A flame propagating through an iron-dust mixture can propagate in two asymptotic regimes. When the characteristic time of heat transfer between particles is much smaller than the characteristic time of particle combustion, the flame propagates in the continuum regime where the heat released by reacting particles can be modelled as a space-averaged function. In contrast, when the characteristic time of heat transfer is much larger than the particle reaction time, the flame can no longer be treated as a continuum due to dominating effects associated with the discrete nature of the particle reaction. The discrete regime is characterized by weak dependence of the flame speed on the oxygen concentration compared to the continuum regime. The discrete regime is observed in flames propagating through an iron dust cloud within a gas mixture containing xenon, while the continuum regime is obtained when xenon is substituted with helium

Goroshin, Samuel

Higgins, Andrew J.

Tang, Francois-David

NASA Technical Reports Server

PROPAGATION REGIME OF IRON DUST FLAMES 
 
François-David Tang
1
, Samuel Goroshin
2
, Andrew J. Higgins
2
 
 
1
European Space Agency, ESTEC; Kaplerlaan 1, Noordwijk, The Netherlands 
2
McGill University, Department of Mechanical Engineering 
817 Sherbrooke St. West, Montreal, Quebec, Canada 
 
Keywords: Iron powder, Combustion, Reduced gravity  
 
Abstract 
 
A flame propagating through an iron-dust mixture can propagate in two asymptotic regimes.  
When the characteristic time of heat transfer between particles is much smaller than the 
characteristic time of particle combustion, the flame propagates in the continuum regime where 
the heat released by reacting particles can be modelled as a space-averaged function.  In contrast, 
when the characteristic time of heat transfer is much larger than the particle reaction time, the 
flame can no longer be treated as a continuum due to dominating effects associated with the 
discrete nature of the particle reaction. The discrete regime is characterized by weak dependence 
of the flame speed on the oxygen concentration compared to the continuum regime.  The discrete 
regime is observed in flames propagating through an iron dust cloud within a gas mixture 
containing xenon, while the continuum regime is obtained when xenon is substituted with 
helium. 
 
Introduction 
 
While the combustion of powdered metals is typically associated in solid-fueled rockets, metallic 
fuels have recently been suggested as a potential energy carrier for transport vehicles as a 
sustainable alternative to fossil fuels [1].  To exploit these applications, a fundamental 
understanding of the metallic dust flames is essential, but experimental results on fundamental 
flame parameters are scarce.  As a result, current models of laminar flames propagating in 
heterogeneous media are simply based on a continuum assumption, which underlines the fact 
that the interparticle spacing lp is much smaller than the flame width ld .  This assumption permits 
the function describing the heat release in the reaction zone to be described as a continuous 
function in space and the governing equations to be expressed as a set of partial differential 
equations  [2,3]. 
 
However, if the interparticle distance lp is on the same order of magnitude as the flame width ld, 
then the continuum fails to describe the propagation of the flame.  The flame exhibits so-called 
discrete characteristics where the propagation of the front is dominated by local ignition 
interactions between neighboring particles. The heat release function becomes dependent on the 
spatial distribution of the particles and the flame can no longer be described by the continuum 
theory [4,5].  The parameter quantifying the regime of propagation is the dimensionless 
combustion time defined as: 
   
   
  
,     (1) 
where    is the characteristic particle reaction time, α is the thermal diffusivity of the gas mixture 
and l is the interparticle spacing.  The discrete regime is realized when     , while the 
continuum is when for       [5]. 
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 In this work, the discrete regime is realized in an experiment where flames propagating through 
clouds of iron particulates are observed in low-thermal diffusivity, oxidizing environment, 
namely xenon-oxygen.  In contrast, the continuum regime is achieved in a helium-oxygen 
mixture, which is characterized by a high thermal diffusivity. The continuum and discrete 
regimes are differentiated using the response of the flame speed to variations of the oxygen 
concentration.  
 
Experimental Details 
 
The dust combustion experiment uses a flame in an open-ended tube methodology that allows 
observation of a constant-pressure laminar flame.  Experiments were performed onboard a 
reduced-gravity parabolic flight aircraft to minimize particle settling and buoyancy-induced 
convective flows.  The schematics of the apparatus are shown in Fig. 1.   
 
 
Figure 1: Schematic of the dust combustion experiment. The top left 
inset illustrates the design of the dust dispersion system and the 
bottom right inset the design of the first stage cooling and filtering 
systems. 
 
