Smoldering propagation and blow-off on consolidated fuel under external airflow

Abstract

Propagation of smoldering combustion and its blow-off phenomena are of practical importance in evaluating the fire dynamics of solid fuels, but the scientific understanding is still limited. In this work, we quantify the smoldering propagation rates on consolidated biomass and the blow-off limits under concurrent and opposed external airflows up to 50 m/s. The incense cylinders with different diameters (1.5-5.0 mm) and densities (720-1,100 kg/m 3) are tested. As the airflow velocity increases, the smoldering propagation rate first increases to its maximum value (Oxygen-limited Regime) and subsequently remains stable (Thermal Regime), regardless of the airflow direction. Afterward, it slightly decreases (Chemical Regime) until blow-off, and the blow-off of opposed smoldering is easier, similar to the pattern of flame spread. The blow-off airflow velocity (13-46 m/s) of smoldering combustion is around ten times larger than that of flaming combustion, and it decreases as the fuel diameter or density increases. This work advances the fundamental understanding of the smoldering propagation, blow-off, and its persistence; thus, helping guide the fire suppression strategies of smoldering.

Full text

S. Lin, T. Chow, X. Huang (2021) Smoldering Propagation and Blow-off on Consolidated Fuel under External Airflow,
Combustion and Flame, 234, 111685. https://doi.org/10.1016/j.combustflame.2021.111685
1
Smoldering Propagation and Blow-off on Consolidated Fuel
under External Airflow
Shaorun Lin1,2, Tsz Him Chow1, and Xinyan Huang1,*
1Research Centre for Fire Safety Engineering, The Hong Kong Polytechnic University, Kowloon,
Hong Kong SAR
2The Hong Kong Polytechnic University Shenzhen Research Institute, Shenzhen, Guangdong, China
*Corresponding to xy.huang@polyu.edu.hk (X. Huang)
Abstract
The propagation of smoldering combustion and the blow-off limit are of practical importance in
evaluating the fire dynamics of solid fuels, but the scientific understanding is still limited. In this work,
we quantify the smoldering propagation rate on consolidated biomass and the blow-off limit under
concurrent and opposed external airflows up to 50 m/s. The incense cylinders with different diameters
(1.5-5 mm) and densities (720-1,100 kg/m3) are tested. As the airflow velocity increases, the smoldering
propagation rate first increases to its maximum value (Oxygen-limited Regime) and subsequently
remains stable (Thermal Regime), regardless of the airflow direction. Afterward, it slightly decreases
(Chemical Regime) until blow-off, and the blow-off of opposed smoldering is easier, similar to the
pattern of flame spread. The blow-off airflow velocity (13-46 m/s) of smoldering combustion is around
ten times larger than that of flaming combustion, and it decreases as the fuel diameter or density
increases. This work advances the fundamental understanding of the smoldering propagation, blow-off,
and its persistence; thus, helping guide the fire suppression strategies of smoldering.
Keywords: smoldering fire; extinction limit; oxygen supply; biomass; wind effect.
1. Introduction
Smoldering is the slow, low-temperature, and flameless burning of porous fuels and one of the
most persistent types of combustion phenomena [1–3]. Smoldering combustion is a heterogeneous
process sustained when oxygen directly attacks the hot fuel surface, different from the flame regarding
the combustion chemistry and transport processes [2,3]. Smoldering can be ignited easily by a weak
heat source [2–4] or even self-ignited, which usually occur in silos and large fuel piles [5], creating a
shortcut to more intensive flaming fires (through smoldering-to-flaming transition). Moreover, it is also
challenging to detect and suppress the hidden smoldering fire. For example, the colossal piles of World
Trade Center debris continued to smolder for more than half a year, despite substantial firefighting
operations [6]. Natural smoldering, such as the underground fires in peatlands or coal mines, is one of
the most extensive and longest-lasting fire phenomena on Earth [7,8]. Therefore, it is vital to deepen
our understanding of smoldering fire dynamics.

S. Lin, T. Chow, X. Huang (2021) Smoldering Propagation and Blow-off on Consolidated Fuel under External Airflow,
Combustion and Flame, 234, 111685. https://doi.org/10.1016/j.combustflame.2021.111685
2
The fire spread (propagation) process is of practical significance in evaluating the impact of fire
events [9–12]. The fire spread is a continuous ignition and burning process [13], depending on both
environment (e.g., wind [10,11,14–16], oxygen [17–19], pressure [20,21], temperature [22,23], and
gravity [24]) and fuel factors (e.g., type/array [25], moisture [16], density [26], orientation [27], and
size [28,29]). Based on the relative direction to the airflow (or wind), fire spread can be classified into
the concurrent and opposed modes [9–11]. In the literature, most studies have focused on the
characteristics of flame spread on solid fuels [9–11,30], rather than the smoldering spread.
Smoldering combustion is controlled by the competition between the oxygen supply and the heat
transfer to and from the reaction zone [3,31,32]. Therefore, the airflow or wind is crucial to smoldering
propagation, because it could increase both the oxygen supply and the heat loss [15,29,33]. By applying
an external airflow (or environmental wind), smoldering propagation may become faster because of the
increased oxygen supply (O2-limit regime) [1,11,17]. Afterward, the excessive airflow may also help
Nomenclature
Symbols
Greeks
a
strain rate (s-1)

