CFD MODELING OF FIRE SPREAD ALONG COMBUSTIBLES IN A MINE ENTRY 

J. C. Edwards, NIOSH - Pittsburgh Rsrch. Lab., Pittsburgh, PA

C. C. Hwang, NIOSH - Pittsburgh Rsrch. Lab., Pittsburgh, PA

Abstract

A computational fluid dynamics (CFD) program was applied to fire

spread along combustibles in a ventilated mine entry. The rate of 

flame spread was evaluated for the ribs and roof of a coal mine entry;

timber sets; and a conveyor belt. The CFD program models char 

forming materials with temperature dependent thermal properties. The

program solves three dimensional time dependent flow equations with 

a mixture fraction model for the gas phase reactions. Radiant heat 

exchange is evaluated for non-scattering gas. The CFD program

predicted a flame spread rate of 0.0145 m / s for an actual coal mine 

fire in which the estimated flame spread rate was 0.0086 m / s. This 

overestimated flame spread rate was a possible consequence of the 

presence of inert materials in the mine entry’s roof and ribs. CFD fire 

spread rate predictions of 0.043 m / s and 0.73 m / s bounded the

measured value of 0.27 m / s for fire spread along Douglas Fir timber 

sets in a tunnel. 

Introduction

Fires in a mine create a hazardous environment for mine 

personnel due to toxic gas and low visibility. The primary toxic gas 

emission is carbon monoxide (CO). Fire spread expands the

emissions source. Important for controlling the spread of a fire over

combustible surfaces is an understanding of how rapidly the fire will 

spread. Fire spread in a coal mine will depend upon the thermal and

physical properties of the material, the imposed ventilation, and the

entry dimensions. Coal mine solid combustibles include coal,

conveyor belts, and wood supports which can undergo the complex 

process of char formation. These fuels, because of their physical 

distribution, can result in fire spread over considerable distances in a

coal mine. Liquid combustibles, such as diesel fuels and transformer 

fluids, will generally be limited to a localized region, although their 

combustion products can be transported by ventilation for extensive

distances. Past research [1] on fire spread has generally been limited 

to one dimensional ignition models which do not consider the char 

formation process within the solid, and the buoyancy generated flow.

With high speed computational capability, it is possible to model fire

spread in a mine entry with particular attention to the entry dimensions,

air ventilation velocity, fuel combustion properties, and char formation 

process. From this capability relationships between fire spread

velocity and ventilation for a particular mine entry configuration can be

developed. This information can be used to develop measures to

control fire spread and to project CO and smoke emissions and their 

transport through the mine ventilation network. 

Fire Spread Model 

To simulate the spread of a fire in a mine entry a fire dynamics 

simulator (FDS) [2] based upon computational fluid dynamics (CFD) 

was used. This CFD program is suitable for defining the geometry of a

mine entry and the combustible fire sources, and the time dependent 

evolution of heat and mass from the ignited combustibles. In this 

simulator the Navier-Stokes equations for multi-component gas flow 

are solved numerically. Gas phase combustion is predicted with a 

mixture fraction model. Radiant heat transfer is solved with a radiative

heat transport equation for an emitting and absorbing, but nonscattering, gray gas. A radiation band model for methane, its 

combustion products, and soot is used to model the blackbody 

radiation absortion coeffcients. In practice, the radiation intensity 

integrated over a wavelength band is solved. Over the wavelength of 

1-200 μ m, the number of bands is from 6 to 10. Turbulence is

simulated in the flow with a large eddy simulation (LES) method. One 

advantage of the LES method over the standard 6- g is the 

instantaneous characterization of the turbulent flow eddys. The 6- g 

model represents a time average of the fluid dynamics equations, and 

loses the irregular characteristics of the gas phase flame. Another 

advantage is the greater spatial and temporal accuracy of the LES 

method. The 6- g model requires the specification of algebraic wall 

functions, which are not required with the LES method. 

