Combustion and Flame 159 (2012) 793–801

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Combustion and Flame

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Micro-alumina particle volatilization temperature measurementsin a heterogeneous shock tube

Patrick Lynch 1, Herman Krier, Nick Glumac ⇑University of Illinois at Urbana–Champaign, Department of Mechanical Science and Engineering, 1206 W. Green St., Urbana, IL 61801, USA

a r t i c l e i n f o a b s t r a c t

Article history:Received 26 February 2011Received in revised form 18 July 2011Accepted 20 July 2011Available online 31 August 2011

Keywords:Aluminum combustionAlOAluminum monoxideCloud extinctionTemperature fitting

0010-2180/$ - see front matter � 2011 The Combustdoi:10.1016/j.combustflame.2011.07.023

⇑ Corresponding author.E-mail addresses: ptlynch@anl.gov (P. Lynch),

glumac@illinois.edu (N. Glumac).1 Present address: Argonne National Laboratory, 97

60439, USA.

Peak flame temperatures in aluminum particle combustion should approach the volatilization tempera-ture of the product alumina. References are divided in assigning this temperature anywhere between3200 and 4000 K, which can provide significant uncertainty not only in numerical models for combustionbut also in the interpretation of flame structure from temperature measurements. We present results inthe controlled conditions of the UIUC heterogeneous shock tube of volatilization temperature, made bymeasuring the extinction of light by nano- and micro-alumina particles at non-resonant wavelengthsat different ambient temperatures. At 10 atm, there is a sharp cutoff at 3860 K beyond which nano-par-ticles volatilize and stop extinguishing within the shock tube test time. Numerical modeling of the evap-oration rate of these particles is used to assign a volatilization temperature of 4340 K at 10 atm. Similarly,a volatilization temperature of 4260 K at 3 atm is measured. From our analysis, the best estimate for thevolatilization temperature at 1 atm was 4189 ± 200 K, which is consistent with the high range of volatil-ization temperature reported in the literature.

� 2011 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

1. Introduction

The peak combustion temperature joins heat release rate amongthe most important performance metrics in energetic metals, oftenused as fuels in solid rocket motors and enhanced blast weapons.High combustion temperatures result in higher thrust in solid rock-et motors. Additionally, in advanced thermobaric weapons, peakcombustion temperatures are important (along with duration), forinstance, in agent defeat. Aluminum is one of the most prevalentlyused energetic additives. Often in aluminum based reactions, spec-tra of the gas phase reaction intermediate AlO are measured [1], andthe B–X Dv = �1 band sequence [2,3] (505–525 nm) can be fit to atemperature, which is thought to closely mirror the peak tempera-ture in the gas phase.

While the product of aluminum with oxygen containing oxidiz-ers, alumina (Al2O3), does not have a stable gas phase, there is a tem-perature above which the alumina vaporizes and quickly volatilizes.According to Glassman [4], peak flame temperatures in aluminumcombustion should approach this volatilization temperature ofAl2O3, and the first studies of large Al particles place the combustiontemperatures at 3800 K and higher. Several other studies measure

ion Institute. Published by Elsevier

krier@illinois.edu (H. Krier),

00 S. Cass Ave., Argonne, IL

peak AlO temperatures consistently near 3200–3250 K in micro-Alcombustion [5–8] both from fitting AlO and by other means. In thestudies of Bazyn, higher temperatures were measured by fittingAlO spectra emitted from the flame zones near larger particles(20 lm and larger) [9] as well as from the flame zones of aluminumparticles ignited with the assistance of a Al/MoO3 thermite reaction[10].

While these similar temperature measurements of 3200–3250 K may be coincidence, the measurements, from differentexperimental ambient conditions (temperature, pressure, oxidizerconcentration, and ignition method), and fit with different codesopen the possibility that there may be a limiting process on thetemperature for the smaller particle sizes. Schlöffel et al. [5] sug-gest that the limiting process may be the volatilization tempera-ture of alumina. Further confounding this issue is that there issignificant ambiguity in the volatilization temperature in trustedreferences. The CRC tables [11] assign the temperature at whichAl2O3 vapor pressure reaches 1 bar (an ill defined concept forAl2O3, but acceptable for the other species reported in that table)is 3248 K. On the other hand, the JANNAF tables [12] maintain thatliquid alumina is present until 4000 K. Glassman uses 4000 K aswell [4].

This difference in the literature can be traced back to the firststudies of the alumina volatilization temperature at 1 atm. Bothstudies were extrapolations from measurements of the partialpressure of vapor species above the liquid phase at lower temper-atures, i.e. effusion studies. The early measurements of Roff and

Inc. All rights reserved.

Fig. 1. Schematic of heterogeneous shock tube and diagnostics when makingvolatilization measurements.

794 P. Lynch et al. / Combustion and Flame 159 (2012) 793–801

Konschak [13] in 1926 likely had higher than reported uncertaintyin the temperatures due to the pyrometric measurements made.The temperature reported from the Wanner pyrometer they wereusing at the time would likely have been outside of the range ofcalibration. It is unclear if there was a secondary calibration avail-able to extend the usefulness of this instrument to higher temper-atures. These measurements were cited in the review of Stull [14]and were later incorporated in the CRC tables. A later study in 1951by Brewer and Searcy [15], which notably cited the Roff and Kons-chak work, obtained a boiling temperature of 3770 ± 200 K. Thisstudy was cited early by Grosse and Conway [16] and later wasincorporated into the JANNAF references.

