COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE
EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China
©2006 Tsinghua University Press & Springer
CFD Analysis of Fire in a Forced Ventilated Enclosure
L. M. Tam 1,2, V. K. Sin 1, S. K. Lao 1*, H. F. Choi 1
1
Department of Electromechanical Engineering, Faculty of Science and Technology, University of Macau, Macau,
China
2
Institute for the Development and Quality, Macau, China
Email: [email protected]
Abstract Due to the rapid development of computer technology and numerical technique, many complex
thermal-fluid phenomena such as fire dynamics can now be simulated by computational fluid dynamics (CFD).
StarCD, a general-purpose CFD package with finite volume method, is used to simulate the experimental data [1]
obtained at the Lawrence Livermore National Laboratory (LLNL). The experiment consists of a fire in a room with a
ventilated exit and an air inlet. An enclosure of 6 m long, 4 m wide and 4.5 m high, with an air intake of 2 m wide and
0.12 m high, has been investigated. Air was ventilated at a constant rate of 0.5 m3/s at the outlet of 0.65 m × 0.65 m. A
heat plate model was implemented to represent the natural pool fire at the center of the floor. Combustion chemical
reactions were excluded [2]. This study employed k-ε model together with discrete ordinates method (DOM) radiation
model to predict the turbulent flow and radiative heat transfer in the enclosure. The energy absorbed by soot particles
as well as the conjugate heat transfer to the wall have been taken into consideration.
The simulation results show good agreement with the experimental data. Moreover, the data indicated that 80% of heat
generated by fire was absorbed by the walls, the floor, and the ceiling. This study demonstrates that StarCD is capable
of modeling fire generated heat transfer in a forced ventilated enclosure.
Key words: Enclosure fire, computational fluid dynamics, conjugate heat transfer, discrete ordinates method.
INTRODUCTION
Macau is under heavily construction in history ever. More and more resorts, hotels and casinos are being built. Some of
them have large space interior, in which fire spread and smoke development are some of the main concerns in fire
safety engineering. One of the smoke control system is the mechanical exhaust method. The amount of exhaust can be
estimated using the CFD model to analyse the fire spread in a ventilated enclosure. The fire following ignition will be
burning freely: the pryolysis rate and the energy release rate are affected only by the burning of the fuel itself and not
by the presence of the boundaries of the enclosure. The fire continues to grow if there is sufficient ventilation. It is well
known that the development of a compartment fire may be divided into three stages [3]:
(1) the growth or pre-flashover stage in which the average compartment temperature is relatively low and the fire is
localized in the vicinity of its origin;
(2) the fully developed or post-flashover fire, during which all combustible items in the compartment are involved and
flames appear to fill the entire volume; and
(3) the decay period, often identified as that stage of the fire after the average temperature has fallen to 80% of its peak
value.
In this study, the main concern is the temperature distribution in the enclosure during the growth and fully developed
stage in order to predict the possible damage caused by the fire. From the point of view in heat transfer, the problem is
equally significant and it is necessary to consider together the three propagation modes: conduction, convection, and
radiation.
Turbulence plays an important role to the development of the fire as well. Mathematical models of turbulence are
employed to determine the Reynolds stresses and turbulent scalar fluxes. The main options are the Reynolds Averaged
Navier Stokes (RANS) technique and the Large Eddy Simulation (LES) model. The solution of the RANS is given by
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the k-ε model and its variants, which comprise transport equations for the turbulent kinetic energy k and its dissipation
rate ε.
There are many codes for CFD analysis of fire and smoke transport. CFAST is the well-known package using zone
model, which usually divides an enclosure into two distinct zones: the hot upper smoke layer and the lower layer of
cooler air. It is assumed that the physical parameters in each zone are uniform. Zone model provides limited
information about the region concerned. Field models [4] divide the enclosure into a large number of cells and solve
the conservation equations inside each cell, hence produce detailed solutions even in complex and large region. FDS is
a fire-specific code using field model, while CFX, FLUENT, PHOENICS, and StarCD are multi-purpose CFD codes
[5].