Most mine combustibles undergo combustion by a gas phase

reaction of the volatiles generated by the pyrolysis of the material. The 

pyrolysis front advances as a reaction front into the solid fuel leaving

behind a char layer. Version 4 of the FDS includes a pyrolysis model

in the CFD model for the fire simulation. This option is employed in the 

present study. The significant parameters for this process are the 

thermal conductivity, specific heat, and density of both the unreacted

coal and the char. The thermal conductivity and specific heat will be

temperature dependent quantities. The surface materials of the tunnel 

are assumed thermally thick. In the code, the material temperature is 

computed through a one-dimensional heat conduction equation. For 

the release of volatiles, the heat of pyrolysis, or vaporization, Hp must

be specified. The mass burning rate, which defines the release rate of

volatiles, is approximated by an Arrhenius rate equation in the FDS.

The maximum burning rate is associated with a specified pyrolysis 

temperature. Combustion of the volatiles with the oxygen is defined by 

the stoichiometric fuel – oxygen mass balance. The heat of

combustion provides the energy for preheating of the solid external 

surface through radiative and convective heat transfer. Heat transfer

internal to the fuel is controlled by the temperature dependent thermal

diffusivity of the solid. For all tunnels, a uniform velocity is assigned at

the inlet and atmospheric pressure is assigned at the exit. At the

tunnel walls, the gas velocity has slip as given by the CFD code. This 

implies that no wall function is used near a wall to accommodate the

no-slip boundary condition. 

Convective and radiative heat transport to the fuel surface

downwind from an initiating heat source will increase the fuel surface

temperature to the pyrolysis temperature. In the CFD application the

initiating heat source can be a localized high temperature surface, or 

an input surface energy flux per unit time. Since the flame spread is 

associated with the emission of pyrolysis gases, the leading edge of

the fuel surface, which is at the pyrolysis temperature, is used to define 

the flame front. Temporal movement of the pyrolysis temperature

along the fuel surface defines the flame propagation. 

Coal Fire Spread

A fire spread CFD model application with the FDS was made to

the 1990 fire at Mathies Coal mine [3]. In appendix K of the MSHA

investigation report [3] it is stated that the fire spread a distance of 

about 900 ft in about 9 hours. The corresponding average flame 

spread rate is about 1.7 fpm (0.0086 m/s). The entry for the simulation

was 7 ft high and 14 ft wide. The ribs and roof were coal, and the floor 

was assigned the value for an inert material. The ventilation air 

reported for the entry was 6000-8000 cfm. For the simulation 

purposes a ventilation of 7000 cfm was assigned, which is a linear air 

velocity of 71.4 fpm (0.363 m / s). The FDS was used to model the fire

1 
spread along the mine entry roof and ribs, which were a continuous 

coal surface. Temperature dependent specific heat and thermal 

conductivity of coal and coke values reported by Merrick [4,5] were

used. The mass density of coal, 1,330 kg / m3

, and coke, 850 kg / m3, 

were reported by Lee et al [6]. The heat of combustion for the coal was 

31,300 kJ / kg based upon a bituminous coal [7]. The stoichiometric 

coal - oxygen reaction was represented in the gas phase by

CH0.74O0.08 + 1.145O2 → CO2 + 0.37H2O +ν COCO +ν soot SOOT (1) 

 

The stoichiometric coefficients, <, for CO and SOOT are related to the 

carbon available in the fuel. The pyrolysis front advances with an

endothermic heat of reaction. There is considerable variation in the

literature values for the heat of pyrolysis, Hp. Values from Mahajan et 

al [8] indicate a value of 209 kJ / kg, and value reported by Hertzberg

et al [9] indicates a value of 1,300 kJ / kg. To investigate the 

sensitivity of the simulation to the heat of pyrolysis, both cases were 

evaluated. For the simulations conducted the thermally inert floor was 

assigned the FDS library values for fire brick. Initiation of the fire

occured by some event for which the details are not known. The

MSHA report [3] concluded that the most likely fire source was that a

roof fall caused energized trolley wire to make contact with steel rails,

creating a high resistance electrical arc, which ignited the fallen coal. 

