Large eddy simulation of compartment fire with solid combustibles

ARTICLE IN PRESS Fire Safety Journal 44 (2009) 349–362

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Large eddy simulation of compartment fire with solid combustibles Shusheng Yuan, Jian Zhang  Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China

a r t i c l e in fo

abstract

Article history: Received 11 November 2007 Received in revised form 30 May 2008 Accepted 16 August 2008 Available online 2 October 2008

For properly describing practical building fire processes with solid combustibles, the pyrolysis kinetics model of solid combustibles and the large eddy simulation (LES) approach are applied to the simulation of the thermal decomposition of the polyurethane foam (PUF) slab and the space fire spread in a compartment. The instantaneous variations of the heat release rate of the PUF slab, the smoke temperature, and the smoke interface height with time are obtained under different ventilation conditions. They are in agreement with the measured data. The ventilation conditions have distinct effects on the interactions between the pyrolysis of the PUF slab and the space fire spread. Influenced by the space fire spread, the heat flux on the top plane of the PUF slab exhibits a non-uniform distribution. The PUF slab is consumed in an asymmetric manner. & 2008 Elsevier Ltd. All rights reserved.

Keywords: Compartment fire Solid combustibles Pyrolysis kinetics model Large eddy simulation Fire spread

1. Introduction A large portion of combustibles in building fires is solid material. Solid combustibles will undergo phase change, pyrolysis, morphological variation, and combustion during the fire processes. The pyrolysis of solid combustibles is coupled with the space fire spread in a room. There exist interactions between them. The volatile species released from solid combustibles are burned in the room space. While the heating from the space fire leads to further pyrolysis of solid combustibles. The fire processes with solid combustibles are quite complex. They are studied primarily by experimental approaches. Reneke et al. [1] conducted experimental studies of the compartment fires with the polyurethane foam (PUF) slab as a fire source. The variations of heat release rate, smoke temperature, interface height, and ceiling temperature with time were measured under different ventilation conditions. Luo et al. [2] studied the fires in a prototype multi-room apartment. The PUF slabs (mattresses) were utilized as fuel. The mass loss rate of the PUF slabs and the evolutions of the smoke temperature and concentrations of CO2 and O2 in each room and corridor were measured in their tests. He [3] experimentally studied the fire flow field in a multi-story compartment building. The fuel load in the burn room is realistic furniture including couch, sofas, tables, and book shelves. Measurements were conducted for the variation of heat release rate with time as well as the evolutions of smoke velocity, temperature, and oxygen concentration at different heights of the burn room door.  Corresponding author. Tel.: +86 10 62772932; fax: +85 10 62781824.

E-mail address: [email protected] (J. Zhang). 0379-7112/$ - see front matter & 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.firesaf.2008.08.002

As an attempt to predict the fire processes with solid combustibles in a room, many numerical simulations were conducted. Novozhilov et al. [4] numerically studied the fire spread of wood in modeled chambers. Hostikka and McGrattan [5] predicted the flame spread in a room with wood linings by employing the large eddy simulation (LES) approach. The pyrolysis kinetics models of the wood were adopted in their computations. Yan and Holmstedt [6] performed numerical studies of room fire growth on the walls lined with particle board. The fire spread in a small compartment using PMMA as solid fuel was simulated numerically by Jia et al. [7]. However, the pyrolysis rate is either presumed empirically or obtained by

Fig. 1. Compartment placed with the PUF slab: A: x ¼ 0.005 m, y ¼ 3.395 m and B: x ¼ 3.295 m, y ¼ 0.005 m.

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Nomenclature A A0 cs D E g h Js p q Q qR qc, qr R s t

pre-exponential factor, m s1 pre-exponential factor, m4 kg1 s1 solid specific heat capacity, J kg1 K1 diffusivity, m2 s1 activation energy, J mol1 gravitational acceleration, m s2 enthalpy, J kg1 sub-grid turbulent mass flux, kg m2 s1 pressure, Pa sub-grid turbulent heat flux, W m2 heat release rate, W radiant heat flux, W m2 convective and radiative heat flux on solid surface, W m2 universal gas constant, J mol1 K1 location of pyrolysis surface, m time, s

assuming the heat balance on the surfaces of solid combustibles in these simulations. PUFs are utilized in a wide variety of living and office commodity. They are solid combustibles commonly found in building fires. LES receives many applications in the prediction of building fires in recent years. For properly describing the real fire processes, the pyrolysis kinetics model of PUF is adopted and combined with the LES approach. They are jointly applied to the simulation of compartment fire with solid combustibles. The interactions between the pyrolysis of PUF slab and the space fire

1800

pyrolysis heat, J kg1 solid mass fraction converting to gaseous combustibles gas and solid thermal conductivity, W m1 K1 gas and solid density, kg m3 sub-grid turbulent stress and laminar stress, N m2

DHv

Z l, ls

r, rs t, tl

Superscripts Farve-filtered quantity filtered quantity

 —

spread is accounted for in the present simulation. The calculated results are compared with the measured data.

