Interaction between Flaming and Smoldering in Hot-Particle Ignition
of Forest Fuels and Effects of Moisture and Wind
Supan Wang1,3, Xinyan Huang2, Haixiang Chen1,*, Naian Liu1
1 State Key Laboratory of Fire Science, University of Science and Technology of China
2 Department of Mechanical Engineering, University of California, Berkeley
3 Jiangsu Key Laboratory of Hazardous Chemicals Safety and Control, College of Safety Science and
Engineering, Nanjing Tech University
The ignition of natural fuels by hot metal particles from powerlines, welding and mechanical treatments may
initiate wildﬁres. In this work, a hot spherical steel particle (6~14 mm and 600~1100 °C) was dropped on the
pine needles with fuel moisture content (FMC) of 6~32% and wind speed of 0~4 m/s. Several ignition
phenomena including direct flaming, smoldering and smoldering-to-flaming transition were observed. The
critical particle temperature for sustained ignition was found to decrease with the particle size and increase
with FMC as (R2=0.85), and the maximum heating efficiency of
particle is found to be . As the particle size increases, the influence of FMC becomes weaker. The
flaming ignition delay times for both direct flaming and smoldering-to-flaming transition were measured,
which decrease with the particle temperature and wind speed, while increase with FMC. The proposed heat
transfer analysis explains the ignition limit and delay time, and suggests that the hot particle acts as both
heating and pilot sources like a small flame for the direct flaming ignition, but only acts as a heating source
for smoldering. This study deepens the fundamental understanding on hot-particle ignition, and may help
provide a first step to understand the mechanism behind the firebrand ignition and the rapid fire spread
observed in extreme wildfires.
Spotting ignition by hot particles such as burning firebrands and inert metal particles is an important
ignition pathway and fire-spread mechanism in wildland and urban fires (Sullivan 2009; Albini et al. 2012).
Burning firebrands often lead to long-distance spotting fires that spread faster than the continuous flame front
(Koo et al. 2010), such as Florida wildfires (1998), Witch Greek fire (2007), Texas wildfires (2011) and Butte
fire (2015). The hot metal particles from human activities, including powerlines, equipment, welding, bullets,
friction in railroads and mechanical cutting (Tanaka 1977; Stokes 1990; Rowntree and Stokes 1994;
Fernandez-Pello et al. 2015), can cause local ignitions, while recently they have also been identified to cause a
large number of wildland fires all around the world.
The spotting process by hot particles is fundamentally different from flame or radiation driven ignition
(Babrauskas 2003; Drysdale 2011). A better understanding of this spotting ignition process is important to
mitigate fire disasters in wildland and wildland-urban interface (WUI) communities (Pagni 1993). The
hot-particle ignition of wildland fuels involves complex physicochemical processes in both the solid and gas
phases (Fernandez-Pello et al. 2015). Once the hot particle has landed, the fuel can be heated, dried,
decomposed, and then ignited with a flame if the particle is hot enough. In addition, more complex smoldering
ignition may be initiated by particle with sufficient energy under a windy environment. Once environmental
condition changes, flaming can transition to smoldering, and the intensive smoldering may also be promoted
Spotting ignition of forest fuels and building structures in WUI initiated by reactive hot particles such as
firebrands (Manzello et al. 2006; Ganteaume et al. 2009; Ellis 2011; Yin et al. 2014) or firebrand showers
(Manzello et al. 2011; Manzello 2014; Suzuki et al. 2016) are often observed. Due to different shape, density,
burning process, etc., of firebrands, the firebrand ignition phenomenon is more complex than the ignition by
an inert hot particle, and lack of fundamental understanding. Therefore, in order to provide a first step to
understand the mechanism behind firebrand ignition, well-designed experiments with controlled fuel bed,
particle and environmental conditions are desired. For this reason, the inert hot particle ignition should be first
studied to remove uncertainty (ember temperature, char layer thickness, combustion characteristics, thermal
properties, etc.) introduced by the reactive and burning firebrand (Hadden et al. 2011). Previous studies in the
literature have studied the hot-particle ignition of high-density powder natural fuels (Hadden et al. 2011; Zak
et al. 2014b; Fernandez-Pello et al. 2015; Urban et al. 2015) and the organic foams as building insulation
materials (Wang et al. 2015a; Wang et al. 2015b). So far, the hot-particle ignition of real forest fuel such as
pine needle beds with various fuel moisture contents (FMC) and wind speeds has not been studied before.
