Journal of Loss Prevention in the Process Industries 43 (2016) 138e146
Contents lists available at ScienceDirect
Journal of Loss Prevention in the Process Industries
journal homepage: www.elsevier.com/locate/jlp
Modeling quenching distance and flame propagation speed through
an iron dust cloud with spatially random distribution of particles
Mehdi Bidabadi a, Mohammad Mohebbi a, Alireza Khoeini Poorfar a, *, Simone Hochgreb b,
Cheng-Xian Lin c, Saeed Amrollahy Biouki a, Mohammadhadi Hajilou a
a
b
c
Combustion Research Laboratory, School of Mechanical Engineering, Iran University of Science and Technology (IUST), Narmak, 16846-13114, Tehran, Iran
Department of Engineering, University of Cambridge, Trumpington Street, Cambridge, CB2 1PZ, United Kingdom
Department of Mechanical and Materials Engineering, 10555 W. Flagler Street, EC 3445, Florida International University, Miami, FL 33174, USA
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 19 October 2015
Received in revised form
4 March 2016
Accepted 18 May 2016
Available online 20 May 2016
In this research combustion of iron dust particles in a medium with spatially discrete sources distributed
in a random way has been studied using a numerical approach. A new thermal model is generated to
estimate flame propagation speed and quenching distance in a quiescent reaction medium. The flame
propagation speed is studied as a function of iron dust concentration and particle diameter. The predicted propagation speeds as a function of these parameters are shown to agree well with experimental
measurements. In addition, the minimum ignition energy has also been investigated as a function of
equivalence ratio and particle diameter. The quenching distance has been studied as a function of particle
diameter and validated by the experiment. Considering random distribution of particles, the obtained
results provide more realistic and reasonable predictions of the combustion physics compared to the
results of the uniform distribution of particles.
© 2016 Elsevier Ltd. All rights reserved.
Keywords:
Flame propagating speed
Quenching distance
Iron
Random particle distribution
Heterogeneous combustion
1. Introduction
Dust explosions are a recognized threat to humans and property
for the last 150 years (Eckhoff, 2003). Many combustible dusts
allow a flame to propagate through the fuel particles if dispersed as
a cloud in air and ignited, in a manner similar to (though not
identical to) the propagation of flames in premixed fuel oxidant
gases (Proust, 2006). Such dusts include common foodstuffs like
sugar flour, cocoa, synthetic materials such as plastics, chemicals
and pharmaceuticals, metals such as aluminum and magnesium,
and traditional fuels such as coal and wood (Abbasi and Abbasi,
2007).
One of the earliest recorded and the most serious of the accidents triggered by dust explosion occurred at Leiden, the
Netherlands, on 12 January 1807 (Abbasi and Abbasi, 2007). Similar
disasters induced by metal dust occurred in 2011 in which three
iron dust flash fires occurred over a period of five months and killed
five workers at the Hoeganaes Corp. facility in Gallatin, Tennessee.
These three events are examples of hazard identification and
* Corresponding author.
E-mail address: Alirezapoorfar@iust.ac.ir (A.K. Poorfar).
http://dx.doi.org/10.1016/j.jlp.2016.05.018
0950-4230/© 2016 Elsevier Ltd. All rights reserved.
general drift in the management of safety barriers. Most of these
accidents occurred during maintenance activities. They could have
been prevented if the risk status of the system had been known. A
comprehensive review of dust explosions cases and causes was
presented by Abbasi and Abbasi (2007). Accidental dust explosions
are highly undesirable in any plant, yet an explosion hazard always
exists wherever dusts are produced, stored or processed, whenever
a threshold quantity of powdered flammable material is present in
the air. With the advancement of powder technologies for materials
processing, and the increase of powder handling processes, hazard
assessment and the establishment of preventive methods for dust
explosions have become more important from the view point of
industrial loss prevention. Therefore, a correct understanding of the
combustion mechanism is necessary in order to minimize the
probability of occurrence of such events in the future.