2. Mathematical model and numerical method Branca et al. [8] studied the thermal response of the PUF slab in a cone calorimeter. The total mass loss of the PUF slab reaches to about 85% and 88% of its original mass under the radiative intensities of 25 and 50 kW/m2, respectively. The charred residue

800

Calculation Experiment

600 Q (kW)

1200 900 600

400 200

300 0

gas, solid, and solid surface temperature, 1C velocity, m s1 sub-grid turbulent reaction rate, kg m3 s1 species mass fraction

Greek letters

Calculation Experiment

1500 Q (kW)

T, Ts, Tw u ¯ W Ys

0

50

100

150 200 t (s)

250

0

300

0

50

100 150 200 250 300 t (s)

400

400

300

300 T (°C)

T (°C)

Fig. 2. Comparison of calculated evolution of heat release rate of the PUF slab with measured data: (a) case 1 and (b) case 2.

200 100 0

x = 0.005,y = 3.395 x = 3.295,y = 0.005 Experiment

0

50

100

150 t (s)

200

200 100

250

300

0

x = 0.005m,y = 3.395m x = 3.295m,y = 0.005m Experiment

0

50

100 150 200 250 300 t (s)

Fig. 3. Comparison of calculated evolution of upper layer temperature with measured data: (a) case 1 and (b) case 2.

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in solid phase was obtained. The experiment shows that the PUF slab is consumed in solid surface reaction mode under the fire environment. It undergoes the processes of pyrolysis and residual char reaction. The thermal decomposition tests conducted in a thermogravimetric analyzer indicate that the total mass of the PUF decreases by about 80% [9]. Thus it is assumed presently that the solid surface reaction of the PUF is dominated by the thermal

decomposition and volatile release. The residual char reaction can be ignored. A series of investigations have been conducted on the thermal decomposition of the PUF by using thermogravimetric analyzers. Different pyrolysis kinetics models of the PUF were proposed for predicting its total mass loss rate [8–10]. Based on the thermogravimetric data of the PUF reported in [9], Wang et al. [11]

2.5

2.5

x = 0.005, y = 3.395 x = 3.295, y = 0.005 Experiment

2.0

z (m)

1.5 z (m)

x = 0.005m, y = 3.395m x = 3.295m, y = 0.005m Experiment

2.0

1.0 0.5

351

1.5 1.0 0.5

0.0 0

50

100

150 t (s)

200

250

300

0.0

0

50

100

150 t (s)

200

250

300

Fig. 4. Comparison of calculated evolution of smoke interface height with measured data: (a) case 1 and (b) case 2.

Fig. 5. Calculated distributions of the smoke temperature on the vertical symmetric plane of the compartment for case 1 (unit: 1C): (a) t ¼ 50 s, (b) t ¼ 80 s, (c) t ¼ 150 s, and (d) t ¼ 200 s.

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proposed a pyrolysis kinetics model of the PUF. It describes the moving speed of the PUF surface due to the thermal decomposition as below:   ds E ¼ A0 fðZÞr0 Y ox exp  (1) dt RT w where ds/dt denotes the local moving speed of the PUF surface, f(Z) is the kinetic function relevant to the reactant concentration, here f(Z) ¼ 1/Z is chosen, Z is the PUF mass fraction converting to the gaseous combustibles, r0 is the air density at 25 1C and takes a value of 1.187 kg m3, Yox is the oxygen mass fraction on the PUF surface, and Tw is the local temperature on the PUF surface. The values of the pre-exponential factor (A0 ) and the activation energy (E) are 3.92  1011 m4 kg1 s1 and 1.53  105 J mol1, respectively. Letting A ¼ A0 f(Z)r0Yox, the local moving speed of the PUF surface is further expressed as   ds E ¼ A exp  (2) dt RT w The PUF slab usually has large volume and surface area in building fires. The temperature in the slab exhibits a non-uniform distribution. Eq. (2) is suitable for describing local mass variation of the PUF slab. It is utilized presently as the PUF pyrolysis kinetics model. Under the conditions that the length and width of the PUF slab are far larger than its thickness, the locally one-dimensional heat conduction equation can be established along the thickness