More importantly, there are very few studies on the smoldering ignition by hot metal particle, and on the
interaction between flaming and smoldering during ignition in wildland fires.
The fuel moisture content (FMC) of forest fuels, usually defined in dry mass basis, is one of the key
parameters determining the wildfire risk, and often varies in a wide range (de Groot et al. 2005). For example,
the FMC of pine needles can vary from 4% under drought conditions to 40% (dead) and over 200% (live)
within one hour after the weather change (Viegas et al. 1992). Valdivieso et al. (Valdivieso and Rivera 2014)
studied the fire spread over wet pine needle beds under different FMCs and wind speeds, and observed
complex interactions between smoldering and flaming. Ganteaume et al. (Ganteaume et al. 2009) showed that
spot fire ignition was easily affected by weather. In general, there is very limited research on the influence of
environmental conditions, such as the wind speed and humidity, during the hot-particle ignition process of
forest fuel bed.
In this work, well-controlled experiments were conducted to study the inert hot-particle ignition process of
pine needle beds with different FMCs and wind speeds. Various ignition phenomena and the interaction
between flaming and smoldering were discovered and analyzed in detail. For the first time, the ignition limit,
correlating the critical particle temperature with both the particle size and FMC, was quantified experimentally.
Two flaming ignition delay times, for (I) direct flaming and (II) smoldering-to-flaming transition, were
measured and analyzed to improve our understanding on the flaming and smoldering process in the
2. Experimental setup
The experimental apparatus, updated from that in the previous work (Wang et al. 2015b), is illustrated in
Fig. 1. In the experiments, a ceramic tube furnace was used to heat a stainless steel particle to a pre-set high
temperature (up to 1200). The tube temperature was monitored by a Pt/Rh thermocouple. When the tube
temperature reached steady state, the steel particle, held by a long-tail spoon, was placed into the center of the
tube. The particle temperature was monitored by a 0.5-mm K-type thermocouple which was in contact with
the particle surface. The temperature difference between the particle and tube was fairly constant (less than
50) for the given particle size and furnace temperature.
Figure 1 Schematic of experimental setup for the hot-particle ignition of pine needles and the top view of the wind wall
and fuel bed (above).
In the experiments, the spherical stainless steel particles with diameter of 6, 8, 10, 12 or 14 mm were tested,
and the preset furnace temperature increased from 600 to 1200 °C in a step of 25 °C. Then, the particle was
quickly heated up and stabilized at a high temperature (). Since the Biot number of these small particles is
about 0.02<0.1 (Wang et al. 2015b), the temperature of the whole particle is relatively uniform after reaching
steady state. Then, the particle was released to slip along the inclined tube (5o slope). The tube outlet lied
almost directly over the fuel bed to minimize the impact of particle’s motion.
The pine needles (Pinus-massoniana Lamb), collected from Sichuan (Southwest China in humid
subtropical climate), were tested as a representative forest fuel. A single needle was measured to have a length
of 12~22 cm and a thickness of about 1.0 ±0.1 mm. These dead pine needles were dried in air of about 15
for 15 days, resulting a FMC = 6 ±1% in equilibrium with the ambient. Then, these dried samples were placed
in an environmental chamber with a pre-set temperature (50 ) and humidity (100%) for 2, 6 and 12 hours,
respectively, to obtain wet samples. The maximum absorbed (saturated) FMC of these dead pine needles is
found to be about 50%. After wetting, these samples were sealed in plastic bags for at least 48 h to equilibrate
the moisture. The FMCs of wet samples were measured before the ignition experiments, by an infrared rays
moisture meter (Sartorius MA145), to be 15%, 25% and 32% [±1%].
