates the high pressure helium gas from the oxidizing environment. The driver to driven pressure ratio is controlled to produce the desired shock strength. The velocity of the shock is measured using four piezoelectric pressure transducers at different axial locations. The ambient temperature and pressure of the gases trailing the incident and reflected shock are calculated with the Gordon-McBride equilibrium code [17] using the known initial driven pressure, composition, and measured shock velocity. The test time of the shock tube can also be found from the pressure transducer traces and is typically near 2 ms. A schematic of the shock tube operation with radial injection and the end section with fiber optic view ports is shown in Fig. 1. This end section allows for photodiode access at multiple axial locations. The end wall has a sapphire view port for further optical access. The fiber optic section is described in further detail in a previous publication [9]. Each test was run with three photodiodes monitoring different axial locations centered at the location of aluminum particle stagnation behind the reflected shock. A nano-aluminum particle has a very small Stokes number, and therefore the particle accelerates quickly behind the incident shock and stagnates within a few microseconds behind the reflected shock. For this reason particle motion behind the reflected shock is neglected. Particles are injected radially into the test gas prior to diaphragm rupture using a pneumatically driven piston. The particles become entrained in the gas flow behind the incident shock and are swept towards the end-wall until the reflected shock stagnates them and they combust. Four particle classes were chosen to vary particle diameter while measuring burn time, temperature, and emission spectra. A Hitachi S-4700 high resolution scanning electron microscope (SEM) was used to accurately characterize the particle size distribution of each sample. Over 100 particle diameter measurements were made from each sample in order to obtain a distribution. Table 1 shows the number average and mass average particle diameters of each nominal sample powder. The SkySpring 18 nm particles were not characterized because the resolution required
Fig. 1. Schematic of shock tube test section with fiber optic access.
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full-width-half-maximum (FWHM). The spectra were time integrated over the entire combustion event; a mechanical shutter was used to avoid emission from particles after the test time of the shock tube. The shutter was fully closed 1.2 ms after the incident shock reflected off of the endwall. This ensured that all of the thermal emission during the nanoparticle heat up and cool down was captured, but any luminosity from events occurring after the test time was rejected. The spectrometer was intensity calibrated using a tungsten calibration lamp with a filament temperature of 3200 K. Pyrometry was performed using a custom-built 3-color pyrometer. A trifurcated fiber bundle imaged the light from the test section through a narrow slit. The trifurcated cable split the light collected from the test into three separate branches. Each branch passed through a collimator, interference filter, and to a photomultiplier. The interference filters each had a 10 nm FWHM bandpass centered at 705, 826, and 905 nm. The shorter wavelengths were measured using Hamamatsu R928 photomultipliers; the 905 nm light was measured using a R636-10 photomultiplier with an infrared-sensitive GaAs photocathode. The outputs of the photomultipliers were amplified using a Stanford Research Systems Quad preamplifier unit with a 300 MHz bandwidth. The time response of the pyrometry system is sub-microsecond. The system was calibrated using a tungsten calibration lamp. Noise level is typically 10–20% of the signal and the measurement uncertainty has previously been estimated to be 150 K for micron sized particles [18]. Photometric burning time measurements were made using photodiodes coupled to different axial locations using the fiber optics in the end section shown in Fig. 1. Three ThorLabs PDA36A amplified photodiodes were used to capture the luminosity from each experiment. The emission was unfiltered because the spectroscopic measurements indicated no molecular emission. The time resolution of the photodiodes is sub-microsecond.