The combustion of metallic particles used in a variety of industrial applications is a highly exothermic event. Basic mechanisms of combustion of such two-phase mixtures are not well
understood because of two major problems facing the research in
combustion of dust particles (Hanai et al., 2000). The first is the
complex nature of processes involving the physical and chemical
properties of the fuel. The second relates to the size, shape and
spatial distribution of the particles. Iron is regarded as a non-
M. Bidabadi et al. / Journal of Loss Prevention in the Process Industries 43 (2016) 138e146
volatile metallic fuel, and the oxidation process takes place as a
heterogeneous surface reaction. The major characteristic feature of
iron combustion is that it burns heterogeneously in air: the
oxidation reaction occurs at the surface of iron particle, and no
flame is observed in the gaseous oxidizer phase. Iron particles do
not evaporate during the combustion process, and the combustion
product, iron oxide, remains in the condensed phase.
Sun et al. (1990), Sun et al. (1998) experimentally examined the
combustion zone propagating through an iron particle cloud and
the process of iron particle combustion. They have demonstrated
that the burning time of an iron particle is proportional to the nondimensional diameter when its diameter is small; as the iron particle diameter becomes larger, the burning time increases with a
power of the non-dimensional diameter. Sun et al. (2006) experimentally studied the concentration and velocity profiles of iron
particles across up- and downward flame propagation in the vicinity of the combustion zone. Bidabadi et al. (2010) proposed a
mathematical model based on utilizing the Lagrangian equation of
motion and the effective thermophoretic, gravitational and buoyancy forces acting on the particles in order to represent the velocity
profile of the micro-iron dust particles. Bidabadi and Mafi (2012,
2013), theoretically investigated the evolution in combustion
temperature and burning time of a single iron particle in air, and
proposed an analytical model that agreed with the experimental
findings. Beach et al. (2007) investigated the combustion of iron
nanoparticles as a potential alternative fuel, in which the burning
time of iron particles was calculated for both spherical and disc
shaped iron particles using the heat balance and chemical kinetic
theories.
There are two general approaches to model dust combustion:
the continuous or macroscopic approach and the discrete or
microscopic approach. From the microscopic viewpoint, the propagation of the flame front is inherently unsteady, as it migrates
from particle to particle (Mukasyan et al., 1996; Rogachev et al.,
1994). The spatial distribution of particles strongly influences the
flame propagation (Tang et al., 2009a,b). In contrast, in the traditional continuous or macroscopic approach to model particles in a
gaseous suspension, the discrete nature of the heat sources is
averaged to yield a mean propagation speed. Continuous models of
dust combustion cannot usually capture the lean flammability limit
concentration or the threshold particle diameter, dust concentration and heat release. Indeed, it can be demonstrated that the
flammability limit depends on spatial distribution of particles
(Rashkovskiy et al., 2010).
A new thermal model has been generated to estimate the flame
propagation speed for micron-sized iron particles under various
dust concentrations and sizes in air. This discrete heat source
method provides a dust combustion model, from ignition process
to the final state, including steady flame propagation, flame
quenching and explosion.
In the current research paper, the combustion of iron particles
distributed uniformly in space is studied. As a further improvement
to the model, a random distribution of particles is used in the
governing equations to predict the flame features, such as; flame
propagation speed, minimum ignition energy, and quenching distance. The model starts by considering single particle combustion
to obtain a space-time temperature distribution. The ensemble
reacting front in the suspended dust combustion is then considered
using the superposition principle to include the effects of surrounding particles. All the burned and burning particles are
considered as heat sources, and the channel walls are assumed to
behave as heat sinks. Finally, the flame propagation speed and
quenching distance in the narrow channel are determined.
139
2. Discrete thermal model
The combustion of dust clouds is a complex process, involving
particle heating, evaporation, intermixing with oxidizer, ignition,
burning and quenching of particles. Particle size and dust concentration and distribution of the particles clearly play very important
roles. Reaction-diffusion phenomena have been modeled extensively in homogeneous media where the reactants are distributed
continuously in space. In a homogeneous system, the heat source
term does not depend on spatial coordinates and a solution can be
obtained by solving a set of scalar, ordinary differential equations.
However, in heterogeneous media, the reactants form a separate
phase within a diffusive medium causing the reaction to occur
locally around the boundaries or inside the sources. Unlike homogeneous media, the reaction is localized at the position of the
heterogeneities and the heat source term depends explicitly on the
coordinates of the reacting sources in the domain (Tang et al.,
2009a,b).
