Combustion and Flame 190 (2018) 25–35

Contents lists available at ScienceDirect

Combustion and Flame

journal homepage: www.elsevier.com/locate/combustflame

An investigation of pyrolysis and ignition of moist leaf-like fuel

subject to convective heating

Babak Shotorban

∗, Banglore L. Yashwanth , Shankar Mahalingam , Dakota J. Haring

Department of Mechanical and Aerospace Engineering, The University of Alabama in Huntsville, Huntsville, AL 35899, USA

a r t i c l e i n f o

Article history:

Received 21 May 2016

Revised 5 November 2017

Accepted 6 November 2017

Keywords:

Pyrolysis

Live fuels

Ignition

Convection

Computational

a b s t r a c t

The burning of a thin rectangular-shape moist fuel element, representing a living leaf subject to con-

vective heating, was investigated computationally. The setup resembled a previous bench-scale experi-

mental setup (Pickett et al., Int. J. Wildland Fire 19 , 2010, 153-162), where a freshly harvested horizon-

tally oriented manzanita ( Arctostaphylos glandulosa ) leaf was held over a flat flame burner and burned

by its convective heating. Computations were performed by FDS coupled with an improved version of

Gpyro3D. This improvement was concerned with the calculation of the mean porosities in the compu-

tational cells to account for the net volume reduction that the condense phase experiences within the

computational cells during moisture evaporation and pyrolysis. The dry mass was assumed to consist

of cellulose, hemicellulose and lignin undergoing the pyrolysis reactions proposed by Miller and Bellan

( Combust. Sci. Technol. 126 , 1997, 97-137) for biomass. The reaction scheme was initially validated against

published experimental and computational TGA results. Then, the burning of leaf-like fuels with three ini-

tial fuel moisture contents (40%, 76%, 120%), selected as per the range of experimentally measured values,

was modeled. The time evolutions of the normalized mass were good for the modeled fuels with 76% and

120% FMCs and fair for the one with a 40% FMC, as compared to the experimental burning results of four

manzanita leaves with unspecified FMCs. The computed ignition time was also in good agreement with

the measurement. The computed burnout time was somewhat shorter than the measurement. Modeling

revealed the formation of unsteady flow structures, including vortices and regions with high strain rates,

near the fuel that acted as a bluff body against the stream of the burner exit. These structures played a

significant role in the spatial distribution of gas phase temperature and species around the fuel, which

in turn, had an impact on the ignition location. Fuel moisture content primarily affected the temperature

response of the fuel and solid phase decomposition.

© 2017 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

1

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. Introduction

The relative importance of the role of external heat transfer

echanisms in wildland fires has been a subject of discussion for

he past few decades [1,2] . Van Wagner [3] suggested three likely

echanisms: (1) flame-fuel contact [4] ; (2) radiation from burn-

ng fuel particles, i.e., embers [5] in pine needle fires in still air

6] , or other fires with low rates of spread; and (3) radiation from

ames, as the main mechanism for sloped beds or surface fires

riven by moderate winds. Anderson [7] performed experiments

nd modeling of fire behavior in otherwise still, ambient air, and

oncluded that between 15% and 40% of the thermal energy re-

uired for fire propagation was supplied by radiation heat flux, and

he remainder was supplied by convection heat transfer. Frankman

t al. [8] concluded that ignition of the fuel element by radiation

∗ Corresponding author.

E-mail address: babak.shotorban@uah.edu (B. Shotorban).

t

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ttps://doi.org/10.1016/j.combustflame.2017.11.008

010-2180/© 2017 The Combustion Institute. Published by Elsevier Inc. All rights reserved

eating alone is more likely under circumstances where the fire

s very intense and even then it may still be dependent on pi-

ot/convective heat sources. Albini [9] developed a simple model

or the radiation-dominated heat transfer case, arguing that radia-

ion dominates for backing, no-wind and some heading fires while

onvection could play a larger role for other heading fires. Rother-

el [10] investigated the relative effects of convection and radi-

tion by performing heading, no wind, and backing burns on fine

uel beds. His temperature-time plots of fuel element and gas tem-

eratures suggested that radiation dominantly preheats fuel in no

ind and backing burns; however, for a heading fire, the fuel is

ignificantly preheated by convection. Pagni and Peterson [11] for-

ulated a simple model that included radiation, convection, and

onduction heat transfer modes and compared the model output

ith laboratory results in pine needle fuel beds [12] . They reported

hat under no-wind ambient conditions, radiation was dominant

hile in wind-aided fire spread, convection was the dominant

ode of heating of yet-to-burn fuel ahead of the fire.

.

26 B. Shotorban et al. / Combustion and Flame 190 (2018) 25–35

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Although the impact of heat transfer mechanisms on overall fire

behavior continues to be an area of study, relatively little work has

been done to examine the relative importance of convective and

radiative heat flux on the initial pyrolysis and subsequent ignition

of thin solid fuels. These processes precede the development of a

spreading fire, and play a significant role in fire spread. Even less

is known in situations involving live solid fuels that are charac-

terized by significant fuel moisture content (FMC). In particular,

the treatment of fuel moisture in previous studies has been sim-

plified or eliminated by considering dead fuels with little to no

moisture content [10,13,14] . Bartoli et al. [15] studied ignition of

dead pine needles and reported that forced convection of ambient

air delayed ignition due to dilution effect of pyrolysis gases and

due to convective cooling. There are several studies focused on the

thermal decomposition of the fuel and the nature of resulting py-

rolysis gases [16–18] . Yedinak et al. [2] reported that flame contact

was essential for fire spreads in their experimental work involving

in deep fuel beds. McAllister et al. [19] conducted experiments on

ignition of lodgepole pine and Douglas-fir needles where thermal

radiation alone was used as the heating mode. They showed that

an additional pilot source was required to initiate ignition. Anand

et al. [20] conducted physics-based modeling of McAllister et al.’s

experiments [19] and found the measured and calculated ignition

times in good agreement. On the other hand, Pickett et al. [21] per-

formed experiments on freshly harvested leaves of several species

including chamise where only convection heating was applied to

the fuel sample. They showed that leaves could ignite without the

aid of a pilot flame; however, it is important to note that their

experiments involved the introduction of a high temperature gas

Fig. 1. (a) Isometric view of computational domain showing thin solid fuel subjected to

domain along a zy -slice at x = 0 . Point A considered for a detailed investigation is located

products of combustion involving a mixture of methane, hydro-

en, nitrogen and oxygen over an FFB with some entrained air)

hich provides a favorable environment to ignite pyrolysis gases

manating from the leaf. Gallacher et al. [22] used a similar setup,

ncluding a radiative panel in the experiments, to investigate the

mpact of convection and combined convection-radiation heat flux.

heir findings indicated that ignition time and solid fuel temper-

ture had a strong dependence on the nature of heating mode

dopted in their experiments. Yashwanth et al. [23] studied the ef-

ects of thermal radiation on the pyrolysis, ignition, and burning of

moist leaf-like fuel element in a setup similar to [21] . They im-

roved and used the coupled FDS-Gpyro3D computational model

24–26] , and showed that it is possible to achieve ignition through

mposed radiation heat transfer provided the heat flux is suffi-

iently large. A shortcoming in Yashwanth et al.’s work was that

he solid fuel dry mass was composed of cellulose only. However,

n addition to this compound, hemicellulose and lignin constitute

he main compounds in biomass [27] and should be included in

he pyrolysis modeling [28,29] .

