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Fire Growth Model for Apartment Buildings
Ser TH1 R4 2 7 no. 734 c. 2 BLDG
National Research Conseil national
Council Canada de recherches Canada
Fire Growth
Model for
Apartment Buildings
CISTI/ICLST NRC/LNRC I n t e r n a l r e p o r t ( I n s t ~ t u t e f T R C Ser ~ N A L Y S E - . V Received on: 03-26-97 I n t e r n a l r e p o r tJ. Cooper and D. Yung
Internal Report No. 734
Date of Issue: January 1997
This is an internal report of the Institute for Research in Construction. Although not intended for general distribution, it may be cited as a reference in other publications.
ABSTRACT
A detailed description of the existing National Research Council of Canada's (NRC) one-zone fire growth model is presented. Several changes to the model are recommended based on recent experimental observations.
The model was compared to the results of three full-scale fire tests performed with different loadings of flexible polyurethane foam in an ASTM/ISO standard room. An accurate prediction of the experimental mass loss rate was found to have the greatest importance in predicting overall fire behavior. The experimental mass loss rate was observed to increase more quickly than the predicted rate and to decay more slowly as a function of fuel depletion. These differences were attributed, respectively, to an
undemrediction of the flame svread rate on the fuel bv the model. and to an (assumed) tendency of polyurethane f o b to resist oxygen pen&tion and flame spread as b m i n g Droeresses. For flashover fires. the inabilitv of the one-zone model to distinmish between iheuhot ceiling layer and the rest of the co&partment resulted in an underpreYdiction of the external heat flux to the fuel, which further impeded the growth of the model fire.
Increasing the flame spread rate by a factor of 2.3. introducing an appropriate decay function for the mass loss rate, and-incorporating a hot layer temperaturein the estimation of the heat flux to the fuel resulted in excellent predictions of the mass loss rate as well as all the other experimental results, demonstrating the suitability of the proposed modelling.
NOMENCLATURE A A" A v o a b B C CD CP F g h h~ H, AHc AHv AHs k kt6
kc
L m, mi&d n q-ig q r Qc Qo Qr QvQw
Ilb
&I Ar T t t16v
Vfo V f wo X Y YArea of wall surfaces or doorway (mZ) Burn area at time t (mZ)
Initial burn area (m2)
Molar stoichiometric coefficient for CO Molar stoichiometric coefficient for CO2 Compartment size factor
Flame heat transfer modulus (m'" s'" W-') Orifice coefficient for compartment ventilation Specific heat of gas, wall or fuel (kJ kg-' K ')
Correction factor for the ventilation rate Gravitational constant (m s ')
Convective heat transfer coefficient for the wall (W m K
')
Heat loss coefficient for upper layer temperature calculation (J K-' niZ) Height of the doorway or window opening (m)
Heat of complete combustion (J kg-' fuel) Heat of vaporization (J kg-' fuel)
Heat of smouldering or pyrolysis (J kg-' fuel)
Thermal conductivity of fuel or wall material (W K')
Constant for calculating oxygen concentration (i' )
Gas absorption coefficient (m
')
Compartment length (m)Mass flow of gases leaving the compartment (m s ') Free vaporization/pyrolysis rate of the fuel (kg niZ s-') Height of the layer interface from base of vent(s) (m)
Minimum external heat flux required to ignite the fuel (W m-') External heat flux to the fuel (W niZ)
Heat release rate of the fire (W)
Heat loss rate through vent openings by radiation (W)
Heat loss rate due to fuel vaporization and heating (W)
Heat loss rate through vent openings by convection (W)
Heat loss rate through the walls by conduction (W) Fuel consumption/buming rate (kg s ')
Fuel vaporization rate (kg s-')
Burning rate enhancement due to heat reradiation (kg m-2 ssl) Temperature of fuel, compartment wall or effluent gases (K) Time (s)
Time at which the oxygen concentration falls below 16% (s) Compartment volume (mi)
Lateral flame speed produced by radiation (m s ')
Actual flame speed as limited by the available oxygen (m 6') Width of the compartment opening (m)
Moles of water produced per mole of carbon burned Mass fraction of OZ, CO, C02 or vapour
Greek Svmbols
P
-
Density of gas, wall or fuel material (kg m-')E - Gas emissivity
v
- Combustion efficiencyCI.
-
Maximum possible combustion efficiency for fuel0
- Compartment equivalence ratioY
- Stoichiometric air to fuel ratioCj
-
Stefan Boltzmann constant (W m-' K - ~ )6 - Wall thickness (m) Subscripts G - W - 1 - 0
-
VAP - 0 2-
02i - PRO-
co
-
C 0 2-
UL-
Gas Wall Inside compartmentOutside compartment, ambient, or vent opening Vapour Post-combustion oxygen Pre-combustion oxygen Product gas Carbon monoxide Carbon dioxide Upper layer
FIRE GROWTH MODEL FOR APARTMENT BUILDINGS by
J. Cooper and D. Yung
1. INTRODUCTION
This report reviews the equations of the original NRC fire growth model by Takeda and Yung [ l ] and documents the modifications required as a result of full-scale validation tests. The predictions of the original model were compared with measurements obtained from full-scale fire experiments. The results of these comparisons were used to make modifications to fire growth and decay rates. The original model was found to underestimate the rate of fire growth for both flaming and flashover fires, and to
overestimate fire decay rates. An accurate prediction of the mass loss rate was found to be essential in correcting these discrepancies and resulted in good overall predictions of fire behaviour.
The report consists of two sections. The first section describes the original model, and the second contains a discussion of the changes made to the model as a result of the experimental findings.
2. MODEL DESCRIPTION
The purpose of the apartment fire growth model is to simulate the ignition and growth of fires in an apartment unit in order to help assess the fire safety performance of apartment buildings. This assessment is done on the basis of the amount, temperature and concentration of the gases generated by the model fire, the speed and effectiveness of various fire protection systems, and the behaviour of building occupants.
The apartment fire growth model calculates the characteristics of compartment fires that have the greatest impact on occupant safety and building damage. These characteristics fall into two categories. The first is the smoke and fire hazard category. Smoke and fire hazard data includes the composition, temperature and flow rate of compartment effluent gases. This information can be used to estimate the potential for smoke spread and fire damage outside the compartment of fire origin. The second categoly is the detection/suppression category. Detection/suppression information includes the time of occurrence of specific fire-detection/suppression-related events, such as the time at which the person@) in the room of fire origin first notices the fire, the smoke detector activation time, the sprinkler activation time, the time to flashover and the time to fire burnout. These times can be used to determine the occupant response and evacuation times.