thermal diffusivity (m2/s)
c
specific heat capacity (J/kg-K)
δ
thickness (m)
d
fuel diameter (mm)
v
stochiometric coefficient (-)
C
fitting coefficient (-) / constant (-)

kinematic viscosity (m2/s)
D
wind tunnel diameter (m)
ρ
density (kg/m3)
Da
Damkohler number (-)
λ
thermal conductivity (W/m-K)
h
convection coefficient (W/m2-K)
ϕ
porosity (-)
hm
mass transfer coefficient (kg/m2-s)

reaction rate (1/s)
∆h
thermal enthalpy difference (J/kg)
∆Hc
heat of combustion (MJ/kg)
I
thermal inertia (J/m2-K-s1/2)
Subscripts
k
permeability (m2)
a
airflow/ambient
L
length (m)
ch
chemical
m"
mass flux (kg/m2-s)
con
concurrent
∆P
pressure difference (Pa)
cond
conduction
q"
heat flux (kW/m2)
conv
convection

regression rate (m/s)
ex
extinction
Re
Reynolds number (-)
f
fire
t
time (s)
F
fuel
T
temperature (K)
o
initial
ua
internal airflow velocity (m/s)
ox
oxygen
Ua
external airflow velocity (m/s)
p
preheating
V
fire propagation rate (cm/min)
r
residence

distance (m)
sm
smoldering
Y
mass fraction (%)
T
thermal

S. Lin, T. Chow, X. Huang (2021) Smoldering Propagation and Blow-off on Consolidated Fuel under External Airflow,
Combustion and Flame, 234, 111685. https://doi.org/10.1016/j.combustflame.2021.111685
3
trigger gas-phase homogenous oxidation under some specific conditions and result in smoldering-to-
flaming (StF) transition [19,34]. However, for flaming fires, flame spread increases with wind speed
due to increased convective heating on the unburnt fuel, rather than increased oxygen supply [33]. On
the other hand, the porosity and permeability of fuel also affect the oxidation-controlled smoldering
processes. For high-permeability fuels, such as cotton [15,35], pine needle [36], and PU foam [37],
oxygen can diffuse into the porous fuel to maintain an internal smoldering propagation. For low-
permeability consolidated fuels like wood [38], fiberboard [1], and coal chunk [8], smoldering can only
propagate from outside to inside like a regression process, because oxygen could only diffuse through
the porous char that is produced from the first-stage pyrolysis process [11]. Further increasing the
airflow velocity, the cooling effect becomes dominant, so eventually, smoldering extinction or blow-
off will occur, just like the blow-off of flame [39].
In the literature, the blow-off of flame on solid fuels has been extensively studied over the last 50
years [4,11]. For example, Loh and Fernandez-Pello [40] showed that the concurrent rate flame spread
over the thin paper first increased with the airflow velocity (< 1 m/s) but became almost constant until
blow-off at about 3 m/s. A similar trend and blow-off wind speed were also observed for the concurrent
flame spread on thin electrical wires [41]. In general, the blow-off of opposed flame spread is easier,
usually at an airflow velocity lower than 1 m/s [42,43]. Comparatively, the research on the blow-off of
smoldering is limited; and generally, it is more difficult to blow off persistent smoldering fire. Palmer
[1] found that the blow-off limit of opposed smoldering propagation over fiberboard was about 7 m/s,
but the concurrent smoldering propagation could still be sustained at 10 m/s [1,11]. Like the flame,
most smoldering extinction processes result from a local energy imbalance, where the cooling rate is
larger than the heat-release rate from exothermic oxidations [4,39,44]. Thus, decreasing oxygen
concentration and pressure promotes the blow-off of smoldering under a smaller airflow [19,20]. So far,
no study has addressed the smoldering propagation at large wind speeds over 10 m/s and the blow-off
limits of persistent smoldering fire; thus, there is a big knowledge gap.
This work investigated both concurrent and opposed smoldering propagations over cylindrical
consolidated biomasses (incenses) with different fuel diameters (1.5-5 mm) and densities (720-1,100
kg/m3). The external airflow velocity of up to 50 m/s in a small wind tunnel was applied to explore the
blow-off limits. The theoretical analysis was proposed to explain the influence of environmental and
fuel properties on smoldering propagation and critical conditions of blow-off.
2. Experimental Methods
2.1. Materials
The cylindrical consolidated rod (i.e., incense), a representative biomass fuel that is prone to
smoldering combustion, was tested in this work (Fig. 1a). The incense is an aromatic biotic material
that is widely used in cultural and religious events in Asia. It mainly consists of mixed wood dust from
the aromatic plants (e.g., from sage and cedar) and has homogenous porosity and composition [45]. The