The current work is motivated by our desire to seek an im-

roved understanding of the physical processes that lead to py-

olysis and subsequent ignition of live fuel subject to convective

eating. Here, the computations are also performed by the cou-

led FDS-Gpyro3D model with an improvement made on Gpyro3D.

n this improvement, the calculation of the mean porosities in the

omputational cells follow a new formulation ( Appendix A ) to ac-

ount for the net volume reduction that the condense phase ex-

eriences within the cells during moisture evaporation and pyrol-

sis. The computational setup resembles a previous bench-scale

convective heating from the burner, (b) two-dimensional view of computational

at y = −0 . 01185 m, x = 0, z = 0 . 051 m.

B. Shotorban et al. / Combustion and Flame 190 (2018) 25–35 27

Table 1

Initial mass fractions of moisture and solid constituents within

the fuel.

FMC (%) Moisture Cellulose Hemicellulose Lignin

40 0.285 0.236 0.236 0.243

76 0.45 0.18 0.18 0.19

120 0.5457 0.1499 0.1499 0.1545

Table 2

Parameters for reactions R1–R4 [32] and R5 [33,34] .

Reaction A (s −1

)E (kJ/mol) �h (kJ/kg)

R1—cellulose 2.8 × 10 19 242.4 0

R2—cellulose 3.28 × 10 14 196.5 225

R3—cellulose 1.3 × 10 10 150.5 −20

R1—hemicellulose 2.1 × 10 16 186.7 0

R2—hemicellulose 8.75 × 10 15 202.4 225

R3—hemicellulose 2.6 × 10 11 145.7 −20

R1—lignin 9.6 × 10 8 107.6 0

R2—lignin 1.5 × 10 9 143.8 225

R3—lignin 7.7 × 10 6 111.4 −20

R4 4.28 × 10 6 108 −42

R5 5.13 × 10 10 88 2260

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x

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Virgin Active

Tar

X Char + (1-X ) Gases

GasesR4

R1

R2

R3

Moisture Water vaporR5

Fig. 2. Generic reactions (R1–R4) of cellulose, hemicellulose and lignin with char

formation mass ratio X = 0 . 35 , 0 . 60 , and 0 . 75 , respectively [32] , and moisture evap-

oration (R5).

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Table 3

Thermophysical properties of solid fuel constituents. Here, ρ is apparent density,

ˆ ρ true density, k thermal conductivity, and c specific heat capacity. Dry fuel is

regarded to any of the species cellulose, hemicellulose and lignin, assumed to

have identical thermophysical properties [32] .

Species ρ (kg/m

3 ) ˆ ρ ( kg / m

3 ) k (W/mK) c (kJ/kg K) Reference

Moisture – 10 0 0 0.596 3.9 [35]

Dry fuel 650 2167 0.1256 2.3 [32]

Char 350 2333 0.0837 1.1 [32]

xperimental setup [21] , where a freshly harvested horizontally

riented manzanita ( Arctostaphylos glandulosa ) leaf was held over

n FFB and burned by its convective heating.

. Problem setup and models

Figure 1 shows a schematic of the considered computational

onfiguration, which resembles the experimental setup used by

ickett et al. [21] for burning manzanita leaves. The solid fuel el-

ment displayed in Fig. 1 (a) is a rectangular cuboid with dimen-

ions 23.7 × 23.7 × 0.51 mm (length × width × thickness) modeled

y Gpyro with a grid resolution of 48 × 48 × 10. The solid fuel di-

ensions are representative of the range of manzanita leaf with a

easured thickness of 0.15 mm to 1.0 mm, length of 20 mm to

0 mm, and width of 13 mm and 26 mm, as reported by Pickett

30] . The modeled fuel dimensions were selected with an objec-

ive of having the mass and surface area as close as possible to

he mean of the empirically measured ones. Pickett et al. [21] re-

orted 5.62 ± 0.39 cm

2 (mean ± s.e.) and 0.2197 ± 0.0127 g for the

easured surface area and mass of manzanita leaves, respectively.

he surface area of the modeled fuel is 5.617 cm

2 , almost identi-

al to the mean of the measured ones. This surface area, combined

ith the selected thickness of 0.51 mm (which is almost in the

iddle of the range of the measured thickness) corresponds to a

uel mass of 0.207, 0.217, 0.230 g for FMCs of 40%, 76%, 120%, re-

pectively. The width and length of the fuel, which are within the

easured ranges [30] , are set identical because otherwise the as-

ect ratio (length/width) would be introduced as a new parameter,

hich in turn, would introduce another parameter as to how the

uel is aligned with respect to the FFB.

The entire computational domain has dimensions

.18 × 0.18 × 0.32 m with a grid resolution of 120 × 120 × 192 in

, y and z directions, respectively. This region excluding the solid

uel domain represents the domain of the gaseous phase mod-

led by FDS. The solid fuel element is centered in the gas-phase

omain and is located at z = 0.05 m. The initial temperature,

MC, pressure, gaseous species mass fractions, and condensed

hase species were set uniform throughout the solid fuel. The

imensions of the FFB exit, which is the source of convective

eating are 0.075 × 0.03 m (length × width) [21,30] . In this paper,

he burner and the gas phase combustion within the burner is not

odeled. Instead, convective heating of the porous solid fuel is

ccomplished by introducing heated air with a uniform velocity

f 1 m/s and temperature of 1100 °C, which enters the domain

hrough this rectangular region shown by burner exit in Fig. 1 .

odeling of the FFB used in the experiments by a hot air source

s reasonable: Pickett [30] measured the height of the FFB flame

o be between 1 and 3 m and the leaf samples were held at 5 cm

bove the FFB, well beyond the reach of the FFB flame. He noted

hat the FFB post-flame leaf-free conditions were 987 ± 12 °C and

0 mol% O 2 at 5 cm above the burner. Our simulations meet this

hermal condition almost exactly, however, the oxygen concen-

ration is somewhat different from that in the air condition. An

pen boundary condition [24] is used on the top, lateral, bottom

xterior boundaries of the FDS domain. The burner is modeled as

n obstacle [24] with a top surface constituting the burner exit,

s illustrated above. The interface boundaries between Gpyro and

DS are treated for consistent heat and gas-phase mass transfer

etween the FDS and Gpyro domains, as illustrated in the previous

aper [23] .