direction of the slab. The temperature distribution on the PUF surfaces is calculated from this equation written as below:   qT q qT (3) rs cs s ¼ ls s qt qz qz The boundary condition on the thermal decomposition surface of the PUF slab is given as ls

qT w ds ¼ qc þ qr  rs DHv dt qz

(4)

where rs and DHv denote the density and the pyrolysis heat of the PUF slab, respectively, qr and qc represent the net radiative and convective heat flux on the PUF surface, respectively. The fire spread and smoke movement in the space of a compartment is described by the instantaneous governing equations for turbulent buoyant flow under low-Mach number. After Favre-filtering to the instantaneous equations by using the box filter, the governing equations for LES are obtained as: Continuum equation:

qr¯ ~ ¼0 þ r  r¯ u qt Momentum equation:   qu~ ~  ruÞ ~ þ rp¯ ¼ r¯ g þ r  sl þ r  s þ ðu r¯ qt

(5)

(6)

Fig. 6. Calculated distributions of the smoke temperature on the vertical symmetric plane of the compartment for case 2 (unit: 1C): (a) t ¼ 50 s, (b) t ¼ 80 s, (c) t ¼ 150 s, and (d) t ¼ 220 s.

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Energy equation: X q ~ ~ ¼ Dp¯ þ r  ðlrTÞ ~ þrqrq þ ~ hÞ r  ðh~ s r¯ Ds rY~ s Þ ðr¯ hÞ þ r  ðr¯ u R qt Dt s

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after each LES calculation of the space fire spread proceeds on three time steps.

(7) 3. Application

Species mass fraction equation:

q ~ ¯s ~ Y~ s Þ ¼ r  ðr¯ Ds rY~ s Þ þ r  Js  W ðr¯ Y s Þ þ r  ðr¯ u qt

(8)

where s, q, and Js denote the sub-grid turbulent stress, heat flux, and mass flux, respectively. They are simulated using the Smagorinsky model [12] and the eddy diffusion model. The turbulent combustion is simulated through the mixture fraction model with fast chemistry. The radiative transport equation for a non-scattering medium is formulated for simulating the thermal radiation. It is solved using the finite volume method [13]. The converted form of the LES governing equations is discretized on a staggered grid. All temporal derivatives are approximated by an explicit second-order predictor-corrector scheme. The spatial discretization employs the second-order difference schemes. The heat conduction equation for the PUF slab is discretized by the implicit Crank–Nicholson scheme. To account for the interactions between the pyrolysis of the PUF slab and the space fire spread, the PUF slab temperature, the pyrolysis rate, and the location of the pyrolysis surface are updated once

The above mathematical model is applied to the simulation of the fire spread and the pyrolysis of the PUF slab in a compartment shown in Fig. 1. The calculation conditions are chosen to be identical to the experimental conditions in [1]. The apartment is 3.4 m wide  3.3 m deep  3.05 m high. It opens to the environment through a door. The floor, ceiling, and walls are manufactured by steel. The fire source is a PUF slab with sizes of 1.8 m  1.8 m  0.15 m. It is horizontally placed at the center of the compartment on a cradle. The cradle is 2 m  2 m in its sizes and suspended 0.3 m above the floor. The igniter is assumed to be a cubic body. It has sizes of 0.06 m  0.06 m  0.06 m and a temperature of 1200 1C. The igniter is set at the center of the up surface of the PUF slab. Then it is removed when stable burning of the PUF slab is reached. The solution domain is half of the compartment space due to symmetry. Uniform spatial grid is arranged in x, y, and z-directions. The total grid number is 80  40  64. To explore the effects of ventilation condition on the pyrolysis of the PUF slab

Fig. 7. Calculated distributions of the smoke velocity vector on the vertical symmetric plane of the compartment for case 1: (a) t ¼ 50 s, (b) t ¼ 80 s, (c) t ¼ 150 s, and (d) t ¼ 200 s.