Before each experimental run, the pine needles were uniformly distributed within a cuboid metal basket
(31×31×4 cm3 with the mesh area porosity of 74%) which was placed above an insulation board. The mass
loss of the pine needle fuel bed in each run was recorded by using a load cell (METTLER TOLEDO
XPl0002S) with 1 Hz. The dry bulk density of fuel bed was controlled to be 40 ±0.5 kg/m3, so the dry fuel
load is 1.6 kg/m2, similar to those in (Santoni et al. 2014; Valdivieso and Rivera 2014; Yin et al. 2014). Based
on a true density of 786 kg/m3 (Santoni et al. 2014), the average porosity of fuel bed was calculated to be
A wind wall system was used to generate a uniform environmental wind field in a large open space for the
ignition experiments. In this system, two SF-8-4 Type axial flow fans (1.5 kW), controlled by two power
transducers (range: 0~50 Hz, resolution: 0.1 Hz), were used to provide the desired wind. The wind speed was
calibrated with the frequency of transducers and ranged from 0 to 4.6 m/s (Jiang and Lu 2013). Before each
experimental run, the centerline wind speed at the leading edge of the fuel bed was measured by a handheld
anemometer (TSI 9545, range: 0~30 m/s, resolution: 0.01 m/s). The default wind speed was controlled at 2
m/s. In order to investigate the influence of wind speed on ignition, additional experiments under other wind
speeds from 0 (no wind) to 4 m/s were conducted for comparison. Because of the complexity and randomness
in fuel and experiment conditions, 10-20 repeated runs were conducted for each experimental condition to
quantify the probability of each experimental outcome. The ignition process was recorded by a video camera
(Sony DSR-SR 300, 25 fps) from a 45° top view.
3. Experimental results
3.1 Ignition phenomena
The main objective of this experimental work is to identify the possible hot-particle ignition phenomena
for forest fuels of different FMCs, and then quantify the ignition limit as a function of particle conditions
( vs. ). The observed phenomena in current hot-particle ignition are categorized as four types: (1) no
ignition, (2) direct ﬂaming ignition, (3) smoldering ignition, and (4) smoldering-to-flaming transition. Note
that in this work, the transient flash, unstable flame-let or sustained charring is not recognized as an effective
ignition, which is different from some other studies (Urban et al. 2015; Wang et al. 2015b).
Figure 2(I) shows a group of snapshots for a typical direct flaming ignition with a 12-mm particle
(1057 °C), FMC of 25%, and 2 m/s wind. This flaming ignition was denoted by a visible and sustained ﬂame
appearing immediately after the particle landed (). Then, the flame quickly spread over the entire fuel
bed within 20 s. This direct flaming often occurs when a high-temperature particle ignites a low-FMC bed.
Figure 2(II) shows a group of snapshots for smoldering ignition with a 14-mm particle (822 °C), FMC of
48%, and 2 m/s wind. Once the hot particle landed, some visible smoke was released from the fuel bed and
around the particle, which could be the water vapor and decomposed gases. Meanwhile, the particle was
gradually immersed into the fuel bed driven by the gravity. In this case, no flame was observed, and the spread
of smoldering became clear after 1030 s, and because of wind, only the forward smoldering occurred (see Fig.
1), consuming more than half while not the entire fuel bed.
Figure 2(III) shows a group of snapshots for smoldering ignition with a 14-mm particle (925 °C) and FMC
of 25% without wind. Compared to (II), an unstable flash quickly appeared and extinguished between 2 and 3
s. This unstable flash could also randomly occur and disappear during the smoldering spread. Nevertheless,
the smoldering dominated the fire spread, and without wind, it spread almost uniformly in each direction and
gradually consumed the entire fuel bed. Such ignition and fire spread was often observed under lower wind
speed and with higher FMC (>25%).
Figure 2 Snapshots of the hot-particle ignition processes of dead pine needles: (I) sustained flaming ignition, (II)
smoldering ignition without flaming, (III) smoldering ignition with unstable flaming, (IV) smoldering ignition transition
to flaming, (V) failed flaming ignition and (VI) failed smoldering ignition, where particle, fuel and environmental
conditions are given in the figures.
Smoldering spread may transition into a sustain flame spread especially under the wind assistance (Rein
2016). Figure 2(IV) shows an example of smoldering-to-flaming transition using the same particle and FMC
condition as (III), but with 2 m/s wind. Compared to (III), similar smoldering ignition and spread phenomena
were observed for the first 198 s. However, a flame appeared afterwards, and became sustained to dominate
the fire spread and fuel consumption.
Figures 2(V) and (VI) present two typical no-ignition cases with an 8-mm hot particle. As the particle was
embedded into the fuel bed, visible smoke was observed and sometimes accompanied by unstable flash (V)
and glowing (VI) around the particle. In a short time, the flash and glowing spots vanished, indicating a failed
ignition. For these no-ignition cases, their fuel mass losses were always less than 5%.