S. Lin, T. Chow, X. Huang (2021) Smoldering Propagation and Blow-off on Consolidated Fuel under External Airflow,
Combustion and Flame, 234, 111685. https://doi.org/10.1016/j.combustflame.2021.111685
4
thermal analysis (TGA-DSC) of this incense was conducted, and the data is shown in Fig. A1 of the
Appendix. The details of the front and cross-section of the incense are also shown in Fig. 1a. Unlike the
cotton bales and plastic foams, the dust particles inside the incense are densely packed, so oxygen is
difficult to flow or diffuse into its internal structure.
Before the test, the incenses were first oven-dried at 75 oC for at least 48 h. Afterward, all samples
were placed into an electronic dry cabinet to avoid the re-absorbing of moisture from the air. To explore
the effect of fuel diameter () and density () on the smoldering propagation, two groups of experiments
were designed:
(Ⅰ) three sample diameters of 1.5, 2.5, and 5.0 mm with a constant fuel density of 720 kg/m3, and
(Ⅱ) three sample densities of 720, 920, and 1,100 kg/m3 with a constant diameter of 1.5 mm.
To help estimate the rate of smoldering propagation, the long incense rod was cut into 10-15 cm samples
and marked like a ruler with an interval of 1 cm (see Fig. 1a).
2.2. Environmental control
The experiments of smoldering propagation and blow-off under external airflow were conducted
inside a small wind tunnel. The customized tubular wind tunnel was made of quartz glass and had an
inner diameter () of 2 cm and a length of 20 cm, as illustrated in Fig. 1(b). The airflow (20.9% oxygen)
from the compressed tank was fed through the bottom of the quartz glass tube, and then homogenized
through a layer of small steel beads. A similar setup was used previously to study the flame spread [24]
and smoldering propagation [19] under opposed flow with different oxygen mass fractions. Before the
test, the airflow velocity ( up to 50 m/s) was controlled and measured by a precision anemometer.
Fig. 1. (a) Photos of cylindrical incenses with different diameters with enlarged details of surface and
cross-section, and (b) schematic of experimental setups for concurrent and opposed smoldering
propagation under external airflow.

S. Lin, T. Chow, X. Huang (2021) Smoldering Propagation and Blow-off on Consolidated Fuel under External Airflow,
Combustion and Flame, 234, 111685. https://doi.org/10.1016/j.combustflame.2021.111685
5
For an internal flow in a circular tube of diameter , the Reynolds number () can be calculated
as 
, where  m2/s is the kinematic viscosity of the air at ambient
temperature [46]. In other words, when the airflow velocity is larger than 2 m/s, the mainstream flow
inside the tube is turbulent (> 2,300) where its velocity profile is relatively flat. Because the inlet
flow is disturbed through a long gas pipeline and a layer of steel bead, it is expected that the downstream
flow through the tube is quite turbulent. On the other hand, the Reynolds number for the external airflow
over the fuel surface (
) is much smaller than the turbulent limit of , so the
boundary-layer flow on the fuel surface is laminar.
2.3. Test procedure
The biomass sample was ignited by a torch at one end, and then inserted into the middle part of
the wind tunnel and fixed vertically at the tube axis by a sample holder, as shown in Fig. 1(b). The
ignited end (~5 mm) was placed on the bottom for the concurrent smoldering propagation, while for the
opposed propagation, the ignited end was on the top. To reduce the effect of ignition, the smoldering
front was allowed to propagate 20-30 mm away from the ignition region before calculating the
smoldering propagation rate. Afterward, wind with prescribed speed was applied, and shortly after, the
smoldering propagation reached the quasi-steady state (see more details in Fig. A2 in Appendix). The
external wind was applied in a step-increase manner from no wind (i.e.,  as the base case) until
the critical airflow velocity for blow-off () was found. To start a new test under a different wind
velocity, a fresh fuel sample was used.
A side-view digital video camera was used to capture the time history of the smoldering front.
Through image analysis frame by frame, the instantaneous smoldering propagation rate () can be
calculated as  
, where  is the required duration for a smoldering front to propagate for a
certain distance of . Then, we could judge whether a steady-state propagation was reached (see Fig.
A2 in the Appendix). For each scenario, tests were repeated at least three times to quantify the standard
deviations, and more repeating tests were conducted near the blow-off limit. In general, good
experimental repeatability was found. During the tests, the ambient temperature () was 23 ± 2 oC, and
the relative humidity was 50 ± 10%.
3. Results and Discussion
3.1. Smoldering phenomena
Fig. 2(a) and (b) shows some typical photos of concurrent and opposed smoldering propagation
under different airflow velocities of 0, 5, and 10 m/s with fuel diameters of 1.5, 2.5, and 5.0 mm. As
the wind velocity increased, the smoldering of incense was stronger due to a better oxygen supply,
where the conical reaction surface was hot enough to emit visible light (glowing incandescence) [11].
However, no smoldering-to-flaming transition was observed in this work, different from the past low-
airflow tests [19–21]. This was probably because the external wind was already large enough to blow