MATHEMATICAL MODEL
The characteristics of the fluid flow within an enclosure are determined by the Navier-Stokes equations, i.e., the mass,
momentum, and energy conservation equations:
∂ρ
∂
+
( ρu j ) = 0
∂t ∂x j
(1)
⎡
⎤
⎛ ∂u ∂u j ⎞ 2 ∂uk
∂p
δ i j − ρ ui′u j′ ⎥ = −
+ gi ( ρ − ρo )
⎢ ρ u j ui − μ ⎜⎜ i +
⎟⎟ − μ
∂xi
⎢⎣
⎥⎦
⎝ ∂x j ∂xi ⎠ 3 ∂xk
∂
∂
( ρ ui ) +
∂t
∂x j
∂u
∂
∂
∂p
∂p
( ρ h ) + ( ρ hu j + Fh, j ) = + u j + τ ij i + sh
∂t
∂x j
∂t
∂x j
∂x j
(2)
(3)
where the u ′ are fluctuations about the ensemble average velocity and the overbar denotes the ensemble averaging
process. The flows generated in enclosure fires generally are turbulent. The terms are given by:
⎛ ∂u ∂u j ⎞ 2 ⎛ ∂uk
⎞
− ρ ui′u j′ = μt ⎜ i +
− ⎜ μt
+ ρ k ⎟ δ ij
⎟
⎜ ∂x j ∂xi ⎟ 3
⎝ ∂xk
⎠
⎝
⎠
(4)
μ ∂h
∂T
− t
+ ∑ hm ρVm , j
∂x j σ h ,t ∂x j m
(5)
Fh , j ≡ −k
where μt is the turbulent viscosity,
k≡
ui′ui′
2
(6)
is the turbulence kinetic energy,
μt = f μ
Cμ ρ k 2
(7)
ε
is the turbulent viscosity, σ h ,t and σ m ,t are the turbulent Prandtl and Schmidt numbers, respectively.
Standard k-ε turbulence modeling is applied in the simulation. The transport equations for turbulence kinetic energy
and turbulence dissipation rate are:
∂
∂
( ρk ) +
∂t
∂x j
∂
∂
( ρε ) +
∂t
∂x j
⎡
⎛
⎛
⎞ ∂u
μt ⎞ ∂k ⎤
2 ⎛ ∂ui
g 1 ∂ρ ⎞
+ ρ k ⎟ i + μt PNL
⎟⎟ − ρε − ⎜ μt
⎢ ρu j k − ⎜ μ +
⎥ = μt ⎜⎜ P −
⎟
3 ⎝ ∂xi
σ k ⎠ ∂x j ⎦⎥
σ h ,t ρ ∂xi ⎠
⎝
⎠ ∂xi
⎝
⎣⎢
⎡
⎛
μt ⎞ ∂ε ⎤
ε
⎢ ρ u jε − ⎜ μ + ⎟
⎥ = Cε 1
σ ε ⎠ ∂x j ⎥⎦
k
⎝
⎣⎢
(8)
⎡
⎞ ∂u ⎤
2 ⎛ ∂ui
ε
ε2
ε
∂u
+ ρ k ⎟ i ⎥ + Cε 3 μt PB − Cε 2 ρ + Cε 4 ρε i + Cε 1 μt PNL (9)
⎢ μt − ⎜ μt
3 ⎝ ∂xi
k
k
k
∂xi
⎠ ∂xi ⎦⎥
⎣⎢
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where
⎛ ∂u ∂u j ⎞ ∂ui
P≡⎜ i +
⎜ ∂x j ∂xi ⎟⎟ ∂x j
⎝
⎠
PNL = −
(10)
ρ ′ ′ ∂ui ⎡
2 ⎛ ∂u ρ k ⎞ ∂ui ⎤
ui u j
− ⎢P − ⎜ i +
⎥
⎟
μt
3 ⎝ ∂xi μt ⎠ ∂xi ⎦⎥
x j ⎢⎣
(11)
The constants appearing in the k-ε turbulence model are: Cμ = 0.09, σ k = 1.0, σ ε = 1.22, σ h ,t = 0.9, Cε 1 = 1.44,
Cε 2 = 1.92, Cε 3 = 1.44, Cε 4 = 0.33, and the empirical coefficient E = 9.0 for smooth walls.