The model uses a standard flexible polyurethane foam to represent the upholstered furniture and bedding typically found in an apartment. Six fire scenarios are employed by the model to represent all possible combinations of 3 fire types (flashover, flaming non- flashover and smouldering) and 2 compartment ventilation conditions (door open or closed) and are as follows:
1. Smouldering fire with the fire origin compartment door open 2. Smouldering fire with the fire origin compartment door closed
3. Flaming non flashover fire with the fire origin compartment door open
4. Flaming non flashover fire with the fire origin compartment door closed
5. Flashover fire with the fire origin compartment door opcn
2.1 General Assumptions
2.1.1 One-Zone Model
Since a large number of calculations are required to assess the lifetime fire safe@ performance of a building, a practical fire growth model for this application needs to be relatively simple. The aim in fire growth modelling is to develop a model that is simple enough to have a practical execution time without making undue sacrifices in accuracy.
Compartment fires are characterized by a hot, upper gas layer caused by buoyancy effects and a relatively cool lower gas layer. The height of the interface between these two layers is time-dependent and decreases as the fire progresses, as does the layer temperature difference. Because of this, two-zone models, which treat the upper and lower gas layers separately, are often used to represent the compartment gas temperature. These models, however, have impractically-long computation times for this application and often predict premature fire extinction if the compartment is underventilated (door closed scenario). The latter is due to the rapid descent of the upper layer predicted by two-zone models under closed-door conditions, which suffocates the fire by reducing the inflow vent area [I]. An additional problem posed by two-zone models is that the
modelling of flame spread over fuel surfaces becomes extremely complicated. A two-zone model incorporating flame spread would require the development of a moving-plume submodel, which would be difficult, time consuming and, because the fire plume is a complex phenomenon, not necessarily very accurate.
Some of the difficulties presented by two-zone models can be eliminated by employing a one-zone model which incorporates lateral flame spread over fuel surfaces to simulate the growth of a fire and calculates a single, transient gas temperature for the compartment. This significantly reduces computation times and allows a more
conservative estimate of underventilated fires. The following conditions and assumptions are employed:
The ceiling, walls and floor of the compartment are fire separations. The comuartment is small (1-2 average-sized residential rooms).
The comuartment gases are well-mixed (at uniform temperature and pressure). Flow thrbugh mulgple compartment openings is weighted by area.
The compartment wall temperatures are uniform and equal. 2.1.2 Heat Transfer Mechanisms
Heat transfer from both the compartment to the rest of the building and from the compartment to the burning fuel occur by radiation, convection, and conduction. In this model, heat transfer to the fuel is assumed to occur mainly by radiation. Heat losses through the compartment boundaries take place by radiation, convection and conduction via the compartment walls, openings and ceiling. The compartment floor is treated as an adiabatic boundary.
2.1.3 Furniture Arrangement
The arrangement of furniture in the compartment can give rise to an infinite number of possible fire scenarios, the statistical occurrence of which would be quite difficult to model. Because of this, a worst-case arrangement is assumed and the furnilre is modelled as a single mass in the centre of the compartment. This facilitates fire spread to the entire combustible load of the compartment and results in a conservative estimate of fire severity. In general, the upholstered surfaces of the furniture determine the progress
of combustion; thus the combustion properties of flexible polyurethane foam are used to simulate the combustion behaviour of apartment furniture.
The furniture in the compartment is assumed to exist as a single mass in the centre of the room and to possess uniform properties.
In the model, the size of the fuel mass reflects the amount of ignitable combustible in the room; large fuel masses are thus used to simulate flashover fires in which all room furnishings ignite, whereas smaller fuel masses are used to simulate the burning of isolated furnishings caused by flaming fires.
2.1.4 Material Properties
Many material properties, such as heat capacity, thermal conductivity and density, vary with temperature. In the temperature range normally experienced by the materials in the fire compartment (20-120O0C), however, only the gas density changes significantly. For the purposes of simplicity, therefore. all material properties, except the gas density, are assumed to remain constant at their ambient values. Since heat capacities and thermal conductivities rise with temperature. this assumption is expected to result in conservative predictions of fire severity.
Material properties are assumed to be constant (unless otherwise stated). 2.1.5 Fire Detection/Suppression
The activation of the fire suppression/detection devices is often difficult to predict as the time required for a given device to activate depends on its location and sensitivity. Simvlifving assumptions are therefore made about the detector activation criteria. These are ioniistint with-the simplicity of the model
The detection of the fire by the occupant of the compartment (fire cue), tbe activation of the smoke detector and the activation of the sprinkler system are assumed to occur in sequence at 35OC, 40°C and 75°C respectively.
Note that the effects of fire suppression are not calculated by the fire growth model, but can be deduced through the activation times of smoke detectors and sprinkler systems [2]. Other assumptions are specific to the model equations and will be discussed in the development below.
2.2 Model Equations
Because of the time-dependent nature of fire, and the interdependence of heat release rates and temperatures, the enclosure fire is represented by four types of transient differential equations that must be solved simultaneously. These are: the species balances, the compartment energy balance, the wall heat conduction equation and the fuel heat conduction equation.
k
well-developed compartment fires, the air supply or ventilation rate generally dictates the rate of burning, the consumption and generation rates of various chemical species and the resulting heat release (temperature). The equations shown below are thus outlined in an order that reflects this relationship to facilitate a physical understanding of the model. (All units employed in calculationsare SI unless otherwise stated.)2.2.1 Compartment Ventilation
The compartment ventilation rate
m
is dependent on buovant forces created bv temperature difference(s) across the compartment'opening(s).in^
the ventilation-. controlled state of well-developed fires. it determines the rates of combustion. snecies production and heat release.As the fire progresses, the upper half of the compartment fills with hot gases and the temperature rises in this hot layer, causing an increase in pressure that drives hot gases through the upper half of the compartment opening, while cool, dense air enters from below. This mechanism for gas flow (in or out of the compartment) is modelled by the following relation from Steckler et al. [3]:
where g is the gravitational constant, CD is the orifice coefficient for the compartment opening, usually 0.68 for inflow and 0.73 for outflow [4], pc, is the gas density at ambient conditions, A, is the area of the opening, To is the temperature outside the compartment,
Tc is the temperature inside the compartment, H, is the total height of the opening and n is the height of the interface between the hot and cool gas layers.
Because the model is a one-zone model employing a single room temperature Tc, the interface between the hot and cool air masses passing through the compartment opening is assumed to be at 0.5K (halfway up the compartment opening(s)). In the simplified model, an average flow coefficient of 0.7 is used for both inflow and outflow.
The factor F is a flow correction based on compartment geometly and is a measure of the compartment's ability to accommodate air circulation. This was correlated from data in Steckler et al. [3] and Quinteire et al. [5] and is given by the following:
Measured Flowrate
F = = 1.19 - 1.77B
+
(0.000625)(TGu)Predicted Flowrate
where
TGu = TG - 273
and the quantity B is a compartment size factor:
and L is the compartment length as measured from the doorway.