Alumina volatilization is not the only mechanism that can sup-press the peak combustion temperature, but it is an interestingcandidate because of this ambiguity in the literature. As the parti-cle size decreases, the reaction rate clearly does not stay constantat the diffusion limited burning rate, as can be noted from burntime data [6,17], but the heat loss from the particle increases withincreasing surface to volume ratio (decreasing diameter), and thewell defined flame front approaches more of a volumetric reactionzone in the transition regime. Still, these processes seem like theyshould be continuous processes without a discrete limiting tem-perature around 3200–3250 K.

The highly controlled environment of the heterogeneous shocktube allows measurements of heated alumina particles in whichthe volatilization temperature of alumina can be measured with-out the need for extensive extrapolation from very low tempera-tures and pressures. Clouds of alumina particles at temperaturesbelow the volatilization temperature should extinguish laserlight. At temperatures beyond the alumina volatilization temper-ature, the transmitted light fraction should reach nearly unitywithin the test time of the shock tube. This temperature at whichalumina particles transition from extinguishing to not extinguish-ing light in the test time was measured to infer the volatilizationtemperature.

Fig. 2. Pressure transducer traces of shock tube event. In this case, the reflectedshock temperature was calculated to be 3886 K and the reflected shock pressure9.7 atm. The estimated test time of 1.7 ms agrees with the drop off of the reflectedshock pressure.

2. Experimental methods

The heterogeneous shock tube facility at the University of Illi-nois generates a high temperature, high pressure controlled envi-ronment ideal for making measurements in combustionconditions. The driven section (the test section) is 8 m long and8.9 cm internal diameter. Other relevant dimensions and descrip-tions of this facility can be found in previous publications [18,9].Through the pressure ratio of the driver and driven sections, astrength selectable shock is sent through the driven section. Asthe shock wave reflects off the endwall, it produces a high temper-ature, high pressure, controlled combustion environment forapproximately 2 ms. Various compositions of test gases can beused. Temperatures exceeding 4000 K and pressures up to 30 atmare achievable. Particles are injected upstream prior to the ruptureof the diaphragms initiating the event and move towards the wall,are stagnated, and are heated under the influence of the gas behindthe incident and reflected shocks.

Figure 1 shows the experimental setup and diagnostics used inexperiments testing the volatilization temperature. Approximately0.1 mg of particles were injected into the shock tube from a porteither 0.38 or 0.78 m from the endwall approximately 1 s beforethe rupture of the double diaphragm section. Light from an80 mW CW frequency doubled Nd:YAG laser (532 nm) was passedthrough the sapphire windows of the shock tube as shown in Fig. 1.The initial pass of the laser occurred 6.3 cm from the endwall. Thelaser light was reflected back through the test section 5 cm fromthe endwall. This location was selected based upon particle trajec-tory modeling and from previous high speed imaging of the event.

The laser light was then reflected approximately 2 m away and fo-cused through a 532 nm bandpass filter onto a Thorlabs PDA36Aphotodiode. The combination of the long distance from the mirroras well as the focusing of the lens ensured that the solid angle col-lected by the photodiode was very small. Indeed the combinationof the small solid angle and the 532 nm bandpass filter was almostalways sufficient for the 80 mW laser to dominate any broadbandemission from the solid particles at these wavelengths. The 532 nmlaser also comes in between the Dv = �1 and Dv = �2 AlO B–Xbands, so any molecular interference is negligible.

A cloud of suspended particles is needed in order to properly ac-count for particle motion during the event and ensure that thediagnostics are properly focused. Two different size distributionsof alumina were studied. Both were purchased from Alfa Aesarand have purities greater than 99.5%. The first size distribution, mi-cro-alumina, had particles in the 0.9–2.2 lm range. The secondpowder, nano-alumina, had a size distribution between 40 and50 nm and specific surface area between 32 and 40 m2/g. Furthercharacterization of the particles as well as the injector are availablein a recent publication [19].

Figure 2 shows traces from the sidewall time of arrival sensorsand endwall pressure transducer during a typical experiment. Re-flected shock conditions were calculated from the incident shockvelocity and initial pressure and temperature. Over the experimen-tal range studied, the incident shock velocity attenuated approxi-mately 1.3%/m near the endwall. Due to the very high

P. Lynch et al. / Combustion and Flame 159 (2012) 793–801 795

temperature conditions not ordinarily studied in this shock tube,viscous effects were corrected for using the model of Petersenand Hanson [20]. Because of the 5 cm distance from endwall inwhich the reflected shock wave is entering a progressively higherpressure incident shock region, the reflected shock temperaturescalculated with this attenuated shock velocity using GASEQ [21]were slightly increased by about 20 K. Changes to the reflectedshock pressure were less than 0.1 atm.

In these experiments, the test time was estimated from the timebetween the incident shock reflection and its second reflection offthe wall once it reflects off of the contact surface. The actual pro-cess must also involve weak refractions during this second ap-proach to the endwall, because in all cases the measured endwallpressure decreases after a relatively constant period which corre-sponds nicely with the estimated test time. Times estimated in thisway ranged from 2.2 ms at 2800 K to 1.3 ms at 4800 K. The testtime at 5 cm was also decreased about 0.2 ms to account for thedistance the shock traveled to the endwall.