Table 1 Summary of average particle diameters. Particle type
Number average diameter (nm)
Mass average diameter (nm)
SkySpring 18 nm SkySpring 50 nm NovaCentrix 80 nm NovaCentrix 110 nm
– 73.2 83.4 100
– 80.9 90.1 110
to characterize these particles accurately was not achievable. Any distribution obtained would have been biased towards the larger particles which were readily resolved while the smaller particles below 18 nm would not have been accounted for. The highest resolution images achieved qualitatively showed the SkySpring 18 nm particle distribution to be significantly smaller than the other sample distributions even though an accurate average could not be quantified. Each sample had a large distribution of particle sizes. Figure 2(a)–(c) shows the histograms of the three characterized samples and Fig. 2(d) shows a corresponding SEM image for the NovaCentrix 80 nm particles. All particles imaged were found to be highly spherical. Nano-aluminum has previously been shown to form both weak and strong agglomerates dependent on the manufacturing process. The images show the particles acquired have weak agglomeration and very little particle necking. The particles acquired from NovaCentrix are specified to be 80–90% aluminum and the oxide-coating thickness is 1.5–2.5 nm. Both samples acquired from SkySpring Nanomaterials are 99.9% pure on a trace metals basis. Emission spectra were collected using an Ocean Optics spectrometer with a 10 lm inlet slit and a 200–550 nm range. The spectral resolution of the spectrometer was approximately 1 nm
(a) Particle size distribution for the SkySpring Nanomaterials 50 nm particles
(c) Particle size distribution for the NovaCentrix 110 nm particles
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(b) Particle size distribution for the NovaCentrix 80 nm particles
(d) Sample Scanning Electron Microscopy (SEM) image of the NovaCentrix 80 nm particles
Fig. 2. Particle characterization.
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3. Experimental results In a previous study [9],we reported nano-aluminum burning times and temperatures for a single class of particles (80 nm) in O2 and CO2. In that study, one of the results was that the degree of temperature overshoot (Tparticle Tambient) depended on oxidizer and pressure. For this study, we have expanded the dataset to include different sized particles while focusing on accurate measurements of burning time and temperature. For temperature, our measurement accuracy and precision are significantly improved by using the results of our recent study on the emissive properties of alumina at elevated temperatures [19]. Since we do not repeat the exact conditions of the previous report, we do not compare results, but the general trends in burning time and temperature overshoot are consistent with the initial study. Current and previous measurements have shown weak or no molecular aluminum monoxide (AlO) emission at pressures below 32 atm for nano-aluminum combustion [9]. Each spectra showed only thermal radiation and no significant gas phase emission, indicating that the primary combustion mechanism involves surface reactions as hypothesized. If gaseous aluminum were present, atomic aluminum lines would likely be seen at 394.4 and 396.1 nm, and banded aluminum monoxide (AlO) emission from the B-X transition would likely be seen in the range from 460–530 nm. It is possible that the gas phase species are present but are not at high enough temperatures to cause detectable spontaneous emission. However, measurements by Lynch et al. showed no aluminum or aluminum monoxide absorption below 1500 K which further suggests that gas phases are not present in significant amounts [20]. The lack of gas phase emission is consistent with a reaction model in which surface processes limit the combustion rate. The average burning times can be seen in Table 2 using the 10%90% area method to calculate the burn time. In order to calculate the 10%-90% area burn time the background intensity in the post combustion environment due to heated particles was subtracted off following the method described in a previous publication [9]. In short, a linear rise is fit from initial noise level to the background intensity level. The rise is assumed to occur from the onset of luminosity to the point of peak intensity where it then remains constant. There is some deviation from the average due to the large particle distribution and also due to the inherent uncertainty in determining the background intensity levels. More important, however, is that the luminosity traces show that as the average particle diameter increases, the photodiode trace becomes wider and the time it takes to reach peak intensity becomes longer. The burning time of the particles spans from 50–200 ls consistently for all samples. The values for the burn time seen in Table 2 compare favorably with those seen previously by Bazyn et al. in similar conditions and are shorter than those seen in micron sized aluminum at higher temperature. Bazyn found burn times near 170 ls for 80 nm aluminum particles in 20% O2 and 80% N2 at higher pressures [9]. It is important to consider the interpretation of the luminosity traces. The emission spectrum showed no evidence of molecular emission, and therefore, the luminosity profiles being shown cannot be directly correlated to the presence of aluminum monoxide,
Table 2 Summary of particle burning time in air calculated using the 10–90% area burn time method of calculation.