For the purpose of the simulation, two virtual heater elements 5 m 

long, 20 cm wide, and 60 cm high, were suspended near the entrance,

and maintained at 1,600 °C for 2,000 s. These radiant heaters 

supplied thermal energy to the coal surfaces to initiate the fire 

development. The pyrolysis temperature of the coal was 525 °C,

based upon [9]. When the surface temperature of the coal reached the 

pyrolysis temperature, the flame front was considered to have reached 

that location. For the simulation the entry length was limited to 151 m, 

which is approximately 53 hydraulic diameters. The coal was assumed 

to be moisture free. Typical inherent moisture content for Pittsburgh 

Seam coal is less than 5 pct. Figure 1 shows the centerline roof

temperature at selected locations downwind from the entrance for a

209 kJ / kg heat of pyrolysis. The intersection of the temperature

curves with the 525 °C isotherm defines the flame movement. 

0

400

800

1200

1600

2000

0 1600 3200 4800 6400 8000

TIME, S

TEMPERATURE, deg C

10 M 50 M

80 M

125 M

525 deg C

Figure 1. Centerline roof coal temperature 

Figure 2 shows the nearly linear increase in 

flame position, as defined by the pyrolysis temperature, with time. Also

shown in figure 2 is the nearly linear increase of flame position with 

time for the 1,300 kJ / kg heat of pyrolysis. Both sets of data are well 

represented by the nearly linear flame spread increase with time, as 

defined by the pyrolysis temperature at the centerline of the roof, of 

0.0145 m/s, which is to be compared with the 0.0086 m / s observation 

determined from [3]. Presence of moisture in the coal, with its 2,470 kJ 

/ kg heat of vaporization, would retard the propagation of the pyrolysis 

temperature along the coal surface. This effect was demonstrated for 

the heat of pyrolysis equal to 1,300 kJ/kg and three different moisture

contents of the coal. For 0 and 5 pct mass fraction of moisture content 

in the coal the fire propagation displacements along the tunnel were

relatively close as shown in figure 3. At an increased moisture content 

of 10 pct the fire propagation ceased at about 2,830 s, as shown in

figure 3. 

0

40

80

120

160

0 2000 4000 6000 8000 10000

TIME, S

FLAME POSITION, m

Hp = 1,300 kJ / kg

Hp=209 kJ / kg

Figure 2. Effect of heat of pyrolysis on flame propagation 

0

40

80

120

160

0 2000 4000 6000 8000 10000

TIME, S

FLAME POSITION, m

MOISTURE FRACTION = 0.

MOISTURE FRACTION = 0.05

MOISTURE FRACTION = 0.10

Figure 3. Effect of moisture content on flame spread

The predicted flame spread rate with the CFD application of

0.0145 m/s was higher than the estimated average flame spread rate

of 0.0086 m/s for the Mathies mine fire. This can be accounted for by 

the presence of inert materials in the mine rib and roof. Inert materials 

such as shale would affect the expected emissions of pyrolysis gases 

and the heat release from the propagating fire, and the thermal 

properties of the fuel. 

The effect of ventilation on flame spread rate is important for 

understanding mine fire control. For a moisture fraction of 0.05 and a

heat of pyrolysis, Hp , of 1,300 kJ / kg , simulations were made for air 

flows of 0.363 m /s, 0.454 m / s, and 0.544 m / s. Figure 4 shows a 

a comparison of the flame spread with time for these three air flows.

The flame spread rates are nearly linear. The flame spread rates 

based upon a linear interpolation of the data in figure 4 are

summarized in Table 1. 