The powder dispersion unit (see top inset in Fig. 1) consists of a dust feeder and a disperser. The 
initially compacted dust is fed via a small syringe-type device.  As it is fed by the piston, the dust 
column is continuously dispersed via the impact of a transverse sonic gas jet produced by a 40-
100 m circular slot at the base of the conical dispersion chamber (see top inset in Fig. 1). The 
conical diffuser connecting the dust dispersion unit with the combustion tube provides expansion 
and laminarization of the initially highly turbulent flow containing the dispersed dust.  The 
combustion tube is a Pyrex glass tube with an internal diameter of 48 mm and 70 cm in length.  
The fuel suspension was ignited by an electrically heated, 100-m-diameter tungsten wire at the 
open end of the tube, with the flame propagating toward the closed end (dispersion system).    
 
The fuel concentration in the suspension is controlled by varying the piston speed via an 
electromechanical linear actuator. The fuel concentration in the suspension can be calculated 
from the feeding rate of the piston, the packing density of the powder and the flow rate of the 
dispersing gas. The mass concentrations of iron powder varied in a range of 900-1,200 g/m
3
. 
 
The exhaust from the combustion tube is passed through a series of cooling and filtering systems 
and ultimately discharged into the aircraft cabin to accommodate the absence of overboard vents. 
The combustion products were drawn into the inlet of the cooling and filtering system by a 
vacuum blower. A wide annular opening between the combustion tube and the filtering system 
158
(see Fig. 1, right bottom inset) ensures unobstructed access of the ambient air to maintain 
ambient pressure inside the combustion tube.  
 
The combustion rack installed onboard the airplane contains four replaceable combustion tube 
assemblies (see Fig. 2). Each assembly is comprised of a combustion tube integrated with an 
individual powder dispersion unit. Four tube assemblies are mounted horizontally parallel to 
each other on the combustion rack, providing an unobstructed view for the optical diagnostics. 
 
 
Figure 2: Photograph of the dust combustion apparatus installed on 
board parabolic flight aircraft. 
 
The propagation of the flame was recorded by a high-speed digital camera viewing the entire 
length of the combustion tube at 300 frames per second.  
 
The use of iron, that burns entirely in the condensed phase was motivated to ensure that the 
reaction occurred in the absence of the formation of vapors in the attempt to reflect the 
heterogeneous characteristics of the modeling.  Five different iron powders were used in this 
investigation and are designated A to D in the Table I.  Scanning electron microscope 
photographs of the iron powders are shown in Fig. 3. 
 
Table I: Characteristics of iron powders used. 
Powder  Particle shape Purity d10 (m) d32 (m) 
(a) Spherical 99.9 3.3 4.3 
(b) Spherical 99.5 7.0 9.6 
(c) Spherical 99.5 9.9 13.7 
(d) Spherical 99.9 26.8 44.7 
 
 
Figure 3: Scanning Electron Microscope (SEM) pictures of iron 
particles. 
159
 The experiments were performed using four separate gas mixtures containing helium or xenon at 
21% and 40% oxygen concentration.  The mixtures were supplied by a commercial gas supplier 
and were certified to be within an accuracy of 2%. 
 
Results 
 
The measured flame speeds from experiments performed in xenon and helium with 21% and 
40% oxygen concentration are shown in Fig. 4. The flame speeds were obtained from the 
analysis of the high-speed videos.  The error bar represents the standard deviation from 5 to 11 
repeated measurements performed with the same gas mixture.   
 
 
 
Figure 4: Flame speed measurements for iron powders A, B, C and 
D in He-O2 and Xe-O2 in 21% and 40% oxygen concentrations. 
  
The flame speed is consistently larger in mixtures containing 40% compared to 21% oxygen. 
However, the difference is more pronounced in mixtures containing helium, compared to 
mixtures containing xenon. 
 
Discussion 
 
The ratios between the flame speeds in 40% and 21% oxygen concentration are shown in Fig. 5 
for helium- and xenon-balanced mixtures and for the different particle sizes.  The ratios 
corresponding to measurements performed in xenon mixtures are consistently lower than those 
for helium mixtures for all particle sizes.  These measurements highlight the fact that flames 
propagating in xenon mixtures are less sensitive to variations of the oxygen concentration     
compared to flames in helium mixtures.  
 