Nano alumina particles were tested in 100% Ar, both 3 and10 atm reflected shock pressure, and reflected shock temperaturesstarting at about 2800 K and increasing to 5000 K. The reflectedshock temperatures were incremented until the photodiode signalshowed little extinction within the shock tube test time andslightly beyond. This cutoff, as well as modeling of the evaporationrates of the particles, was used to determine a volatilization tem-perature at the reflected shock pressure. Additionally, micro-alu-mina particles were tested at 10 atm. These larger particles didnot volatilize appreciably within the shock tube test times untiltemperatures higher than the volatilization temperature. However,the volatilization rates were predicted from the numerical schemefor evaporation and fit to a volatilization temperature lower thanthe test ambient temperature.

2.1. Processing

Two criteria were used to determine when a cloud of nano-alu-mina particles had significantly volatilized and was no longerextinguishing laser light. The first was that the transmitted lightintensity, which always dropped somewhat shortly after the meet-ing of the reflected shock with the cloud, had to recover to 95%transmissivity within the test time (temperature dependent, butabout 1.5 ms at 3900 K). At high pressures, this recovery often oc-curred rapidly, sometimes within 200 ls. However, at lower pres-sures, this recovery required more time. The second criterion wasthat once the shock tube test time was reached, the average trans-missivity beyond the test time was required to be within 5% of100%. This criterion was to ensure that the cloud of particles hadvolatilized and not simply moved out of the test volume. The re-flected shock, which reflects again off of the contact discontinuityin the shock tube, would sometimes bring the particles back intocollection volume and the transmitted light intensity would subse-quently drop. If the signal passed both of these criteria, it was as-sumed that there was limited extinction and the particles hadvolatilized substantially within the test time. These criteria, whilenot the only criteria that could be applied, were deemed satisfac-tory as they produced sharp cutoffs in extinction with temperaturefor both the low pressure and high pressure data.

This defined sharp cutoff, however, is not the volatilization tem-perature of the alumina. Because of the exponential nature of thevapor pressure with temperature, there can be significant evapora-tion of the particle at temperatures below the volatilization tem-perature. With such small particles, the alumina can evaporateand then dissociate within the test time at temperatures hundredsof degrees below the volatilization temperature. This particle evap-oration was modeled, allowing for the calculation of a volatiliza-tion temperature for the different pressures.

2.2. Volatilization model

The model for evaporation assumes that at each ambient tem-perature below the volatilization temperature, there is a rate ofevaporation and dissociation of the alumina. The numericalscheme calculates this rate, which changes as the particle temper-ature and diameter change, and determines if, for an assumed vol-atilization temperature, it would be possible for a particle toevaporate during the shock tube test time. The volatilization tem-perature is then iterated to achieve the temperature for which par-ticles subjected to a lower experimental ambient temperaturewould not evaporate.

Also, an assumption is made that there is a finite volume inwhich the products dissociated from alumina particles can buildup into. This assumption comes from the finite spacing that theparticles have, which was estimated by imaging using an acrylicsection on the shock tube. Measurements of the fraction of the0.1 ± 0.05 mg of particles injected which are actually entrained inthe narrow cloud which passes the lasers (based on the ratio ofthe total intensity from this region to the total intensity every-where in the tube) reveal this number to only be approximately32 ± 6%. Further, using this high speed imaging of the shock tubeevent, the extent of this narrow cloud of particles was measuredto be 3.5 ± 0.8 cm. These observations led to an estimate of theaverage spacing between particles of 84 ± 28 diameters.

This spacing effectively limits the volume into which the prod-ucts can diffuse and causes the buildup of dissociated products inthis volume. This buildup increases the concentration of theseproducts which slows the rate of evaporation, which is limitedby the concentration gradient. As equilibrium is reached, the parti-cle ceases to evaporate. Because there is not a stable Al2O3 gasphase species, the alumina was assumed to have broken down intocomponents calculated with the Gordon McBride equilibrium sol-ver [22] (more than 90% of which was Al, AlO, and O). These prod-ucts were averaged into a single species, subscripted A, whichdiffused into the volume between particles.

The rate of evaporation, _m, is driven by the difference in massfraction of the species A between the surface yA,s and the environ-ment, yA,amb:

_m00 ¼ qDd2

ln 1þyA;ambðtÞ � yA;s

yA;s � 1

!ð1Þ

where d is the particle diameter, D is the mass diffusivity of theaveraged species A into the bulk gas, and q is the gas density. Eq.(1) is the quasi-steady state, spherically symmetric mass conserva-tion equation for high mass transfer rates. This approach assumesthat the droplet is a single species, in this case species A, and thegas is a single species (almost entirely Ar) and negligibly solublein the droplet [23]. These assumptions are reasonable for Al2O3 vol-atilization in an Ar bath gas. D was estimated using the methods de-scribed in Law’s text [24], accounting for ambient temperature,pressure, and species concentration. D was calculated to be2.08 cm2 s�1 for the 10 atm studies. For the 3 atm studies, this num-ber increased to 7.4 cm2 s�1, not just because of the difference inthe pressure and temperature, but also because of the slight differ-ence in mole fractions of the dissociating species. D does not have tobe recalculated with different time steps since it is dependent onthe pressure and the ambient temperature, both of which do notchange. The buildup of species dissociated from the particle con-trols the mass fraction in the environment as described above.The surface mass fraction is assumed to be equal to the vapor pres-sure at the particle temperature:

yA;s ¼PAMAl2O3

PMaveð2Þ

Fig. 3. Predictions of the evaporation of particles for different input volatilizationtemperature for an ambient temperature near 3850 K. The ambient pressure is10 atm.