2 
0

20

40

60

80

100

120

140

0 1000 2000 3000 4000 5000 6000 7000

TIME, s

FLAME POSITION, m

VEL = 0.363 m / s

VEL = 0.454 m / s

VEL = 0.544 m / s

Figure 4. Effect of ventilation velocity upon flame spread 

 Table 1. Flame spread vs air flow

Air flow, m / s Flame spread rate, m / s 

0.363 0.0156

0.454 0.0235

0.544 0.0320

For the range of air flows considered, a linear fit between flame

spread rate Vf

 and air flow Va is established with an R square value, 

coefficient of correlation, equal to unity. 

Vf = 0.0904Va - 0.0173 (2) 

A linear dependence of flame spread upon ventilation was 

reported by Roberts and Blackwell [10] for wood lined ducts 0.3 m by 

0.3 m square cross section. The constant term in the flame spread

rate relationship is a consequence of the nonlinear effects such as 

radiant heat transfer. When the flame had advanced to the 115 m

position along the entry, the fire heat release rates were 16 MW, 19

MW, and 22 MW for the three air flows. For air flows less than 0.326

m / s, continuous flame propagation could not be established for the

same source fire intensity and duration. The flame ceased

propagation about 1,500 s after the source fire was extinguished for a

ventilation velocity of 0.326 m / s, with propagation not extending to the

70 m station. 

The dominant mode of heat transfer to the coal surface was 

radiant energy. The radiant energy transfer dominated the convective

heat transfer. For example, at the 50 m and 100 m locations along the

tunnel roof, the ratio of the radiant heating to convective heating was 

approximately one order of magnitude when the flame front reached

these locations. 

 

Fire Characteristic 

Roberts and Blakwell[10] analyzed the propensity of a fire in a 

fuel lined roadway to transition from an oxygen rich mode into a fuelrich mode. The characteristic parameter R for the transition was 

defined by 

R = KAB/( ρ Q) (3) 

Where A = fuel burning area 

 B = fuel surface burning rate 

 K = air / fuel ratio from stoichiometric equation 

 ρ = air density (1.2 kg / m3 ) 

 Q = volumetric air flow 

Roberts [10] showed that if R exceeded a critical value of 

approximately 0.4, the fire is expected to transition from an oxygen rich 

state to a fuel rich state. An evaluation was made of R to compare the

value at the termination of the heat source for a ventilation velocity of 

0.363 m/s in a coal lined fire tunnel for the two values of heat of

pyrolysis. For a coal fire the value of K was 11.27. The coal was 

moisture free. The CFD predictions for burning rate along the ribs and

roof of the entry were used to evaluate the terms A and B in equation

3. A heat of pyrolysis of 209 kJ / kg resulted at 1,000 s in a R value

2.56, and at 5,000 s in a R value 3.49. After the external heat source

was turned off at 2,000 s the fire continued to be fuel rich. At an

increased heat of pyrolysis of 1,300 kJ / kg the R values at 1,000 s and

5,000 s were 2.39 and 2.96 respectively. The continued propagation

of the fire for these cases was associated with a fire intensity which 

was about 16 MW for each fire. 

Timber Set Fire Spread 

Another combustible source in a mine is timber sets, which are

used for roof supports. Warner [11] investigated the effect of timber 

set spacing on fire propagation in a ventilated timbered roadway. Fire

spread experiments were conducted in a 53 m long tunnel with a cross 

section 4.57 m wide and 1.83 m high. Each timber set consisted of an

overhead element at the roof supported by a leg element on each rib. 

The linear air flow was 1.78 m/s. A kerosene ignition fire source near 

the entrance had an effective heat release rate of 3,194 kW/ sq m, with 

a total heat release rate of 12 MW. Mineral wool was used as a

thermal insulation on the tunnel sides and roof to protect the tunnel 

exposed surfaces. Fire brick, with a thermal diffusivity about three

times that of rock wool, provided thermal insulation to the tunnel floor.