3.2 Ignition probability and limit
In the direct flaming ignition case, the flame quickly spread over the surface and consume the entire fuel
bed. In the smoldering ignition case, more than half or the entire fuel beds were consumed with the influence
of FMC and wind. In the smoldering-to-flaming transition case, once a flame appeared, it became sustained to
dominate fire spread and fuel consumption. Based on mass loss percentage, there are two clear final states for
the fuel bed: burnout (mass loss percentage > 50%) and no burn (mass loss percentage < 5%), which can
distinguish the successful and failed ignition (or identify the fire point) (Drysdale 2011). Here the burnout
includes various intermediate ignition phenomena (direct flaming, smoldering ignition and
smoldering-to-flaming transition). Because of 10-20 repeating runs for each tested condition, we report the
ignition probability as the ratio between the successful ignition numbers () and the number of repeating
The ignition limit is defined by the critical FMC and particle conditions at .
Figure 3 shows the measured hot-particle ignition probability and the fitted ignition limit ( ) as a
function of critical particle size () and temperature () for pine needle beds with FMCs of 6%, 15%, 25%
and 32%. Each colored circle in the ﬁgure corresponds to a set of at least ten repeating runs, and the color bar
scales the ignition probability from 0% (black) to 100% (white). Because of the complex ignition process, an
ignition transition zone with different ignition probabilities is found. The temperature range for the transition
region reflects the complexity and uncertainty of experiment, which is found to be 100~200 °C and is
independent of the particle size. For simplicity, if the particle condition is above the limiting curve, fuel bed
has a high ignition risk by the hot particle either through flaming or smoldering; while if below the limit curve,
the fire risk is low.
Figure 3 Ignition probabilities () as function of the initial temperature and diameter of hot particles for the forest fuel
bed with 6%, 15%, 25%, and 32% FMCs. Black line shows the critical temperature for ignition ( ).
For each FMC, there is similar hyperbolic relationship between the critical particle temperature ()
and size (): for a smaller particle, a higher temperature was needed for ignition. For example, in order to
ignite a pine needle bed of 6 % FMC with a 50% probability, the particle temperature needs to increase from
636 to 970 °C as the particle diameter decreases from 14 to 6 mm. Such hyperbolic relationship has also been
observed in (Hadden et al. 2011; Zak et al. 2014b; Fernandez-Pello et al. 2015; Urban et al. 2015; Wang et al.
2015b). It suggests that the ignition outcome for the smaller particles is more sensitive to the particle size,
(as well as the particle energy); while for the larger particles, it is more sensitive to the particle temperature
() where a minimum critical temperature () may exist. Note that within the tested particle size range,
such minimum critical temperature is not observed, and the limiting curve still has a clear decreasing trend for
large particles. Therefore, the particle energy still plays an important role for those large particles.
In order to better quantify the influence of FMC, Fig. 4(a) compares the hot-particle ignition limit curves
for FMC = 6% and 32%, where the error bar is bounded by the ignition probability of 5% and 95%. Clearly,
for a given particle size, the required particle temperature is higher for a higher FMC. For example, for an
8-mm particle, an increment of about 430 °C is needed as the FMC increases from 6% (air dried) to 32%,
while for a 10-mm particle, only an increment of 140 °C is needed. Therefore, as the FMC increases, the
ignition capability becomes substantially weaker for smaller particles. On the other hand, as the particle size
increases, the influence of FMC on the ignition limit becomes smaller. Figure 4(b) further shows that as the
FMC increases, the critical particle temperature increases significantly. For the large 14-mm particle, the
temperature (as well as the energy) increment is almost linear for FMC increasing from 6 to 32%.
Figure 4 The measured critical particle temperature () as a function of (a) particle size (d), and (b) FMC, with 2 m/s
wind. The error bars are bounded by the 5% and 95% ignition probability.
3.3 Flaming ignition delay time
The ignition delay time of sustained flaming () can be deﬁned as the interval between the landing of the
particle () and the appearance of the sustainable flame. Thus, two different flaming ignition delay times
are found for (a) directly flaming (<10 s) and (b) the transition time from smoldering to flaming (>100 s). The
ignition delay time for pure smoldering is difficult to quantify in experiment because of the lack of accurate
judging standard, which is not analyzed here.