Using the shrinking core model of particle combustion, the oxygen concentration     is related 
linearly to the particle combustion time            ) [6].  Hence, flame speeds measured in 
xenon mixtures are less sensitive to changes of the particle reaction time    compared to 
mixtures containing helium. 
160
  
 
 
Figure 5: Ratio of the flame speeds between 21% and 40% O2 in 
helium and xenon mixtures. 
 
The stronger dependence of the flame speed on the reaction time    in mixtures containing 
helium compared to mixtures balanced with xenon can be attributed to a transition of the 
propagation regime from continuum to discrete.  When substituting the balance inert gas from 
helium to xenon in 21% O2, the dimensionless combustion time    decreases from approximately 
3.4 (continuum) to 0.6 (discrete).  
 
Previous numerical work has shown that the discrete regime is characterized by a front speed 
that is independent of the reaction time    [7].  In other words, variations of the oxygen 
concentration do not affect the flame speed in the discrete regime. The flame speed ratio 
characteristic of the discrete regime reflects the insensitivity of the flame speed on the reaction 
time   : 
 
      
      
|
     
  .    (2) 
 
The distinctive relationship between the flame speed and the reaction time    in the discrete 
regime is in sharp contrast with the front speed predictions in a continuum. Using thermal theory, 
the flame speed   is expected to vary with the reaction time    as     √   ⁄ [8].  This behavior 
results in a ratio of the flame speeds             ⁄  : 
 
      
      
|
     
 √
       
       
 √
  
  
    .  (3) 
 
In the discrete regime, the fact that flames exhibit a different behavior to change of the oxygen 
concentration from the predictions of the thermal theory highlights the breakdown of the 
continuum assumption.  In the discrete regime, the heat release around particles becomes 
161
localized to the point that the propagation of the flame becomes limited by the heat diffusion 
between neighboring particles.  When the flame is controlled mainly by heat diffusion, the 
increase of the reaction rate of particles does not cause an increase of the flame speed.    
 
In contrast, in a continuum, the limiting mechanism is assumed to be the particle reaction rate.  
This assumption underlines the fact that the reaction rate is treated as continuous function in 
space, where particles form a dense cloud of particles characterized by an interparticle spacing 
much smaller than the flame width.   
 
Conclusion 
 
The regime of propagation was investigated by varying the transport properties of the gas 
mixture as a means to change the dimensionless combustion time. Reduced experiments were 
performed in xenon- and helium-balanced mixtures to observe discrete and continuum flames, 
respectively. It was found that flames propagating in xenon-balanced mixtures were less 
sensitive to the oxygen concentration than flames propagating in helium-balanced mixtures.  
This observation reflects the distinct behavior of the flame propagation between the discrete and 
the continuum regimes.  
 
Acknowledgement 
 
This work was supported under Canadian Space Agency contract 9F007-052073/001/ST. The 
authors would like to thank the Flight Research Laboratory of the National Research Council of 
Canada. 
 
References 
 
1. K. Kleiner, “Powdered Metal: The Fuel of the Future,” New Scientist, 2522 (2005), 34- 
2. S. Goroshin, M. Bidabadi, J.H.S. Lee, “Quenching Distance of Laminar Flame in 
Aluminum Dust Clouds,” Combustion and Flame, 105 (1996), 147-160. 
3. A.G. Merzhanov, E.N. Rumanov, “Physics of Reaction Waves,” Reviews of Modern 
Physics, 71 (1999), 1173-1211. 
4. J.M. Beck, V. Volpert, “Nonlinear Dynamics in a Simple Model of Solid Flame 
Microstructure,” Physica D, 182 (2003), 86-102. 
5. S. Goroshin, J.H.S. Lee, Y. Shoshin, “Effect of the Discrete Nature of Heat Sources on 
Flame Propagation in Particulate Suspensions,” Symposium (International) on 
Combustion, (27) 1998, 743-749. 
6. J.C. Yang. “Heterogeneous Combustion,” Environmental Implications of Combustion 
Processes, ed. I.K. Puri (Boca Raton, FL: CRC Press, 1993), 127-128. 
7. S. Goroshin, F.D. Tang, A.J. Higgins, “Reaction-diffusion fronts in media with spatially 
discrete sources,” Physical Review E, 84 (2011), 027301. 
8. L.P Yarin and G. Hetsroni, Combustion of Two-Phase Reactive Media (Berlin: Springer-
Verlag, 2004), 301. 
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Propagation Regime of Iron Dust Flames

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