THE EFFECT OF THERMAL RADIATION ON THE DYNAMICS OF FLASHOVER IN A COMPARTMENT FIRE

Transcription

1 The 6th ASME-JSME Thermal Engineering Joint Conerence March 16-20, 2003 TED-AJ THE EFFECT OF THERMAL RADIATION ON THE DYNAMICS OF FLASHOVER IN A COMPARTMENT FIRE W. W. YUEN Department o Mechanical and Environmental Engineering University o Caliornia at Santa Barbara Santa Barbara, Caliornia, USA yuen@engineering.ucsb.edu Shousuo HAN Department o Building Services Engineering The Hong Kong Polytechnic University Hong Kong, China r@polyu.edu.hk W. K. CHOW Department o Building Services Engineering The Hong Kong Polytechnic University Hong Kong, China bewkchow@polyu.edu.hk Keywords: ire, lashover, radiation, zonal method ABSTRACT Flashover is a phenomenon describing a room ire changed rom the growth stage to the development stage. There is a rapid increase in size and intensity. The radiant heat lux back to the uel surace and the loor o the room is known to be one o the key parameters leading to lashover. Indeed, a heat lux (largely due to radiation) o 20 kw/m 2 to the room loor is oten taken to be the condition o lashover. To understand the importance o radiation, a zone model is developed to simulate the transient ire growth in a compartment. Heat and mass transer correlations available in the literature are used to simulate the non-radiative eect. A three-dimensional non-gray soot radiation model is used to simulate the radiative exchange between the uel surace, the hot gas/particulates layer and the surrounding wall. Results show that the hot layer temperature alone may not be an eective indicator or lashover. Other parameters such as particulates volume raction in the hot layer, venting area and heat transer to the surrounding wall are also important in determining the occurrence o lashover.

2 NOMENCLATURE a = the total potential heat lux generated by the ree burning ire, parameter used in Eq. (5) A = area o the uel surace A w = surace area o the wall o the compartment b = an exponential coeicient used in Eq. (5) c p = speciic heat o hot gas/particulates layer C 2 = the second radiation constant D = ractional height o the discontinuity plane v = particulates volume raction g = gravitational constant G = rate o energy gain o the hot gas/particulates layer H C = heat o combustion H R = height o the cubical compartment H vap = heat o vaporization H V = height o the vertical vent k = an empirical constant used in the deinition o absorption coeicient o hot gas/particulates layer K = a lame spread constant L = rate o energy loss o the hot gas/particulates layer L R = length o the cubical compartment L = equivalent length o the ire base m = mass o hot gas/particulates layer N = ractional height o the neutral plane R = radius o the ire at the compartment loor R edge = the distance over which the eect o the edge o the uel is elt R max = the maximum radius o the ire Sr = stoichiometric ratio t = time T = temperature o the hot gas/particulates layer T a = ambient temperature V = lame spread rate U c = an adjustable parameter or the wall temperature W R = width o the cubical compartment W V = width o the vertical vent Z d = discontinuity height H = increase in enthalpy o hot gas/particulates layer due to mass increase H I= net enthalpy low rate out o the vent o m = mass low rate o air into the compartment a m = rate o volitalisation m o = mass low rate out o the vent q = heat lux rom the ire to the ire base q, surr= heat lux rom the surrounding (hot layer and walls) to the ire base q b = radiative heat lux to the base o the compartment gs x = exchange actor between the hot layer and wall element x (x = l, r, i, o, t, b, v stand or the let, right, inner, outer, top, bottom wall and vent opening respectively) sxs y = exchange actor between wall element x and wall element y (x,y = l, r, i, o, t, b, v) χ = combustion eiciency ρ 0 = density o hot gas/particulate mixture ε = emissivity κ = absorption coeicient INTRODUCTION The importance o the phenomenon o lashover in compartment ire is well known or many years [1]. Physically, lashover is a term used to characterize the rapid transition o a relatively small local ire to a large ire in which the whole compartment is involved. When lashover occurs, the ire jumps rom the growth stage to the development stage, and great damages to the building structure and properties would be resulted. Flashover has been consistently observed in disastrous ires [2] leading to severe losses o human lives and properties. Experimentally, studies on lashover were reported both in actual ires and in ull-scale burning tests. Two quantitative criteria were consistently observed as conditions or the onset o lashover. They are: a. upper gas layer temperature exceeds 600 C b. heat lux at the loor exceeds 20 kw/m 2 A summary o the conditions