Figure 5(a) presents two types of flaming ignition delay time () versus the particle temperature () and
size () for 6% FMC with 2 m/s wind. Each data point is an averaged value over 10-20 repeating runs, and the
error bar shows the standard error. For high-temperature particles (), the direct flaming ignition is
preferred (see Fig. 5(a) (I)). For a rapid direct flaming, the hot particle acts as both the heating and pilot source,
and the ignition time may correspond the piloted ignition time of the radiation ignition process. The asymptote
of the flaming delay time and particle temperature (analogous to radiation heat flux) seems similar with the
relationship of the radiation ignition time and critical heat flux (Quintiere 2006). As the particle temperature
decreases, the smoldering ignition becomes more likely, and with wind its transition to flame occurs after a
long delay when the smoldering front clearly spreads out (see Fig. 2(IV)). For the smoldering-to-flaming
transition, the hot particle acts as the heating source, and the ignition time may be analogous to the
spontaneous ignition time of the radiation ignition process.
Figure 5(b) further shows the flaming ignition delay time () versus the FMC under the fixed particle
condition. Clearly, the ignition delay time increases with increasing FMC for both flaming phenomena. For
°C, only smoldering-to-flaming transition occurs. While for °C, direct flaming occurs
with FMC < 24% (Fig. 5(b) (I)), and smoldering-to-flaming transition becomes more likely with FMC > 24%
(Fig. 5(b) (II)).
Figure 5 Ignition time for (I) direct flaming, and (II) smoldering-to-flaming transition as the function of (a) the initial
particle temperature () and diameter () for pine needle bed of 6% FMC with 2 m/s wind; (b) the fuel moisture content
(FMC) with a 14-mm hot steel particle ( = 822 or 925 °C) and 2 m/s wind; (c) the wind speed with the 6% FMC, for the
given particle conditions.
Figure 5(c) shows the effect of wind speed on the flaming delay time with 6% FMC for several particle
conditions. In general, as the wind speed increases, the ignition probability () increases and the flaming
delay time () decreases, no matter whether it is the direct flaming or the transition from smoldering. In
addition, it is observed that as the wind speed () increases, smoldering is more likely to transition to
flaming. Wind can help cool the particle, while it also boosts the convective heat transfer between particle and
fuel. Experimental results indicate that the particle cooling by wind is weaker than the corresponding
enhancement in fuel heating. On the other hand, wind also increases the oxygen supply to the smoldering zone
to increase both the smoldering spread rate and the probability of smoldering-to-flaming transition (Valdivieso
and Rivera 2014; Rein 2016). Note that although not observed in current experiments, further increasing the
wind speed, its cooling effect may become dominant to reduce the fire risk of hot particle.
4.1 Maximum heating efficiency of particle
Because of the complexity in the fuel bed and the randomness of the particle’s landing process, the
detailed heat transfer process between hot particle and fuel bed is extremely difficult to model. Nevertheless,
based on the experimental observations and heat-transfer principles, the particle’s heating efficiency could be
estimated. At the ignition limit, we define a maximum overall heating efficiency as
where is the particle’s effective heating distance in the fuel bed; , , and are the surface area,
volume, density and specific heat, respectively, with subscripts “” for particle and “” for fuel bed;
MJ/kg is the heat of water evaporation; (Valdivieso and Rivera 2014; Rein 2016) is the
characteristic smoldering temperature; is the critical particle temperature at the ignition limit which is
higher than (see Fig. 5). Both and  are much higher than the ambient temperature (
), so and are assumed throughout the following discussion.
Note that a large particle energy is not necessary to ignite the fuel. For example, a warm () while
very large particle can have a large energy, but it will not lead to ignition. In addition, the particle has to be at
least hot enough to heat the local fuel above to get a smoldering ignition, and to be even hotter to pilot a
flame. Therefore, it would also be useful to quantify a maximum specific heating efficiency as
Clearly, further increasing the particle temperature above the critical value () for ignition is a waste
of energy, and reducing both heating efficiencies.
Because of a small Biot number (), the effective heating (or the self-cooling) time of the
particle () can be estimated by a lumped transient heat equation (Incropera et al. 2011):
where the particle is cooled from its initial temperature () to the minimum effective heating temperature (
Then, the effective heating time is
which increases with both the temperature and size of particle. Interestingly, based on the critical particle
initial temperature () found in Fig. 3, the calculated critical heating time () is not sensitive to
either the critical particle temperature or size, while it clearly increases with FMC, as shown in Fig. 6(a).