as has previously been done. When monitoring molecular emission such as AlO the assumption is that the luminosity trace corresponds to the presence of AlO, which indicates combustion because AlO is a key intermediate species in the gas phase combustion process. However, in this case the luminosity is due to thermal radiation evidenced by the emission spectra. Therefore, we are correlating burn time to particle temperature which is a different assumption than that made when monitoring emission filtered around an aluminum monoxide band as is normally the case for micron sized particles [4]. The three color pyrometry measurements indicated a rise in particle temperature above the ambient gas temperature. Multiple tests were performed for each particle size at 1500 K and 20 atm in 20% O2–80% N2. Table 3 shows the peak temperature calculated at the location of peak intensity tabulated for each particle class. The average temperature remains relatively constant for all particle sizes. The average peak temperature is between 3200–3500 K for all cases. Bazyn et al. [9] similarly found peak temperatures for nano-aluminum combustion near 2500 K for 8.5 atm pressures and 3500 K for 32 atm pressures. The values of the peak temperatures at 20 atm found in these tests range between the values found by Bazyn. These temperatures are near the boiling temperature of aluminum which varies from 3040 K at 4 atm to 3600 K at 32 atm. In a surface-process limited combustion mechanism the peak temperature increases with pressure since the reaction rate (heat release rate) is proportional to the number density of oxidizer in the vicinity of the particle. A low pressure test performed at 3.5 atm gave a peak temperature of 2375 K, which is again consistent with the trend predicted by the surface-process limited combustion model. The high peak temperatures and relatively long burn times observed in this work and previously by Bazyn [9] suggest that heat transfer from the particles must be relatively slow compared to that suggested by common models. In the continuum limit (Nu 2), the nano-aluminum particle would need to fully combust in less than 0.5 ls in order for the particle to reach 3200 K in the ambient conditions of the experiment. Using a non-continuum expression valid for the transition regime (Nu = 0.3/Kn), the burning time is only extended to 1.5 ls. The data suggest this is not the case. A more detailed heat transfer analysis is presented in the next section.
4. Model description A nano-aluminum combustion model was developed to further investigate the heat transfer of the particles. The model is an energy balance of the particle that assumes a surface-process limited combustion mechanism and heat transfer through conduction to the ambient gas and radiation to the walls of the shock tube at 300 K. Figure 3 depicts facets of the combustion model. The reaction surface is the initial surface area of the particle and does not change because diffusion of oxidizer and fuel are assumed to occur much faster than the limiting surface process (i.e., surface diffusion or chemical reaction).
Table 3 Summary of peak temperature of combusting nano-aluminum particles in air.
Particle type
Burning time (ls)
Deviation (ls)
Particle type
Peak temperature (K)
Deviation (K)
SkySpring 18 nm SkySpring 50 nm NovaCentrix 80 nm NovaCentrix 110 nm
74.5 119.5 129.2 134.3
20.5 6.4 9.6 6.7
SkySpring 18 nm SkySpring 50 nm NovaCentrix 80 nm NovaCentrix 110 nm
3301 3274 3169 3472
251 338 482 252
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The influx of heat to the particle is assumed to be due to the chemical reaction between the oxygen and aluminum following Eq. (1), which releases 1.85(1018) joules of energy for each collision of oxygen molecule resulting in reaction with the aluminum surface. The rate of reaction is calculated using the number density of oxygen at the particle surface (Eq. (2)), thermal velocity (Eq. (3)), the collision frequency (Eq. (4)), and a sticking probability / which is a variable parameter in the model. The velocity distribution in Eq. (3) assumes a maxwellian distribution. This assumption ignores the chemical reaction occurring at the surface of the aluminum particle which consumes the oxidizer molecules; however, it will be shown that the model predicts very small sticking coefficients (0.001), and in the limit of small sticking coefficients the velocity distribution approaches that of a maxwellian distribution, and the assumption is considered valid. The sticking probability represents the percentage of collisions that react and has a value between zero and one. A sticking probability of zero represents no reaction, and a sticking probability of one indicates each collision results in chemical reaction. The sticking probability is assumed to remain constant during the combustion of the aluminum particle. Eqs. (2)–(6) represent the calculation for the heat due to the reaction. An effective area