An application was made with the FDS to the results reported in [11]

for the evaluation of fire spread along Douglas Fir timber sets in a

ventilated entry. Thirteen Douglas fir timber sets, each 0.30 m by 0.30 

m square, were formed by two vertical sections along the tunnel wall,

with a cross beam along the roof connected to the vertical beams. The

separation distance between the timber sets was 2.34 m. The 

moisture content of the wood was 18 pct. Thermal and physical

properties for Douglas Fir wood and char reported by Parker [12], and 

Hostikka and McGrattan [13], were used in the simulation. The heat of 

vaporization of 1,820 kJ / kg is specified in [14] for Douglas Fir. Figure

5 shows a comparison of the CFD predicted and measured flame

spread rate. The flame spread in [11] was defined by the temperature

immediately behind the roof timber and approximately 2 cm below the 

beam reaching 538 °C. The measured flame propagation in figure 5 is 

nearly linear with time with an approximate rate of 0.27 m / s. The

CFD prediction can be broken into two approximately linear segments 

with time. For the initial 1.1 minutes the flame propagation rate is 

approximately 0.73 m / s, followed by an 0.043 m / s propagation rate

for an additional 3.4 minutes propagation to the end of the tunnel.

Figure 6 shows a comparison of the measured gas temperature with 

the CFD predicted gas temperature at the ninth timber set,

approximately 18.6 m downwind from the first timber set. The

agreement between the CFD prediction and measured gas 

temperature is very good during the temperature increase and

decrease. The maximum temperature is overestimated with the CFD

program. 

Conveyor Belt Fire Spread 

CFD simulations were made for fire spread along a conveyor belt 

in a fire tunnel for which experimental data are available [15]. The

dimensions of the tunnel are 28 m x 3.6 m x 2.4 m with the conveyor

belt suspended horizontally 1.2 m above the floor as shown in Figure

7. The conveyor belt is 1.5 m wide by 10 m long. 

3 
0

5

10

15

20

25

30

35

0 1 2 3 4 5

TIME, min

DISTANCE, m

MEASUREMENT CFD

Figure 5. Comparison of CFD predicted flame spread with measured

values for Douglas fir timber sets

0

200

400

600

800

1000

0 4 8 12 16 20

TIME, min

TEMP, deg C

CFD MEASURED

Figure 6. Comparison of CFD predicted gas temperature with

measured values at Douglas fir timber set 

Figure 7. Schematics of a tunnel (not to scale) for conveyor-belt fire 

spread. 

Typical time-temperature traces obtained from the thermocouples

along the centerline of the sample are shown in Figure 8. The flame is 

assumed to spread to the front where the material surface temperature

reaches the ignition temperature. The air speed was 4. m / s. Sample 

plots of the flame front, , with different source-fire intensities from 

500 to 1,000 kW / m

Xig

2

 are shown in Figure 9. 

T im e , s

Temperature, °C

0 1 0 0 2 0 0 300 400 5 0 0 0

4 0 0

8 0 0

1

T im e , s

Temperature, °C

0 1 0 0 200 300 4 0 0 5 0 0 0

400

800

3

T im e , s

Temperature, °C

0 1 0 0 2 0 0 300 400 5 0 0 0

4 0 0

8 0 0

5

T im e , s

Temperature, °C

0 1 0 0 2 0 0 300 400 5 0 0 0

4 0 0

8 0 0

7

T im e , s

Temperature, °C

0 1 0 0 2 0 0 300 400 5 0 0 0

4 0 0

8 0 0

9

T he rm ocouple

p o sitio n, m

Figure 8. Time-temperature traces of fuel surfaces thermocouples at

distances from 2 m to 10 m 

X

X

X

X

X

X

X

X

X

X

X

X

X

X

Time, s

Xig, m

0 100 200 300 400 0

2

4

6

8

10

500 kW/m2

600 kW/m2

800 kWm2

1000 kW/m2 X

Figure 9. Flame front versus time for different source-fire strength.

