Paper # 070DE-0104 Topic: Detonations, Explosions, and Supersonic Combustion 8 th U. S. National Combustion Meeting Organized by the Western States Section of the Combustion Institute and hosted by the University of Utah May 19-22, 2013 Heat Transfer Effects in Nano-Aluminum Combustion David Allen, Herman Krier,& Nick Glumac Department of Mechanical Engineering, University of Illinois Urbana-Champaign, 1206 W Green St. Urbana, IL 61801 Nano-aluminum combustion remains poorly understood, as evidenced by recent paradoxical measurement results. While nanoscale Al is often assumed to burn in the kinetic limit, optical temperature measurements of nano-aluminum particles combusting in a heterogeneous shock tube at pressures near 20 atm showed peak temperatures above 3000 K in ambient air at 1500 K. This temperature overshoot and the simultaneous burning times measurements greater than 100 μs cannot be described from an energy balance considering continuum heat transfer losses from the particle. A conservative estimate assuming all reaction energy is used for sensible heating of the aluminum particle requires complete combustion in less than 1 μs to reach peak temperatures of 3000 K suggesting deviation from continuum mechanics. Similar heat transfer effects are seen in laser induced incandescence (LII) experiments of various nano-particles. In the shock tube and LII experiments the particle Knudsen number is near unity and non-continuum heat transfer effects and slip conditions can be expected. Previous work by Igor Altman suggests a formula which predicts an upper limit on the energy accommodation coefficient (EAC) which characterizes the energy transfer between a gas particle and surface. A simple model considering surface combustion and an energy balance using various heat transfer loss mechanisms shows that an upper limit of 0.005 for the EAC predicted by Altman’s theory agrees well with experimental data. An EAC of 0.0035 produces a best fit of the thermal profile for varying nano-aluminum particle sizes and predicts the temperature overshoot at high pressures. The decrease in the EAC for nano-aluminum has significant implications in the application and modeling of nano-aluminum used in explosives and solid rocket motors where ideally the particle transfers energy to the surrounding atmosphere. In such cases of low EAC radiation plays a more significant role in particle heat transfer. 1. Introduction Nano-aluminum combustion is of interest because of its proven ability to increase the burn rate in propellants and its potential for use in enhancing explosives. Fine metal particles are known to be highly reactive. However, replacing micron sized aluminum particles with nano-aluminum in explosive applications has been met with contradictory results. In certain applications the use of nano-aluminum has been shown to increase the detonation velocity, while other studies have shown little effect [5]. The mechanism for nano-aluminum combustion is still not fully understood and is the subject of much debate [7,14,15]. For nano-scale particles in most environments the transition from continuum mechanics to the free molecular regime of particle and gas phase interaction occurs. This transition in particle interaction plays a potentially dominant role in the particle temperature and heat transfer characteristics, but has yet to be experimentally investigated in nano-aluminum combustion. A 20 nm aluminum particle is approximately 100x the size of a surrounding air molecule and Knudsen numbers greater than one are easily achievable at combustion temperatures and pressures. These effects are considered in laser induced incandescence experiments to determine particle size distributions of nano-particles in flows [8] and must also be considered when determining the transient thermal profile of a combusting nano-aluminum particle. Theoretical and experimental work performed by Altman suggests that at high particle and gas temperatures, nano- particles have very small energy accommodation coefficients and become conductively isolated from the ambient gas [1, 2]. Radiation consequently becomes a more significant pathway for heat transfer in the low accommodation coefficient regime. The experimental work 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 estimate [2]. 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
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Paper # 070DE-0104 Topic: Detonations, Explosions, and Supersonic Combustion
8th
U. S. National Combustion Meeting
Organized by the Western States Section of the Combustion Institute
and hosted by the University of Utah
May 19-22, 2013
Heat Transfer Effects in Nano-Aluminum Combustion
David Allen, Herman Krier,& Nick Glumac
Department of Mechanical Engineering, University of Illinois Urbana-Champaign, 1206 W Green
St. Urbana, IL 61801
Nano-aluminum combustion remains poorly understood, as evidenced by recent paradoxical
measurement results. While nanoscale Al is often assumed to burn in the kinetic limit, optical temperature
measurements of nano-aluminum particles combusting in a heterogeneous shock tube at pressures near 20 atm
showed peak temperatures above 3000 K in ambient air at 1500 K. This temperature overshoot and the
simultaneous burning times measurements greater than 100 μs cannot be described from an energy balance
considering continuum heat transfer losses from the particle. A conservative estimate assuming all reaction energy
is used for sensible heating of the aluminum particle requires complete combustion in less than 1 μs to reach peak
temperatures of 3000 K suggesting deviation from continuum mechanics. Similar heat transfer effects are seen in
laser induced incandescence (LII) experiments of various nano-particles. In the shock tube and LII experiments
the particle Knudsen number is near unity and non-continuum heat transfer effects and slip conditions can be
expected. Previous work by Igor Altman suggests a formula which predicts an upper limit on the energy
accommodation coefficient (EAC) which characterizes the energy transfer between a gas particle and surface. A
simple model considering surface combustion and an energy balance using various heat transfer loss mechanisms
shows that an upper limit of 0.005 for the EAC predicted by Altman’s theory agrees well with experimental data.