A detailed description of the mathematical formulation and nu-

erical approaches of Gpyro3D-FDS can be found in Refs 23–26 .

or Gpyro, a new formulation was developed in the current study

o calculate the mean porosities in the computational cells while

ccounting for the net volume reduction that the condense phase

xperiences within the cells during moisture evaporation and py-

olysis. Details of this formulation are given in Appendix A .

Initially, the fuel consisted of moisture, cellulose, hemicellulose,

ignin in the solid phase and the gas phase within the solid fuel

onsisted of standard air (nitrogen and oxygen). The respective ini-

ial mass fractions of moisture and dry constituents are given in

able 1 . The percentage mass distributions of cellulose, hemicellu-

ose and lignin in the dry fuel were 33, 33 and 34%, respectively

31] . The initial temperature was set to an ambient temperature of

00 K.

The reaction scheme proposed by Miller and Bellan [32] for dry

iomass was utilized in this work (see Fig. 2 ). Each of the dry

pecies, i.e., cellulose, hemicellulose and lignin, undergoes four re-

ctions R1–R4 as shown in Fig. 2 . Reactions R1–R3 are primary

eactions and R4 is a secondary reaction. The primary reactions

28 B. Shotorban et al. / Combustion and Flame 190 (2018) 25–35

500 600 700 800Temperature (K)

0

0.2

0.4

0.6

0.8

1

Dim

ensi

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ss r

esid

ual m

ass

5K/min (K89)20K/min (K89)80K/min (K89)5K/min (MB97)20K/min (MB97)80K/min (MB97)5K/min (present study)20K/min (present study)80K/min (present study)

Fig. 3. Dimensionless residual mass in TGA experiments by Koufopanos

et al. [36] (K89), and their zero-dimensional model of Miller and Bellan [32] (MB97)

and of the current study.

0 5 10 15 20 25Time (s)

0

0.2

0.4

0.6

0.8

1

m / m

0

Exp #1Exp #2 Exp #3 Exp #4 FMC 40%FMC 76%FMC 120%

0 5 10 15 20 25Time (s)

0

0.01

0.02

0.03

0.04

0.05

0.06

Mas

s lo

ss r

ate

(g/s

)

a

b

Fig. 4. Time histories of (a) mass normalized by initial mass, and (b) mass loss

rate; Exp #1–4 are for experiments performed on four manzanita leaves with un-

specified FMCs [21] . FMC 40%/76%/120% are three different FMCs modeled in the

current study.

a

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0 5 10 15 20 25

Time (s)

0

200

400

600

800

1000

1200

Tem

pera

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(°C

)

FMC 76%

0 5 10 15 20 25

Time (s)

0

0.1

0.2

0.3

0.4

0.5

0.6

Moi

stur

e m

ass

frac

tion

FMC-40%FMC-76%FMC-120%

Fig. 5. Time histories of (a) temperature for FMC of 76% and (b) moisture mass

fraction for various FMCs at point A (see Fig. 1 ).

0 5 10 15 20 25

Time (s)

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Hea

t rel

ease

rat

e (k

W)

FMC 40%FMC 76%FMC 120%

Fig. 6. Time history of heat release rate for various initial FMCs.

are concerned with the conversion of the virgin species to an

active state which later breaks down to lower molecular weight

gases and char. The secondary reaction R4 is concerned with the

breakdown of tar to low molecular weight gases. In Fig. 2 , R5 de-

notes the water evaporation reaction, a single reaction proposed by

Bryden and Hagge [33] for both free and bound moisture. These re-

ctions with kinetic parameters given in Table 2 have been incor-

orated in Gpyro3D. The thermophysical properties are assumed

dentical between dry fuel species, i.e. active and virgin cellulose,

emicellulose and lignin [32] . The values of these properties for

he dry species and moisture are tabulated in Table 3 . Molecular

eights for the pyrolysis gas and tar are 28 and 40, respectively

B. Shotorban et al. / Combustion and Flame 190 (2018) 25–35 29

0 5 10 15 20 25

Time (s)

0

0.2

0.4

0.6

0.8

1M

ass

frac

tion water

cellulose (v)hemicellulose (v)lignin (v)cellulose (a)hemicellulose (a)lignin (a)char

Fig. 7. Time evolution of mass fractions of condensed phase species including virgin

(v) and active (a) dry species at point A for a fuel with an initial FMC of 76%.

a

0

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nd the thermal conductivity and specific heat for both are

.025 W/mK and 1.005 kJ/kg K, assumed to be air’s.

A simplified stoichiometric relation is used to model the chem-

cal reaction between air and fuel vapor, where the latter is mod-

ig. 8. Contours of the water mass fraction at (a) t = 9.5 s (b) t = 11 s on an xy -slice l

5115 m, for a fuel with an initial FMC of 76%.

led as methane:

H 4 + 2(O 2 + 3 . 76N 2 ) → CO 2 + 2H 2 O + 7 . 52N 2 . (1)

It is noted that the main pyrolysis gases produced by cellulose,

ontain carbon dioxide, carbon monoxide and hydrogen in addition

o methane. Yang et al. [27] showed that methane is a main gas

roduct during the pyrolysis of cellulose, hemicellulose and lignin.

ccordingly, this simplification is utilized in this paper.