or the onset o lashover reported by dierent studies is shown in Table 1[3-12]. Qualitatively, another criterion used to characterize the onset o lashover is the visual observation that at the time immediate prior to lashover, lames begin to come out o the vents. Numerical and theoretical studies o lashover have ocused primarily on predicting the behavior o the gas layer temperature in a compartment ire using various orms o the zone model [13-15]. The concept o thermal instability in compartment ire was initiated by Thomas et. al. [11]. This concept led to urther works [16,17] in which the onset o lashover is predicted by computational techniques o nonlinear dynamics [18,19]. In all o the existing numerical and theoretical studies, the gas layer temperature is the primary dependent variable and the gas temperature criterion (> 600 C) is used as the quantitative criterion or lashover. It is interesting to note rom Table 1 that in all o the reported lashover in which data or both criteria are available, both the gas temperature and heat lux criteria or the onset o lashover are satisied. Physically, the heat lux criterion is expected to be more critical since the secondary ignition o the combustibles in a compartment is a major actor leading to lashover. The heat lux to the loor (and more speciically, radiant heat lux) is the main source o energy leading to the secondary ignition. However, gas layer temperature exceeding 600 C without a radiation source (such as the wall or soot particulates which can serve as a radiating medium) is insuicient to generate the necessary heat lux at or loor required or lashover. To generate a loor heat lux o 20 kw/m 2 or a temperature dierence o 600 C based only on convection, or example, would require a heat transer

3 coeicient o about 33 W/( m 2 -K). This value exceeds the range o heat transer coeicient generally expected in a compartment ire environment (natural convection and low speed orce convection). The importance o the radiant eedback mechanism in the onset o lashover is recognized by almost every theoretical study o lashover [13-17]. But due to the complexity o radiation and the uncertainty o the radiation model used in the analysis, all o the existing studies do not use the heat lux criterion as a actor in determining the condition o lashover. Over the past ten years, signiicant advances have achieved both in the understanding o the radiative properties o the various combustion species in a ire and the mathematical modeling o three-dimensional radiative transport in a participating medium [20]. These advances can be readily implemented in a zonal model to give an improved assessment o the onset o lashover. The objective o the present work is to implement two speciic advances in radiation heat transer into a zone model to analyze the transient behavior o a compartment ire and the onset o lashover. Since smoke particulates are expected to be a major component contributing to the radiative emission and absorption o the hot gas/particulates layer in the room during a compartment ire, a simpliied model [21] is used to account or the non-gray absorption behavior o the smoke particulates. This model yields the relationship between smoke particulates volume raction, gas layer temperature with the radiative emission and absorption o the hot layer. Computationally, the three-dimensional radiative exchange between the hot layer, the ire base and the surrounding walls must be evaluated accurately to determine the radiant eedback to the loor. An eicient and accurate zonal method [22], which is shown to be applicable or all participating media in enclosures with three-dimensional geometry, is used. Numerical data are generated to show the importance o various parameters on the onset o lashover both rom the perspective o the hot gas/particulates layer temperature and the radiant heat lux to the loor. ANALYSIS A simpliied two zone compartment ire model [16] is used as the basis o the present study. While this model can give only an overall picture with no ine details, it contains all the relevant physics and is suicient or the present purpose, which is to illustrate the importance o using an accurate radiation model in assessing lashover. Conservation Equations The compartment is assumed to be a cubical enclosure as shown in Fig. 1. The ire is assumed to be a circular region in the center o the loor with radius R. Following the mathematical development o Bishop et. al. [16,19], the temperature o the hot gas/particulates layer is governed by dt G L H = (1) dt c m p The gain rate o the hot layer depends on whether the ratio o the mass air low rate to the uel volatilisation rate is greater than (uel controlled ire) or less than (ventilation controlled ire) the stoichiometric ratio. Assuming that all energy o combustion goes