S. Lin, T. Chow, X. Huang (2021) Smoldering Propagation and Blow-off on Consolidated Fuel under External Airflow,
Combustion and Flame, 234, 111685. https://doi.org/10.1016/j.combustflame.2021.111685
6
off the flame (usually < 5 m/s [40–43]). On the other hand, except for oxygen supply, the permeability
of a fuel and its ability to remain consolidated may also affect this transition [33]. Nevertheless,
increasing the oxygen concentration could promote the transition to flame in a smaller airflow [34].
Moreover, compared to the opposed propagation, the glowing zone is brighter for the concurrent
propagation under the same airflow velocity. The length of the glowing zone ( or smoldering front
thickness) increased as the fuel diameter increased, but it was insensitive to the airflow velocity unless
near the blow-off limit. The flat leading edge of the glowing region (not the tip of conical shape) was
used to track the smoldering front. The glowing tip might not be the perfectly conical shape or clearly
observed, because an ash layer sometimes remained and covered the conical tip, just like the burning
cigarette (see the supplementary video). Fig. 2(c) also shows a typical blow-off process for the
smoldering over a 2.5-mm thick incense, where the opposed airflow velocity was increased to 15 m/s.
Gradually, the smoldering (glowing) zone became weaker, flatter, and smaller. After maintaining for
about 3 min, the smoldering was eventually blown off.
Fig. 2 Smoldering propagation on incense rods of 1.5, 2.5, and 5.0-mm diameters under (a) concurrent, and
(b) opposed airflow velocities of 0, 5, and 10 m/s; and (c) blow-off for smoldering on a 2.5-mm incense
under the opposed airflow velocity of 15 m/s.
3.2. Smoldering propagation rate vs. airflow direction
Fig. 3 compares the rate of smoldering propagation at different airflow directions. As expected,
the concurrent smoldering propagation is much faster than the opposed propagation, and the trend of
which is essentially the same as flame spread [11]. For example, for a 2.5-mm thick incense, the

S. Lin, T. Chow, X. Huang (2021) Smoldering Propagation and Blow-off on Consolidated Fuel under External Airflow,
Combustion and Flame, 234, 111685. https://doi.org/10.1016/j.combustflame.2021.111685
7
smoldering propagation rate is around 1.9 cm/min under a concurrent airflow of 5 m/s, tripling that
under an opposed airflow.
In general, the fire spread can be viewed as a continuous ignition process [9,11]. Thus, its rate is
driven by the heat transfer from the oxidation zone () and resisted by the fuel thermal inertia ()
[11] as
 
 


where , ,  , and   are the fuel bulk density, specific heat capacity,
smoldering temperature, and enthalpy change, respectively. The effect of permeability or porosity ()
could be reflected by the difference in bulk density () as , where  is the solid
density of biomass sample. For smoldering fire propagation, the preheated length () from glowing
char-oxidation zone to the unburnt zone is close to the thermal penetration depth (, i.e., ,
because both are the characteristic length of heat conduction in solid fuel [11].
As illustrated in Fig. 3(b), for concurrent smoldering propagation, the airflow can directly attack
the conical reaction front, so partial airflow may permeate into the porous glowing zone in the form of
a Darcy flow. The excessive oxygen supply intensifies the char oxidation and increases smoldering
temperature (see intense incandescence in Fig. 2(a)), so a larger preheating flux () will be conducted
from the reaction front to the preheated zone. In addition, the conical glowing zone may preheat the
airflow boundary layer, which can preheat the downstream unburnt fuel via convection. Both effects of
the concurrent airflow can speed up the smoldering propagation.
Fig. 3. (a) Comparison of smoldering propagation rate under external concurrent and opposed airflow,
where the markers show the average values and error bars show the standard deviations, and (b) schematic
diagrams of smoldering propagation under concurrent and opposed airflow.
In contrast, for the smoldering propagation under opposed airflow, the cool airflow can directly
cool the unburnt zone, reducing the preheating from the hot glowing zone () to the preheat zone.