To verify and validate the kinetic model described above, a

impler problem is considered first. It is the computational mod-

ling of the thermogravimetric analysis (TGA) experiments of

oufopanos et al. [36] , where wood samples were heated at the

ates of 5, 20 and 80 K/min. A zero-dimensional version of Gypro

s used here to model their experiments. It is noted that most

ench-scale pyrolysis experiments that have been conducted to

ate by design are zero-dimensional [25] . Since the experiments

id not use a moist specimen, the reaction R5 for moisture is dis-

arded during this validation exercise. The dimensionless residual

ass is displayed against temperature in Fig. 3 for experiments of

oufopanos et al. [36] , simulations of Miller and Bellan [32] and

imulations in the current study. It is seen that the residual mass

s. temperature in the current study is in excellent agreement with

he one in [32] for all three heating rates.

ocated at z = 0.051 m and (c) t = 9.5 s (d) t = 11 s on an xy -slice located at z =

30 B. Shotorban et al. / Combustion and Flame 190 (2018) 25–35

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3. Results and discussion

Figure 4 (a) shows the time evolution of the fuel mass normal-

ized by the initial mass m / m 0 . The curves labeled ‘Exp’ in the fig-

ure are experiments of Pickett et al. [21] with four manzanita leaf

samples. They did not specify the properties, e.g., FMC, mass etc.,

Fig. 9. Color contours of temperature in °C (a, d), oxygen mass fraction (b, e), and mas

assing x = 0 for a case with an initial FMC of 76%.

f these samples but reported that the FMC ranges between 44%

nd 107% for manzanita leaves. Fuels with three FMCs of 40%, 76%

nd 120%, were chosen to model in the current work. The time

istory of the normalized mass in each of the modeled cases seen

n Fig. 4 (a) is characterized by four time intervals: an initial short

nterval during which mass does not exhibit a substantial change,

s fraction of water vapor (c, f) at t = 3 s (a–c) and t = 11 . 5 s (d–f) on an zy -slice

B. Shotorban et al. / Combustion and Flame 190 (2018) 25–35 31

-0.05 0 0.05x (m)

0

500

1000

1500

2000

Tem

pera

ture

(°C

)

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Mas

s F

ract

ion

-0.05 0 0.05x (m)

0

500

1000

1500

2000

Tem

pera

ture

(°C

)

Temperature

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Mas

s F

ract

ion

O2

H2O

CO2

a

b

Fig. 10. Mass fraction of tracked gas species versus x at time (a) 3 s (b) 11.5 s at

y = 0 and z = 0.06 m in the gas phase domain for an initial FMC of 76%.

f

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ollowed by the second interval during which mass decreases al-

ost linearly, followed by a rapid decrease when the third inter-

al begins, followed by the fourth interval when fuel mass has

lateaued. The duration of the first interval seems identical among

he three modeled cases. The second interval is longer for a larger

MC and the duration of the third interval is almost the same for

ll FMCs. Figure 4 (a) shows a good agreement between the model-

ng and experimental results for FMC 76% and 120%. Specifically,

he modeled residual dimensionless masses for these two cases

re within the range of 0.17 and 0.2, where the residual dimen-

ionless masses of four experiments lie. The modeled residual di-

ensionless mass is 0.3 in this case. The modeled residual mass

s larger for a smaller FMC because a fuel with larger FMC has a

arger overall mass fraction of moisture and smaller mass fraction

f dry species. Hence, the residual mass, which is almost exclu-

ively char, when normalized by the initial mass, is smaller for a

arger FMC.

To gain a better insight into the time evolution of mass, the

ass loss rates (MLR) are plotted against time in Fig. 4 (b) for the

ame cases shown in panel (a). Four time intervals, introduced in

he previous paragraph, are more distinguishable in this figure. In

he first interval, starting from time zero, MLR gains no apprecia-

le value, as in this interval, the fuel heats up without experienc-

ng significant moisture evaporation. After the temperature of the

olid fuel increases sufficiently, the fuel moisture evaporates. This

rocess commences around the same time for all FMCs but takes

onger to complete for a fuel with larger FMC. The local minimum

orresponds to the time where the second interval ends, and as

een in Fig. 4 (b), this interval is longer for a larger FMC. Since the

nitial mass of all three modeled fuels is close, a fuel with a larger

MC in this figure has substantially more moisture. The third in-

erval, which starts from the local minimum and extends to the

ime at which MLR levels off has a spike. During this interval, py-

olysate gases are released. It is seen that the peak is higher for

fuel with a smaller FMC, as it has a larger dry mass. Given that

ickett et al. [21] smoothed the experimental data to generate MLR

lotted here, we still see a fair comparison between experimental

nd modeled results in Fig. 4 (b).

A classical combustion model for a thermally thin fuel element

ssumes that before ignition, all moisture first evaporates from the

ample at a temperature near the boiling point of water [10] . Pick-

tt et al. [21] discuss that when a combustible mixture of pyrolysis

ases is produced, ignition occurs shortly after moisture evapora-

ion is complete. To further investigate this behavior, the time his-

ories of temperature and mass fraction of moisture are plotted in

ig. 5 at a fixed point in the fuel. This point is indicated by A in

ig. 1 , which is located on the edge of the solid fuel which is par-

llel to the x axis.

Temperature increases nearly linearly with time as evident in

ig. 5 (a) until about t = 11 s when ignition occurs, and subse-

uently, temperature increases rapidly. After a flame is formed in

he gas phase, temperature rises further with time and the temper-

ture fluctuations, which have begun at around t = 10 s, become

ubstantially more pronounced. The moving average temperature

owever decreases and plateaus at approximately t = 13 s, while

he instantaneous temperature fluctuates between 400 ° and 700 °.he gas phase temperature close to point A fluctuates because of

he entrainment of the ambient gas into the burner exit flow and

he unsteady vortex shedding. Hence, the solid fuel at point A is

ubject to a hot stream of the burner exit at one instance and a

ool stream of the ambient gas at another. The air entertainment

nd vortex shedding are also active early on as the fuel is heated

p but the temperature fluctuation of the fuel at point A becomes

oticeable after 10 s. This amplitude increase is attributed to the

ecrease of the fuel thermal response time which is proportional

o the fuel mass. As evident in Fig. 4 (a), the fuel mass at initial

imes is much larger (by a factor of five for 76% FMC) than that at

ater times. Specifically, as seen in Fig. 5 (b), the fuel losses mass

rst by the moisture evaporation and then by the pyrolysis gas as

he virgin dry species become active and then char. The charring

rocess occurs very fast, starting at 9 s and completing at 12 s,

s will be seen in Fig. 7 , during which the local mass loss occurs

aster and the amplitude of temperature fluctuations increase sub-

tantially. It is seen in Fig. 5 (b) that the moisture evaporation is

ompleted earlier for the fuel with a smaller initial FMC; however,

he time of this completion differs by only one second, at most,

rom the fuel with the smallest FMC to the one with the highest.

he initial steadiness of the mass fractions of moisture is due to

he fact that the fuel at point A is not hot enough to lose water by

vaporation.

The time history of the heat release rate (HRR) is plotted in

ig. 6 . HRR quantifies the amount of heat generated by the sto-

chiometric reaction of pyrolyzate gases with oxygen in the gas

hase. A rapid increase of HRR seen in this figure indicates igni-

ion. So dependent on the FMC, the ignition times range between

and 13 s. A comparison of this figure to Fig. 5 (b) reveals that the

vaporation of moisture at point A is completed prior to ignition.

rom Fig. 6 , it could be said that the burnout time ranges between

2 and 17 s. The ignition and burnout times reported in the exper-

ments for a sample manzanita leaf with no specified mass or FMC

re 9 and 22 s [21] .