Fig. 4. The evaporation time of four particle sizes vs. the temperature differencefrom the volatilization temperature at 10 atm. The evaporation time of four particlesizes vs. the temperature difference from the volatilization temperature at 10 atm.The temperature at which particles would not significantly volatilize during theshock tube test time was measured to calculate the volatilization temperature.

796 P. Lynch et al. / Combustion and Flame 159 (2012) 793–801

where P is the ambient pressure, MAl2O3 is the alumina molecularweight, and Mave is the average molecular weight of the environ-ment, mostly Ar, but it does change slightly. The vapor pressureof species A is assumed to follow the Clapeyron equation with theparameters of the reactant species, Al2O3:

PA ¼ P exp �DHv

Ru

1Tp� 1

Tvol

� �� �ð3Þ

P is the pressure tested, either 3 or 10 atm, and DHv is 1860 kJ/mol[4]. DHv is temperature dependent. However, this temperaturedependence was ignored because there would be significant uncer-tainty associated with fitting this value along with the volatilizationtemperature. Additionally, the reference value for the heat of vola-tilization is as uncertain as the volatilization temperature itself, so1860 kJ/mol was assumed an acceptable value across the tempera-tures studied. Tvol is the volatilization temperature, which is iteratedin the calculation.

The ambient mass fraction of the volatilizing species yA,amb,increases as the mass of species A in the environment, mA,amb, in-creases. The mass of the remaining particle mp, decreases by thissame amount.

mpðtÞ ¼ mpð0Þ �mA;amb ð4Þ

The numerical model accounts for three modes of heat transferfor the particle, convection/conduction (with corrections for non-continuum effects) from the ambient gas, radiation to the wall,and the vaporization of the particle.

Several initial diameters are chosen to probe the diameter ef-fect, namely 50 nm, 500 nm, 2 lm, and 3 lm. The 50 nm particlesize was chosen as representative of the nano-alumina particles.Similarly, the 2 lm particles were representative of the micro-alu-mina particles. While the injection strategy and the passage of thenormal shocks should break up most agglomerates, any agglomer-ation present would increase the average particle size. At 2 lm, theagglomeration of a few particles would greatly increase the evap-oration time. The particle heat up time is approximately 5 ls forthe 50 nm particles and approximately 30 ls for the 2 lm parti-cles. This heat up time is small relative to either the shock tube testtime or the evaporation time of any particle tested. Although par-ticle motion (i.e. stopping of the particles in the stagnant gasbehind the reflected shock) is neglected, the particle heat up timesare still very representative of the actual heat up time after thepassage of the reflected shock.

This model was implemented in an explicit forward-differencetime marching scheme with the volatilization temperature as theiterant until either the diameter reached 2.5 nm or the test timewas exhausted. 2.5 nm was chosen for the minimum diameter inall cases as it represented a 95% reduction of the diameter of thesmallest particle size simulated. If the particle size reachedd = 2.5 nm before the test time, then the volatilization temperaturewas too low relative to the ambient temperature and a higher in-put volatilization was the next iterant. The particulars concerningthe implementation of the numerical scheme are detailed inAppendix B of [25].

Figure 3 shows the predicted decrease in the diameter of a50 nm particle as it evaporates, for four different iterations of thevolatilization temperature in a 3850 K, 10 atm ambient. For exam-ple, if the first temperature selected, (the first iterant) was a vola-tilization temperature of 4180 K, the evaporation rate would be toorapid and the particle would evaporate within 300 ls. For a guessof 4260 K, the particle would evaporate within 500 ls. As the vol-atilization temperature guess eventually reaches 4315 K, the evap-oration rate would be insufficient to evaporate the particle withinthe test time; however, it would be extremely close to being com-pletely volatilized within a few hundered microseconds. Only at

even higher iterant temperatures (in this case 4335 K), would par-ticles stop volatilizing within the test time. If the volatilizationtemperature were this temperature, particles subjected to theambient temperature at the cutoff would still be present afterthe test time. At ambient temperatures below the cutoff, particleswould continue to be present during the test time, but at temper-atures just beyond the cutoff, they would evaporate within the testtime. Interestingly, near the cutoff temperature, the evaporationprofile with time quickly becomes more shallow with relativelysmall changes in temperature. This profile indicates that the actualchoice of volatilization temperature in this regime between whichparticles stop evaporating within the test time and disappear with-in the test time is not particularly ambiguous, as this region of tem-peratures is as narrow as 25 K. Experimental uncertainty anduncertainty in the numerical scheme will certainly be higher thanthe uncertainty in this choice of volatilization temperature.

Figure 4 shows the calculated evaporation time of four differentparticle sizes with temperature for 10 atm ambient pressure. Theevaporation time was defined as the time required for the particleto reach 2.5 nm. Approximately 450 K below the volatilizationtemperature at 10 atm, there was very little evaporation even forthe smallest particles. The nano particles were able to evaporatewell within the shock tube test time for temperatures 300 K belowthe volatilization temperature and even faster for higher tempera-tures. Predictably, the micro-particle evaporation times were long-er, and, for instance, for the 3 lm particles, typically required

P. Lynch et al. / Combustion and Flame 159 (2012) 793–801 797

ambient temperatures beyond the volatilization temperature in or-der to evaporate during the test time. The 2 lm particles wouldevaporate faster, but still required times comparable to the testtime 100 K below the volatilization temperature.