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and the space fire spread, two cases of simulations are conducted. The compartment door has a height of 2 m. Its widths are 0.9 m and 0.23 m for cases 1 and 2, respectively. The total time for simulation is taken to be 600 s. The time step is determined by the CFL condition to satisfy the stability criteria. The simulation starts from t ¼ 0, i.e., the time when the igniter is set at the surface of the PUF slab. Free boundary conditions are imposed on the open door. The walls, floor, and ceiling of the compartment are treated as thermally thin boundaries. Both radiative and convective heat transfer between their outer surfaces and the surrounding air are taken into account. The pyrolysis surface of the PUF slab is approximated by a stairstep shape in the simulation. The heat exchange between the horizontal surfaces of the PUF slab and the hot smoke is considered. The vertical surfaces of the PUF slab are taken to be adiabatic. The internal grid number along the slab thickness direction is set at 30. The PUF slab is a polymer material. Its surface emissivity is chosen to be 0.92 [7]. While all the other solid surfaces are made of steel plates. Their emissivity is taken to be 0.82 [14]. The surrounding environment has a temperature of 20 1C. The density and the pyrolysis heat of the PUF slab are 20 kg m3 [15] and 1215 kJ kg1 [2], respectively. The decomposed PUF is assumed to convert entirely to the gaseous combustibles whose molecular formula is C6.3H7.1NO2.1 [15]. It leads to Z ¼ 1 and f(Z) ¼ 1 in the pyrolysis kinetics model of the PUF. Yox in this

model is taken presently as the environment oxygen concentration, i.e., Yox ¼ 0.21. Then it gives A ¼ 9.77  1010 m s1. A fire dynamics simulator (FDS version 4.0) program [16] is employed in the present study.

4. Results and discussion Figs. 2(a) and (b) show the comparison of the calculated evolutions of heat release rate of the PUF slab with the measured data for cases 1 and 2. The heat release rate is obtained from the mass loss rate and the combustion heat of the PUF slab. It is seen that the heat release rate of the PUF slab calculated by the pyrolysis kinetics model increases gradually with time, reaches a peak, and then decreases gradually. The predicted evolution of heat release rate of the PUF slab for case 2 agrees with the measurement. While the results for case 1 are in generally agreement with the measured data. The calculated peak for this case is higher than the measurement. The descent of the heat release rate with the time is faster than the measured data for both cases. Comparing Fig. 2(a) with Fig. 2(b), it is seen that the peak of the heat release for case 1 with a wide door is obviously higher than that for case 2 with a narrow door. The ventilation condition has pronounced effects on the combustion of the PUF slab. Increasing the width of the door leads to fast heat release of

Fig. 8. Calculated distributions of the smoke velocity vector on the vertical symmetric plane of the compartment for case 2: (a) t ¼ 50 s, (b) t ¼ 80 s, (c) t ¼ 150 s, and (d) t ¼ 220 s.

ARTICLE IN PRESS S. Yuan, J. Zhang / Fire Safety Journal 44 (2009) 349–362

the PUF slab. The discrepancy between the calculation and the measurement for case 1 suggests that the one-dimensional heat conduction equation may not be adequate for the PUF slab subject to relatively large heat release rate. It should be further improved. Figs. 3(a) and (b) present the comparison of the calculated evolutions of upper layer temperature and the measured data for

0.75

mre (kg/s)

Case 1 Case 2

0.50

0.25

0.00

0

50

150

100

200

t (s) Fig. 9. Calculated evolutions of air mass inflow rate through the door.

250

355

cases 1 and 2. The experimental results are measured at two vertical positions of x ¼ 0.005 m, y ¼ 3.395 m, and x ¼ 3.295 m, y ¼ 0.005 m and averaged for the upper layer data. The predicted results are also obtained by averaging the calculated upper temperature at the same positions. It is seen that the predictions agree with the measurements for both cases. The upper layer temperature increases with time at first. It reaches a peak and then decreases gradually with time. The smoke temperature is affected obviously by the ventilation condition. The peak value of the smoke temperature evolution for case 1 is higher than that for case 2. But the smoke temperature descends more rapidly with time for the former than for the latter. Figs. 4(a) and (b) show the comparison of the calculated evolutions of smoke interface height with the measured data for cases 1 and 2. The measured test data is taken from two vertical positions. One is at x ¼ 0.005 m and y ¼ 3.395 m and the other is at x ¼ 3.295 m and y ¼ 0.005 m. The predicted results are the smoke interface heights at the same positions. The predictions agree generally with the measurements. The smoke interface height descends gradually with time, reaches a valley, and then rises gradually. The valley values are close for both cases. The presence of this valley value is relevant to the peak value of the heat release rate of the PUF slab. After reaching the valley value, the smoke interface height rises faster for case 1 than for case 2. The ventilation condition exhibits influences on the smoke interface height at the late stage of the fire.

Fig. 10. Calculated distributions of the oxygen volume fraction on the vertical symmetric plane of the compartment for case 1: (a) t ¼ 50 s, (b) t ¼ 80 s, (c) t ¼ 150 s, and (d) t ¼ 200 s.