is used for the influx of heat to model the reduction in the amount of aluminum surface area at the reaction surface during combustion. The effective area is determined by calculating the surface area of the remaining mass of aluminum at each time step as if it were a sphere. The assumption is that the reaction occurs at the outer surface of the particle, but as the particle burns the amount of reactive area decreases as a function of time following Eq. (5). A variable reaction area is chosen to account for changes in reactivity as the aluminum is depleted. As reaction occurs and oxide builds up on the surface, this barrier most likely impedes the oxidizer from reaching fresh metal. This effect can be simulated in our simplistic model by reducing either sticking probability (/) and/or reaction area (A) as a function of reaction extent. We, somewhat arbitrarily, choose the latter approach. The effect of including a time varying / or A alters the predicted transient temperature profile. Assuming the sticking probability or reactive surface area decreases with time results in the particle attaining an initial peak temperature followed by a temperature decay, which is similar to what was seen in experiment. If the product / A is constant, then the particle temperature rises and remains at the peak temperature until particle burnout. The value of the peak temperature is unaffected by this treatment, as the peak temperature occurs at the beginning of particle combustion when the reactive surface area is nearly equal to the outer particle surface area. The burn time is increased by less than 15% using the decreasing reactive area, and therefore this assumption does not significantly affect the conclusions.
Fig. 3. Depiction of the surface process nano-aluminum combustion and heat transfer model.
2 Al þ 3=2 O2 ! Al2 O3 þ 1:85 ð1018 Þ NO2 ¼
J Collision O2
X O2 P T a kb
1=2 8 kb T a c¼ mO2 p c f ¼ NO2 4 2=3 6 mal Aeff ¼
qal p
Ein ¼ Aeff fq/
ð1Þ ð2Þ ð3Þ ð4Þ ð5Þ ð6Þ
The conduction of heat to the surrounding gas is the key effect of interest in the present study. As previously mentioned, Altman predicts a decrease in the accommodation coefficient at high temperatures. Altman puts an upper limit on the accommodation coefficient aE following Eq. (7), where h is the Debye temperature of the solid. For the conditions in this study Eq. (7) puts the upper limit of the accommodation coefficient at approximately 0.006. The heat transfer to the surroundings through conduction in the free molecular regime is calculated following Eq. (8). Eq. (9) shows the corresponding heat transfer equation assuming continuum mechanics, where k is the thermal conductivity of the gas, Nu is the Nusselt number, and d is the particle diameter. The radiation to the walls follows the Stefan–Boltzmann law using Eq. (10) with an emissivity of 0.1 for alumina [19]. The temperature of the particle changes as shown in Eq. (11).
1 h2 2 CRv þ 1 T g T s aE P c c þ 1 ðT p T a Þ Esur ðtÞ ¼ 8 Ta c 1 k Esur ðtÞ ¼ Nu ðT p T a Þ A d
aE <
Erad ðtÞ ¼
r T 4p T 4w A
Ein Esur Erad DTðtÞ ¼ mparticle cp
ð7Þ ð8Þ ð9Þ ð10Þ ð11Þ
5. Discussion The model has two unknown parameters which must be fit to experimental data. These parameters are the sticking probability, /, and the energy accommodation coefficient, aE. The two independent unknowns are fit by comparing the predicted dependent variables of model peak temperature and burning time to the values obtained in the shock tube experiments. Figure 4(a) and (b) show the model predictions graphically for an 80 nm particle. The burn time calculated in the model is independent of the heat transfer of the particle with the assumptions provided, and is plotted in black on the log scale. The particle is considered fully burned in the model once 90% of the original mass is reacted. A sticking probability of zero represents no reaction and therefore the burn time asymptotes towards infinity at this value. The particle temperature increases with increasing sticking probability as expected because a larger percentage of the collisions result in exothermic heat release. Seven potential temperature profiles are plotted for comparison, each using a different accommodation coefficient or heat transfer assumption. Five accommodation coefficients, a correlation for the Nusselt number deduced from laser induced incandescence on nano-particles [12], and a Nusselt number of 2 are considered. For a given sticking probability the burning time and
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(a) Model results for an 80 nm particle comparing burn time and peak temperature at ambient conditions of 1500 K and 20 atm in air for sticking probabilities between 0-0.5
(b) Model results for an 80 nm particle comparing burn time and peak temperature at ambient conditions of 1500 K and 20 atm in air for sticking probabilities between 0-0.01 Fig. 4. Comparison of burn time and peak temperature using various heat transfer models.