2.1. Uniform distribution
In the uniform distribution approach, dust particles are assumed
to be uniformly dispersed in air as shown schematically in Fig. 1.
The ignition system provides the minimum necessary energy to
the dust cloud, raising the temperature of some particles to the
ignition temperature. As these particles start to burn, they act as a
heat source and cause the temperature of the surrounding region to
rise. The temperature rise in the other particles is calculated as the
linear superposition of thermal effects from the burned and
burning particles. Particle ignition is assumed to take place once the
particle reaches a minimum temperature Tig ¼ 850 K (Tang et al.,
2009a,b), and the combustion process propagates to other particles. The mixture is assumed to be stagnant, so that the temperature increase of particles in the preheated zone is assumed to be an
exclusive result of conduction heat transfer through the gaseous
medium (Bidabadi et al., 2013).
The thermal model generated in this study for the uniform
particle distribution model is based on heterogeneous combustion
in three-dimensions. The model relies on the following
assumptions:
1. Each particle is spherical in shape, and the associated flame
diameter remains constant and equal to the particle diameter
(Sun et al., 1990).
2. No oxide layer surrounds the iron particles.
3. The thermal properties of the medium and particles are independent of temperature.
Fig. 1. Spatial distribution of particle in a uniform dust cloud: layer n 1 represents
(burned particles), layer n (burning particles), and layer n þ 1 (preheating particles).
140
M. Bidabadi et al. / Journal of Loss Prevention in the Process Industries 43 (2016) 138e146
4. The Biot number for the burning iron particles is negligible, so
particles have a single temperature (Bidabadi and Mafi, 2012).
5. There is an equal and constant spacing between the particles in
the uniform model.
6. The reaction of a particle proceeds at a fixed rate, releasing a
proportional rate of energy.
7. The micron sized iron particle is assumed to burn in a diffusioncontrolled regime (Bidabadi and Mafi, 2012, 2013), corresponding to infinitely fast reaction rate relatively to diffusion.
The combustion process is represented by a one-step irreversible reaction form as:
nF F þ nO2 O2 /nP P
(1)
where F, O2 and P denote fuel, oxygen and product, respectively,
and the quantities nF, nO2 , and nP denote the respective stoichiometric coefficients. The stoichiometric chemical reaction equation
between Iron and Oxygen is defined as follows:
3Fe þ 2O2 /Fe3 O4
(2)
The burning time of a single iron particle in a diffusioncontrolled regime (t), is explained by Glassman and Yetter (2008)
and can be evaluated from the following expression:
t¼
rp dp;0 2
8r∞ Do2 ;∞ ln 1 þ nYo2 ;∞
(3)
where all variables are defined in the nomenclature section. The
heat transfer in single-particle combustion, and the temperature
distribution throughout the domain is modeled as a purely
conductive process in spherical coordinates, for the temperature
rise Ta ¼ T T∞ relative to the ambient temperature T∞:
1 v 2 vTa ðr; tÞ 1 vTa ðr; tÞ
r
¼
vr
a vt
r 2 vr
(4)
where r is the radial distance from the origin of the coordinate
system, t is time, and a is the gas phase diffusivity. The boundary
and initial conditions for the equation above are:
kp A
v
Ta ðr; tÞ ¼ q_ H ðt tÞ;
vr
at r ¼ rp ;
(6)
The solution to equation (4) for temperature rise was obtained
through the whole domain by Bidabadi et al. (2013) as:
Ta ðr; tÞ ¼ Tf T∞
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
r rp
4erfc
r
4at
r
2
p
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2ffi3
r rp 5
Hðt tÞerfc
4aðt tÞ
(8)
Ta is the space-time distribution of temperature around a single
burning particle and beyond, Ts is the total effect of burning and
burned particles which is indicative of the temperature of medium
fluid around a particle in the preheated zone and r is the radial
distance, rp is particle radius, t is time, t is the burning time and Erfc
is the complementary error function. The solution for any point in
the domain is assumed to be given by the linear superposition of
the solutions for all burning and burned particles which is presented in equation (8).
The spacing between the target particle and each particle placed
at i, j, k is presented by:
ri;j;k ¼ L
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
i2 þ j2 þ k2
(9)
where L is the spacing between two adjacent layers and determined from the mass dust concentration cd:
L¼
pd3p rp
!1=3
(10)
6Cd
The resulting flame propagation speed is defined as the ratio of
the space between two adjacent layers to the difference of their
ignition times in the discrete domain (Goroshin et al., 1998).