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Figs. 5(a)–(d) present the calculated distributions of the smoke temperature on the vertical symmetric plane of the compartment at four different times for case 1. The first two times are within the increasing period of the heat release rate, while the last two are in the decreasing period of the heat release rate. From Fig. 5(a), it is seen that the fire plume over the PUF slab is generally symmetric and convergent at t ¼ 50 s or the initial stage of the fire. The location of the smoke interface is relatively high and the temperature is relatively low. As shown in Fig. 5(b), the fire plume inclines slightly to the door and its width becomes large at t ¼ 80 s. The upper layer smoke temperature near the rear wall is higher than that near the door. While the lower layer temperature near the door is higher than that near the rear wall. The smoke temperature at this moment increases over that at t ¼ 50 s, but the interface height becomes low. The distribution of the smoke temperature at t ¼ 150 s is given in Fig. 5(c). It shows that the fire plume inclines more to the door and the width of the plume increases further. The upper layer smoke temperature near the door is higher than that near the rear wall. While the lower layer temperature near the rear wall is higher than that near the door. The smoke interface height maintains to be low. The hot smoke temperature is still high. As seen in Fig. 5(d), the fire plume is found only near the rear wall and the temperature of the hot smoke descends evidently at t ¼ 200 s. Figs. 6(a)–(d) show the calculated distributions of the smoke temperature on the vertical symmetric plane of the compartment

at four different times for case 2. It is seen that the fire plume developing processes are similar to case 1. The fire plume is nearly symmetric at t ¼ 50 s (Fig. 6(a)). The smoke interface is relatively high. The fire plume becomes wide at t ¼ 80 s (Fig. 6(b)). A decrease in the smoke interface height is found. When t ¼ 150 s (Fig. 6(c)), the fire plume inclines to the door and the smoke interface height decreases further. The fire plume inclines to the rear wall at t ¼ 220 s (Fig. 6(d)). The smoke interface height is still low. Figs. 7(a)–(d) present the calculated distributions of the smoke velocity vector on the vertical symmetric plane of the compartment at four different times for case 1. A nearly symmetric fire plume is found at t ¼ 50 s, as shown in Fig. 7(a). Air is entrained into the room through the door but the inflow velocity is low. More air is seen to be entrained into the room at t ¼ 80 s from Fig. 7(b). It moves towards the floor and reaches the bottom of the fire plume. The fire plume becomes wide and inclines slightly to the door. Fig. 7(c) shows that the air inflow velocity on the door opening increases further at t ¼ 150 s. The entrained air moves to the bottom of the fire plume. The plume has large width and inclines more to the door. Air continues to be entrained into the room and reaches to the rear wall at t ¼ 200 s, as seen in Fig. 7(d). The fire plume tends to diminish. Figs. 8(a)–(d) show the calculated distributions of the smoke velocity vector on the vertical symmetric plane of the compartment at four different times for case 2. The fire plume maintains

Fig. 11. Calculated distributions of the oxygen volume fraction on the vertical symmetric plane of the compartment for case 2: (a) t ¼ 50 s, (b) t ¼ 80 s, (c) t ¼ 150 s, and (d) t ¼ 220 s.

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to be nearly symmetric at t ¼ 50 and 80 s. No air flows into the room through the door at t ¼ 50 s (Fig. 8(a)). The air entrainment from surroundings becomes evident at t ¼ 80 s (Fig. 8(b)). It increases further and the fire plume inclines to the door at t ¼ 150 s (Fig. 8(c)). The air inflow velocity becomes less and the fire plume is found near the rear wall at t ¼ 220 s (Fig. 8(d)). Figs. 9(a) and (b) present the calculated evolutions of air mass inflow rate through the door for cases 1 and 2. Along with the developing of the fire processes, the air entrainment from surroundings increases gradually with time, reaches a peak, and then decreases gradually. The air inflow rate for case 1 is larger than that for case 2. Furthermore, the air entrainment starts at earlier time for case 1 than for case 2. Thus increasing the width of the door is favorable to entraining air from surroundings. Figs. 10(a)–(d) present the calculated distributions of the oxygen volume fraction on the vertical symmetric plane of the compartment at four different times for case 1. From Fig. 10(a), it is seen that the oxygen in the room is consumed not too much at t ¼ 50 s. The cold air layer still has certain height. Along with the increase in the heat release rate, the oxygen concentration decreases obviously and the air layer height becomes low at t ¼ 80 s, as shown in Fig. 10(b). Fig. 10(c) exhibits further decrease in the oxygen concentration and the air layer height at t ¼ 150 s. The oxygen concentration at t ¼ 200 s is depicted in Fig. 10(d). It is seen that when the PUF slab is close to the end of consumption,