into the hot layer, G is given by m a χmh c i Sr m G = m a m a χ Hc i < Sr Sr m where χ is the combustion eiciency, m a is the mass low rate o air into the compartment, m is the rate o volitalisation, H c is the heat o combustion and Sr is the stoichiometric ratio. The volitalisation rate o uel depends on the heat transer rom the ire and the compartment surrounding to the ire base. It is given by where q, surr q ( +, ) vap (2) q q surr A m = (3) H is the heat lux rom the ire to the ire base, is the heat lux rom the surrounding (hot layer and walls) to the ire base, H vap is the heat o vaporization and A is the area o the uel surace given by A 2 = π R () Following Emmons [13], the ire is assumed to have the orm o a cone and the heat lux rom the lame to the base is given by br ( 1 ) q = a e (5) where a is the total potential heat lux generated by the ree burning ire and b is an exponential coeicient. The ormulation o q, surrdepends on the radiation model, it will be discussed in the next section. The mass low rate o air into the compartment is assumed to be driven by buoyancy low [23] and is given by 2 T D = 2 1 ( ) + (6) 3 T 2 3/2 a ma CDρ0WvH g N D N v with D being the ractional height o the discontinuity plane given by

4 D Z d = (7) H v where Z d is the discontinuity height. N is the ractional height o the neutral plane, it is taken empirically to be ( 1+ D) 2 N = D+ (8) 2 The rate o energy loss rom the hot layer is given by L= H + Q (9) o w where H o is the net enthalpy low rate out o the vent given by ( ) H = m c T T (10) o o p a with m o being the mass low rate out o the vent. Assuming that there is no accumulation o mass in the compartment, m is related to m and m by o m = m + m (11) o a Q w is the heat loss rom the hot gas/particulates layer to the wall. Its expression depends on the radiation model and will be discussed in the next section. A consequence o Eq. (11) is that there is no mass increase within the compartment. This leads to H = 0 (12) and the mass o the hot gas/particulates layer is given by a ( ) m= ρ L W H Z (13) 0 R R R D In Eq. (13), the concentration o particulates is assumed to be suiciently low such that the density o the hot gas/particulates layer remains essentially constant at ρ 0. Finally, the dierential equation or the rate o change o the ire radius is given by dr = V 1 e dt R Rmax Redge (1) where R edge is the distance over which the eect o the edge o the uel is elt and R max is the maximum radius, representing the size o the uel sample. V is the lame spread rate which can be taken as [2] V K m a = ρ WNH 0 v v (15) with K being a lame spread constant. Radiation Model o Previous Works In nearly all o the existing theoretical works [13-17] on lashover, q, surrandq w are generated by assuming a constant value o emissivity, ε, or the gas/particulates layer. For example, Bishop et. al. [16] used the ollowing expressions ( ε) q, surr= σ εt + 1 Tw T a (16) ( εσ [ ]) Q w = Aw T Tw + ht T Tw (17) with h t being a convective heat transer coeicient and A w is the surace area o the surrounding wall given by ( ) ( ) ( ) A = 2 LW + 2 L H + 2 HW (18) w R R R R R R To complete the mathematical description o the model, the wall temperature is assumed to be between the layer temperature T and the ambient temperature T a given by ( ) T = U T T + T (19) w c a a with U c being an adjustable parameter between 0 and 1. A undamental diiculty o this radiation model is that it provides no physical correlation between the layer emissivity ε and measurable parameters such as particulates volume raction and temperature o the hot layer which are known to have an eect on hot layer emissivity. The model also does not account or the eect o the compartment geometry (dimensions, size o vent and radius o ire base) on the radiation transport. The Current Radiation Model In the current model, particulates in the hot layer are assumed to be the primary species or radiative emission and absorption. Assuming that the size o the particulates are small so that the Rayleigh s limit o particle absorption is valid, the absorption coeicent o the hot gas/particulates layer can be written as [21] 3.6k v T κ = (20) C2 where v is the particulates volume raction, k is an empirical constant in the range o 3.5 to 7.5 (depending on the uel) and C 2 is the second radiation constant. Since the size o the ire grows with a growth rate given by Eqn. (1), the volume raction o the hot gas/particulates layer is assumed to be proportional to the ire radius R. Speciically, the current model assumes