For most fuels, approximately 30 percent of the heat liberated in the flame is radiated to the environment and the rest is
dispersed convectively in the buoyant plume [3]. Several numerical methods have been developed to predict radiative
heat transfer in an enclosure with participating media. The zone method [6] and Monte Carlo method [7] both requires
huge computational resource in solving the radiative transfer equations (RTE). The six-flux model can take advantage
of the simplicity and low computational requirements while dealing with fires smaller than 100 kW [8]. The discrete
transfer (DT) radiation model [9] which involves tracking of beams, requires its own geometrical description. The
discrete ordinates method (DOM) [10] does not perform beam tracing but solves field equations for radiation intensity
associated with a fixed direction s, representing one discrete solid angle [11].
sˆi ⋅∇I i = − ( kaλ + k sλ ) I i + kaλ I bλ +
ks n
∑ wj I j
4π i =1
(12)
where kaλ is the absorption coefficient at wavelength λ , w j are the quadrature weights that depend on the chosen
ordinates, I bλ is the black-body intensity in the wavelength band and n is the number of ordinates.
COMPUTATIONAL DETAILS
The fire experiments were conducted in a ventilated enclosure (Fig. 1) in LLNL. A fire case MOD8 was chosen to be
compared with numerical results obtained by CFD method. Liquid fuel isopropanol from a pressurized reservoir flows
through a calibrated rotometer to an opposed jet nozzle located in the center of a steel pan on the center of the floor. It
quickly evaporates and burns before it contacts pan surface. The resulting fire has every appearance of a natural fire.
The fire size was estimated to be 400 kW.
Figure 1: Schematic diagram of the fire test enclosure
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1. Geometry and boundary conditions The dimension of the enclosure is 4.5 m high, 4.0 m wide and 6.0 m long. The
fire took place at the center of the enclosure floor. The rate of heat release was controlled at around 400 kW. An
extraction rate of 0.5 m3/s was maintained by an air-extraction system at the exit. The 0.65 m square exit opening was
on the vertical centerline of the west wall, with its center 3.6 m located above the floor. Fresh air was supplied from
four rectangular openings (0.5 m long x 0.12 m high each) on the lower part of the north wall with the horizontal
centerline 0.1 m above the floor. These rectangular openings were simplified into one horizontal rectangle (2.0 m long
x 0.12 m high). The floor, walls and ceiling consist of a 10-cm thick Al2O3-S1O2 refractory, with the physical properties
listed in Table 1. They were maintained at 20 °C before the fire ignition. Since the boundaries are low thermal
conductants, heat is hard to transfer from the inner surfaces to the outer surfaces. The outer surfaces of the enclosure
were assumed to be thermal insulated.
Table 1 Physical properties of walls and ceiling
Property
Floor and walls
Ceiling
3
Density ρ (kg/m )
1440
1920
Thermal conductivity k (W/m⋅K)
0.39
0.63
Heat capacity Cp (J/kg⋅K)
1000
1000
Emissivity ε
0.95
0.95
2. Fire specification Two different strategies have been performed to simulate the heat release by fire. In the first case,
Case A, the fire starts at t = 0 of the simulation and grows according to a well known t-squared relation [12]. The rate
of heat release from the fire relates with the square of time through a factor α (Eq. 13). Normally, fast t-squared with α
= 0.0469 kW/s2 performs well for an enclosure fire [13]. The rate of heat release grows to a peak value of 400 kW in 92
s, then keeps constantly at 400 kW.
Q = αt2
(13)
In the second case, Case B, the rate of heat release remains 400 kW just after the fire started. The fire source was
approximated as a 0.5 m square heat plate representing an isopropanol fire. The heat plate is located 0.25 m above the
floor. Combustion and fire spread were not considered in both cases.
3. Monitoring Positions Three thermocouple trees were placed on either side of the fire source (east rake and west
rake) and along the center vertical line in the south wall surface, as shown in Fig. 1. Another three thermocouples were
positioned inside the enclosure in the simulation as listed in Table 2.
Table 2 Thermocouple positions in the simulation
Position (m)
Thermocouple
number
x
y
z
1
1.5
0.3
2.0
2
3.0
2.25
0.01
3
5.98
3.6
2.0
NUMERICAL ANALYSIS
The computational domain of the fire simulation consists of two major parts: the fluid region inside the enclosure and
the extended region at the exit opening; the second part was the solid structure with conjugate heat conduction and heat
storage. The heat transfer within the solid was three dimensional. Non-uniform mesh distribution was employed to
reduce the calculation time. In the region near the wall, a finer mesh (0.025 m) was used. Coarser mesh (0.25 m) was
used in the region where temperature gradient is small. Total cell number is about 65,000 cells.
The standard high Reynolds number k-ε turbulence model is used in this study to analyze the fire-induced air flow with
the field modeling technique. It is employed for analyzing the turbulent behavior of the buoyant flow. Spatial
discretization is performed using a second order scheme called the Monotone Advection and Reconstruction Scheme
(MARS) [14].