Equation (2) was developed from differences between measured gas flow rates and gas flow rates predicted by Eq. (1) for four different compartment size factors, B. In predicting the mass flow, data from Steckler et al. [3] for the same experimental
compartment, was used to estimate the ambient temperatures T,. The latter were absent from the data in Qlllntiere et al. [S] and were ohseived to increase with the temperature of
the lower layer. The assumed relationship between the ambient and the lower layer temperature is shown in Fig. 1.
Figure 1: Increase in ambient temperature with lower layer temperature
-- 70 --
60 --
so --
A plot of F against upper layer temperature for various compartment size factors B, is shown in Fig. 2 with the corresponding experimental points. The simple dependency of F on compartment upper layer temperature and compartment geometry B. given by Eq. (2), is shown to be adequate for all 4 data groups. The scatter observed in the data may indicate that other factors, such as fire intensity and size, which ranged from 30-120 kW and 0.46-1.84 m (line burner width) respectively, may also affect gas ventilation rates. The behaviour of F with B shows that Eq. (1) has a tendency to
underpredict mass flow rates for large compartments with comparably small openings, and
T. = 13.2 + 0.24T,,
Estimated relationdrip for change in
ambient teqerature due to hog
companment gases (valid beyond ./--'
,+-A*
T=L = 15 "C) .-H'
overp~cdict flow ratcs for small compartments with large openings. Because ventilation ratcs havc a direct cffect on firc severity. however, Eq. (2) is applied only if the correction
I
40 --
30 --
20 --
10 -- --Regression line
factor is greater than 1.0 to allow a conservative prediction of compartment ventilation rates.
F = 1.19
-
1.77 B + 0.000625 (TGU)0 SO 100 150 200 250 300 350 400 Aver.ge Upper Layer Temperatore (c)
Figure 2 : Mass flow rate correction factor vs. compartment temperature, where B is
the compartment size factor and Wo is the width of the compartment opening in m.
2.2.2 Flame spread
The rate of flame spread from the point of ignition directly affects the fuel mass loss and burning rates. The current compartment flame spread model assumes that the lateral flame spread rate depends on the net external radiative heat flux to the combustible and the O2 concentration in the compartment [I] :
YO>< - 0.1 1
for Yo,, > 0.1 1
Vf = 0.0 for YO,< < 0.1 1
where Vfis the lateral flame spread velocity and Yozi is the oxygen mass fraction in the compartment. Vr, is the radiation-dependent flame velocity and has been correlated by Quintiere and Harkleroad [6] as:
where q,j, is the critical heat flux for ignition, q, is the net external radiant heat flux to the fuel surface and C is the flame heat transfer modulus. Both q,i, and C are properties of the combustible and can be obtained from experimental flame spread velocity data. The graphical data obtained by Quintiere and Harkleroad [6] are shown in Fig. 3, where C is the slope of the line and qOi,is the intercept. Note that the line shown represents a
conservative prediction of flame spread based on the highest flame spread rates observed for a given external radiant heat flux. The flame heat transfer modulus and other
properties for several typical apartment combustibles are given in Table 1.
External Heat flux
(w/mZ)
Figure 3: Experimental flame spread velocity plot for polyurethane foam
The net external heat flux to the fuel surface, q, is the heat fed back to the fuel by the compartment enclosure. This can be expressed in terms of the radiative fluxes from the compartment gases and walls:
where E is the gas emissivity and TG. Twl and Ts are the gas, inner wall and fuel surface
temperatures, respectively. In the current model, the surface temperature of the burning fuel is assumed to be tied to TG ; this is discussed in the Fuel Surface Temperature section. This assumption is conservative and prevents the occurrence of negative heat fluxes in
Eq. (7) during the beginning of the fire.
The gas emissivity depends on the gas volume and concentration as given by Takeda and Yung [I]:
where L is the compartment length and kc is the gas absorption coefficient, which is assumed to vary linearly with the product gas concentration :
where k~~ is a constant derived from experiments (approximately 2.0 m-' for polyurethane foam) and Y p ~ o is the mass fraction of product gases (see the Species Concentration section).
The area of the fuel covered by flame grows during the fuel-controlled stage of the fire until the maximum burning radius is reached. The ignited area of the fuel is
considered to be roughly circular and thus grows according to the relationship:
where A,, is the initial burning area and Vf is the flame spread velocity.
Table 1: Property Data for Some Typical Furniture Materials
(Data compiled from T e w m n and Pion [7]. Quintiere and Harkleroad [GI
.
Tewarsoa [8]. and Surnathipda and Monene [9]) 2.2.3 Mass Loss Rate for Flaming FiresThe distinction between the fuel mass loss rate and the fuel burning rate is that the first refers to all of the vapour that is driven from the heated fuel, whereas the second refers only to the portion of evolved vapour that is converted into products. The mass loss rate of the fuel for flaming fires depends on the ignited area, the concentration of 02in the burning environment and the radiative heat flux to the fuel.
In unenclosed areas, the combustion of a given fuel sustains itself via flame radiation to the fuel surface. The mass loss rate arising from free combustion is termed the "ideal" mass loss rate. The "ideal" mass loss rate, keasured under normal atmospheric conditions, is a propem of the fuel being burned. When the fuel is burned in an enclosed environment, such as an apartment, the ideal mass loss rate is reduced due to the limited oxygen available to the fuel. This, however, is counteracted by increased radiative feedback from the heated surfaces (walls and ceiling) of the enclosure which causes an increase in the mass loss rate of the fuel.
The complete relationship for the fuel mass loss rate for flaming fires is thus given by Tewarson and Pion [7]:
where Y02i is the mass fraction of 0 2 present before combustion, Av is the ignited area and
Ar is the enhancement to the mass loss rate due to heat reradiation by the compartment walls.
The mass loss enhancement is given by:
9,
&=-
AHv where q, is defined by Eq. (7).
2.2.4 Buming Rate for Flaming Fires
The burning rate of the fuel is related to the mass loss rate through the combustion efficiency:
where RB is the fuel burning rate, RML is the fuel mass loss rate and p is the combustion efficiency.
The combustion efficiency depends on the ability of fresh oxygen to reach the vaporized fuel. In most combustion situations involving thermoplastic materials, the fuel vaporization (mass loss) rate exceeds the burn rate because of poor air-fuel vapour
mixing, or insufficient oxygen. The degree to which the vaporized fuel can be completely burned is frequently correlated with an equivalence ratio
4,
which expresses thecombustible fuel vapour to oxygen ratio as a fraction of the stoichiometric fuel vapour to oxygen ratio.