5 R v = v,0 (21) Rmax with v,0 being a characteristic volume raction which is a unction o the uel. Assuming that the uel surace can be treated as a square o length L given by L = π R (21) exact expressions or the exchange actor between the ire base, the hot gas/particulates layer and the surrounding wall can be readily obtained using the tabulated data and superposition procedure as outlined in Yuen and Takara [22]. The deinition o exchange actor and its mathematical properties are described in reerence [21]. For a cubic enclosure with W R = L R = H R = 0 cm, Z d = 0 (i.e. the hot layer ills the whole compartment) and a ire base with L = 30 cm, or example, the exchange actor between the ire base and the hot layer (s g), the exchange actor between the ire base and the top wall (s s t ) and the exchange actor between the hot layer and the top wall (gs t ) are shown in Figs. 2a, 2b and 2c respectively. It is important to note that these actors depend strongly on the absorption coeicient. The radiation transport thus depends strongly on the hot layer temperature and the particulates volume raction. Based on the concept o exchange actor, the expression or q, surr can be written as Aq σt gs ( κ) ( κ ) + ss ( κ ) ( ) ( ) o vs( κ w) ( κ ) =, surr ss t w l w + σt + s s κ + ss κ + s + σt s s w r w i w a v a (22) where gs ( ) layer and the ire base. s s ( x= t,, l r,, i o v, v) κ is the exchange actor between the hot stands or the exchange actor between the top wall (t), let wall (l), right wall (r ), inner wall (i), outer wall (o), the vent opening (v) and the ire base respectively. The subscript o-v stands or the outer wall section minus the vent opening. The subscript in the absorption coeicient κ indicates the temperature (wall, vent or hot layer temperature) at which it is evaluated. In a similar manner, the expression or Q is given by w x a v a gst( κ) + gsb( κ) ( ) ( ) + gsi( κ ) + gso( κ ) t( κw) + gsb ( κw) ( ) ( ) gsi( κw) gso v( κw) ( κ ) Q w = σt + gsl κ + gsr κ gs σtw + gsl κw + gsr κw + + σt gs (23) where the subscript b stands or the bottom loor. Equations (1) to (15), together with Eqns. (19) to (23) constitute a complete mathematical description o the present transient compartment ire model. In addition to predicting the transient behavior o the hot layer temperature, the radiative heat lux to the compartment loor can be readily evaluated by Q = L W q = σ κ σ κ b R R b T gsb a v b a ( ) + T s s ( ) t b( κw) + ss l b( κw) ( ) ( ) s s ( κ ) ss + σt + s s κ + ss κ + o v b w w r b w i b w (2) Equation (2) can be used as a basis o evaluation or the heat lux criterion o lashover. RESULTS AND DISCUSSION Numerical data are generated to examine the eect o vent opening W v, particulates volume raction v,0 and the wall temperature parameter U c on the transient temperature rise o the hot gas/particulates layer and the radiative heat lux to the compartment loor. These parameters are selected because they are expected physically to be important parameters aecting the occurrence o lashover. The eect o other parameters will be investigated in uture works. For the value o other parameters, the present work ollows the approach o Bishop et. al. [16]. They are chosen to describe a typical ire burning on a circular PMMA slab developed on a scaled (i.e. 0 cm inside cube) compartment. A listing o the parameters is shown in Table 2. For a direct comparison, numerical data are also generated with the previous radiation model with a layer emissivity o ε = 0.1 (value used in reerence [16]). For the case with U c = 0 (T w = T a, the cold wall case), the layer temperature or dierent vent openings are shown in Figs. 3a to 3e. The corresponding heat lux to the compartment loor are shown in Figs. a to e. The layer temperature illustrate an interesting relation between radiation and vent openings. When the vent opening is small (or example, W v = 5 cm) and the ire is ventilation

6 controlled, the primary eect o radiation appears to be the heat loss to the surrouding wall. The case with the smaller particulates volume raction (hence less radiation heat loss) has the higher layer temperature. An increase in the particulates volume raction increases the radiative heat loss (to the surrounding) and thus lowers the layer temperature. When the vent opening is large (W v > 10 cm) and the ire is uel controlled, the eect o radiative eedback to the uel surace appears to be more important. The layer temperature increases with increasing particulates volume raction. The increased radiative eedback to the uel surace increases the burning rate and thereore the layer temperature. It is interesting to note that result o the previous radiation model (which does not depend on particulates volume raction) agrees with the optically thick (high particulates volume raction) case or the ventilation controlled ire (W v = 5 cm) and it agrees with the optically thin (low particulates volume raction) case or the uel controlled ire. This result demonstrates the physical diiculty o the previous radiation model. By assuming a constant emissivity or the hot gas layer and the wall in