3. Results and discussion

3.1. 10 atm volatilization experiments

Experiments conducted in 100% Ar at 10 atm with aluminanano-particles showed a high degree of repeatability. The trans-mitted light intensity for similar temperatures was very similarin duration and peak extinction levels. Figure 5 shows photodiodetraces through nano-alumina clouds at 10 atm for various temper-atures tested. In almost all cases, there were two brief deviations(approximately 5 ls in duration) from the background signalaround t = 0. These deviations, most often a drop in intensity, butsometimes a slight increase in intensity, were attributed to theschlieren effect from the large deinsity gradients in the incidentand reflected shocks as they pass the laser beams [26]. Aftert = 0, the reflected shock, as it passes through, stagnates the testgas. The stagnant test gas decelerates most particles, which driftinto the test section, heat up, and volatilize.

The photodiode data are by no means monotonic. The fluctua-tions in transmitted light intensity are real and cannot be attrib-uted either to photodiode noise or instability in the laser. Beforethe passage of the reflected shock, the noise level is small andthe intensity is relatively flat, and the photodiode was calibratedto be linear. After the passage of the reflected shock, variations inthe transmitted light intensity can be attributed to the turbulentnature of the particles within the cloud, the rich flow structure ofthe cloud observed in the shock tube, as well as some beam steer-ing. The high speed imaging in the acrylic test section show thateven though the bulk gas has stagnated after the passage of the re-flected shock, there is still significant particle movement. Particlesmove in and out of the test volume of the two passes of the laserbeam. In all cases, the bulk of the cloud is very near the center ofthe two passes of the laser beam.

Figure 5 also shows some of the predicted trends of the exper-iments. At low temperatures, for example the lowest temperatureshown here of 2848 K, the transmitted intensity dropped sharplyto transmissivities on the order of 0.2, and did not recover withinthe test time. However, as temperature increased, for example toaround 3600 K, not only did the peak drop in transmitted intensitydecrease (i.e. the minimum transmitted light intensity was closerto 1), the recovery in intensity began during the test time. Eventu-

Fig. 5. The transmitted light intensity through clouds of nano-alumina particles atexample ambient temperatures in which there was significant extinction for 10 atmpressure.

ally, as temperature was increased around 3800 K, reduction intransmitted intensity was small and the transmissivity appearedto recover within the test time. Here it was more difficult to assignqualitatively if there was extinction within the test time or not.However, often there were secondary drops in transmitted lightintensity just beyond the shock tube test time. These intensityreductions were likely particles which were entrained in the testsection by the reflected shock after it had again reflected off ofthe contact discontinuity. The second extinction criterion of lim-ited deviations in average transmissivity outside of the test timewas an important distinction and used to ensure that, when extinc-tion of the cloud was no longer observed, it was because the parti-cles were volatilizing and not simply moving out of the testvolume.

Figure 6 shows examples of the transmitted light intensity forclouds at higher temperatures. At temperatures beyond 3853 K,the transmitted light intensity was high and any peaks seen, par-ticularly those right after shock reflection, returned to transmittedintensity approaching 1 within the test time, and indeed oftenwithin 200 ls. While these photodiode traces qualitatively looksimilar to those at 3800 K, as in Fig. 5, the distinction often ap-peared if there was any extinction beyond the test time. The pho-todiode traces looked very similar for temperatures beyond4500 K.

The quantitative extinction criteria were applied to all tests atthe different temperatures and the results are shown in Table 1.The extinction criteria produced a sharp cutoff at 3860 K for10 atm. This cutoff temperature was then inserted into the evapo-ration model as described in Section 2.2 in order to model the vol-atilization temperature. The volatilization temperature at 10 atmwas calculated to be 4340 K.

The nearly 400 K difference between the experimentally ob-served cutoff temperature and the calculated volatilization tem-perature from the numerical model suggested tests were neededto confirm this large offset. According to the evaporation modeling,conditions which predict steeper trends for evaporation time withtemperature include larger particle sizes and lower pressure.Therefore tests were also conducted in these conditions.

Classically, a strong pressure dependence on evaporation timeis not predicted because the product of diffusivity and density ispressure independent. There is a very small effect of appliedpressure on the vapor pressure [27], however despite the increasedpressure to 10 atm from 1 atm, this effect would only account for a0.03% difference in the vapor pressure, well within the uncertainty.The evaporation model, however, indirectly allows for pressuredependence because it allows the accumulation of volatilized

Fig. 6. The transmitted light intensity through clouds of nano-alumina particles atexample ambient temperatures in which there was not significant extinction for10 atm pressure.

Table 1The extinction of the light through the particle cloud at different ambient temper-atures at 10 atm. The extinction criteria produced a sharp cutoff at 3860 K for 10 atmpressure. This cutoff was then modeled to be the result of a volatilization temperatureof 4340 K at 10 atm.