Figure 7 displays the time history of the virgin species and

ater at point A. As water mass fraction decreases by evapora-

ion, the mass fractions of the virgin species, i.e., virgin cellulose,

emicellulose and lignin increase. The peaks of the mass fractions

f the virgin species occur after water evaporation is complete. The

32 B. Shotorban et al. / Combustion and Flame 190 (2018) 25–35

Fig. 11. Contours of oxygen mass fraction and velocity vectors on an (a) xz slice

passing y = 0 and (b) yz slice passing x = 0 at t = 11 . 5 s for an initial FMC of 76%.

Fig. 12. Iso-surfaces of heat release rate (HRR) per unit volume with 24 kW/m

3 at

(a) t = 11 s, (b) t = 11 . 5 s, (c) t = 12 s for a case with an initial FMC of 76%. .

h

l

c

f

t

f

o

F

a

a

a

x

t

t

f

peaks are somewhat wide as the temperature is not high enough

yet to initiate the heterogeneous reactions. As the temperature of

the solid fuel increases, the virgin species transform to the active

species and then break down to char, pyrolysis gases, and tar. This

transformation is completed the earliest for hemicellulose and the

latest for cellulose.

The contours of the water mass fraction along two xy slices

passing through the solid fuel are displayed in Fig. 8 at two dif-

ferent times t = 9 . 5 and 11 s. These times are slightly before and

after ignition. It is seen in this figure that the fuel still contains

an appreciable amount of moisture when ignition occurs. Fig. 8 (c)

shows that drying fronts are formed and propagate from the top

and bottom edges toward the center in y direction. Later, as seen

in Fig. 8 (d), the drying fronts propagates from the center toward

the left and right edges in x direction. The reason for a higher rate

of water evaporation at the top and bottom edges is a wider length

of the burner opening in y direction. Overall, the regional variation

of the evaporation rate is a result of non-uniform heating mainly

caused by the non-uniformity of the flow of the surrounding gas

flow including the formation of vortices above the fuel.

Figure 9 displays the contours of temperature and mass frac-

tions of oxygen and water vapor in the FDS domain at t = 3 s (top

row) and t = 11 . 5 s (bottom row). There is a flame at the latter

time. Contour patterns are in part dictated by flow structures in-

cluding vortex shedding above the fuel. Vortices are formed by the

passing of burner exit flow over the solid fuel that acts as a bluff

body. These structures will be discussed later in this section. The

ot region right above the fuel at t = 11 . 5 s in Fig. 9 (d), which is

acking at t = 3 s in Fig. 9 (a), indicates the flame location. A high

oncentration of water vapor around and mainly above the solid

uel at t = 3 s, as seen in Fig. 9 (c), is originated from the fuel mois-

ure evaporation. Once the water vapor is released from the solid

uel and transported into the gas-phase domain, it displaces the

xygen around the solid fuel, reducing its mass fraction, as seen in

ig. 9 (b). On the other hand, a lower concentration of oxygen and

higher concentration of water vapor around and above the fuel,

s seen in Fig. 9 (e) and (f), is due to the combustion reaction.

The mass fractions of H 2 O, CO 2 , O 2 and temperature immedi-

tely above the solid fuel in the gas phase are plotted against the

coordinate at times t = 3 and 11.5 s in Fig. 10 . It is seen that at

ime 3 s ( Fig. 10 a), temperature at x = 0 has a local minimum with

wo peaks on the sides with slightly larger temperatures. The mass

raction of H O varies similarly. On the other hand, it is seen that

2

B. Shotorban et al. / Combustion and Flame 190 (2018) 25–35 33

w

A

f

t

f

i

i

c

f

t

h

i

x

c

F

m

t

f

o

p

t

a

t

a

d

a

F

4

h

w

t

a

f

e

F

F

s

a

i

d

t

m

e

e

w

i

w

t

m

d

w

f

f

C

v

T

w

t

c

t

m

d

b

m

t

r

t

t

f

f

n

t

w

h

a

m

a

s

A

R

B

S

E

b

t

J

A

a

d

1

T

s

r

c

f

G

a

s

s

s

i

ν

O

t

r

ν

w

s

t

t

c

(

here H 2 O is high, O 2 is low because of the oxygen displacement.

t time 11.5 s ( Fig. 10 b), when there is a flame, temperature has

our local peaks that correspond to the peaks of H 2 O and CO 2 . By

his time, all the moisture has evaporated from the fuel and H 2 O is

ormed as a result of combustion. Here, CO 2 follows a trend sim-

lar to H 2 O. From this figure, it could be said that O 2 is deficient

n the reaction zone because of two reasons: consumption during

ombustion and displacement by water vapor. However, the mass

raction of O 2 has a pronounced local peak close to the center of

he solid fuel.

In order to gain a better insight into oxygen distribution and

ow it is correlated with the velocity field, instantaneous veloc-

ty vectors and contours of oxygen mass fraction on two yz and

z slices are shown in Fig. 11 . Four vortices, symmetrically lo-

ated and separated by regions with high strain rates are visible in

ig. 11 (a). The outer vortices are unsteady, which are formed and

ove up, and the new ones are formed. Since a vortex is essen-

ially a low pressure region, two inner vortices displace the species

rom the mid part of the domain above the fuel to the edges. Two

uter vortices displace them further away from the fuel. This dis-

lacement explains the reason for the appearance of the peaks in

he profiles of the products of combustion, as displayed in Fig. 10 .

An iso-surface of HRR per unit volume of 24 kW/m

3 is shown

t three different times right after ignition in Fig. 12 . It is seen

hat ignition takes place at a region very close to the edges that

re parallel to x axis ( Fig. 12 a). These edges are where the fuel

ries more rapidly than other areas ( Fig. 8 ). As the flame is formed

nd grows, the iso-surface spreads to the other areas, as seen in

ig. 12 (b) and (c).

. Summary and conclusions

A kinetic mechanism for the chemical reactions of pyrolysis of

emicellulose, cellulose and lignin, and the evaporation of water

as incorporated in improved Gypro3D, which was coupled to FDS,

o model multi-component decomposition, ignition and burning in

thin, rectangular leaf-like fuel subject to convective heating. The

uel was oriented horizontally and heated up, to model previous

xperiments of the burning of individual manzanita leaves in an

FB apparatus [21] . Fuels with identical sizes but three different

MCs with a range consistent with the reported range of the mea-

ured ones for manzanita leaves were modeled. The surface area

nd mass of the modeled fuel matched the averages of the empir-

cally measured ones. The modeled fuel thickness was in the mid-

le of the range of the measured ones, and the length and width of

he modeled fuel were within the ranges reported in experiments.