S ¼ L tig;nþ1 tig;n
(11)
The ignition time of a single particle in a layer is assumed to be
representative of its layer ignition time. Every experimental apparatus in dust combustion uses an igniter. To study the effect of this
component, the energy release is assumed to be sudden and it is
presented by Dirac delta function in the present paper.
The igniter’s distance to the nearest layer is assumed to be L and
the energy release occurs in a plane parallel to layers. The 1D energy equation for the igniter presented in Cartesian coordinates is
also given by the heat equation:
1 vTa;ig ðx; tÞ
¼
a
vt
vx2
Ta;ig ¼ T T∞
where q_ is the rate of heat release of a single particle during the
burning time, and H is the Heaviside function. The rate of heat
release is assumed to behave as (Hanai et al., 2000):
Ta ri;j;k ; tig;i
i¼1 j¼1 k¼1
(5)
q_ ¼ AkP Tf T∞ rp1
n X
n X
n
X
v2 Ta;ig ðx; tÞ
Ta ð∞; tÞ ¼ 0;
Ta ðr; 0Þ ¼ 0;
Ts ¼
The boundary conditions of this equation are:
Ta;ig ðx; 0Þ ¼ 0
k
v
1
T ðx; tÞ ¼ Q dðtÞ
vr a;ig
2
at x ¼ 0
(13)
where x is the distance of a particle in layer of n from the igniter’s
origin, equal to x ¼ nL and Q is the total energy released from
igniter and considered to be the minimum energy that needed to
ignite first layer and d(t) is the Dirac delta function.
The solution to Eq. (12) yields:
Ta;ig ðx; tÞ ¼
(7)
(12)
2
Qa 1
x
pffiffiffiffiffiffiffiffi exp
k
4at
pat
(14)
Equation (14) is assumed as an initial condition for the calculation of flame features, such as; flame propagation speed and
quenching distance.
M. Bidabadi et al. / Journal of Loss Prevention in the Process Industries 43 (2016) 138e146
preheating of the layers is influenced by burning of the preceding
layers, in addition to the ignition system.
2.2. Random distribution
The model discussed in the previous section is limited to a
system with particles distributed uniformly and statically in a
reacting medium. In reality, dust particles may not be distributed
regularly in space, so that a random placement with a given mean
distance can be more realistic.
Therefore, in order to create a reaction media with randomly
distributed particles, a number of nodes Ne uniformly distributed
within the medium is considered. Each empty node shows the
location where a particle can be placed. The particles in the model
are randomly distributed, generating a dust cloud with N particles.
The domain size is constant and equal to the one in the uniform
distribution model. The variable b defines the fraction of filled
locations:
b¼
N
Ne
(15)
For uniform distribution of particles, b ¼ 1, and for random
distribution, b < 1.
In order to maintain the same overall mass concentration as in
the uniform distribution model, a modified distance between two
adjacent layers, Lr, is defined as:
Lr ¼
bpd3p rp
!1=3
6Cd
(16)
so that the total volume is (NeL3r ) and the total particle mass is
(NrpVp), and therefore the total mass concentration per unit volume
is maintained. The random model employs the same governing
equations used in the case of uniformly distributed particles.
An algorithm illustrating how the ignition times are obtained is
shown in Fig. 2. Following the energy release by the ignition system, the temperature of the first layer at the considered location is
calculated. When the temperature of the particles in the first layer
reaches the ignition temperature, it is recorded as the ignition time
of the first layer, and the calculations are continued to find the
ignition times of the other layers. Beyond the first layer (n > 1),
Fig. 2. Flowchart for calculating the ignition time of iron particles.
141
2.3. Quenching distance
The analysis of flame propagation or extinction in narrow
channels can take into consideration the heat loss to the walls. At
first, combustion of single particle is studied to obtain a space-time
temperature distribution. The generated heat diffuses to the preheat zone through conduction. Based on the superposition principle, the space-time temperature distribution of particles, as heat
sources, and the heat loss to the walls, as heat sinks, are the two
parameters that affect the temperature of the preheat zone. The
particles ignite when their temperature reach the ignition point.