⎯ 225 ⎯
The thermal radiation was treated using DOM with 24 ordinates (S4). It was assumed that there was no scattering of the
radiation. The gas absorption coefficient was assumed to be 0.2 m-1 to implement the heat absorbed by the soot and
particles generated by the fire.
An initialized analysis was performed without any heat source inside the enclosure to establish the flow field of
ventilation maintained at 20 °C constantly until the residuals of velocities drop below 10-3. This initial data was used in
the simulation just after ignition of fire. A variable time step strategy was used to decrease the calculation time as well
as to maintain accuracy. Table 3 lists the detailed information about time step. About 9 hours CPU time was necessary
to complete the analysis on an Intel Pentium 4 PC with a CPU speed of 2.8 GHz.
Table 3 Time steps
Physical time (s)
Time step (s)
Step number
0~1
0.02
50
1~2
0.05
20
2~5
0.1
30
5 ~ 10
0.2
25
10 ~ 30
0.5
40
30 ~ 120
1
90
120 ~ 1200
2
540
RESULTS AND DISCUSSION
The temperature development histories at three key locations listed in Table 2 are shown in Fig. 2. In Case A, it shows
that the gas temperature slowly increased in the first minute, then rapidly rose in the following two minutes. This is
because fast growth rate for the fire has been implemented in the simulation. The temperature increased slowly and
linearly afterwards. The main difference between Case A and B is in the first 4 minutes. In Case B, the temperature
rapidly increased just after the fire started. The results also indicate that the temperature developments are remarkably
similar in both cases after 4 minutes. The temperatures at those monitoring points are nearly identical at 20 minutes.
(a) fast growth fire
(b) constant rate of heat release
Figure 2: Predicted temperature histories at three monitoring points.
Temperature distribution along the east rake and the west rake 20 minutes after fire ignition are compared with
measured data in Figs. 3 and 4. In order to validate the results using zone models, Steckler’s two-layer equivalency
technique was applied to these temperature profiles. This technique simplifies profile data into the two distinct layers.
It is observed that the numerical results can be used reasonably as a prediction of the temperature distribution along
both rakes.
⎯ 226 ⎯
(a) fast growth fire
(b) constant rate of heat release
Figure 3: Temperature distribution along east rake at 20 minutes.
(a) fast growth fire
(b) constant rate of heat release
Figure 4: Temperature distribution along west rake at 20 minutes.
(a) fast growth fire
(b) constant rate of heat release
Figure 5: Vertical temperature distribution along the center of the south wall at 20 minutes.
⎯ 227 ⎯
Fig. 5 shows a comparison between measured and numerical results of the vertical temperature profile along the
surface center on the south wall. It gives a relative good numerical results 2.0 m above the floor. The increase in
temperature 1 m to 1.5 m above the floor is caused by the “ray effect” of the discrete ordinates radiation model, since
the energy is propagated through discrete directions instead of into the whole discrete solid angle [15]. Using a higher
number of ordinates may reduce the ray effect.
LLNL experiment [1] reported that approximately 83 percent of the energy from the fire was deposited in the enclosure
walls and ceiling. Fig. 6 shows the rate of heat release by fire and the rate of heat absorption by the walls and ceiling. It
was calculated that 81 percent of energy has been absorbed by the walls and ceiling in fully developed stage for both
cases. Using the t-squared fire model, a sudden change in the rate of heat absorption occurs at 92 seconds, when the rate
of heat release reached 400 kW. The numerical results of the energy transfer give a very good agreement with the
experimental data.
(a) fast grow fire
(b) constant rate of heat release
Figure 6: Rate of heat release by fire and rate of heat absorption by the walls and ceiling
CONCLUSIONS
It can be concluded that the general-purpose package StarCD is an efficient and powerful tool when dealing with
simulation of fire in a ventilated enclosure, even for the case without considering complex chemical reactions of
⎯ 228 ⎯
combustion. The experimental data and Steckler values were used to validate the predictions made by the code. The
second order differencing scheme MARS gives accurate results. DOM provides an easy way to solve the RTE,
although the ray effect of DOM overestimates temperature in some areas. Higher order DOM is required to reduce the
ray effect. The fire characteristic is mainly affected by the rate of heat release. This paper also accurately verified the
percentage of heat absorption by the enclosure walls and ceiling.
Acknowledgements
The authors acknowledge the support team at CD adapco China for their help with StarCD.
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