an ad-hoc ashion, the model cannot yield a consistent interpretation o the physics, even in a limiting sense. From the lashover perspective, results in Figures 3a and 3e and the temperature criterion would suggest that lashover occurs in the ventilation controlled case with low particulates volume raction ( v, or W v = 5 cm, v, or W v = 10 cm). The temperature criterion is also satisied or the high volume raction case ( v, ) with W v = 20 cm. The temperature criterion is never satisied or all particulates volume raction or the uel controlled ire (W v = 30, 0 cm). The conclusion about lashover, however, is quite dierent i the heat lux criterion and results in Figs. a to e are utilized. Speciically, heat lux criterion is not satisied or all particulates volume raction or the ully ventilation controlled ire (W v = 5 cm) and the ully uel controlled ire (W v = 0 cm). For the W v = 5 cm case, the high layer temperature is attained when the particulates volume raction is small. There is insuicient emission and thereore the radiative heat lux to the compartment loor remains low. For the W v = 0 cm case, the temperature o the hot layer is not high enough to generate the necessary radiative heat lux. Results in Figs. b to d suggest that lashover occurs in cases with high particulates volume raction ( v,0 = 10-3, 10 -, 10-5 ) or ires which are neither totally ventilation controlled nor totally uel controlled (W v = 10, 20, 30 cm). Note that in the W v = 30 cm case, the heat lux criterion is satisied even though the hot layer temperature is only about 800 K (500 C). It is important to note that the association o lashover with high particulates volume raction is consistent with the observation that the presence o smoke and luminous lame is a necessary condition or lashover. Results in Figs. 3a to 3e and a to e demonstrates readily that the temperature criterion alone might not be an adequate condition or the identiication o lashover. An accurate model or thermal radiation heat transer and a correct assessment o the radiative heat lux to the compartment loor are necessary or an eective assessment o the lashover. Temperature results with U c = 1 (T w = T, the hot wall case), are shown in Figs. 5a to 5c and the corresponding heat lux to the compartment loor are shown in Figs. 6a to 6c. The slight oscillation in the numerical result is due to the explicit numerical scheme used in the present calculation. It has no impact on the accuracy o the result. The transient temperature behavior or dierent W v are quite similar. Since there is no heat loss rom the hot layer to the wall, the steady state temperature is independent o the radiative properties o the layer and is thus quite insensitive o the particulates volume raction. There is also less dierence in the layer temperature between the uel controlled ire and the ventilation controlled ire. The radiative heat lux to the compartment loor also show similar behavior or dierent vent opening and particulates volume raction. In general, the radiation o the wall dominates the heat transer and has a major eect on the inal steady state hot layer temperature and heat lux to the compartment loor. Because o the large radiative heat lux rom the wall, the two lashover criteria are readily satisied in all cases. It is interesting to observe that all the predicted lashovers are quite catastrophic as there is a nearly vertical jump both in the temperature and in the radiative lux to the compartment loor. Physically, this suggests that a ire in a highly insulated compartment will likely lead to a lashover. This is consistent with physical expectation. CONCLUDING REMARKS The present work shows that radiative heat transer is clearly a dominant actor in the determination o lashover. A theroretical model with an inaccurate model o radiation can lead to conclusions with uncertain accuracy. Using a non-gray particulates radiation model and the zonal method, a zone model is developed to determine the conditions leading to lashover. Numerical data are presented to illustrate the eect o vent opening, particulates volume raction and the wall temperature on the transient temperature rise and lashover. Results demonstrate that the hot gas layer temperature alone might not be a suicient criterion or lashover. Both high temperature in the hot layer and high emissivity rom the gas/particulates layer are necessary to generate a heat radiative heat lux to the compartment loor. I the compartment is well insulated, the radiation rom the wall can also become a dominant eect leading to lashover. The present model can be used as a basis or a more detailed non-linear analysis to identiy the dierent type o instabilities and their relation to the transition to lashover. This task is currently under consideration and will be reported in a uture publication.