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the oxygen concentration increases and the air layer height is still low. Figs. 11(a)–(d) show the calculated distributions of the oxygen volume fraction on the vertical symmetric plane of the compartment at four different times for case 2. The lower cold air layer is relatively high except near the fire source region at t ¼ 50 s (Fig. 11(a)). It is seen that the air layer height in the room descends evidently at t ¼ 80 s (Fig. 11(b)). The oxygen concentration becomes less due to the consumption of combustion. The air layer height in the compartment descends further at t ¼ 150 s (Fig. 11(c)). The oxygen tends to be consumed out except the air layer near the floor. This happens due to that the air inflow rate to the room for case 2 is less than that for case 1. The PUF slab approaches to finishing the pyrolysis at t ¼ 220 s (Fig. 11(d)). The oxygen concentration in the lower space of the compartment ascends slightly. Figs. 12(a)–(d) present the calculated distributions of the R smoke integral radiant intensity ( 4p Iðx; sÞ dO) on the vertical symmetric plane of the compartment at four different times for case 1. From Fig. 12(a), it is seen that the radiant intensity in the compartment approaches a symmetric distribution at t ¼ 50 s. The radiant intensity is high in the region over the PUF slab and low in the other region. As shown in Fig. 12(b), the region with high radiant intensity expands evidently at t ¼ 80 s. It is up close to the ceiling and declines slightly to one side of the room near the

Fig. 12. Calculated distributions of the smoke radiant intensity on the vertical symmetric plane of the compartment for case 1 (unit: kW/m2): (a) t ¼ 50 s, (b) t ¼ 80 s, (c) t ¼ 150 s, and (d) t ¼ 200 s.

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Fig. 13. Calculated distributions of the smoke radiant intensity on the vertical symmetric plane of the compartment for case 2 (unit: kW/m2): (a) t ¼ 50 s, (b) t ¼ 80 s, (c) t ¼ 150 s, and (d) t ¼ 220 s.

Fig. 14. Calculated distributions of the heat flux on the top plane of the PUF slab for case 1 (unit: kW/m2): (a) t ¼ 50 s, (b) t ¼ 80 s, (c) t ¼ 150 s, and (d) t ¼ 200 s.

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(Fig. 13(b)). But the region with high radiant intensity expands up to the ceiling. At t ¼ 150 s (Fig. 13(c)), the region with high radiant intensity diminishes and leans to the door. This region keeps to be relatively small at t ¼ 220 s (Fig. 13(d)). But it leans to the rear wall. Fig. 13, jointly with the Fig. 6, shows that the region with high radiant intensity corresponds to the region with high gas temperature. It leads to radiative heat transfer from the fire plume to other regions. Figs. 14(a)–(d) present the calculated distributions of the heat flux on the top plane (z ¼ 0.45 m) of the PUF slab at four different times for case 1. As shown in Figs. 14(a) and (b), the heat flux distributions on the top plane of the PUF slab are generally symmetric at t ¼ 50 and 80 s or the increasing stage of the heat release rate. The heat flux is high near the center of the top plane at t ¼ 50 s. The region with high heat flux expands outwards from

door. Fig. 12(c) shows that the radiant intensity is high in the region close to the door and relatively low near the rear wall at t ¼ 150 s. The radiant intensity becomes low except in the local region near the rear wall at t ¼ 200 s, as seen in Fig. 12(d). Comparing Fig. 12 with Fig. 5, it is seen that the fire plume region with high temperature is also large in radiant intensity. As a result, the radiation will transmit heat from the fire plume region to other regions of the compartment and the PUF slab will be further heated. Figs. 13(a)–(d) show the calculated distributions of the smoke integral radiant intensity on the vertical symmetric plane of the compartment at four different times for case 2. The smoke radiant intensity is symmetric in its distribution at t ¼ 50 s (Fig. 13(a)). It is high in the local region over the PUF slab. The radiant intensity still exhibits generally symmetric distribution at t ¼ 80 s

Fig. 15. Calculated distributions of the heat flux on the top plane of the PUF slab for case 2 (unit: kW/m2): (a) t ¼ 50 s, (b) t ¼ 80 s, (c) t ¼ 150 s, and (d) t ¼ 220 s.

0.9

0.9 y = 1.7m z (m)

z (m)

y = 1.7m 0.6 0.3

0.5

1.0

1.5

2.0

2.5

0.6 0.3

3.0

0.5

1.0

1.5

0.9

z (m)

z (m)

0.3 1.5

2.0 x (m)

3.0

y = 2.5m

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1.0

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0.9

y = 2.5m

0.5

2.0 x (m)

x (m)

2.5

3.0

0.6 0.3

0.5

1.0

1.5

2.0

2.5

3.0

x (m)

Fig. 16. Calculated residual configurations of the PUF slab along x-direction for case 1: (a) t ¼ 50 s, (b) t ¼ 80 s, (c) t ¼ 150 s, and (b) t ¼ 200 s.