The time evolutions of the modeled MLR and dimensionless

ass for FMCs of 40%, 76% and 120% were compared against the

xperimental ones obtained for four leaves with unspecified prop-

rties. The time evolutions of the modeled dimensionless mass

ith 76% and 120% FMCs were in good agreement with the ones

n experiments. This agreement was fair between the modeled fuel

ith a 40% FMC and the fuels burned in the experimens. Four

ime intervals characterized the time progression of the heated fuel

ass in the modeling. An initial short interval during which mass

id not exhibit a substantial change since in this interval, the fuel

as heated but the fuel did not reach a temperature high enough

or moisture evaporation. In the second interval, which was wider

or the fuel with a larger FMC, the mass decreased almost linearly.

loser to the end of this interval, the dry species converted from a

irgin state to an active state with some pyrolysate gases released.

he third interval, when the MLR started from a local minimum,

hich coincided roughly with the ignition, and extended to the

ime at which it leveled off. During this interval, pyrolysate gases

ontinued releasing and the MLR had a spike, which was due to

he flame formed above the leaf. In the fourth interval, the fuel

ass plateaued, as the charring process was completed.

The range of the ignition times calculated in the modeling for

ifferent FMCs included the experimental ignition time that had

een reported for a fuel sample with an unspecified FMC and

ass. The largest modeled burnout time was somewhat smaller

han the experimental burnout time of the fuel sample. The cur-

ent study showed that when ignition occurred, almost all mois-

ure had evaporated from the fuel. Although the moisture and

he solid species were initially uniformly distributed within the

uel, the moisture loss and pyrolysis occurred nonuniformly, as the

uel was heated. This nonuniformity was mainly attributed to the

onuniformity of the convective heat transfer to the fuel, which in

urn was attributed to the flow nonuniformity around the fuel. It

as characterized by a flow separation, vortices and regions with

igh strain rates, caused by the fuel that acted as a bluff body

gainst the burner exit flow. Given uncertainties in the experi-

ents cited and the uncertainties associated with thermophysical

nd chemical kinetic parameters used in the model, additional re-

earch is required to perform a comprehensive validation.

cknowledgments

The authors acknowledge the useful discussions with David

. Weise of the USDA Forest Service and Thomas H. Fletcher of

righam Young University. This work was supported by Joint Fire

ciences Program project 11-1-4-19 and DOD/EPA/DOE Strategic

nvironmental Research and Develop Program project RC-2640,

oth administered by the USDA Forest Service PSW Research Sta-

ion through cooperative agreements 11-JV-11272167-103 and 16-

V-11272167-025 with The University of Alabama in Huntsville.

ppendix A. Mathematical formulation

Gpyro assumes that each condensed phase reaction k consumes

single condensed phase species ( A k ) and forms a single con-

ensed phase species ( B k ) plus gases ( G k ):

kg A k → νB k kg B k + (1 − νB k ) kg G k . (A.1)

he unit kg is noted to indicate that this reaction is on a mass ba-

is and νB, k is the solid fraction of reaction k . As an example of

eaction (A.1) , refer to Fig. 2 where, for instance, active cellulose is

onsumed and char is formed in reaction R 3 . It is noted that char

ormation mass ratio X defined therein is the equivalent of νB, k . In

pyro3D [26] , a more general form of reaction (A.1) , where there

re consumed gases, and both consumed and produced gases con-

ist of different gaseous species. However, the form shown here is

ufficient for the ensuing discussion without losing the generality.

To correlate the solid fraction with the densities of the con-

umed and formed condensed species, a factor χ k is introduced

n Gpyro3D:

B k = 1 +

(ρB k

ρA k

− 1

)χk . (A.2)

n the other hand, Eq. (A.1) indicates that if δm A k and δm B k

denote

he masses of the consumed and formed condensed phase species,

espectively, then

B k =

δm B k

δm A k

=

ρB k

ρA k

δV B k

δV A k

, (A.3)

here δV A k and δV B k are the volumes of the consumed and formed

pecies, respectively. Eq. (A.3) is the key for further clarification of

he discussions made by Lautenberger [26] , allowing for the condi-

ions under which swelling, shrinkage and no volume change oc-

urs. If δV A k > δV B k , then shrinkage occurs. Using Eqs. (A.2) and

A.3) , one can readily show that this inequality is satisfied if

34 B. Shotorban et al. / Combustion and Flame 190 (2018) 25–35

w ∑

t

Y

r

ρ

w

s

ψ

T

i

s

w

t

s

c

m

Q

c

v

o

m

w

t

a

c

t

a

[

c

d

n

t

i

r

a

v

v

s

ρB k > ρA k

and χ k < 1; or if ρB k < ρA k

and χ k > 1. In contrast, if

δV A k < δV B k , then swelling occurs, a condition which is satisfied if

χ k > 1 and ρB k > ρA k

; or if χ k < 1 and ρB k < ρA k

. If δV A k = δV B k ,

i.e., no volume changes, then νB,k = ρB k /ρA k

and χk = 1 . On the

other hand, the nonnegativity of νB k is satisfied for ρB k

< ρA k if

χk ≤ ρA k / (ρA k

− ρB k ) . Using these criteria with the values given for

char formation mass ratios for charring reaction R3 in Fig. 2 , densi-

ties in Table 3 , and the values calculated for χ k in Eq. (A.2) , shrink-

age occurs in the cellulose charring whereas swelling occurs in the

hemicellulose and lignin charring. In the moisture evaporation re-

action R5, the moisture is consumed without the formation of any

other condensed phase species so one may say that an extreme

case of shrinkage occurs in the evaporation reaction. When a ma-

terial is comprised of multiple condense-phase species undergoing

shrinkage or swelling, there will be a net volume change of the

condensed phase.

The expansion or contraction of a pyrolyzating material, includ-

ing moisture evaporation, can be taken into account in the mod-

eling by changing the volumes of the computational cells (finite

volumes) and/or changing the mean porosities of the cells, accord-

ingly [37] . This porosity change can be justified by formation of

voids (including cracks) at subgrid scales as a result of the inter-

nal contraction of the condensed phase species and the moisture

evaporation. In the existing two- and three-dimensional version of

Gpyro, the cell volume change capability is lacking and the condi-

tion χk = 1 is imposed for heterogeneous reactions. However, for

given consumed and formed condense phase species densities, Eq.

(A.2) with χk = 1 , may not be satisfied. This condition is relaxed

in the current study by changing the mean porosities of the cells

through a new formulation to offset the contracted volume with-

out changing the cell volume.