Temperature (K) Extinguishing laser light after test time

2848 Yes2993 Yes3324 Yes3479 Yes3599 Yes3786 Yes3848 Yes3876 No3980 No4274 No4353 No

798 P. Lynch et al. / Combustion and Flame 159 (2012) 793–801

species in the finite volume assumed by the modeling, which willhave a different quantity of Ar initially present in the same volumewith different pressures, leading to different ambient mass frac-tions with pressure. The finite volume into which alumina canfreely evaporate and diffuse is calculated from measurements ofthe average particle spacing relative to the average size. This aver-age spacing was calculated to be 84 particle diameters. This spac-ing may be weakly pressure dependent as the entrainment ofparticles into the free stream (one of the measured quantities inthis calculation) is not solely dominated by the settling time of par-ticles but also weakly on the test gas initial pressure, and otherpressure effects. All those measurements were conducted in6 atm pressure, intermediate to the 3 atm and 10 atm conditionssimulated. This limited volume causes the buildup of dissociatedproducts to slow the rate of evaporation due to the concentrationgradient between the surface and the environment. As equilibriumis reached, the particle ceases to evaporate. At lower pressure, themass fraction in the environment can more quickly equilibratewith the mass fraction at the surface. Thus at each temperature,for lower pressure, the evaporation rate is lower, and temperaturescloser to the volatilization temperature are needed to completelyevaporate a particle in the test time.

Figure 7 shows selected photodiode traces of the transmittedlight intensity through clouds of 2 lm micro-alumina particles atvarious temperatures for reflected shock pressures near 10 atm.As expected, significant extinction during the test time was presentat temperatures 3815 K and higher. The data were noisier than forthe nano-alumina particles. This higher noise level was attributedto two factors. First the size distribution of the micro-aluminaparticles undoubtedly lent itself to some larger particles. Because

Fig. 7. The transmitted light intensity through clouds of micro-alumina particles atexample ambient temperatures for 10 atm pressure.

of the strong diameter dependence on particle evaporation time,for the nano-particles, evaporation time differences between40 nm and 60 nm particles are relatively small compared to thedifference between 1 lm and 3 lm particles. Any agglomeratesthat are present, even after the passage of two shocks, will there-fore have an even greater effect. Additionally, since the mass in-serted into the injector was the same for nano-alumina andmicro-alumina particles, the number of particles in the free streamwas smaller by several orders of magnitude. Smaller numbers ofparticles should enhance variability of the particle clouds, by mak-ing the environment even less uniform.

Because temperatures tested were above the volatilization tem-perature so that they may properly evaporate within the shocktube test time, the evaporation time was fit to the curve predictedby the evaporation code for micro sized particles at the volatiliza-tion temperature calculated with the nano-alumina particles. Be-cause of the increased noise level, the evaporation time wasrelaxed to be the first time in which the transmitted light intensityrecovered to 95% and the average transmitted intensity beyondthat point had to be above 90%.

Figure 8 is the plot of these evaporation times vs. temperatureat 10 atm reflected shock pressure. There is some variability atsimilar temperatures, but, in general, the data fit reasonably wellto 2 lm particles with a volatilization temperature of 4340 K, thatwhich was calculated from the nano-alumina data. Because of thesignificant uncertainty in the particle distribution, there was no at-tempt to fit the volatilization temperature and particle size simul-taneously, however, as the measurements of the particle sizesuggest, the surface area average of the particle size is likely largerthan 2 lm, which would suggest that the volatilization tempera-ture of 4340 K could be slightly high on the order of 100 K butnot significantly higher. However, this small difference is likelywithin the uncertainty already present in the 4340 K calculation.

3.2. 3 atm volatilization experiments

Experiments at lower pressures were required because they re-sulted in smaller offsets between the volatilization temperatureand the observed temperature at which particles stop extinguish-ing light within the test time. The 3 atm nano-alumina transmittedintensity photodiode traces were by far the noisiest that were col-lected. The reason for this is unclear, however it has been observedthat at very high temperatures and particularly as pressuredecreases, the dynamics behind the reflected shock are less ideal,particularly due to increased thickness of the turbulent boundarylayer at lower pressure [20]. This could affect the clouds of

Fig. 8. A fit of the evaporation time of micro-alumina particles at 10 atm fordifferent ambient temperatures. A fit of the evaporation time of micro-aluminaparticles at 10 atm for different ambient temperatures. The data fit reasonably wellto a 4340 K volatilization temperature and a 2 lm particle size.

Fig. 10. Example transmitted light intensity through clouds of nano-aluminaparticles at ambient temperatures above 4050 K and at 3 atm pressure. Theseclouds do not extinguish laser light after the shock tube test time.

Table 2The extinction of the light through the particle cloud at different ambient temper-atures at 3 atm. The extinction criteria produced a sharp cutoff at 4050 K for 3 atmpressure. This cutoff was then modeled to be the result of a volatilization temperatureof 4260 K at 3 atm.

Temperature (K) Extinguishing laser light after test time

P. Lynch et al. / Combustion and Flame 159 (2012) 793–801 799

particles at low pressures. Figure 9 shows example transmissivitytraces for several temperatures at 3 atm. The 3 atm data did notfollow clear qualitative trends like were seen in the 10 atm datafor both the nano-alumina and micro-alumina data. The peak dropin transmitted light intensity changed unpredictably, and the timeat which the peak drop happened was not always consistent. Oftenthere were sharp drops in transmissivity which slowly recovered,not always within the test time, like those seen in the micro-alu-mina data, for instance like at 3831 K. There were however, alsoexperiments that showed a modest, late drop in transmissivitywhich never recovered. This phenomenon was exhibited, for in-stance in the 3164 K data. Even at higher temperatures, like inthe photodiode traces seen in Fig. 10, it was difficult to qualita-tively assign an extinction cutoff.

However, using the quantitative criteria, the results of whichare shown in Table 2, an extinction cutoff was assigned for the3 atm data, which was 4050 K. The photodiode signals for whichthe nano-alumina particles volatilized within the test time areshown in Fig. 10. When the evaporation model was used in orderto assign a volatilization temperature to this extinction cutoff,the temperature at 3 atm was 4260 K. Again, while the extinctioncutoff temperature was almost 200 K higher than at 10 atm, be-cause of the comparative steepness of the evaporation curve, thevolatilization temperature at 3 atm was lower than at 10 atm, asexpected.