Gottuk [lo] defines the combustion efficiency of enclosure fires as:
where p, is
an
experimentally-determined maximum efficiency for the fuel (about 0.9 for polyurethane foams) and+
is the plume equivalence ratio. The plume equivalence ratio is the ratio of the fuel vaporization rate to the plume oxygen entrainment rate, normalized by the stoichiometric fuel to oxygen ratio.Because the plume oxygen entrainment rate is usually difficult to determine, many experiments are conducted at steady state in a manner that allows the oxygen entrainment rate to be estimated from the mass flow of oxygen entering the enclosure [l 11. For non-
steady state conditions, however, equivalence ratios calculated from ventilation rates could give rise to premature extinction for fires in compartments where the door is closed, as the high concentrations of oxygen initially in such compartments are not considered.
In the current fire growth model, a more conservative compartment equivalence ratio is defined. This is consistent with the assumptions of well-mixed combustion employed in the species and energy balances. Only the reactants (oxygen and vaporized fuel) present in the compartment are considered, and the compartment equivalence ratio is calculated as the normalized fuel vapour to oxygen mass ratio present in the compartment.
This eliminates the dependency of
I$
on the ventilation rate in the early stages of the fire and is thus more likely to give low predictions ofI$
for fires in sealed compartments.This is done by considering the mass ratio of vaporized fuel to oxygen present in the compartment:
where
4
is the compartment equivalence ratio, V is the compartment volume, y is the stoichiometric air to fuel ratio and Y v A p and YOoz~ are the mass fractions of vaporized fuel and oxygen, respectively.Note that the above ratio considers all the fuel vapour and oxygen that will contact the compartment during a given time period, At. Values of
4
< 1 apply to the developing fire situation, where oxygen is in excess and the fuel vaporization rate controls the burning rate (fuel-controlled); values ofI$
> 1 indicate that the fire has reached the ventilation- controlled state, where the rate of oxygen supply to the fuel becomes the limiting factor for the buming rate.2.2.5 Mass Loss and Burning Rates for Smouldering Fires
Smouldering fires are fires that occur without flame. Because of this, the mechanism for flame spread described above does not apply to smouldering fires. The fuel mass loss rate for smouldering fires can be correlated with the elapsed time through a .relationship given by Quintiere et al. [I21 :
where t is the elapsed time. The buming rate
RB
for smouldering fires is then calculated from4
as for flaming fires.2.2.6 Species Concentrations
The species being considered in the fire growth model are oxygen, the product gases (mainly CO and COZ ) and unburned fuel vapour. The concentrations of these species depend on reaction stoichiometly and the ventilation, fuel mass loss and bum rates. Since the model consists of time-discretized equations. a suitable average oxygen, product gas and fuel vapour concentration value for each timestep must be calculated. This can be done by treating the com?ar!ment as a well-stirred batch reactor that is filled at the beginning of each timestep and emptied to its initial volume just before the end of each timestep, requiring that the concentrations be calculated on the basis of the total mass of gas contacting the compartment over a given timestep. (This includes the gas present in the compartment at the beginning of the timestep.)
2.2.7 Oxygen Concentration
Two oxygen concentrations are calculated by the model. The first is the "pre- combustion" mass fraction of oxygen in the compartment, which is the concentration of oxygen that would exist in the compartment if no chemical transformation of the
vaporized fuel had taken placz. This is calculated by adding the mass of oxygen already in the compartment to the mass injected over the current timestep and dividing by the total mass of all the gas that will have contacted the compartment during the current timestep:
where YOzF represents the oxygen mass fraction in the compartment at the end of the previous timestep and p~ is the gas density.
The second oxygen concentration calculated by the model includes the oxygen consumption term. This is the "true" oxygen concentration at the end of each timestep when both fuel vaporization and chemical reaction have taken place:
where RML is the fuel mass loss rate as defined previously and y and p are the
stoichiometric air to fuel ratio and the combustion efficiency. Note that the combustion efficiency is based on the numerator of Eq. (17) instead of Eq. (18) because the former omits the consumption term and is thus a more conservative estimate of the total amount of oxygen that is available to bum the evolved fuel vapour during a given timestep.
When the oxygen concentration Yo2i falls below 16%, an asymptotic scheme, instead of Eq. (17), is used to calculate YO2, for burning under vitiated (reduced) oxygen conditions:
where
and t16 is the time when an oxygen concentration of 16% is reached. This permits an asymptotic approach to the fire extinction value of lo%, where the value of 16% is taken to be the transition point from normal burning to burning under vitiated oxygen
conditions. This asymptotic depletion of oxygen in the late stages of the fire is considered to be more representative of true fire behaviour than the use of Eq. (1 7) and prevent9 the premature extinction of the fire. Note that the value of YOzi is used to limit flame spread as well as the burning rate.
2.2.8 Product Gas Concentration
The mass fraction of product gases in the compartment at the end of each timestep is found in a manner similar to that employed in Eq. (17):
where YOm.0 represents the product gas mass fraction from the previous timestep. The second term in the numerator represents the combination of oxygen and fuel to form product gases. The numerator in equation (20) represents the mass of product gas that will have contacted the compartment during the current timestep, whereas the
denominator again represents the mass of gas that will have contacted the compartment. (Note that, although the oxygen that reacts with the fuel appears in the numerator as a separate quantity, it is in fact part of the product gases at the end of the timestep as a result of chemical transformation.)
2.2.9 Fuel Vapour Concentration
Vaporized fuel that fails to burn, either because of insufficient oxygen or imperfect fuel/air mixing, accumulates in the compartment with the other gaseous species. The average concentration of fuel vapour in the compartment for a given timestep is calculated similarly to that of oxygen in Eq. (17), by including a production and depletion term:
where Y0vAp represents the concentration of vapour previously in the compartment and (1-p) represents the unburned fraction of vapour produced over the time period At. The denominator is the same as in Eqs. (17), (18) and (20).
2.2.10 Product Gas Composition - Flaming Fires
For flaming combustion of foams, plastics and other synthetic substances, the simplified product gas is assumed to consist of water vapour, CO and C02. The relative proportion of these is determined by the reaction stoichiometry for the fuel in question. This takes the general form:
where the equation above is normalized so that:
and X is the number of moles of water produced in the normalized stoichiometry The mass ratio of CO to C02 is assumed to be linear for the purposes of this analysis. The relationship that is assumed for this model is based on the fact that C02 production increases with the amount of oxygen available in the ambient air and relates the molar stoichiometric coefficients a and b by:
where Y 0 2 F is as in Eq. (18) and K is a tunable constant that depends on the fuel type
(about 260 for polyurethane foam).
Once Eqs. (22) and (23) have been simultaneously solved for a and b, the product gases can be further subdivided into CO and C 0 2 fractions through the following
2.2.1 1 Product Gas Composition - Smouldering Fires
For smouldering fires, where chemical reaction is less vigorous, the following correlations are employed for the relative proportions of CO and GOz:
Note that the unaccounted fraction of Y p ~ ~ consists of a wide variety of gases including HZO.