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wall. Comparing Fig. 15 with Fig. 14, it is seen that the maximum heat flux on the top plane of the PUF slab for case 1 with larger air inflow rate is higher than that for case 2. The former is 50 kW/m2, while the later is 40 kW/m2. Figs. 16(a)–(d) show the calculated residual configurations of the PUF slab along the x-direction at four different times for case 1. Since the heat flux distributions on the PUF slab surface are generally symmetric at t ¼ 50 and 80 s, the pyrolysis of the PUF slab and the changes in its configuration proceed in nearly symmetric manner, as seen in Figs. 16(a) and (b). The heat flux is high near the center of the slab surface. The pyrolysis and configuration change starts from the central region of the slab and extends outwards gradually. The fire plume leans to the door and the PUF slab surface close to the door receives more heat flux at t ¼ 150 s. Thus the pyrolysis and configuration change of the PUF slab near the door is faster than that close to the rear wall, as

the center at t ¼ 80 s. From Figs. 14(c) and (d), it is seen that the region with relatively high heat flux shifts to the corner of the slab at t ¼ 150 s. The pyrolysis of the PUF slab is close to the end at t ¼ 200 s. Relatively high heat flux is found only at the corner of the PUF slab near the rear wall. Figs. 15(a)–(d) present the calculated distributions of the heat flux on the top plane (z ¼ 0.45 m) of the PUF slab at four different times for case 2. The heat flux on the top plane of the PUF slab exhibits symmetric distribution at t ¼ 50 s (Fig. 15(a)). It is high near the center of the top plane. Arriving at t ¼ 80 s (Fig. 15(b)), the heat flux on the top plane of the PUF slab is still nearly symmetric in its distribution. But the region with high heat flux deviates from the plane center. The heat flux on the top plane close to the door is higher than that near the rear wall at t ¼ 150 s (Fig. 15(c)). At t ¼ 220 s (Fig. 15(d)), the local region with high heat flux remains only on the top plane of the PUF slab close to the rear

0.9

0.9 x = 1.65m

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x = 1.65m

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2.1

2.3 y (m)

2.5

0.6

0.3

2.7

1.7

1.9

2.1

2.3 y (m)

Fig. 17. Calculated residual configurations of the PUF slab along y-direction for case 1: (a) t ¼ 50 s, (b) t ¼ 80 s, (c) t ¼ 150 s, and (d) t ¼ 200 s.

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y = 1.7m

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z (m)

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y = 1.7m

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2.0 x (m)

2.5

3.0

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Fig. 18. Calculated residual configurations of the PUF slab along x-direction for case 2: (a) t ¼ 50 s, (b) t ¼ 80 s, (c) t ¼ 150 s, and (d) t ¼ 220 s.

ARTICLE IN PRESS S. Yuan, J. Zhang / Fire Safety Journal 44 (2009) 349–362

0.9

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0.9 x = 1.65m

z (m)

z (m)

x = 1.65m

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2.7

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0.3

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Fig. 19. Calculated residual configurations of the PUF slab along y-direction for case 2: (a) t ¼ 50 s, (b) t ¼ 80 s, (c) t ¼ 150 s, and (d) t ¼ 220 s.

shown in Fig. 16(c). The fire plume leans to the rear wall at t ¼ 200 s. The PUF slab near the rear wall is gradually consumed out, which can be seen from Fig. 16(d). Figs. 17(a)–(d) present the calculated residual configurations of the PUF slab along the y-direction for case 1 at t ¼ 50, 80, 150, and 200 s, respectively. From these figures, it is seen that the pyrolysis and configuration change of the PUF slab starts from the slab center and then extends outwards gradually. Therefore, the pyrolysis and consumption of the PUF slab is not uniform along the thickness direction. The local mass variation rate lies on the net heat flux received by the local surface of the slab. Figs. 18(a)–(d) show the calculated residual configurations of the PUF slab along the x-direction at four different times for case 2. As seen in Figs. 18(a) and (b), the pyrolysis of the PUF slab and the changes in the configuration are generally symmetric about its center at t ¼ 50 and 80 s. The pyrolysis of the PUF occurs in the central region of the slab at first. Then it spreads gradually to the outer region of the slab. From Fig. 18(c), it is seen that the pyrolysis and the configuration change of the PUF slab close to the door is faster than that near the rear wall at t ¼ 150 s. At t ¼ 220 s, the pyrolysis of the PUF slab near the rear wall continues and tends to its end, as shown in Fig. 18(d). Figs. 19(a)–(d) present the calculated residual configurations of the PUF slab along the y-direction for case 2 at t ¼ 50, 80, 150, and 220 s, respectively. Along the y-direction, the pyrolysis and configuration change of the PUF slab starts from the central region. It extends gradually to the outer region of the slab.