The new formulation is developed through local spatial averag-

ing similar to the so-called homogenization technique [38] . Let δV

be a finite volume consisting of a condensed phase medium (solid

phase or liquid phase) with a volume of δV c and void with a vol-

ume of δV v such that δV = δV c + δV v . If the condensed phase con-

sists of multiple species, then δV c =

∑

i δV i , where δV i is the vol-

ume of species i . Three different volumetric averages are defined

for a property such as α:

〈 α〉 c =

1

δV c

∫ δV c

αdV, (A.4)

〈 α〉 v =

1

δV v

∫ δV v

αdV, (A.5)

α =

1

δV

∫ δV

αdV. (A.6)

It can be shown that these three volume averages satisfy

α = (1 − ε) 〈 α〉 c + ε〈 α〉 v , (A.7)

where ε = δV v /δV is the volume fraction of the void. If the volume

fraction of the species i is denoted by X i = δV i /δV c , it can be shown

that

〈 α〉 c =

∑

i

X i αi , (A.8)

where αi is the α property of species i , which is assumed uni-

formly distributed within δV i . On the other hand, by definition

of density, 〈 ρ〉 c =

∑

i δm i / ∑

i δV i , where ρ is the apparent density

and δm i is the mass of the species i , one can derive

〈 ρ〉 c =

∑

i

X i ρi =

( ∑

i

Y i ρi

) −1

. (A.9)

here Y i = δm i /δm is the mass fraction of the species i and δm =

i δm i . Both equalities in Eq. (A.9) are obtained by δm i = ρi δV i ,

hrough which one can also show that

i = X i

ρi

〈 ρ〉 c . (A.10)

Setting α ≡ρ in Eq. (A.7) and noting that 〈 ρ〉 v ≈ 0, one can de-

ive

= (1 − ε) 〈 ρ〉 c . (A.11)

Let us assume that the condensed-phase species i is porous

ith porosity ψ i . Using the definition of the porosity, one can

how that 〈 ψ〉 c =

∑

i X i ψ i and

= (1 − ε) 〈 ψ〉 c + ε. (A.12)

his equation is consistent with Eq. (A.7) since the porosity of void

s 〈 ψ〉 v = 1 . Here, ψ is the mean porosity in δV .

The three-dimensional condensed-phase equations of mass,

pecies and energy conservation are, respectively,

∂ ρ

∂t = − ˙ ω

′′′ f g , (A.13)

∂ ( ρY i )

∂t = ˙ ω

′′′ f i − ˙ ω

′′′ di , (A.14)

∂ (ρ ˜ h

)∂t

= −∇ · ˙ q

′′ − ˙ Q

′′′ s −g , +

∑

k

˙ Q

′′′ s,k −

∂ ˙ q ′′ r

∂z +

∑

i

(˙ ω

′′′ f i − ˙ ω

′′′ di

)h i ,

(A.15)

here ˙ ω

′′′ f g

, ˙ ω

′′′ f i

and ˙ ω

′′′ di

are the volumetric reaction rates of to-

al gas formation, species i formation and species i destruction, re-

pectively, ˙ Q

′′′ s −g is the volumetric rate of heat transfer from the

ondensed phase to the gas, which is correlated with the volu-

etric rate of heat release due to homogeneous gaseous reactions,˙

′′′ s,k

is the volumetric rate of heat release (or absorption) due to

ondensed phase reactions, ˙ q

′′ = −k ∇T is the conduction heat flux

ector, ˙ q ′′ r is the in-depth radiative heat flux, and h i is the enthalpy

f species i , and

˜ h =

∑

i Y i h i is the mass-based averaged enthalpy.

For the gas phase, the following three-dimensional equations of

ass and species conservations are solved:

∂ (ρg ψ

)∂t

+ ∇ · ˙ m

′′ = ˙ ω

′′′ f g , (A.16)

∂ (ρg ψ Y j

)∂t

+ ∇ ·(

˙ m

′′ Y j )

= −∇ ·(j ′′ j

)+ ˙ ω

′′′ f j − ˙ ω

′′′ dj , (A.17)

here ˙ m

′′ = − K ν (∇P − ρg g ) , j ′′

j = −ψ ρg D ∇Y j , Y j is the mass frac-

ion of the gas species j , and ν , K , and D are viscosity, permeability

nd diffusivity, respectively. Here, g indicates the gravitational ac-

eleration vector. Under the assumption that the gas phase is in

hermal equilibrium with the condensed phase, i.e., the local gas-

nd condensed-phase temperatures are identical.

The set of Eqs. (A .13) –(A .17) is similar to the one given in Gpyro

26] for a three dimensional domain that experiences no volume

hange. However, there is an important difference which is hid-

en in the definition of the variables with an overbar. Gpyro does

ot account for void, requiring δV v = 0 during pyrolysis. This condi-

ion, which is equivalent to setting ε = 0 or α = 〈 α〉 c in Eq. (A.7) ,

s valid if δV c = δV is fixed. This restriction is relaxed in the cur-

ent work by letting δV c reduce while δV is fixed and the imbal-

nce between these two volumes is remedied by introducing the

oid volume δV v = δV − δV c . Hence, noting that δV represents the

olume of a computational cell, the modeling of the fuel domain

hrinkage, which is a complex matter in a full three dimensional

B. Shotorban et al. / Combustion and Flame 190 (2018) 25–35 35

s

h

m

o

t

i

R

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

etup, is avoided. To include for the effect of void in Gpyro, we

ave revised it by introducing ε in the code and making adjust-

ents on the calculation of all properties that will be a function

f it through Eq. (A.7) . It is noted that Gpyro is capable to handle

he domain shrinkage in a one-dimensional configuration but not

n a two- or three-dimensional one.

eferences

[1] X. Zhou , S. Mahalingam , D.R. Weise , Modeling of marginal burning state offire spread in live chaparral shrub fuel bed, Combust. Flame 143 (3) (2005)

183–198 .

[2] K.M. Yedinak , J.D. Cohen , J.M. Forthofer , M.A. Finney , An examination of flameshape related to convection heat transfer in deep-fuel beds, Int. J. Wildland

Fire 19 (2010) 171–178 . [3] C.V. Wagner , Calculations on forest fire spread by flame radiation, Canada De-

partment of Forestry and Rural Development (1967) . Forestry Branch Depart-mental Publication No. 1185

[4] G.M. Byram , H.B. Clements , E.R. Elliott , P.M. George , An experimental study ofmodel fires, Technical Report, 1964 . DTIC Document.

[5] P.H. Thomas , D.L. Simms , H.G. Wraight , Fire spread in wooden cribs, Fire Saf.