2.2.12 Compartment Temperature
The compartment containing the fire is being treated as a well-mixed combustor for which a single transient energy balance can be written to obtain the room temperature TG. Because of the limited knowledge of chemical kinetics for large-scale fires, the temperature in the compartment is based on the heat of combustion for the fuel involved instead of being linked to the production of individual species. The ventilation and fuel mass loss rates also affect the compartment temperature, as these quantities dictate the net energy flux across the compartment boundaries. The energy balance for the compartment is therefore given by:
where Cp, is the gas specific heat, V is the compartment volume, p~ is the gas density, Qc is the rate of heat release to the room by combustion, Qw is the rate of heat loss through the compartment walls, Qv is the rate of heat loss through the compartment opening by convection, Qo is the rate of heat loss rate through the compartment opening by radiation and Qr is the rate at which heat is transferred from the room to the fuel for vaporization and heating.
The fire heat release rate is given by the following:
Qc = AHc
,
R
p ( 2 9where AHc is the heat of combustion per unit mass of fuel burned. (Note that for
smouldering fires, the heat release rate is calculated using the heat of pyrolyis, AHs, which is considerably smaller than the heat of complete combustion.)
The rate of heat loss through the walls is expressed as the sum of the convective and radiative heat fluxes to the wall surface:
where h is the convective transfer coefficient for the wall, Tw, is the inner wall temperature, and AW is the total wall and ceiling surface area in the compartment.
The convective heat loss through the compartment opening is:
where Cpc, m, and RML are as defined previously. This energy term represents the heat loss from the room due to the convection of gases in and out of the room and the heat lost to the vaporized fuel in heating it from Ts to TG.
The radiative heat loss through the compartment opening is:
where A, is the area of the compartment opening and the other variables are as defined previously. The above represents the radiant exchange between the compartment gas and walls and ambient space at To.
The heat requirement for solid fuel heating and vaporization is expressed as:
where AHv is the heat required to create one unit mass of vapour. The first term . represents the energy conducted into the fuel in order to heat it, and the second term
represents the energy required to vaporize the fuel at Ts.
2.2.13 Wall Temperature
The wall temperature TW for each wall varies with distance from the heat source and is calculated on the basis of one dimensional heat conduction:
where x is the wall thickness coordinate, p~ is the material density, Cpw is the specific heat and k is the thermal conductivity. Solution of this equation yields a wall temperature profile in x which is the same for all of the walls and independent of the space coordinates yz for each wall.
The above equation requires the definition of two boundary conditions, one for the inside surface of the wall and one for the outside wall surface. These boundary conditions are, respectively:
where k is the thermal conductivity of the wall material, and h is the convective heat transfer coefficient. These boundary conditions represent the radiative and convective exchanges between the inner and outer wall surfaces and the surrounding gas. For the purpose of simplicity, the emissivities, E. of the compartment walls and surfaces outside
the compartment are assumed to be 1 .O. Other relevant wall properties are shown in
Table 2.
Table 2: Property Data for Typical Wall Materials
(Data compiled fmm Holman [13], and Sumathipala and Monette [9] )
Material
Pine Gypsum board
Concrete
2.2.14 Fuel Surface Temperature
The temperature of the fuel surface is assumed to be controlled by the same mechanisms that control the temperature of surfaces in the lower portion of the
compartment. This assumption is n e c e s s q in order to give a more conservative estimate of the heat flux to the fuel as mentioned previously. The fuel and lower compartment surfaces are thus modelled as a conductive body between two radiative heat flux boundaries: Ps kn/m" 430 1440 1900
where ks is the fuel conductivity, Cps is the fuel specific heat and ps is the fuel density. (Note that this is not totally accurate for thermoplastic materials such as polyurethane foam which burn at their ignition temperature, but is expected to have no adverse effect on the predicted compartment temperatures because TS is only employed in the calculation of q, and used conservatively in Eq. (33).)
The fuel is assumed to radiate to a temperature equal to the ambient temperature To from its base and to a temperature equal to the compartment gas temperature TG from its surface. The radiation boundaries of the fuel are thus similar to those for the walls, but without the convective heat transfer term:
CPW Jlkg K 2800 840 880
ks
Wlm K 0.112 0.48 1.07 h Wlm' K 53 55 55where Tsi and Tk are the temperatures of the fuel surfaces facing the ceiling and floor of the compartment, respectively. The above equations contain the assumption that the floor under the fuel remains close to the ambient temperature.
2.3 Computation Algorithm
The time-dependent differential equations outlined above were solved
simultaneously through the use of numerical methods. The wall and fuel heat conduction equations were solved using Patanka's [I41 finite volume approach for one-dimensional heat conduction. A flow diagram of the Visual Basic computer algorithm is shown below to illustrate the iterative nature of solution.
T A R T L O O P F O F I R S T I N E X T S O L V E F O R iii, F U E L S U R F A C E iiii T E M P E R A T U R E
1
iii: C A L C U L A T E VENTILATION RATE S O L V E W A L L ---. H E A T C O N D U C T I O N:iz
-1::::
E Q U A T I O N :if: ~~~ ....Figure 4: Flowchart of computation algorithm (FGM = F i e Growth Model)
...
The algorithm for the fire growth model begins with a user interface. At the beginning of a run, the user can specify the compartment dimensions, the initial room temperature, the fuel and wall materials, the fuel load and surface area, the number and sizes of door and window openings, whether the door is open or closed and the type of fire (smouldering or flaming) being simulated. The fuel and wall chemical and thennal properties are accessed through a fuel and wall material database. The fuel options in this database currently include polyurethane, PMMA and wood, whereas the wall material options are gypsum board, wood and concrete (see Tables 1 and 2).
Other input data for the model are: the area of the fuel that is initially ignited, the window breakage temperature, and the activation temperatures of the various fire
detection and suppression devices. The latter are treated as expert data and require adjustment only in cases of unusual fire situations, such as when the suppression
equipment is known to be dysfunctional or when the window glass is non-standard. The initial bum area affects the speed of the fire's progress and must thus suit the nature of the ignit con ' source.
The program consists of two nested loops, an inner loop to perform the iterative calculations and check solution convergence and an outer loop for proceeding forward in time (upon successful completion of the inner loop). The inner loop incorporates a timestep length adjustment which halves the timestep if the number of iterations for a given timestep exceeds 100 and doubles the timestep if the number of iterations is less than f 0 (up to a maximum of 2 s).