The flame propagates in a narrow channel with infinite length and
constant width. If the flame quenches in the channel, the channel
width is defined as equal to/or less than the quenching distance.
The burned and burning particles are heat sources. In this
model, the particles are structurally placed within the spacing
shown in Fig. 1. The spacing between two adjacent layers is calculated by Eq. (10). Because of symmetry, a single particle of a layer
can be representative of the whole layer to determine the ignition
time of all the particles of that layer. This particle is assumed to be
positioned at the origin of the local coordinate system.
The flame propagates through the layers and ignites them one
by one, and their temperature is represented as
Tsource; p ¼
n X
n X
n
X
T ri;j;k ; tig;i
(17)
i¼1 j¼1 k¼1
where the ignition time of layer i is indicated as tig,i, and the local
temperature defines whether the particle has ignited at the given
temperature.
2.3.1. Heat sink
The present model estimates the quenching distance of a specific mixture by means of two parameters: dust concentration and
channel width. In this model, the walls play the role of heat sinks, as
described in Fig. 3. The heat transfer to walls by the thermal conductivity of the mixture is considered to be one-dimensional and
perpendicular to wall surface. A layer in the preheat zone is
considered as a lumped capacitance mass with uniform temperature. The heat loss causes the reduction in the temperature of the
particles, and all the particles in one layer are ignited at the same
time. Walls are at temperature Tw, the lumped capacitance average
temperature of layer is Tlayer and the channel width is D. The rate of
heat loss to the walls of the channel is obtained from the work done
by Bidabadi (1996).
Fig. 3. Schematic of lumped capacitance assumption for layers and one-dimensional
heat transfer to walls. The quenching distance is obtained for a parallel flat plates
configuration.
142
q_ loss ¼
M. Bidabadi et al. / Journal of Loss Prevention in the Process Industries 43 (2016) 138e146
2kA Tlayer Tw
Table 1
Thermo-physical properties of iron particles and air used in calculations.
(18)
D=2
The total heat loss of one layer in the preheat zone, from time
zero to time tr is:
Ztr
Qloss ¼
q_ loss dt
(19)
0
Using the lumped capacitance assumption, the temperature
reduction of that layer is expressed as Tsink ¼ rQCloss
.
pV
The temperature reduction over a time tr becomes:
Tsink ¼
4k
rCp D2
Ztr Tlayer Tw dt
(20)
0
2.3.2. Sink and sources superposition
Because the heat equation is linear in temperature, it is again
possible to calculate the total effect in the preheat zone as the
algebraic sum of the temperatures of all the heat sinks and sources.
Tlayer ¼ Tsource Tsink
Tlayer ¼
n X
n X
n
X
T ri;j;k ; tig;i i¼1 j¼1 k¼1
(21)
4k
rCp D2
Ztr Tlayer Tw dt
0
(22)
The present study uses an iterative method to obtain and
calculate the integral part in Eq. (22). When the temperature of the
target particle of layer n þ 1 in the preheat zone reaches the ignition temperature, this layer starts to ignite and burn. The calculations assume the values of atmospheric pressure of P ¼ 101 kpa,
initial ambient temperature of T∞ ¼ 300 K and the adiabatic flame
temperature of Tf ¼ 1990 K (Tang et al., 2009a,b). Iron dust flames
were studied experimentally in the context of laminar flames
propagating in suspensions of iron particulates by Mamen (2006)
and Tang et al. (2009a,b). Their experiments were performed in a
reduced-gravity environment onboard a parabolic flight aircraft to
minimize particle settling and buoyancy-induced convective flows
that cause flame disruptions. The experiment consisted of producing a suspension of iron particulates inside a glass tube at the
initial atmospheric pressure and ambient temperature and initiating a propagating flame at the open-end of the tube. Quenching
plate assemblies forming rectangular channels with variable
widths were installed inside the tube as depicted in figure. Pass and
quench events across the channel were used to find the quenching
distance. Flame propagation was recorded by a high-speed digital
camera. The iron dusts used by (Tang et al., 2009a,b) are (Alpha
Aesar, Atlantic Equipment Engineers, Inc.), were characterized using the Mie scattering technique with a Malvern Mastersizer 2000E
system; the arithmetic mean particle size of the powders used, are
given in Table 1.