An EAC of 0.0035 produces a best fit of the thermal profile for varying nano-aluminum particle sizes and predicts
the temperature overshoot at high pressures. The decrease in the EAC for nano-aluminum has significant
implications in the application and modeling of nano-aluminum used in explosives and solid rocket motors where
ideally the particle transfers energy to the surrounding atmosphere. In such cases of low EAC radiation plays a
more significant role in particle heat transfer.
1. Introduction
Nano-aluminum combustion is of interest because of its proven ability to increase the burn rate in propellants and its
potential for use in enhancing explosives. Fine metal particles are known to be highly reactive. However, replacing
micron sized aluminum particles with nano-aluminum in explosive applications has been met with contradictory results.
In certain applications the use of nano-aluminum has been shown to increase the detonation velocity, while other studies
have shown little effect [5]. The mechanism for nano-aluminum combustion is still not fully understood and is the
subject of much debate [7,14,15].
For nano-scale particles in most environments the transition from continuum mechanics to the free molecular regime
of particle and gas phase interaction occurs. This transition in particle interaction plays a potentially dominant role in the
particle temperature and heat transfer characteristics, but has yet to be experimentally investigated in nano-aluminum
combustion. A 20 nm aluminum particle is approximately 100x the size of a surrounding air molecule and Knudsen
numbers greater than one are easily achievable at combustion temperatures and pressures. These effects are considered in
laser induced incandescence experiments to determine particle size distributions of nano-particles in flows [8] and must
also be considered when determining the transient thermal profile of a combusting nano-aluminum particle.
Theoretical and experimental work performed by Altman suggests that at high particle and gas temperatures, nano-
particles have very small energy accommodation coefficients and become conductively isolated from the ambient gas [1,
2]. Radiation consequently becomes a more significant pathway for heat transfer in the low accommodation coefficient
regime. The experimental work 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 estimate [2]. 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
2
collision with gas molecules becomes inefficient, leading to particle temperatures much higher than those expected using
continuum regime expressions.
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 [8]. 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 [12]. 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 tests times near 2 μs. Low temperatures were used for this study to test nano-aluminum combustion
which has been shown to ignite at temperatures below 2000 K [3]. The combustion of the nano-aluminum 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 diameter. A converging duel 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. Figure 1 shows an example of the pressure transducer traces which give very accurate time of
arrival measurements. The ambient temperature and pressure of the gases trailing the incident and reflected shock are
calculated with the Gordon-McBride equilibrium code [13] 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.
Figure 1 Example piezoelectric pressure transducer signals used as time of arrival measurements to calculate the
shock velocity.
3
A schematic of the shock tube operation with radial injection and the end section with fiber optic view ports is
shown in Figure 2. 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 previous publication
[3]. 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 instantaneously behind the reflected shock. For
this reason particle motion behind the reflected shock is neglected.
Figure 2 Schematic of shock tube test section with fiber optic access
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 18 nm particles were not characterized because the resolution required 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 18 nm particle distribution to be significantly smaller than the other
sample distributions even though an accurate average could not be quantified.