The calculations for the fire growth model begin with the ventilation rate, which governs the supply of oxygen to the fire. The lateral flame spread is then calculated from the initial burn area, the amount of oxygen in the room and the net radiation heat flux to the f k l surface; then the mass loss rate of the fuel is calculated based on the newly ignited area of fuel. Using the ventilation rate, the concentration of accumulated fuel vapour, and the precombustion oxygen concentration, the combustion efficiency is determined and used to calculate the bum rate of the fuel. Based on this bum rate, the species balances are solved for the oxygen, product gas (CO and COz) and vaporized fuel concentrations. The compartment temperature is then obtained from the compartment energy balance using the new heat release rate of the fire (calculated from the burn rate), which gives rise to new wall and fuel temperatures through the solution of the conduction equations. Finally, a convergence check is done on the compartment temperature. If the relative error for two consecutive iterations exceeds 0.01%, the solution has not converged and the whole inner loop repeats itself until the convergence criteria are satisfied. If the relative error for consecutive iterations is less than 0.01%, a check is done to see whether the simulation time has been reached and the simulation is either terminated or continued on into the next timestep.
2.4 Numerical Testing
Because the run time of the program was relatively short (20-60 sec), no attempt was made to optimize the above sequence. Numerical tests thus focused on program stability and time and space discretization criteria.
2.4.1 Stability
The factors having the largest influence on stability were the nonlinear radiation boundary conditions for the second order heat conduction equations, and the size of the chosen timestep.
The radiation source t e r n in the conduction equations were stabilized by a
linearization which is necessary in order to convert the equations to their discretized forms [14]. This had the effect of damping the oscillations produced by these terms. The
timestep length requirement was expected to vary over the duration of the simulation because of the relative stability of ventilation-controlled combustion with respect to fuel- controlled combustion. The attainment of the maximum burning radius by the fire proved to be most critical, as the slope of the temperature-time curve often changes at this point. These variations were accommodated by allowing the timestep length to change during the course of a model run as described above.
The program was then run for a wide range of compartment sizes (1.0 m2
-
30 m2 floor area) to test its stability over a range of conditions. The smallest compartments gave rise to the largest program execution times (a measure of instability) because of the higher temperatures reached by the gases in these compartments. All of the runs, however, executed successfully in less than 1 min (for fuel loads of 100 kg or less and fire durations of 1 hour).2.4.2 Effect of Time Discretization
The predicted compartment temperatures were somewhat sensitive to the size of the initial timestep, which is an input to the program. This effect, however, was not significant from a predictive point of view. Temperature predictions obtained for the fuei- controlled portion of the fire for timestep lengths of 5 s differed from those obtained witk 1 s time steps by at most 2-5 degrees, which amounts to less than 2% relative error for the temperatures involved. The predicted species concentrations showed almost no change, which was expected because of the relatively slow changes in species concentrations with time. Initial time steps of 2 s can thus be expected to yield reasonable results without increasing computer time too much.
2.4.3 Effect of Space Discretization
Since the compartment itself is not considered spatially, the issue of space
discretization applies only to the one-dimensional heat conduction equations. Because of the highly non-linear nature of the temperature profiles in the walls of the compartment, the choice of 6x for the numerical integration is extremely important. The fuel
temperature has less effect on model predictions because of the considerably smaller area of the fuel, so the discretization of the fuel is not as critical.
The effect of 6x was tested by running the model for typical apartment dimensions (7.0 x 7.0 x 2.44 m) using the flashover fire scenario and a wall thickness of 0.3 m. Trial 6x values of 0.075,0.016,0.01,0.006, and 0.004 m were used, corresponding to 5,20, 30,50, and 80 wall temperature nodes, respectively. A reference run employing 100 fuel and wall temperature nodes was used to represent the "correct" solution. (Runs with more nodes gave identical solutions.) The wall thickness represented typical values for apartment buildings so that an accuracy standard could he set for general model use.
The results of the test showed that an insufficient number of temperature nodes in
the wall significantly affected the time required to attain the maximum compartment temperature, as well as the value of that maximum. This occurred because the use of a coarser discretization grid caused the inner wall surface temperature to be underestimated, resulting in a greater gas-wall temperature gradient. This facilitated radiative and
conductive heat transfer from the compartment to the wall. In the severest case tested (5 temperature nodes), the maximum compartment temperature was underestimated by 150 degrees (as compared to the reference run). This effect was greatly reduced for the
20 and 30 node tests but the deviation of the shape of the compartment temperature-time curve from tbat observed in the reference run was still significant.
The predicted window breakage times for the 20 and 30 node tests differed from the time predicted in the reference run by several minutes. The 80 node test was identical to the reference run and yielded the same breakage time as the 50 node test, indicating that at least 50 nodes are necessary to obtain an accurate prediction of the window breakage event for the chosen conditions. The shape of the temperature-time curve for the 50 node test, however, still differed from that of the reference run, indicating that the ideal number of nodes is even higher. The node requirement would likely increase for thicker fuel slabs, or smaller compartments where the wall area has a larger effect on gas temperature. A minimum of 100 fuel and wall nodes should be adequate in ensuring a reasonable
integration of the wall and fuel temperature profiles in most instances. This limit should, however, be retested every time a new fire scenario is employed as other factors could also affect the node requirement.
3. COMPARISON WITH EXPERIMENTAL DATA
3.1 Summary of Modifications to Original Model
The original model described above was tested by comparing predicted
temperatures, species concentrations and fuel mass loss rates to those obtained during full- scale fire experiments involving several different fuel loadings.
It was found that the model underpredicted the fire growth rates for both flaming and flashover fires, and overpredicted fire decay rates. An accurate prediction of the fuel mass loss curve was observed to be most critical in obtaining good overall representations of fire behaviour. 'lbc fuel mass loss relationship of the model was therefore the focus of the modifications. Incorporating a new mass loss relationship that increased the rate of flame spread on the fuel and decayed with fuel mass produced significant improvements in the model predictions. This improvement was most marked for the flashover fire, where it was found tbat the original model significantly underpredicted the external heat flux to the fuel surface.
The mass loss rate determines the heat release rate of the fire and the rate of evolution of product gases. All the changes to the model were therefore based on
matching the shape of the experimental mass loss curve. This was achieved by increasing the rate of flame spread on the fuel by a factor of 2.3 and changing the mechanism for the mass loss rate given by Eq. (1 1) as follows:
where m, is the initial mass of the fuel and
m
is the mass of fuel that has been consumed by the fire. The mass loss rate was found to decay with the remaining mass of the fuel. This was attributed to a diffusion resistance posed by the surface of the foam as burning progresses, preventing O2 from reaching the surface. As the relationship for such a resistance is unknown, the above represents an assumption based on the observations.In Eq. (40), the effect of the oxygen dependency was extended to include the burning rate enhancement, Ar, because the latter was found to dominate for well- developed fires, producing unreasonably high mass loss rates. A lower limit of 0%,
instead of
5%,
was chosen for the oxygen decay function to allow a smooth transition to fire extinction and to provide a conservative estimate of fire duration.For flashover fires, which occur for higher fuel loads, the above changes were insufficient to predict the observed increases in the mass loss rate. This was attributed to the limitations of a one-dimensional flame spread model in simulating the observed 2-dimensional burning of thicker fuel slabs, and to the uossible undemrediction of the external heat flux to t6e fuel through the use of the average compa&ent temperature
TG
in Eq. (7) instead of the much hotter upper layer temperature. Since a 2-dimensional flame spread relationship would complicate the fire growth model considerably, only the external heat flux was corrected. An estimation of the hot layer temperature was obtained from Deal and Beyler 1151 as:
where TUL is the estimated upper layer temperature, Qc is the fire heat release rate, m, is the gas outflow rate, CpG is the gas specific heat and A is the room surface area,
conservatively limited to that of the ceiling.