Particle properties of kg/m3, J/kg-K,and W/m2-K are used in the
calculation. In other words, there may be a minimum effective heating duration, below which the hot-particle
ignition becomes impossible. Such heating duration increases with FMC, but is insensitive to the particle size.
During the cooling of the particle, the fuel bed is also heated by the hot particle. At the end of heating (
), a fuel layer within a short distance next to the particle is heated to . Such a heating process can be
described through a simplified one-dimensional heat equation (Quintiere 2006) as
where is the effective thermal conductivity of fuel bed;
. Then, we can estimate this heating distance, i.e. the characteristic char-layer thickness generated by the
particle heating, as
where kg/m3, W/m-K, and J/kg-K for fuel bed are used in the calculation.
Figure 6 At the ignition limit, (a) Estimated effective heating time of particle (), and heating length in fuel () as a
function of fuel moisture content (FMC); and (b) overall (, blue solid point) and specific (, black empty point)
heating efficiency of particle.
Fig. 6(a) shows that at the ignition limit () this critical heating distance is found to be almost
constant ( mm), independent of FMC. Such results reflect the principle of ignition and fire spread: no
matter what ignition protocol can be such as by hot particle, firebrand, flaming, lightening or self-ignition, a
self-sustained reaction front (i.e. fire inception) needs to be generated for fire spread. During ignition, such
reaction front should exceed a threshold thickness (maybe called as “quenching distance”) to overcome the
Thus, at the ignition limit ( ) the maximum overall and specific heating efficiencies become
Their values are calculated and shown in Fig. 6(b). Clearly, only a small portion (3~5%) of the particle’s
overall energy is used for ignition, and the rest of the particle’s energy was lost by the radiative, convective
cooling and preheating fuel beyond the ignition zone. Moreover, as the particle size increases, a decreasing
indicates that the overall heating from the particle to fuel bed becomes less efficient. Such trend does not
change with FMC.
Figure 6(b) further shows that the maximum specific efficiency is also small, but to be almost
constant (10%), independent of particle size and FMC. Therefore, is a more useful and physically
meaningful parameter to estimate the fire risk of hot-particle ignition of wildland fuels. More importantly, for
a given fuel bed, once a critical ignition condition (critical particle temperature and size) is determined, the
constant may be estimated to predict the critical conditions for other particles.
Based on the particle and fuel properties as well as in Eq. (8b), an empirical correlation for
hot particle ignition is obtained:
where these coefficients for [mm] and FMC [%] may change with the particle metal type and the fuel
properties (e.g. fuel type and bulk density). The R2 of Eq. (9) was 0.85, by fitting all 50% ignition probability
data in Fig. 3. Considering the large complexity of experiments, this correlation provides a good description of
the experimental results. Interesting, we find that the data for 50% ignition probability of α-cellulose (with
only one FMC) by stainless steel particles in the paper of Zak et al. (Zak et al. 2014a) can be fitted as
with R2 > 0.90, which holds the same functional form with Eq. (9).
4.2 Delay time for direct flaming
For a rapid direct flaming, the hot particle acts as both the heating and pilot source (Wang et al. 2015b).
Therefore, the classical pilot ignition theory for the thermally thin fuel (Quintiere 2006) is adopted to estimate
its ignition delay:
where is the pilot ignition temperature of fuel; is the characteristic length of fuel which is the
diameter of pine needle (about 1 mm) in current discrete and porous fuel bed; and
heat flux from particle to fuel with the effective heating coefficient, which increases with wind speed
(Wang et al. 2015b).
Equation (10) clearly shows that the ignition delay time (1) decreases with the increasing particle
), agreeing with Fig. 5(a) (I), (2) increases with FMC (), agreeing with Fig. 5(b)
(I); and (3) decreases with the wind speed because of the increasing , agreeing with Fig. 5(c) (I).
For heat exchange between particle and fuel, assuming
, the values of and
can be optimized based on the measurement of in Fig. 5(a) (I).
Thus, it is estimated that W/m2-K and
kW/m2. Note that these values are very
similar to the heat flux level from a small flame (Gollner et al. 2013). Therefore, the directly flaming ignition
of wildland fuels by hot-particle is similar to the ignition by the direct flame contact.