3. Results and discussion
Fig. 4 shows the variation of the mean flame propagation speed
as a function of dust concentration for iron particles of 5 mm
diameter, for cases where iron particles are uniformly or randomly
distributed in reaction media. Each realization was assigned a
Value
Particle properties
Cp
447
kp
80.2
rp
7860
1990
Tf
Tig
850
n
0.2846
Air properties
Do2 ;∞
22.5 106
0.233
Yo2 ;∞
r∞
1.1614
T∞
300
Unit
Ref.
J/kg K
W/m K
kg/m3
K
K
e
Incropera and DeWitt (2002)
Incropera and DeWitt (2002)
Incropera and DeWitt (2002)
Incropera and DeWitt (2002)
Tang et al. (2009a,b)
Bidabadi and Mafi (2013)
m2/s
e
kg/m3
K
Incropera and DeWitt (2002)
Bidabadi and Mafi (2013)
Incropera and DeWitt (2002)
Assumed
different random distribution of particles, containing the same
overall concentration and the total number of particles.
According to Fig. 4, under uniform distribution, increasing the
dust concentration results in an approximately linear increase in
flame propagation speed. The flame speed under random distribution using a specific dust concentration depends on the particular distribution of particles. The flame speed increases with dust
concentration.
The variation in the fluctuation in flame speed values is seen to
increase with the value of b, which characterizes the level of nonuniformity. The results are compared with the experimental work
of Sun et al. (1998). The model results for both uniform and random
distribution show good agreement with the published experimental data, regardless of the value of b. The simulations slightly
overestimate the flame propagation speed in general, but deviate
from the experimental results at low concentrations.
The role of particle diameter on the flame propagation speed is
shown in Fig. 5, for three different diameters, as a function of dust
concentration. The increase in particle diameter leads to a decrease
in flame velocity and a decrease in the relative fluctuation in the
simulations. This is due to the fact that larger particles require
much more energy to be ignited as compared to smaller ones, and
that the inter-particle distance of larger particles is lower than that
of smaller particles.
Fig. 6 illustrates the behavior of flame speed as function of
particle diameter for a particular overall equivalence ratio. The results for uniform and random distributions in the current research
paper are compared with the experimental data reported by Tang
et al. (2009a,b) for a fuel-rich iron/air suspension with equivalence ratio f ¼ 1.43e1.90 with fuel particles having specific surface
area, ranging from 0.013 to 0.175 (m2/g) in a reduced-gravity
environment. The results for the uniform and individual realizations of the random distribution model are shown as a function particle diameter. Clearly the results for each realization
depends on the spatial distribution of particles. Similarly to Figs. 5
and 6 shows that an increase in particle diameter leads to a lower
flame speed. This is a result of the fact that larger particles take
longer to reach the specified ignition temperature. The obtained
results from the present model are in very good agreement with the
experimental findings (Tang et al., 2009a,b).
Fig. 7 shows how the minimum ignition energy increases nearly
linearly as a function as a function of particle diameter for a mixture
with a stoichiometric dust concentration. As the particle size increases, the assumed distance between neighboring particles (L)
will rise according to Eq. (15) and the minimum ignition energy
required to ignite the mixture should increase nearly linearly.
The variation of the MIE for a layer in a uniformly distributed
medium is illustrated in Fig. 8 as a function of the equivalence ratio
for a particle diameter of 10 mm. The minimum ignition energy
M. Bidabadi et al. / Journal of Loss Prevention in the Process Industries 43 (2016) 138e146
143
Fig. 4. Flame propagation speed as a function of iron dust concentration for the uniform and random distribution of particles for dp ¼ 5 mm, T∞ ¼ 300 K, P ¼ 101 kpa and different
values of b: a) b ¼ 0.9, b) b ¼ 0.64, c) b ¼ 0.32.
decreases strongly for lower concentrations, f < 1. Beyond an
equivalence ratio of unity, the rate of reduction in MIE decreases for
larger concentrations. The reason is that with the rise of dust
concentration the assumed distance between of neighboring particles reduces and leading to a lower energy for ignition of dust
cloud.