The factor hK is a heat loss coefficient given by:
where kw, pw and Cpw are the wall conductivity, density and specific heat, t is the clapsad time and 6 is the compartment wall thickness.
Because the basic assumptions of the existing model include a fixed layer interface height that limits the gas outflow area to half the vent area, the above correlation results in excessive postflashover temperatures. An upper limit of 1200°C was therefore set for the ceiling layer to simulate the temperature limit that would occur if a higher outflow was permitted. The temperature resulting from Eq. (41) was used instead of
TG
in thecalculation of the net external radiative heat flux to the fuel and averaged with TG to drive the compartment ventilation rate. To further ensure a conservative estimate of flashover fire intensity, the conduction heat flux through the walls was assumed to be negligible and only the beat losses through the compartment ceiling were considered.
The flame spread model also posed problems during the simulation of flashover fires in that the corrected net heat flux to the fuel exceeded the minimum ignition heat flux. Since Eq. (6) is infinite for heat fluxes equal to q,,i,, the maximum flame speed was limited to 0.01 m/s (excluding the correction factor of 2.3) to avoid sudden changes in the burn area arising from unrealistic flame speeds.
To accommodate another characteristic of flashover fires, the model was also modified with respect to the way it simulated oxygen depletion. Oxygen levels in flashover fires often drop well below 16% and then recover as the fire dies out. This recovery is omitted from the asymptotic model given by Eq. (19). The use of Eq. (19) in situations where Y02~ is greater than Y02i could thus lead to premature extinction of the fire in cases where the conditions in the compartment are sufficient to allow reignition.
Equations (5) and (1 1) were therefore written in terms of YOZF for flashover fires. This prolongs the fire because the fuel is consumed more slowly initially and because reignition of the fuel is allowed to occur with oxygen recovery. The lower flame spread limit for oxygen of I I % in Eq. (5) was considered to he too high and was dropped to 5% in order to prevent premature restrictions on fire growth.
The above argument also extends to flaming fires with sufficient intensity to bring oxygen levels below 16%. For this reason, the modified version of the fire growth model bypasses Eq. (19) and uses Eq. (18) in all decay functions.
3.2 Results
Comparisons of the predicted and experimental mass loss. temperature and
concentration profiles for three full-scale fire tests are shown below. The modified model described above produced significantly better results for all of the three tests shown. Both the curves generated by the original model and those generated by the modified model are shown to demonstrate the improvement in the predictions.
3.2.1 Polyurethane Foam - 0 Burner Tests (Non-Flashover)
Flexible polyurethane foam is used as the representative fuel for apartment fires. Residential fires almost always involve upholstered furniture or bedding, which is well represented by synthetic foams. The full-scale polyurethane foam tests were conducted with foam thicknesses of 50, 100 and 150 mm (3.9,7.7 and 11.5 kg respectively) to study the effect of different fuel loads.
The foam tests were conducted in an ASTM/ISO standard room with the door open. Details on the configuration of this room and that of the representative fuel are given in Sumathipala et al. [16]. The walls of the room were concrete and had an approximate thickness of 0.2 m. The mode of ignition in the tests was a propane-fired 0-burner applied at the centre20f the specimen. This bumer was estimated to give rise to an initial burn area of 0.003 m
.
The maximum hum area of the foam in each test was assumed to be equal to the total surface area of the fuel. Fuel mass loss, temperature and concentration profiles obtained from the experiments were compared with modelpredictions for similar conditions. The shapes of the mass loss and temperature profiles for the three foam thicknesses were similar. indicating that the foam burns with a consistent type of fire spread.
3.2.2 50 mm Foam Tests
Figures 5-9 show the fuel mass loss, temperature and concentration profiles for the 50 mm foam tests. Figure 5 shows a comparison between the experimental fuel mass loss profile and that obtained from the model. The prediction of the original model deviates significantly from the experimental result; the predicted mass loss rate is initially too slow and shows none of the decay evident in the experimental one. This decay is the same in both the 50 and 100 mm tests (see Figs. 5 and 10) and is not due to falling oxygen levels, as the oxygen level in both of these tests remained at or near atmospheric levels. The decay can therefore be assumed to he due to some function of fuel depletion, possibly a heat and mass transfer resistance posed by increasing amounts of vapour leaving the fuel surface, or a gradual reduction in the amount of "fresh" fuel surface available for flame spread. The initial underprediction of the fuel mass loss rate can be attributed to an incorrect correlation of the flame spread rate. The flame heat transfer modulus for polyurethane foam.. is often difficult to measure becausc the evolution of volatile
combustibles nrevents flame attachment 191. Thc value of C givcn in Tablc 1 may thus bc incorrect for tbe foam used in the exper&ents. -
Figure 5: Comparison of predicted and experimental fuel mass loss profiles for 50 mm polyurethane slab
I
0 1 2 3 4 5 6 7 8 9 10
Time (min)
Figure 6: Comparison of predicted and experimental temperature profiles for
When the model is adjusted to reflect a decay in the mass loss rate with the square of the remaining fuel fraction and the flame spread rate increased by a factor of 2.3, the experimental mass loss curve is reproduced with reasonable accuracy. An improvement of similar magnitude can be seen in the predictions of temperature and concentration (see Figs. 6.7 and 8).
Figure 6 shows a comparison between the predicted and experimental
compartment temperatures. Since the model employs the well-mixed assumption, the predicted compartment temperature is also the temperature of the effluent gases. The experimental temperature profile shown was measured at the top of the doorway and thus represents the worst-case effluent temperature.
The temperatures predicted by the original model rise too slowly and decay vely r~pidly after the maximum temperature is reached. The predicted maximum temperature exceeds the experimental maximum temperature by 100°C and occurs almost 4 minutes too late. The performance of the modified model is significantly better. The predicted temperatures are very close to the experimental door temperatures, and the areas under the predicted and experimental curves are very similar, which is indicative of similar fire intensities. The decay of the predicted temperature curve is slightly too fast, indicating that the conductivity modelled for the walls may be too high, or that the decay mechanism for the burning rate may change as the fire progresses.