4.3 Delay time for smoldering-to-flaming transition
The fundamental mechanism to trigger the smoldering-to-flaming transition is still poorly understood
(Rein 2016). Various experiments have shown that the occurrence of this transition tends to increase with the
increasing wind speed (Palmer 1957; Valdivieso and Rivera 2014), oxygen concentration and external
radiation (Bar-Ilan et al. 2005). The delay time for this transition can be very long, and has been observed to
last from a few minutes to hours, depending on the fuel properties, fire and environmental conditions (Rein
2016). Based on observations in the literature, one hypothesis is proposed: the smoldering-to-flaming
transition occurs as a spontaneous ignition after the pyrolysis gas mixes with the hot air. The air is preheated
by a stronger exothermic secondary char oxidation in a thick char layer. As the thickness of char layer
increase, the charring zone has a high probability to initiate the secondary char oxidation and a long residence
time to preheat air. Therefore, the thickness of self-sustained char layer can play an important role in the
Figure 7 Illustration of (a) the smoldering process before the transition to flaming, here is generated by the direct
heating from the hot particle (), and the self-sustained smoldering spread (); and (b) the delay time of the direct
flaming () and smoldering-to-flaming transition () varying with initial particle temperature and size, here the delay
time of smoldering-to-flaming transition () is generated by the effective heating time () and the self-sustained
smoldering spread time ().
For simplicity, we propose a critical char-layer thickness () to characterize this transition. As illustrated
in Fig. 7(a), is generated first by the direct heating from the hot particle (), and then the self-sustained
smoldering spread ():
This thickness should be constant for the fixed fuel bed and environmental condition. Thus, the delay time
of smoldering-to-flaming transition is
where and have been evaluated through Eqs. (5) and (7), respectively; and the self-sustained spread of
charring front () is irrelevant to the hot particle, while only depending on the fuel properties and wind
condition. Then, the delay time for this transition becomes
which is related to the fuel and particle properties as well as the wind condition, but is independent of the
particle temperature and size.
Equation 12(b) indicates that the required time in self-sustained smoldering spread () decreases with
both increasing initial temperature and size of particle, in opposite to the effective heating time of particle ()
seen in Eq. (5). Note that this flaming delay time is more than 100 s (see Fig. 5(a) (II)), and is less than 35
(see Fig. 6(a)). Therefore, and the self-sustained smoldering spread accounts for the major
component in the overall delay time. Figure 7(b) qualitatively illustrates the delay time for the transition to
flame varying with the particle initial temperature and size (dashed line for reducing particle size), agreeing
well with the experimental observations in Fig. 5(a) (II). Further increasing the particle temperature, the direct
flaming ignition becomes more likely, as illustrated in Fig. 7(b).
In the literature there are very few experiments for the smoldering spread rate () over pine needles and
its dependence with the fuel moisture and wind speed. For other fuels like saw dust (Palmer 1957) and peat
(Huang et al. 2016; Prat-Guitart et al. 2016), it has been found that the smoldering spread decreases with FMC
as , and increases with wind speed as (forward smoldering). Such trend could also
be expected for the smoldering pine needles. That is, the delay time of smoldering-to-flaming transition
increases with the FMC and decreases with the wind speed, agreeing with experimental results in Figs. 5(b) (II)
and 5(c) (II).
In this work, several ignition phenomena, including direct flaming, smoldering and smoldering-to-flaming
transition, were observed for the hot-particle ignition of pine needle beds. The critical particle temperature for
sustained ignition was found to decrease with the particle size and increase with FMC as
, and the maximum heating efficiency of particle is found to be . It is also
found that as the particle size increases, the effect of FMC on the ignition limit becomes weaker.
The flaming ignition delay time was measured for both direct flaming and smoldering-to-flaming transition.
Both ignition delays decrease with the particle temperature and wind speed, while increase with FMC.
Simplified heat transfer analysis successfully explains the limit condition and delay time for hot-particle
ignition, and improves the understanding on the interaction between flaming and smoldering. The theoretical
analysis also suggests that the hot particle acts as both heating and pilot sources for the direct flaming, but
only acts as a heating source for smoldering and its later transition to flaming. This study deepens the
fundamental understanding on the hot-particle ignition process, and may be a first step to understand the
ignition mechanism behind firebrand ignition and the rapid fire spread observed in extreme wildfires.
This work was sponsored by National Natural Science Foundation of China (51576184) and National Key
Research and Development Program (No. 2016YFC0800104 & 2016YFC0800604) H.C. was supported by
Fundamental Research Funds for the Central University (WK2320000036). The authors would like to thank
Dr Guillermo Rein (Imperial College London) for his valuable comments.
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