Fig. 9 shows the variation of quenching distance in terms of
various iron particle diameters. By increasing the value of particle
diameter, the amount of energy release per unit volume is
decreased during the combustion process therefore the preheating
time is increased for the layers, and the flame propagation speed is
decreased. The reduction in preheating time means the reduction
of heat loss. Therefore, a bigger particle diameter leads to a higher
heat loss and quenching distance, as shown in Fig. 9. This prediction
144
M. Bidabadi et al. / Journal of Loss Prevention in the Process Industries 43 (2016) 138e146
Fig. 5. Flame propagation speed as a function of dust concentration for different particle diameters for the uniform and random distribution of particles for T∞ ¼ 300 K, P ¼ 101 kpa.
Fig. 6. Flame propagation speed as a function of particles diameter for a rich mixture, with 4 ¼ 1.63, T∞ ¼ 300 K, P ¼ 101 kpa.
Fig. 7. Minimum ignition energy as a function of particles diameter for 4 ¼ 1, T∞ ¼ 300 K, P ¼ 101 kpa and uniform particle distribution.
was validated by the experimental data for two different iron particle diameters reported by Mamen (2006).
Fig. 10 demonstrates how an increase in dust concentration results into smaller quenching distance. The amount of energy
release per unit volume increases with dust concentration during
the combustion process. Therefore, the ratio of heat release to heat
losses to the wall decreases, so that the flame propagation speed is
increased and the quenching distance becomes narrower.
4. Conclusion
In the present study, flame propagation of iron dust particles in a
medium with spatially discrete sources is numerically investigated,
both for a uniform as well as for a random distribution of particles
for a given concentration and diameter. In addition, the variation of
quenching distance is also considered as a function of the same
variables.
M. Bidabadi et al. / Journal of Loss Prevention in the Process Industries 43 (2016) 138e146
145
Fig. 8. Minimum ignition energy as a function of equivalence ratio for dp ¼ 10 mm, T∞ ¼ 300 K, P ¼ 101 kpa and uniform distribution.
Fig. 9. Experimental validation of the quenching distance of various iron particle diameter for 4 ¼ 1, T∞ ¼ 300 K, P ¼ 101 kpa.
Fig. 10. Quenching distance of 9 mm iron particles as a function of dust concentration in T∞ ¼ 300 K, P ¼ 101 kpa.
The simulation results show that the flame propagation speed
for of both uniform and random particle distributions are the same
on the mean. Both sets of simulations are able to reproduce the
behavior of experimental data with both diameter and concentrations rather well.
The flame propagation speed in iron-air suspensions decreases
as the particle size increases significantly. More energy is required
for the ignition of larger particles relative to the smaller ones as
compared to the smaller ones. The calculated minimum ignition
energy is shown to increases with an increase in particle size and
decrease with bulk equivalence ratio for selected cases using uniform distribution. Finally, the calculated quenching distances
appear to capture reasonably well the threshold for quenching
distances, providing an effective model both for flame propagation
as well as quenching of dust clouds. As in combustion physics of
dust cloud, particles are distributed randomly in the reaction
146
M. Bidabadi et al. / Journal of Loss Prevention in the Process Industries 43 (2016) 138e146
medium, therefore taking into account this phenomenon in the
governing equations, the predicted results are more realistic. The
presented thermal model can be developed to consider particle size
distribution to enhance the obtained results in comparison with the
experimental data.
Nomenclature
A
Cd
d
D
DO2
H
i,j,k
kp
L
r
t
tr
T
P
N
Ne
Q
Qloss
q_ loss
Lr
Area (m2)
Dust concentration (kg/m3)
Diameter (m)
The channel width (m)
Oxygen diffusivity coefficient (m2/s),
Heaviside function
Components of Cartesian coordinate
Conduction coefficient (W/m K)
Distance of two adjacent particles or layers (m)
Radial distance (m)
Time (s)
The relative time between the ignition of two neighbor
layers
Temperature (K)
Pressure (Pa)
Total number of particles
Total number of empty location before distributing
particles
Energy released from igniter (j)
The total heat loss of one layer (j)
The rate of heat loss to the walls (j)
The modified distance between two adjacent layer (m)
Greek symbols
a
Thermal diffusivity (m2/s)
r
Density (kg/m3)
t
Particle burning time (s)
4
Equivalence ratio
Subscripts
a
Burning zone
f
Flame
g
Ambient gas
ig
Ignition
p
Particle
w
Wall
∞
Ambient property
References
Abbasi, T., Abbasi, S., 2007. Dust explosionsecases, causes, consequences, and
control. J. Hazard. Mater. 140, 7e44.