3164 Yes3482 Yes3563 Yes3623 Yes3736 Yes3787 Yes3831 Yes3991 Yes4118 No4138 No4160 No4177 No4250 No4503 No4551 No

3.3. Error analysis of evaporation model

Even though intuitive trends result from the calculation of thevolatilization temperature, and fits of larger particles to the mod-el’s evaporation rates seem reasonable, there is still significantuncertainty associated with the volatilization temperature at thesetwo pressures, and it must be accounted for if those points are tobe used to extrapolate a volatilization temperature at 1 atm. A de-tailed error analysis was conducted on four possible sources oferror.

The first source was an uncertainty in ambient temperature atwhich the particles stopped volatilizing within the test time. Whileit is clear that there was some arbitrariness in the criteria that werechosen to implement the cutoff in extinction as defined previously,it was consistent, repeatable and produced a sharp well definedcutoff, especially for the 10 atm data. Even so, there were threesources of uncertainty in the ambient temperature calculation.The first was the uncertainty from calculation of the reflectedshock conditions from measurement of the incident shock velocity.This uncertainty is as low as 1% of the reflected shock temperature,

Fig. 9. Example transmitted light intensity through clouds of nano-aluminaparticles at ambient temperatures below 4050 K and at 3 atm pressure. Theseclouds extinguish laser light after the shock tube test time.

or about 40 K. The second was the uncertainty in the adjustment ofthe reflected shock temperature at a distance of 5 cm. This was ta-ken as the full value of the adjustment, or 20 K. The third uncer-tainty comes from the effect of temperature rise in the entirereflected shock region with time. This was estimated using Peter-sen and Hanson’s method [20]. Using the endwall pressure trans-ducer traces as well as the photodiode extinction traces, acharacteristic time in which to run this calculation was 0.5 ms aftershock reflection. Using this characteristic time, temperaturedependent temperature rises in the reflected shock region ofapproximately 75 K were obtained. Adding these three sources inquadrature, the uncertainty in ambient temperature was taken tobe 87 K.

The next source of error is the measurement of the spacing ofthe particles which defines the region into which products can vol-atilize. Based on a large number of imaging studies performed withthe acrylic test section, this spacing was calculated to be about 84particle diameters. Statistical uncertainty in this calculation was33% from the propogation of one standard deviation in the quanti-ties entering into the calculation, i.e. mass injected, percentage ofthe total intensity in the cloud, and the cloud extent. However, ifthe model is sensitive to spacing much larger than 33% higher, itcould be observed in the fixed mass fraction error analysis whichfollows. Upon the onset of the error analysis, it was thought thatthis assumption and number, upon which the evaporation modeldepends, would very strongly affect the evaporation/volatilization

Table 4Results and uncertainty analysis.

Pressure (atm) Volatilization temperature (K) Uncertainty (K)

10 4340 2173 4260 213

Table 5Extrapolation of the volatilization results to 1 atm.

Calculation Volatilizationtemperature (K)

Uncertainty(K)

Heat of dissociation(kJ/mol)

Best estimate 4189 200 2313Using reference DHv 4163 200 1860

800 P. Lynch et al. / Combustion and Flame 159 (2012) 793–801

rate. The sensitivity is quite low though. Furthermore, the mea-surement error appears much smaller than the statistical uncer-tainty. The extent of the cloud is clearly observable by imagingwith the acrylic section and uncertainties in the mass of particlesin the cloud are raised to the 1/3 power.

Mass diffusivity directly enters into the volatilization rate in Eq.(1) and could be a source of error as the calculation for each speciesis only known approximately. Additionally, it is unclear if theassumption that the vapor phase alumina decomposes (to its equi-librium concentration no less) immediately upon vaporization anddiffuses away is valid. It is true that there is no stable gas phase ofAl2O3, but the exact composition of the gas which diffuses from theparticle is unknown. To test this effect, the calculated mass diffu-sivity was increased and decreased by 25%.

Finally, as a check of the assumption that the buildup of prod-ucts of the dissociation of alumina in the environment eventuallystop the particle from evaporating further, different fixed environ-ment mass fractions were assumed. This test also serves as a test ofthe assumption of the uniform distribution. Fixing the mass frac-tion of the environment also affects the gradient of the mass frac-tion, which truly controls the evaporation rate. The fastest particleevaporation would occur if the mass fraction of dissociated speciesremained zero throughout. This mass fraction represents the extre-mely unlikely event that the particle spacing was severely underpredicted (unlikely as described above, but possible). In the secondtest, the mass fraction of the environment was fixed at the value atwhich one half of the mass (or 1/8 of the diameter) had evaporated.This fixed mass fraction in the environment initially slows theevaporation of the particle and is representative of what wouldhappen if gradient of the mass fraction was over-predicted andthe vaporization and especially diffusion away into a uniform dis-tribution was slower. The third fixed mass fraction was calculatedto be the slowest the particles could volatilize with a uniform massfraction, i.e. with a mass fraction equal to the value at which theentire mass of the particle had evaporated. This simulation repre-sents a severe over-prediction of the mass fraction gradient.