The source fire area was 0.75 m2

, and the air speed was 4 m / s. For 

this case, the flame-spread rates are insensitive to the source-fire

intensity. Figure 10 shows the flame-spread rate as a function of the air 

speed entering the tunnel. Although the CFD results show a much 

stronger effect of the air speed on the flame-spread rate than the

experimental results, the agreement with experimental values of

Lazzara and Perzak [15] is good for air speeds between 0.8 and 1.8

m/s. The experimental results of Green et al [16] are also shown in the 

figure, for which the CFD predictions are less favorable. 

4 
Figure 10. Flame-spread rate as a function of the air speed at the

tunnel inlet 

 

Conclusions 

1. Fire propagation along a fuel surface which undergoes pyrolysis with 

char formation can be accounted for with a CFD model which predicts 

the spatial advance of the pyrolysis temperature along the fuel surface. 

2. The observation that a coal mine fire propagated with an average

spread rate of 1.7 fpm (0.0086 m / s) was simulated with the CFD

program to yield a flame propagation rate of 2.9 fpm (0.0145 m / s).

Based upon the sparse information with regard to the unobserved mine 

fire, the result is reasonable. The presence of inert materials in the 

mine roof and ribs, which were coal for the model computations, would 

moderate the effective flame spread rate. 

3. CFD analysis showed the coal lined tunnel flame spread rate was 

relatively insensitive to the heat of pyrolysis, but strongly sensitive to 

the coal moisture content and the ventilation. A linear dependence of 

flame spread rate upon imposed ventilation was predicted with the 

CFD computations for a moisture fraction of 0.05.

4. CFD prediction of flame spread in a tunnel lined with Douglas Fir 

timber sets initially overestimated the measured fire propagation rate,

and subsequently underestimated the measured flame propagation 

rate. The measured fire propagation rate was 0.27 m / s. The CFD

fire spread rate prediction was 0.73 m / s for an initial linear fire spread

rate, which was followed by a 0.043 m / s fire spread rate. 

5. CFD prediction of the dependence of flame spread along a conveyor

belt upon air speed showed good agreement with measurements of

Lazzara and Perzak [15] for air speeds less than 2 m/s. 

CFD modeling provides an important tool to facilitate the 

dependence of fire spread upon the material properties, inlet air flow, 

and entry dimensions for applications to fires in mines. The extent of

the fire spread can be used to project the smoke and CO emissions,

and their transport through the mine network. Additional CFD 

investigations need to be undertaken to determine the effect of flame 

spread upon ventilation. With this capability, an analytic method can

be provided for mine fire emergency planning. 

References 

1. Quintiere, J.G. “Surface Flame Spread”, The SFPE Handbook of

Fire Protection Engineering, Section 1 Ch 24, eds. P.J. DiNenno 

et al, Society of Fire Protection Engineers, Boston, MA, 1988. 

2. “Fire Dynamics Simulator (Version 4) Technical Reference Guide”

NIST Special Publication 1018, ed. K. McGrattan, U.S. Dept. of

Commerce, July 2004, 85 pages.

3. “Non-Injury Underground Coal Mine Fire Mathies Mine (ID No. 36

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(1949) 11 pages 

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atmosphere” Fuel, vol. 55, no.1, 1976, pp.63-69. 

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1969, pp.699-709. 

11. Warner, B.L. “Evaluation of Potential Fire Hazard Caused by

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Report (Contract No. H0144068) March 1975. 

12. Parker, W.J. “Prediction of the Heat Release Rate of Douglas Fir”,

Fire Safety Science-Proceedings of the Second International

Symposium (ed. T. Wakamatsu, Hemisphere Publishing

Company, New York) 1989, pp. 337-346. 

13. Hostikka, S. and McGrattan, K., “Large Eddy Simulation of Wood 

Combustion”, International Interflam Conference, 9th Proceedings,

vol.1, Sept. 17-19, 2001, (Interscience Communications Ltd,

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14. SFPE Handbook of Fire Protection Engineering, (ed. P. DiNenno, 

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Pretoria, South Africa, Oct. 1987. 

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1989. 

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