particle temperature considering one of the seven heat transfer models satisfy the energy balance of the system. It is evident that an accommodation coefficient between 0.001– 0.005 is necessary in order to achieve burn times greater than 100 ls and peak temperatures of 3300 K as indicated by the highlighted section of Fig. 4(b). The dashed box indicates the experimentally determined possible peak temperatures for sticking probabilities that give burning times also in the experimentally observed range. The best fit values for the accommodation coefficient and sticking probability are 0.0035 and 0.0009 respectively. The values obtained for the accommodation coefficient here match extremely well with the value of 0.005 found experimentally by Altman in previous work. These results clearly suggest that the nano-aluminum particles are experiencing thermal isolation from the ambient gas due to low energy accommodation coefficients. Further comparison of the simple model with the experiment can be made by comparing the luminosity trace to the relative model-predicted thermal radiation intensity (i.e., T4). Figure 5(a)–(d) shows the predicted luminosity compared to photodiode traces from the experiment at 1500 K and 20 atm in air. For these traces the best fit accommodation coefficient of 0.0035 and sticking probability of 0.0009 were chosen. The comparison between model and experiment is quite good. The model predicts the peak temperature for each particle size to be approximately 3400 which is below the 3450 K boiling
temperature of aluminum at 20 atm within uncertainty. It is likely that as the particle heats up some of the aluminum is volatilized and reacts at the surface of the particle limiting the peak temperature of the system to the boiling temperature of the aluminum at the given pressure. The peak temperature does not change significantly in the model with particle size because all modes of heat transfer scale similarly. The heat loss scales with d2 and the heat due to chemical reaction scales with the effective area, but the peak temperature occurs near the start of the particle reaction when the effective area is very near the initial area of the particle. The transient temperature profiles change with particle size due to the effective area approximation as seen in Fig. 5(a)–(d). The model prediction that the peak temperature remains constant independent of the particle diameter agrees with the experimental data shown in Table 3 within experimental uncertainty. The comparison extends to lower pressures as well. The model predicts a peak temperature of 2600 K at a pressure of 3.5 atm using the accommodation coefficient (0.0035) and sticking probability (0.0009) as those used to fit the data at 20 atm. Pyrometry measurements found the temperature to be 2375 K at 3.5 atm. The model slightly over predicts the temperature, but the accommodation coefficient used was fit to a system with the peak particle temperature of 3100 K and an ambient gas temperature of 1500 K. In the case of lower pressure, the peak temperature is lower and following Eq. (6), a lower particle temperature implies a higher accommodation coefficient. Scaling the accommodation coefficient by this difference in expected temperature brings it to a value of approximately 0.0047. Using this value further drops the predicted temperature to 2500 K which is within the experimental value of 2375 ± 150 K. Clearly the accommodation coefficient may vary as the particle temperature changes during the combustion event, but here it is assumed constant. The possible effect of particle agglomeration on the results and conclusions is worthy of consideration. If nanoparticles agglomerate rapidly or are not efficiently de-agglomerated, then large agglomerates may still readily ignite at low temperatures but will coalesce and burn as larger particles. If agglomerates contain enough primary particles, the coalesced particulate may be large enough to burn in the diffusion limit, with correspondingly high temperatures. In our arrangement, breakup of agglomerates is strongly promoted during injection and by the shock waves. During injection, the dispersed aerosolized particles are entrained in a jet of gas, then sent through an array of fine meshes that have been shown to effectively produce a well-dispersed cloud [21]. Petersen used a much milder form of injection [22] and directly measured particle