7 Reerences Hagglund [] Parker and Lee [5] Fang [6] Lee and Breese [7] Babrauskas [8] Budnick and Klein [9] Fang and Breese [10] Thomas [11] McCarey and Quintiere [12] Temperature Near the Ceiling C 600 No data ± Radiation Heat Flux (kw/m 2 ) No data Table 1: Observations o the lashover criteria. Compartment Parameters H R = 0 cm W R = 0 cm L R = 0 cm H V = H R = 0 cm Fuel Parameters R max = 15 cm R edge = 1 cm K = 1/2000 Sr = 8.25 H vap = 1,008,000 J/kg H c = 2,900,000 J/kg T = 1300 K Fluid Parameters C D = 0.7 ρ 0 = 1.25 kg/m 3 T a = 300 K c p = J/kg-K Heat Transer Parameter h t = 7 W/m 2 -K χ = 0.65 a = 102,000 W/m 2 b = 1.12 m -1 Figure 2a: Exchange actor between the ire base and the hot layer (with W R = L R = H R = 0 cm, L = 30 cm, and Z d = 0). Figure 2b: Exchange actor between the ire base and the top wall (with W R = L R = H R = 0 cm, L = 30 cm, and Z d = 0). Table 2: Speciied parameters in numerical examples. H V H R W R W V Figure 1: Geometry and dimensions o the cubical compartment. L R Figure 2c: Exchange actor between the hot gas layer and the top wall (with W R = L R = H R = 0 cm, L = 30 cm, and Z d = 0).

8 Figure 3a: Temperature o the hot layer or W v = 5 cm and dierent particulates volume raction. Figure 3d: Temperature o the hot layer or W v = 30 cm and dierent particulates volume raction. Figure 3b: Temperature o the hot layer or W v = 10 cm and dierent particulates volume raction. Figure 3d: Temperature o the hot layer or W v = 0 cm and dierent particulates volume raction. Figure 3c: Temperature o the hot layer or W v = 20 cm and dierent particulates volume raction. Figure a: Radiative heat lux to the compartment loor or W v = 5 cm and dierent particulates volume raction.

9 Figure b: Radiative heat lux to the compartment loor or W v = 10 cm and dierent particulates volume raction. Figure e: Radiative heat lux to the compartment loor or W v = 0 cm and dierent particulates volume raction. Figure c: Radiative heat lux to the compartment loor or W v = 20 cm and dierent particulates volume raction. Figure 5a: Temperature o the hot layer or W v = 5 cm, U c = 1, and dierent particulates volume raction Figure d: Radiative heat lux to the compartment loor or W v = 30 cm and dierent particulates volume raction. Figure 5b: Temperature o the hot layer or W v = 20 cm, U c = 1, and dierent particulates volume raction

10 Figure 5c: Temperature o the hot layer or W v = 0 cm, U c = 1, and dierent particulates volume ractions. Figure 6c: Radiative heat lux to the compartment loor or W v = 0 cm, U c = 1, and dierent particulates volume ractions. ACKNOWLEDGEMENT This work was based on work conducted by one o the author (WWY) during a sabbatical leave at the Polytehnic University at Hong Kong. It is also supported by the PolyU conerence grant and account no. G W136. Figure 6a: Radiative heat lux to the compartment loor or W v = 5 cm, U c = 1, and dierent particulates volume ractions. Figure 6b: Radiative heat lux to the compartment loor or W v = 20 cm, U c = 1, and dierent particulates volume ractions. REFERENCES [1] Drysdale, D. D., An Introduction to Fire Dynamics, Wiley, Chichester, [2] Rasbash, D. J., Major Fire Disasters Involving Flashover, Fire Saety Journal, Vol. 17 (1991), pp [3] Peacock, R. D., Reneke, P. A., Bukowski, R. W. and Babrauskas, V., Deining Flashover or Fire Hazard Calculations, Fire Saety Journal, Vol. 32 (1999), pp [] Hagglund, B., Jannson, R. and Onnermark, B., Fire Development in Residential Rooms ater Ignition rom Nuclear Explosion, FOA C20016-DG (A3), Forsvarets Forskningsanstalt, Stockholm, 197. [5] Parker, W. J. and Lee, B. T., Fire Build-up in Reduced Size Enclosures, A Symposium on Fire Saety Research, NBS SP-11 (197), National Bureau o Standards, pp [6] Fang, J. B., Measurement o the Behavior o Incidental Fires in a Compartment, NBSIR National Bureau o Standards, Gaithersburg, Maryland, [7] Lee, B. T. and Breese, J. N., Submarine Compartment Fire Study Fire Perormance Evaluation o Hull Insulation, NBSIR , National Bureau o Standards, Gaithersburg, Maryland, [8] Babraukas, V., Full Scale Burning Behavior o Upholstered Chairs, NBS-TN 1103, National Bureau o Standards, Gaithersburg, Maryland, [9] Budnick, E. K. and Klein, D. P., Mobile Home Fire Studies: Summary and Recommendation, NBSIR

11 , National Bureau o Standards, Gaithersburg, Maryland, [10] Fang, J. B. and Breese, J. N., Fire Development in Residential Basement Rooms, NBSIR , National Bureau o Standards, Gaithersburg, Maryland, [11] Thomas, P. H., Bullen, M. L., Quintiere, J. D. and McCarey, B. J., Flashover and Instabilities in Fire Behavior, Combustion and Flame, Vol. 39 (1980), pp [12] McCarey, B. J., Quintiere, J. D. and Harkleroad, M. F., Esitmating Room Temperatures and the Likelihood o Flashover using Fire Test Data Correlation, Fire Technology, Vol. 17 (1981), pp [13] Emmons, H. W., Prediction o Fires in Buildings, Proceeding o the Seventeenth (International) Symposium on Combustion, 1978, pp [1] Quintiere, J. D., Fundamentals o Enclosure Fire Zone Models, Journal o Fire Protection Engineering, Vol. 1, No. 2 (1989), pp [15] Chow, W. K., Predictability o Flashover by Zone Models, Journal o Fire Sciences, Vol. 16 (1999), pp [16] Bishop, S. R., Holborn, P. G., Beard, A. N. and Drysdale, D. D., Nonlinear Dynamics o Flashover in Compartment Fires, Fire Saety Journal, Vol. 21 (1993), pp [17] Graham, T. L., Makhviladze, G. M. and Roberts, J. P., On the Theory o Flashover Development, Fire Saety Journal, Vol. 25 (1995), pp [18] Thompson, J. M. T. and Steward, H. B., Non-linear Dynamics and Chaos, Wiley, Chichester, [19] Liang, F. M. and Chow, W. K., Preliminary Study on Flashover Mechanism in Compartment Fires, Accepted or publication, Journal o Fire Sciences, April (2002). [20] Siegel, R. and Howell, J. R., Thermal Radiation Heat Transer, th Ed., Taylor and Francis, New York, [21] Yuen, W. W. and Tien, C. L., A Simpliied Calculation Scheme or the Luminous Flame Emissivity, Proceeding o the 16 th Symposium o Combustion, 1976, pp [22] Yuen, W. W. and Takara, E. E. The Zonal Method, a Practical Solution Method or Radiative Transer in Non-Isothermal Inhomogeneous Media, Annual Review o Heat Transer, Vol. 8 (1997), pp [23] Rockett, A. J., Fire Induced Gas Flow in an Enclosure, Combustion Science and Technology, Vol 12 (1976), pp [2] Takeda, H., Transient Model o Early Stages o Fire Growth, Mathematical Modelling o Fires, Ed. J. R. Mehaey, ASTM, Philadelphia, 1987, pp