S. Lin, T. Chow, X. Huang (2021) Smoldering Propagation and Blow-off on Consolidated Fuel under External Airflow,
Combustion and Flame, 234, 111685. https://doi.org/10.1016/j.combustflame.2021.111685
8
Furthermore, the oxygen can only reach the char surface via diffusion of the boundary layer, rather than
the pressure-driven Darcy flow under concurrent airflow. Thus, the oxygen supply from the opposed
airflow is less sufficient, slowing down the smoldering propagation. The relatively limited oxygen
supply of opposed smoldering is also reflected by a weaker glowing zone in Fig. 2(b).
3.3. Effect of airflow velocity
Fig. 3 also illustrates the effect of airflow velocity on the smoldering propagation rate, where a
similar trend is found for both concurrent and opposed propagations (see more comparisons in Figs. 4a-
b and 5a-b). That is, as the external airflow velocity increases, the smoldering propagation rate first
increases rapidly to the maximum value (O2-limited Regime) and then remains constant over a wide
range of airflow velocities (Thermal Regime). Subsequently, the propagation rate slightly decreases
(Chemical Regime) until blow-off, following a similar pattern of concurrent flame spread [41,42].
In a small-airflow regime, the smoldering temperature increases with airflow velocity, indicated
by a brighter glowing zone. Therefore, oxygen supply controls the smoldering propagation in this
regime, while the cooling effect of airflow is negligible. For example, as the concurrent airflow velocity
increases from 0 m/s to 3 m/s, the rate of smoldering propagation on the 2.5-mm thick fuel
monotonically increases from 0.8 cm/min to 1.6 cm/min. Such an increasing trend is defined as the O2-
limited Regime, referring to the terminology widely used for the opposed flame spread [11,14,17].
For a consolidated fuel, the smoldering propagation could be regarded as a burning or fuel-
regression process, similar to the burning of a candle or the premixed flame [11,15,29]. Therefore, the
smoldering propagation rate () is the same as the regression rate () as
 




(O2-limited Regime)
where  is the velocity of internal airflow inside the conical porous char. Its magnitude could be
estimated by Darcy’s law dominated in the concurrent smoldering and by the diffusion within the
boundary layer dominated in the opposed smoldering as







 




(concurrent)






(opposed) 
where the Nusselt number changes with flow velocity and diameter as  with 
. For opposed smoldering propagation, the internal airflow velocity still changes with the external
airflow () but is several orders of magnitude smaller than that of concurrent smoldering propagation.
Therefore, the smoldering propagation rate at the O2-limited Regime increases with the airflow velocity,
regardless of the flow direction (see Fig. 3a).

S. Lin, T. Chow, X. Huang (2021) Smoldering Propagation and Blow-off on Consolidated Fuel under External Airflow,
Combustion and Flame, 234, 111685. https://doi.org/10.1016/j.combustflame.2021.111685
9
Continuously increasing the airflow velocity, the smoldering propagation rate becomes stable. For
example, the concurrent propagation rate on the 2.5-mm thick fuel remains at 2.1 ± 0.3 cm/min from 7
m/s to 23 m/s in Fig. 3(a), regardless of the airflow velocity. In this large-airflow regime, the unlimited
oxygen supply no longer affects the smoldering propagation rate. Instead, the thermal conduction within
the fuel ( ) starts to dominate the smoldering propagation [11]. This behavior is
similar to the Thermal Regime of the flame spread, where the preheating of flame controls the rate of
flame spread [42,47]. Based on Eq. (1), the smoldering propagation rate at the Thermal Regime is free
of oxygen effect and reach the maximum value as
  
  
 
(Thermal Regime)
where  and  are the fuel thermal conductivity and diffusivity, and  is the thermal length within
the fuel. Therefore, the Thermal-Regime smoldering propagation rate is insensitive to the external
airflow velocity.
Fig. 4 Effect of fuel diameter on the rate of smoldering propagation under (a) concurrent and (b) opposed
airflow, (c) maximum smoldering propagation rate and (d) blow-off limits.
Further increasing the external airflow velocity, the smoldering propagation rate eventually starts
to decrease, where the cooling effect of external airflow (see Fig. 3b) on char-oxidation reaction at the

S. Lin, T. Chow, X. Huang (2021) Smoldering Propagation and Blow-off on Consolidated Fuel under External Airflow,
Combustion and Flame, 234, 111685. https://doi.org/10.1016/j.combustflame.2021.111685
10
smoldering front can no longer be neglected. Then, the smoldering propagation rate is controlled by the
competition between smoldering heat release and environmental cooling as
 
 

 


 (Chemical Regime) 
where  and  are the rate and heat of smoldering reaction, respectively. Analogous to the flame
spread [11,17], such a smoldering propagation is called the Chemical Regime [11]. Thus, as the airflow
increases, the convective cooling (
 ) increases to slow down the smoldering propagation. Eventually,
the cooling rate of airflow may equal or exceed the heat release rate of smoldering (
 