5. Conclusions The large eddy simulation of the space fire spread and the pyrolysis of the PUF slab in a compartment is conducted. The pyrolysis kinetics model of the PUF is utilized in the simulation. The following conclusions are reached. By considering the interactions between the thermal decomposition of the PUF slab and the space fire spread, the instantaneous mass variation rate of the solid combustibles can be computed and obtained. It is not necessary to set the heat release rate of the fire source in advance.

The calculated evolutions of the heat release rate of the PUF slab, the smoke temperature, and the smoke interface height in the compartment are in agreement with the measured data under different ventilation conditions. The heat flux on the top plane of the PUF slab exhibits a nonuniform distribution. The pyrolysis and configuration change of the PUF slab starts from the surface center with relatively high heat flux. Then it extends outwards gradually. The pyrolysis and consumption of the PUF slab proceeds in an asymmetric manner. When the fire plume inclines to one side of the room, the slab close to this side has a fast mass loss rate. The ventilation conditions have pronounced effects on the interactions between the pyrolysis of the PUF slab and the space fire spread in a compartment. When the height of the door keeps unchanged, increasing the width of the door opening will lead to faster mass loss of the PUF slab, higher peak value of the heat release rate, and higher maximum heat flux on the PUF slab surface.

Acknowledgment This study was supported by the China NKBRSF Project no. 2001CB409600. References [1] P.A. Reneke, M.J. Peatross, W.W. Jones, C.L. Beyler, R. Richards, A comparison of CFAST predictions to USCG real-scale fire tests, NISTIR 6446 (2000). [2] M.C. Luo, V. Beck, A study of non-flashover and flashover fires in a full-scale multi-room building, Fire Saf. J. 26 (1996) 191–219. [3] Y.P. He, Measurement of doorway flow field in multi-enclosure building fires, Int. J. Heat Mass Transfer 42 (1999) 3253–3265. [4] V. Novozhilov, B. Moghtaderi, D.F. Fletcher, J.H. Kent, Computational fluid dynamics modeling of wood combustion, Fire Saf. J. 27 (1996) 69–84. [5] S. Hostikka, K. McGrattan, Large eddy simulation of wood combustion, NIST Report, 2001. [6] Z.H. Yan, G. Holmstedt, CFD and experimental studies of room fire growth on wall lining materials, Fire Saf. J. 27 (1996) 201–238. [7] F. Jia, E.R. Galea, M.K. Patel, The numerical simulation of the noncharring pyrolysis process and fire development within a compartment, Appl. Math. Modelling 23 (1999) 587–607. [8] C. Branca, C.D. Blasi, A. Casu, V. Morone, C. Costa, Reaction kinetics and morphological changes of a rigid polyurethane foam during combustion, Thermochim. Acta 399 (2003) 127–137.

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[9] C.Y.H. Chao, J.H. Wang, Comparison of the thermal decomposition behavior of a non-fire retarded and a fire retarded flexible polyurethane foam with phosphorus and brominated additives, J. Fire Sci. 19 (2001) 137–156. [10] M.L. Hobbs, G.H. Lemmon, Polyurethane foam response to fire in practical geometries, Polym. Degradation Stability 84 (2004) 183–197. [11] J.H. Wang, C.Y.H. Chao, W.J. Kong, Experimental study and asymptotic analysis of horizontally forced forward smoldering combustion, Combust. Flame 135 (2003) 405–419.

[12] J. Smagorinsky, General circulation experiments with the primitive equations. I. The basic experiment, Month. Weather Rev. 91 (1963) 99–164. [13] G.D. Raithby, E.H. Chui, A finite-volume method for predicting radiant heat transfer in enclosure with participating media, J. Heat Transfer 112 (1990) 415–423. [14] J.P. Holman, Heat Transfer, ninth ed, McGraw-Hill, New York, 2002. [15] FDS-database4 /http://fire.nist.gov/fds/S. [16] K. McGrattan, G. Forney, Fire dynamics simulator—(version 4) technical reference guide, NIST Spec. Publ. 1018 (2004).