sizes in the resulting cloud, finding little agglomeration of aluminum nanoparticles within the first minute after injection. Furthermore, it has been shown that the strong shear forces of the shock waves are effective at breaking weak agglomeration in nano-particles [23–25]. Thus, the experimental evidence to date suggests clouds formed in the shock tube are, at the least, resistant to the formation of agglomerates. Post shock agglomeration should also be relatively slow. Calculations considering an evenly dispersed thin cloud of particles behind the incident and reflected shock using the Smoluchowski monodisperse model, which ignores electrostatic forces, suggest that each particle will conservatively collide with less than two other nano-particles during the test time. In order for a nanoparticle to increase in size from 100 nm to 500 nm, it would require an agglomerate consisting of approximately 125 primary particles assuming spherical geometry. Heat transfer analysis of a 500 nm particle using the non-continuum heat transfer approximation still shows that the agglomerate particle must combust in less than 15 ls in order to reach 3000 K, still well below what is seen in
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D. Allen et al. / Combustion and Flame xxx (2013) xxx–xxx
(a) Model radiation for SkySpring 18 nm particles at 1500 K and 20 atm in air compared to experimental data
(c) Model radiation for NovaCentrix 80 nm particles at 1500 K and 20 atm in air compared to experimental data
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(b) Model radiation for SkySpring 50 nm particles at 1500 K and 20 atm in air compared to experimental data
(d) Model radiation for NovaCentrix 110 nm particles at 1500 K and 20 atm in air compared to experimental data
Fig. 5. Comparison of model radiation and experimental luminosity measurements for each particle class.
experiment. Furthermore, the lack of significant AlO and Al emission during nano-particle combustion at 1500 K also suggests that it is not particles burning in the diffusion limit that is responsible for the measured temperature overshoot [20].
6. Conclusions It has been shown that in order for nano-aluminum particles to achieve the burning time and peak temperatures observed experimentally, the heat transfer from the burning particles must be significantly slower than would be expected assuming energy accommodation coefficient values approaching 1. This effect was theoretically described by Altman and shown to be true in experiments using laser irradiation. In those experiments the energy accommodation coefficient was found to be approximately 0.005. It has been shown here with a simple surface based heat transfer model, that the best fit for the energy accommodation coefficient is 0.0035 which agrees very well both with the experiments performed by Altman and the upper estimate described previously in Eq. (6). It is therefore concluded that at the high ambient temperatures recorded in the shock tube, the particles are experiencing thermal isolation from the surrounding gas. More complex combustion reaction models can be implemented; however, without
accounting for the low energy accommodation coefficient it is not possible to correctly predict the particle temperatures and burning times seen in experiment. This effect has important consequences for modeling of nanoaluminum combustion. In particular, particle temperatures will likely be much higher than current models predict, and radiation effects may be enhanced. It is expected that similar results will arise for other metal condensed phase nano-particles combusting at high temperatures, as suggested by Altman.
Acknowledgments This project was supported by the US Air Force under Contract FA9300-11-M-2004. Additional support was obtained from DTRA under Grant HDTRA1-10-1-0003. The project manager is Dr. Suhithi Peiris. The Scanning Electron Micrographs were taken in the Frederick Seitz Materials Research Laboratory Central Facilities, University of Illinois, which are partially supported by the US Department of Energy under Grant DEFG02-9-ER45439. Special thanks to Ed Dreizin and Michael Zachariah for helpful discussion on the issue of temperature overshoot. Thanks also to Sam Goroshin for providing us with the references on thermal isolation which made this work possible.
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