Beach, D., Rondinone, A., Sumpter, B., Labinov, S., Richards, R., 2007. Solid-state
combustion of metallic nanoparticles: new possibilities for an alternative energy carrier. J. Energy Resour. Technol. 129, 29e32.
Bidabadi, M., 1996. An Experimental and Analytical Study of Laminar Dust Flame
Propagation. Department of Mechanical Engineering, McGill University.
Bidabadi, M., Haghiri, A., Rahbari, A., 2010. Mathematical modeling of velocity and
number density profiles of particles across the flame propagation through a
micro-iron dust cloud. J. Hazard. Mater. 176, 146e153.
Bidabadi, M., Mafi, M., 2012. Analytical modeling of combustion of a single iron
particle burning in the gaseous oxidizing medium. Proc. Inst. Mech. Eng. Part C
J. Mech. Eng. Sci. 227 (5), 1006e1021.
Bidabadi, M., Mafi, M., 2013. Time variation of combustion temperature and burning
time of a single iron particle. Int. J. Therm. Sci. 65, 136e147.
Bidabadi, M., Zadsirjan, S., Mostafavi, S.A., 2013. Propagation and extinction of dust
flames in narrow channels. J. Loss Prev. Process Ind. 26, 172e176.
Eckhoff, R., 2003. Dust explosions in the process industries: identification, assessment and control of dust hazards, third ed. Gulf Professional Publishing, Boston,
Mass, USA.
Glassman, I., Yetter, R.A., 2008. Combustion, fourth ed. Academic Press, Burlington,
MA.
Goroshin, S., Lee, J., Shoshin, Y., 1998. Effect of the discrete nature of heat sources on
flame propagation in particulate suspensions. In: Symposium (International) on
Combustion. Elsevier, pp. 743e749.
Hanai, H., Kobayashi, H., Niioka, T., 2000. A numerical study of pulsating flame
propagation in mixtures of gas and particles. Proc. Combust. Inst. 28, 815e822.
Incropera, F., DeWitt, D., 2002. Fundamentals of Heat and Mass Transfer, fifth ed.
John Wiley & Sons, New York.
Mamen, J.N., 2006. On the Structure of an Aluminum Dust Flame. Department of
Mechanical Engineering, McGill University.
Mukasyan, A., Hwang, S., Sytchev, A., Rogachev, A., Merzhanov, A., Varma, A., 1996.
Combustion wave microstructure in heterogeneous gasless systems. Combust.
Sci. Technol. 115, 335e353.
Proust, C., 2006. A few fundamental aspects about ignition and flame propagation
in dust clouds. J. Loss Prev. Process Ind. 19, 104e120.
Rashkovskiy, S.A., Kumar, G.M., Tewari, S.P., 2010. One-dimensional discrete combustion waves in periodical and random systems. Combust. Sci. Technol. 182,
1009e1028.
Rogachev, A., Shugaev, V., Kachelmyer, C., Varma, A., 1994. Mechanisms of structure
formation during combustion synthesis of materials. Chem. Eng. Sci. 49,
4949e4958.
Sun, J.H., Dobashi, R., Hirano, T., 1990. Combustion behavior of iron particles suspended in air. Combust. Sci. Technol. 150, 99e114.
Sun, J.H., Dobashi, R., Hirano, T., 1998. Structure of flames propagating through
metal particle clouds and behavior of particles. In: Symposium (International)
on Combustion. Elsevier, pp. 2405e2411.
Sun, J.H., Dobashi, R., Hirano, T., 2006. Velocity and number density profiles of
particles across upward and downward flame propagating through iron particle
clouds. J. Loss Prev. Process Ind. 19, 135e141.
Tang, F.D., Goroshin, S., Higgins, A., Lee, J., 2009a. Flame propagation and quenching
in iron dust clouds. Proc. Combust. Inst. 32, 1905e1912.
Tang, F.D., Higgins, A.J., Goroshin, S., 2009b. Effect of discreteness on heterogeneous
flames: propagation limits in regular and random particle arrays. Combust.
Theory Model. 13, 319e341.