 ), so
the blow-off or the quenching by airflow occurs (discussed more in Section 3.4). Similar smoldering
extinction behaviors were also observed in the quenching by the cold wall [29] and fuel moisture.
3.4. Smoldering blow-off limits
Table 1 and Fig. (4d, 5d) summarize the blow-off limits of both concurrent and opposed
smoldering propagation over incenses with different fuel diameters and densities. Clearly, the blow-off
of concurrent smoldering propagation is much more difficult than opposed smoldering propagation. For
example, for 2.5-mm thick incense, the blow-off limits of concurrent and opposed smoldering
propagation are 30 m/s and 14 m/s, respectively. As discussed in Section 3.2 and Fig. 3(b), compared
to the smoldering propagation under concurrent airflow, the opposed airflow can directly attack the
preheated zone, thus increasing cooling efficiency on the unburnt fuel. Therefore, smoldering
propagation is easier to achieve blow-off under opposed airflow. Such a trend is also similar to the
flame spread, where the blow-off of opposed flame spread can be achieved in a smaller wind speed [24].
On the other hand, as shown in Fig. 4(d), when the fuel density is 720 kg/m3, as the fuel diameter
increases from 1.5 mm to 5.0 mm, the blow-off airflow velocity () of smoldering propagation
decreases from 46 m/s to 24 m/s under the concurrent airflow and from 15 m/s and 13 m/s under the
opposed airflow, respectively. Similarly, as shown in Fig. 5(d), the blow-off limits of both concurrent
and opposed smoldering decrease as the fuel density increases from 720 kg/m3 to 1,100 kg/m3 with the
same fuel diameter of 1.5 mm (see more analysis in Section 3.5 and 3.6).
More importantly, all the blow-off airflow velocities of smoldering (13-46 m/s) in the present work
are higher than those of flame spread, for example, the concurrent flame spread over the thin wire (2
m/s) [41] and thin cellulose (~5.5 m/s) [48], or the opposed flame spread over PMMA rod (~3m/s) [24],
thin paper/PMMA sheet (~1 m/s) [42] and thin cellulose (0.4-1 m/s) [43]. The observed blow-off airflow
velocity of incense is also higher than 7 m/s of the opposed smoldering propagation over fiberboard [1].
Approximately, the blow-off airflow velocity of smoldering propagation is about one order of
magnitude larger than that of flame spread, so that smoldering is much more persistent than flaming.
From Eq. (5), the blow-off or the quenching by airflow occurs (i.e.,  ) when the cooling rate
of airflow equals to the heat release rate of smoldering as 
 
 , where the cooling flux at the

S. Lin, T. Chow, X. Huang (2021) Smoldering Propagation and Blow-off on Consolidated Fuel under External Airflow,
Combustion and Flame, 234, 111685. https://doi.org/10.1016/j.combustflame.2021.111685
11
extinction limit could be further expressed as [46]

 


For simplicity, by assuming , we obtain

 
 
 
 
Fig. 5 Effect of fuel density on the rate of smoldering propagation under (a) concurrent and (b) opposed
airflow, (c) maximum smoldering propagation rate, , and (d) blow-off airflow velocity, .
To further evaluate the cooling effect of external flow, a smoldering Damkohler number ()
could be proposed referring to the Da of flame, as the ratio of the flow residence time scale () to the
reaction time scale () [11] as


 



 

 
Similar concept was also proposed for heterogenous combustion of carbon by Tsuji and Matsui [49].
At the blow-off limit, a critical smoldering Damkohler number can be defined from Eqs. (7,8) as

S. Lin, T. Chow, X. Huang (2021) Smoldering Propagation and Blow-off on Consolidated Fuel under External Airflow,
Combustion and Flame, 234, 111685. https://doi.org/10.1016/j.combustflame.2021.111685
12


 
which is essentially a constant depending on fuel properties and flow conditions, like the conventional
critical Damkohler number for the blow-off limit of flame[9]. Note that as the fuel size and geometry
changes, the flow field ( and ) will change, so that the value of 
 will change accordingly.
Table 1. The maximum smoldering propagation rate () and blow-off airflow velocity () over
incenses with different fuel diameters and densities.
Diameter
 (mm)
Density
 (kg/m3)
Maximum smoldering rate, (cm/min)
Blow-off limit,  (m/s)
Concurrent
opposed
Concurrent
opposed
1.5
720
3.2
0.9
46
15
2.5
720
2.1
0.7
30
14
5.0
720
1.2
0.5
24
13
1.5
920
2.1
0.8
37
11
1.5
1,100
1.3
0.6
18
8
3.5. Effect of fuel diameter
Fig. 4(a-b) further compares the effect of fuel diameter () on smoldering propagation under
external airflow. For both concurrent and opposed smoldering propagations, the propagation rate
increases as the fuel diameter decreases. It is consistent with the trend of flame spread in the literature,
i.e., a faster flame spread for a smaller-diameter fuel [28,50]. For example, under the airflow velocity
of 5 m/s, as the fuel diameter increases from 1.5 mm to 5 mm, the concurrent smoldering propagation
rate decreases from 2.1 cm/min to 1.1 cm/min, and the opposed smoldering propagation rate declines
from 0.9 cm/min to 0.5 cm/min. Clearly, the maximum smoldering propagation rate also decreases with
the fuel diameter, as further compared in Fig. 4(c). From Eqs. (2,3), the internal airflow velocity ()
inside the conical porous char is inversely correlated with fuel diameter (), thus the rate of oxygen
supply decreases as the fuel diameter increases. As a result, the rate of smoldering propagation decreases
with the fuel diameter, agreeing with the experimental results in Fig. 4.
The concept of  number (i.e., Spalding mass transfer number) has been widely used to estimate
the flaming burning rate of liquid droplet fuels and solids [51–53]. Compared to conventional
gasification mass transfer driven by the flame sheet and heat conduction in the gas phase, the pyrolysis
surface for smoldering is driven by the char-oxidation and heat conduction in the solid phase. Thus, the
same concept can be adopted in describing smoldering burning (or propagation). For a cylindrical rod,
the smoldering propagation is two-dimensional in axial and radial directions (see the top view of control
volume in Fig. 6). Considering the smoldering propagation in the radial direction and the analogy with