Comparisons of the predicted and experimental 0 2 , CO and COz profiles are
shown in Figs. 7,8 and 9. Both the original and modified models predict a higher consumption of O2 than given by the experimental data, but this is likely due to the fact that the experimental 0 2 concentrations were taken in the exhaust duct and were increased
by dilution with additional air being entrained into the duct. The experimental CO and
C Q
concentrations, however, are corrected to reflect the concentrations leaving the0 1 erperimeota1 ... 0dgln.I Model ModlBed Model
1
0 4 I 0 1 2 3 4 5 6 7 8 9 10 Time (min)Figure 7: Comparison of predicted and experimental 0 2 profiles for 50 mm
i
0.14t
.
coeq, . : ,.
-
... Odghsl Model . . ,.
.o. .
0 1 2 3 4 5 6 7 8 9 10 Time (min)Figure
8:
Comparison of predicted and experimental CO profiles for 50 mmpolyurethane foam slab
0 1 2 3 4 5 6 7 8 9 10
Time (min)
Figure 9: Comparison of predicted and experimental CO* concentration profiles for
experimental room and are thus reasonably accurate reflections of the actual CO and C 0 2 levels. The original model overpredicts these concentrations significantly. The modified model predicts considerably lower CO and C02 maxima and the locations of these maxima are closer to those observed in the experiments.
3.2.3 100 mm Foam Tests
Figures 10-14 show the predicted and experimental profiles obtained for the 100 mm foam slab. In general, the results of these comparisons support the chancres made .A
-
to the model based on the 50 mm foam tests.
Figure 10 shows the predicted and experimental fuel mass loss cuives. As mentioned previously, the same mass loss trend was observed for all the fires in the presence of oxygen, supporting the theory that the mass loss rate decays as some function of fuel consumption. The predictions of the original and modified models show the same trends observed in the 50 mm tests, with the modified model giving an even better
agreement with the experimental mass loss rate for this test. The good representation, in both tests, of the shape of the mass loss curve appears to support the proposed changes to the mass loss and flame spread mechanisms.
0 1 2 3 4 5 6 7 8 9 10
Time (min)
Figure 10: Comparison of predicted and experimental mass loss profiles for 100 mm
polyurethane foam slab
The shape of the experimental doorway temperature profile, shown in Fig. 1 1, is similar to that shown in Fig. 5, demonstrating the reproducible nature of the fire spread for the foam. The original model shows the same discrepancies observed for the previous test, whereas the modified model again gives significantly improved predictions. The temperatures predicted by the modified model after t = 2 min are slightly too high, but, aside from this, the agreement with doorway temperatures is quite good, both in the magnitude and the shape of the temperature curve.
... Odglnal Model
Mobin& Model
0 1 2 3 4 5 6 7 8 9 10
Time (min)
Figure 11: Comparison of predicted and experimental temperature profiles for 100 mm polyurethane foam slab
Figures 12, 13 and 14 show the corresponding predicted and experimental 02, CO and C02 concentrations. The degree of improvement in the predicted profiles is similar to that observed in Figs. 7-9. The modified model consistently gives better predictions than the original model; this is reflected in both the magnitude and shape of the predicted concentration curves.
The improved predictions obtained with the modified model were due to a better representation of the experimental mass loss rate. This indicates that correct modelling of the fuel mass loss rate is one of the most important factors in formulating an accurate fire growth model. The consistent overprediction of the CO and
C G
concentrations by the model is probably due to the presence of other species in the room that were notaccounted for in the model's reaction stoichiometry, or to experimental error in the corrected duct concentrations.
Figure 12: Comparison of predicted and experimental 0 2 profiles for 100 mm
polyurethane foam slab I 0
."
-... 0 I 2 3 4 5 6 7 8 9 10 Time (min) * U e;6
g
I0 -- 3-
0"
5.- 07Figure 13: Comparison of predicted and experimental CO profiles for 100 mm polyurethane foam slab
-. -.. -.-., .. .-.. ... . . ' ... M0dlUed Madel
...
Odglnsl Model1
0 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 Time (min)0 1 2 3 4 5 6 7 8 9 10 Time (min) 10 9 --
-
8 . --
e 0.=
7 -- ce i-
5 6 - - U cFigure 14: Comparison of predicted and experimental C 0 2 profiles for 100 mm
polyurethane foam slab
3.2.4 Polyurethane -
0
Burner Tests (Flashover)The results for the 150 mm foam tests are shown in Figs. 15-19. This fuel load, equivalent to about 13 kg of foam, gave rise to a flashover fire, which had to be extmguished after t=3 min. Unlike the previous tests, where the maximum temperature reached only 200°C and the difference between the compartment floor and ceiling temperatures was relatively small (150°C), the maximum temperature in this test was 100O0C, and the floor-to- ceiling temperature range was more than 800°C. The effects of such temperature d~fferences in the compartment are poorly represented by one-zone models, in which the temperature being calculated is an average, without the addition of some external heat source to compensate for the effects of the flame and hot layer. This is most evident in Figs. 15-19 from the increased slope of the experimental profiles beyond t=2 min, where the increased wall and ceiling back-radiation first starts to have a noticeable effect.
A comparison of the predicted and experimental mass loss rates is shown in Fig. 15. Here, extreme departure from a uniform room temperature of TG is evident at t
-
2 3 min,where the discrepancies between the predictions of the original model and the experimental mass loss curve begin to grow. The modified model, with its increased radiation to the fuel, is able to predict the slope change in the mass loss curve because of the square power effect of q, on the flame speed in Eq. (6), which in turn increases the bum area.
A comparison of predicted and experimental temperature profiles shows a similar pattern. The original model underpredicts the heat release rate of the fire because both the bum area A, and the burning rate enhancement are underpredicted. This is shown in Fig. 16.
The temperature predictions of the modified model show a significant improvement, as would be expected from the good prediction of the bum rate shown in Fig. 15.
. .
.
, ... OddnaI Model . . ..
,.
..
,..
.
..
..
.Time (min)
Figure
15:
Comparison of predicted and experimental mass loss profiles for 150 mmpolyurethane foam slab
1 2
Time (min)
Figure 16: Comparison of predicted and experimental temperature profiles for
The trends for the concentration profiles show a similar trend, in that the shapes of the curves predicted by the modified model are in good agreement with those obtained from the experimental compartment. The consistent underprediction of the O2 level is again due to the fact that the experimental 0 2 concentrations are duct concentrations and
thus include any oxygen in the additional air being entrained into the duct. The sharp peaks in the experimental CO and C02 profiles are due to the sensitivity of the analyzers
and are thus not necessarily indicative of concentration fluctuations in the room.
0"
s Original Model-Modlfled Model
0
4
0 1 2 3
Time (min)
Figure 17: Comparison of predicted and experimental O2 profiles for 150 mm
0 9 Original Madel -Modified Model
0.5
1. 2
Time (min)
Figure 18: Comparison of predicted and experimental CO profiles for 150 mm
polyurethane foam slab
1 2
Time (min)
Figure 19: Comparison of predicted and experimental C01 profiles for 150 mm polyurethane foam slab