These four modifications were applied to the numerical scheme,and the volatilization temperature was recalculated. Table 3 showsthe error analysis for the conditions at 10 atm, the results weresimilar for the error analysis for the conditions at 3 atm. Uncer-tainty in the ambient temperature introduced an error of 3.5% forthe 10 atm conditions and about another 3.5% comes from particlespacing calculation. On the other hand, suprisingly the mass diffu-sivity calculation did not strongly affect the volatilization temper-ature measurement. This result is likely because of the overallassumption that any volitilized species diffuse out in a uniform dis-

Table 3Error analysis for conditions of nano-particles in 10 atm. The temperature at whichthe particles ceased extinguishing laser light during the test time was Tamb = 3860 K,and nominally produces a volatilization temperature of 4340 K.

Error source Error introduced % Volatilizationtemperature (K)

% Change

Ambient mass fraction, Tamb

3860 K +87 K +2% 4470 3.5%3860 K �87 K �2% 4225 3%

Particle spacing, S84 diameters +28 diameters +33% 4360 <1%84 diameters �28 diameters �33% 4210 3.5%

Mass diffusivity, D2.1 cm2/s +0.52 cm2/s +25% 4340 <1%2.1 cm2/s �0.52 cm2/s �25% 4340 <1%

Ambient mass fraction, yA,amb

yA,amb variable yA,amb = 0 – 5050 16%yA,amb variable yA,amb = 0.008 – 4290 1%yA,amb variable yA,amb = 0.017 – 4290 1%

tribution around the particle. Any increase in the rate of the vola-tilization is balanced by quicker accumulation of product speciesslowing the rate.

For both the 10 atm and 3 atm data, when the ambient massfraction was fixed to an intermediate value, the percent changein the recalculated volatilization temperature was small (always<2%). However, when the ambient mass fraction was fixed at zero,very large volatilization temperatures (relative to the ambient par-ticle temperature) were needed in order to prevent the particlesfrom volatilizing within the test time. These values are unrealistic;however, they confirm that the volatilization temperature at itsminimum, must be larger than the temperature at which particlesstop extinguishing within the shock tube.

Overall, uncertainty was added in quadrature, resulting in 5%for both data points. Table 4 shows the summary of the data anderror analysis.

3.4. Extrapolation to 1 atm volatilization temperature

Three atm was the low pressure limit for the experiments. At1 atm, for instance, the evaporation times would exceed the testtime for the smallest particles for temperatures of interest. Addi-tionally, as the data became noisier at low pressure conditions, thistrend should render unusable data. Two data points as shown inTable 4 are available to extrapolate the volatilization temperatureto 1 atm, though.

Using these two points and (3), a volatilization temperature of4189 K at 1 atm was calculated as shown in Table 5. The heat ofdissociation between these two points was 2313 kJ/mol. Addition-ally, a least squares fit can obtain the volatilization temperature at1 atm using Eq. (3) if a heat of volatilization is assumed. Using thereference value of 1860 kJ/mol [4], this least squares fit was per-formed and yielded a temperature of 4163 K. This fit is plotted inFig. 11. Both extrapolations carry uncertainties of at least 200 K.These values are high compared to the reference literature, butthe data fall within the range of the uncertainty for the JANNAF ref-erence numbers. The values are significantly larger than the valuein the CRC tables [11] and also significantly larger than 3200 K.This result lends credence to the values in the JANNAF tables andstrongly suggests that a lower alumina volatilization temperatureis not the limiting temperature in AlO temperature measurementsof burning aluminum micro-particles.

4. Conclusion

An experimental study of the volatilization temperature ofalumina particles was conducted in a shock tube for slightly ele-vated pressures by examining the extinction from a cloud of parti-cles at a non-resonant wavelength (532 nm). The volatilization

Fig. 11. Extrapolation of the volatilization results to 1 atm.

P. Lynch et al. / Combustion and Flame 159 (2012) 793–801 801

temperature was then modeled from this temperature at whichclouds stop extinguishing:

1. In nano-alumina particles, at 10 atm, there is a sharp cutoff at3860 K at which particles volatilize and stop extinguishingwithin the shock tube test time. This result corresponds to amodeled volatilization temperature of 4340 K at 10 atm.

2. In micro-alumina particles at 10 atm tested at higher tempera-tures, the evaporation time of the particles as measured fromthe transmitted light intensity nicely follows the trends of 2 lmparticles with a volatilization temperature of 4340 K at 10 atm.

3. In nano-alumina particles at 3 atm, there is a sharp cutoff at4050 K at which particles volatilize and stop extinguishingwithin the shock tube test time. This result corresponds to avolatilization temperature of 4260 K at 3 atm.

4. Extrapolating from these pressures, the best estimate for thevolatilization temperature at 1 atm from experimental datawas 4189 K with a heat of dissociation of 2313 kJ/mol. Usingreference values for the heat of dissociation (1860 kJ/mol) givesa 1 atm temperature of 4163 ± 200 K, certainly far higher than3200 K, reported in the CRC handbook.

5. Alumina volatilization is therefore not the temperature limitingprocess during micro-aluminum combustion.

Acknowledgments

This research was sponsored by the Defense Threat ReductionAgency under contracts HDTRA1-07-1-0011 and DAAE30-1-9-0080 (Program managers Drs. William Wilson and Suhithi Peiris).The helpful discussions with Dr. Irvin Glassman were greatlyappreciated. The translations of the early German work by JohnRudolphi were also appreciated. Thanks also go to James Hum,Laura Chen, and Mark Figge for technical assistance.

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