Sci. 537 (1964) 1 . [6] H.E. Anderson , R.C. Rothermel , Influence of moisture and wind upon the char-

acteristics of free-burning fires, Symp. (Int.) Combust. 10 (1965) 1009–1019 .Elsevier.

[7] H.E. Anderson , Heat transfer and fire spread, Intermountain Forest and RangeExperiment Station, Forest Service, US Department of Agriculture, 1969 .

[8] D. Frankman , B.W. Webb , B.W. Butler , D.J. Latham , Fine fuel heating by radiant

flux, Combust. Sci. Technol. 182 (2010) 215–230 . [9] F.A. Albini , A model for fire spread in wildland fuels by-radiation, Combust.

Sci. Technol. 42 (1985) 229–258 . [10] R. Rothermel, A mathematical model for predicting fire spread in wildland fu-

els, U.S. Department of Agriculture, Intermountain Forest and Range Experi-ment Station, Ogden, UT, 1972 Research paper INT-115 . http://www.treesearch.

fs.fed.us/pubs/32533 .

[11] P.J. Pagni , T.G. Peterson , Flame spread through porous fuels, Symp. (Int.) Com-bust. 14 (1973) 1099–1107 . Elsevier.

[12] R.C. Rothermel , H.E. Anderson , et al. , Fire spread characteristics determined inlaboratory, 1966 .

[13] A .M. Grishin , V.A . Perminov , Mathematical modeling of the ignition of treecrowns, Combust. Explos. Shock Waves 34 (1998) 378–386 .

[14] B. Porterie , J.C. Loraud , L.O. Bellemare , J.L. Consalvi , A physically based model

of the onset of crowning, Combust. Sci. Technol. 175 (2003) 1109–1141 . [15] P. Bartoli , A. Simeoni , H. Biteau , J.L. Torero , P.-A. Santoni , Determination of the

main parameters influencing forest fuel combustion dynamics, Fire Saf. J. 46(2011) 27–33 .

[16] C.W. Philpot , Influence of mineral content on the pyrolysis of plant materials,Forest Sci. 16 (1970) 461–471 .

[17] R.A. Susott , Characterization of the thermal properties of forest fuels by com-

bustible gas analysis, Forest Sci. 28 (1982) 404–420 . [18] J.M. Rogers , R.A. Susott , R.G. Kelsey , Chemical composition of forest fuels af-

fecting their thermal behavior, Can. J. Forest Res. 16 (1986) 721–726 .

[19] S. McAllister , I. Grenfell , A. Hadlow , W. Jolly , M. Finney , J. Cohen , Piloted igni-tion of live forest fuels, Fire Saf. J. 51 (2012) 133–142 .

20] C. Anand , B. Shotorban , S. Mahalingam , S. McAllister , D.R. Weise , Physics-basedmodeling of live wildland fuel ignition experiments in the fist apparatus, Com-

bust. Sci. Technol. 189 (2017) 1551–1570 . [21] B.M. Pickett , C. Isackson , R. Wunder , T.H. Fletcher , B.W. Butler , D.R. Weise , Ex-

perimental measurements during combustion of moist individual foliage sam-ples, Int. J. Wildland Fire 19 (2010) 153–162 .

22] J.R. Gallacher , V. Lansinger , S. Hansen , D. Jack , D.R. Weise , T.H. Fletcher , Effects

of season and heating mode on ignition and burning behavior of three speciesof live fuel measured in a flat-flame burner system, Spring Technical Meeting

of the Western States Section of the Combustion Institute, Pasadena, CA (2014) .23] B. Yashwanth , B. Shotorban , S. Mahalingam , C. Lautenberger , D. Weise , A nu-

merical investigation of the influence of radiation and moisture content onpyrolysis and ignition of a leaf-like fuel element, Combust. Flame 163 (2016)

301–316 .

24] K. McGrattan , S. Hostikka , R. McDermott , J. Floyd , C. Weinschenk , K. Over-holt , Fire dynamics simulator technical reference guide volume 1: mathemat-

ical model, U.S. Department of Commerce, National Institute of Standards andTechnology (2013) . Special Publication 1018-6.

25] C.W. Lautenberger , Gpyro3D: a three dimensional generalized pyrolysis model,Fire Saf. Sci. 11 (2014) 193–207 .

26] C.W. Lautenberger , Gpyro: a generalized pyrolysis model for combustible solids

technical reference. Version 0.800, Technical Report, Reax Engineering Inc.,2014 .

[27] H. Yang , R. Yan , H. Chen , D.H. Lee , C. Zheng , Characteristics of hemicellulose,cellulose and lignin pyrolysis, Fuel 86 (2007) 1781–1788 .

28] J.J. Manya , V. Enrique , L. Puigjaner , Kinetics of biomass pyrolysis: a reformu-lated three-parallel-reactions model, Ind. Eng. Chem. Res. 42 (2003) 434–441 .

29] T.R. Rao , A. Sharma , Pyrolysis rates of biomass materials, Energy 23 (1998)

973–978 . 30] B.M. Pickett , Effects of moisture on combustion of live wildland forest fuels,

Brigham Young University, Provo, Utah, 2008 MS thesis . [31] D.R. Prince , T.H. Fletcher , A combined experimental and theoretical study of

the combustion of live vs. dead leaves, 8th US National Combustion Meetingof the Combustion Institute, Park City, UT (2013) .

32] R.S. Miller , J. Bellan , A generalized biomass pyrolysis model based on superim-

posed cellulose, hemicellulose and lignin kinetics, Combust. Sci. Technol. 126(1997) 97–137 .

33] K.M. Bryden , M.J. Hagge , Modeling the combined impact of moisture and charshrinkage on the pyrolysis of a biomass particle, Fuel 82 (2003) 1633–1644 .

34] W. Mell , A. Maranghides , R. McDermott , S.L. Manzello , Numerical simulationand experiments of burning douglas fir trees, Combust. Flame 156 (2009)

2023–2041 .

35] K.M. Bryden , K.W. Ragland , C.J. Rutland , Modeling thermally thick pyrolysis ofwood, Biomass Bioenergy 22 (2002) 41–53 .

36] C.A . Koufopanos , A . Lucchesi , G. Maschio , Kinetic modelling of the pyrolysis ofbiomass and biomass components, Can. J. Chem. Eng. 67 (1989) 75–84 .

[37] Y.B. Yang , V.N. Sharifi, J. Swithenbank , L. Ma , L.I. Darvell , J.M. Jones ,M. Pourkashanian , A. Williams , Combustion of a single particle of biomass, En-

ergy Fuels 22 (2007) 306–316 . 38] S. Whitaker , Simultaneous heat, mass, and momentum transfer in porous me-

dia: a theory of drying, Adv. Heat Transfer 13 (1977) 119–203 .