S. Lin, T. Chow, X. Huang (2021) Smoldering Propagation and Blow-off on Consolidated Fuel under External Airflow,
Combustion and Flame, 234, 111685. https://doi.org/10.1016/j.combustflame.2021.111685
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flaming burning of droplet [13,52] or cylindrical rod [53], the burning flux (
) of incense can also be
approximated as

  

where  is a fitting correlation, and  is a constant for a given fuel. Thus, the smoldering rate in the
axial direction is comparable to the observed smoldering rate in the radial direction as
  



which decreases with the fuel diameter [52], agreeing with the experimental results in Fig. 4(a-c).
Because of the curvature effect, the conductive heat flux concentrates towards a smaller radius. A
similar expression is also derived from Eq. (4), with the diameter as the thermal length () as
 


As seen from Fig. 2, the smoldering front thickness () increases as the fuel diameter increases ().
Fig. 6. Schematic diagram of the 2-D (radial and axial) smoldering propagation on a cylindrical fuel and
the primary heat transfer processes.
On the other hand, as discussed in Section 3.4, the blow-off limit of smoldering was found to
decrease as the fuel diameter increases (Fig. 4d). This trend is opposite to the flame spread, where the
blow-off of a thinner fuel occurs at a smaller airflow velocity and the same critical strain rate (
) [24,41]. Fundamentally, the concept of strain rate can be used for flame because the external
wind can pull and bend the gaseous flame sheet. Nevertheless, the smoldering front in the solid phase
cannot be bent like a flame sheet by the external flow. Therefore, the definition of critical strain rate for
blow-off may not be applicable to smoldering combustion.
To explain the influence of fuel diameter on the smoldering blow-off limit (), a simplified
energy conservation equation is applied to the near-limit reaction zone (see the front view of control
volume in Fig. 6). At the blow-off extinction limit, the smoldering rate is zero; the reaction-zone

S. Lin, T. Chow, X. Huang (2021) Smoldering Propagation and Blow-off on Consolidated Fuel under External Airflow,
Combustion and Flame, 234, 111685. https://doi.org/10.1016/j.combustflame.2021.111685
14
thickness is minimal ( ); and the bottom size is already quenched by the large wind. Then, the
heat generation in the oxidation reaction zone is equal to the convective heat loss due to the airflow (
)
and the conduction to the preheat zone (
 ) as

   

where the convective heat loss from the side for the thin oxidation zone is neglected, and the oxidation
rate from the side has reached a maximum (
 ) and can no longer increase with airflow.
Then, the required convective cooling coefficient () can be derived, which also increases with the
increased airflow velocity and the decreased fuel diameter, as


 


where  
   is a smoldering constant, and  is assumed for
simplicity. Thus, by rearranging Eq. (13), the dependence of blow-off airflow velocity with fuel
diameter can be expressed as   

Therefore, as the fuel diameter () increases, the required external airflow velocity to blow off
smoldering fire decreases, agreeing with experimental results in Fig. 4(d). Note that if the fuel diameter
further decreases below 1 mm (i.e., an ultra-thin fuel), the strong wind may easily break and remove
the smoldering zone. Then, the extinction is no longer a blow-off but a fuel-removal, which needs
further experimental verification.
3.6. Effect of fuel density
Fig. 5(a-b) also shows the effect of fuel (bulk) density on the concurrent and opposed smoldering
propagation rate, where the maximum rate of smoldering propagation was further compared in Fig. 5c.
As expected, as the fuel density decreases, the smoldering propagation rate increases, agreeing with the
theoretical analysis of Eqs. (1,2) where the maximum propagation rate is inversely proportional to the
fuel density ( ). For example, as the fuel density increases from 720 to 1,100 kg/m3 under
the wind velocity of 10 m/s, the smoldering propagation rate decreases from 2.1 cm/min to 1.3 cm/min
for the concurrent spread and from 0.9 cm/min to 0.5 cm/min for the opposed spread, respectively.
As the (bulk) fuel density of porous media increases ( ), its porosity and
permeability decrease. Thus, at the blow-off limit, the maximum airflow into the porous fuel (
 )
decreases, which reduces the value of  in Eq. (14). Moreover, the thermal conductivity of fuel
increases with the density (), so that the radial heat conduction from the reaction zone to the
preheat zone also increases. From Eq. (14), we can see the required blow-off airflow velocity ()
decreases as the fuel density increases, agreeing with the experimental results in Fig. 5(d).

S. Lin, T. Chow, X. Huang (2021) Smoldering Propagation and Blow-off on Consolidated Fuel under External Airflow,
Combustion and Flame, 234, 111685. https://doi.org/10.1016/j.combustflame.2021.111685
15
4. Conclusions
In this work, we use experimental approaches to investigate the smoldering propagation and blow-
off over cylindrical incenses under concurrent and opposed external wind up to 50 m/s. There are no
experimental data on the smoldering propagation at large wind speeds over 10 m/s and the blow-off
limits of persistent smoldering fire before this study. For concurrent smoldering propagation, partial
airflow may permeate into the porous glowing zone in the form of a Darcy flow, while the oxygen can
only reach the char surface via diffusion for opposed smoldering propagation. Also, the conical glowing
zone may preheat the concurrent airflow boundary layer to preheat the downstream unburnt fuel, which
further promotes the concurrent smoldering propagation faster than the opposed propagation.
We also found that the smoldering propagation rate is very sensitive to the airflow rate. As external
airflow velocity increases, the smoldering propagation rate first increases (O2-limited Regime), and then
remains stable at its maximum value for a wide range of airflow velocity (Thermal Regime). Afterwards,
it slightly decreases (Chemical Regime) until blow-off. Comparatively, the flame-spread rate increases
with the wind speed due to increased convective heating rather than increased oxygen supply. This is a
significant difference between smoldering and flaming spread, because smoldering combustion is
controlled by both oxygen supply and heat loss.
We report for the first time that the blow-off airflow velocity of smoldering propagation (13~46
m/s) is around one order of magnitude larger than that of flame spread, and it decreases as the fuel
diameter or density increases. Blowing-off concurrent smoldering propagation is also more difficult
than opposed propagation, similar to the blow-off of flame spread. Future numerical simulations are
needed to reveal the underlying physical and chemical process of smoldering propagation and blow-off
under different airflow velocities.
CRediT authorship contribution statement
Shaorun Lin: Investigation, Writing-original draft, Formal analysis, Resources. Tsz Him Chow:
Investigation, Resources. Xinyan Huang: Conceptualization, Supervision, Writing-review & editing,
Funding acquisition.
Declaration of competing interest
The authors declare no conflicts of interest.
Acknowledgments
This research is funded by the National Natural Science Foundation of China (NSFC) No. 51876183
and the Society of Fire Protection Engineers (SFPE) Educational & Scientific Foundation. The authors
thank Dr. Supan Wang (Nanjing Tech Univ.) for helping conduct thermal analysis of the incense
sample. The comments from Dr. Han Yuan (Hong Kong PolyU) are also acknowledged.

S. Lin, T. Chow, X. Huang (2021) Smoldering Propagation and Blow-off on Consolidated Fuel under External Airflow,
Combustion and Flame, 234, 111685. https://doi.org/10.1016/j.combustflame.2021.111685
16
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Appendix
The incense sample was firstly pulverized into powders for TGA-DSC tests. The initial mass of
peat was about 5 mg, and samples were heated at the constant rates of 10 K/min. Two oxygen
concentrations were selected, 0% (nitrogen) and 21% (air). Experiments were repeated twice for each
case, and good repeatability is shown. Fig. A1 shows the mass-loss rate (DTG) and heat flow (DSC)
curves, respectively. Regardless of the oxygen concentration, the mass-loss rate rapidly increases at
around 250°C, which can be defined as the pyrolysis temperature. The heat of smoldering () can
be calculated by integrating the heat flow curve, and it is about 18 MJ/kg for this incense.
Fig. A1 TGA-DSC results of incense sample under air and nitrogen flow at a heating rate of 10
K/min, (a) normalized mass loss rate; and (b) heat flow as a function of temperature.
Fig. A2 shows some examples of required duration () for a reaction front to propagate through a
certain distance of  under different airflow directions and velocities. Good linearity between  and
 indicates the steady-state of smoldering fire propagation, where the slopes of the fitting lines are the
corresponding smoldering propagation rates ().
Fig. A2. Examples of smoldering front position () vs. the experimental duration () over the incense
with different diameters under different airflow velocities.