ahead of the flame. This in turn depends on the size and location of the flame (causing radiant heating), the air flow direction (causing convective heating), the thermal properties of the fuel (affecting the rate of temperature rise), and the flammability of the fuel (Drysdale, 2011).
Heating ahead of the flame will be more rapid if there are heat sources in addition to the flame itself, such as radiation from a layer of hot gases under the ceiling. Air movement is very important. Flame spread will be much more rapid with air flow in the direction of spread (‘wind aided’) than air flow in the other direction (‘wind opposed’). Upward flame spread is always rapid because the flame can rapidly preheat the material ahead of the burning region.
Flames tend to spread most rapidly on surfaces which have a high rate of temperature increase on exposure to heat flux. These are materials with low thermal inertia which are also more susceptible to ignition. Materials such as low density plastic foams experience rapid flame spread and fire growth for this reason.
Figure 3.1 A burning sofa in a furniture calorimeter test. If this sofa was burning in a room, the room would be full of toxic smoke
3
2
1
0
Large hood tests
F32 (sofa) F31 (loveseat) F21 (single chair)
Time (s)
200 400 600 800 1000
0
Rate of heat release (MW)
Figure 3.2 Heat release rate for furniture items. Reproduced from Babrauskas (2008) by permission of Society of Fire Protection Engineers
Burning rates for some liquid and solid fuels are given in Table 3.2 (derived from Babrauskas, 2008). These are based on a constant rate of burning per square metre of exposed surface area.
The figures for liquids and plastics are measurements from open‐air burning experiments. The figures for liquids are for pool fires over 2 m in diameter. The figures for wood are based on a constant regression rate of 40 mm/h which is typical for burning of wood in a fully developed room fire. The values for wood furniture will be similar to those given for wood cribs. Table 3.2 shows how the surface regression rate, the mass loss rate and the burning rate are all related, and they can be combined with the calorific value of the fuel to give the heat release rate.
These figures can be used to estimate the rate of heat release in a large open air fire, such as may occur in an industrial building after the roof has collapsed.
3.4.2 Burning Items in Rooms
The heat release rate of burning items of furniture or other fuel in the open air has been discussed in the previous section. Burning objects can behave differently when they burn inside a room. The convective plume of hot gases above the burning object will hit the ceiling and spread horizontally to form a hot upper layer. In the early stages of the fire, the rate of burning may be significantly enhanced by radiant feedback from this hot upper layer. Later, Table 3.2 Burning rates for some liquid and solid fuels
Density Regression rate
Mass loss rate
Surface burning rate
Specific surface
Total burning rate
Net calorific value
Heat release rate
(kg/m3) (mm/h) (kg/h) (kg/s/m2) (surface)
(m2 surface m2 floor)
(kg/s/m2) (floor)
(MJ/kg) (MW/m2) (floor) Liquids
LPG (C3H8) Petrol Kerosene Ethanol
585 740 820 794
609 268 171 68
356 198 140 54
0.099 0.055 0.039 0.015
1.0 1.0 1.0 1.0
0.099 0.055 0.039 0.015
46.0 43.7 43.2 26.8
4.55 2.40 1.68 0.40 Plastics
PMMA Polyethylene Polystyrene
—
—
—
—
—
—
—
—
—
0.054 0.031 0.035
1.0 1.0 1.0
0.054 0.031 0.035
24.0 44.0 40.0
1.34 1.36 1.40 Wood
Flat wood 1 m cube 100 mm in crib
25 mm in crib Softboard
500 500 500 500 300
40 40 40 40 108
20 20 20 20 32
0.056 0.056 0.056 0.056 0.009
1.0 6.0 20 47 1.0
0.0056 0.033 0.11 0.26 0.009
16 16 16 16 16
0.09 0.53 1.8 4.2 0.14
PMMA, poly(methyl methacrylate).
the rate of burning may be severely reduced because of limited ventilation, which can restrict the transport of incoming air and outgoing combustion products through the openings, and reduce the oxygen concentration in the lower layer.
Figure 3.3 shows a fire in a room, at an early stage when only a single item is burning, before any spread of flame to linings or other items. The room has only one opening for ven- tilation. The combustion reaction requires the input of oxygen, initially obtained from the air in the room, but later from air coming in through the opening. The energy released by the fire acts like a pump, pulling cool air into the room, entraining it into the fire plume and pushing combustion products out through the top of the opening. The fire plume provides buoyant convective transport of combustion products up to the ceiling. The plume entrains a large amount of cold air which cools and dilutes the combustion products. The diluted combustion products form a hot upper layer within the room. The thickness and temperature of the hot layer increase as the fire grows. The lower layer consists of cooler incoming air which is heated slightly by mixing and radiation from the upper layer (Figure 3.4).
When the plume reaches the ceiling, there is a flow of hot gases radially outwards along the underside of the ceiling, called the ceiling jet. The direction of the ceiling jet will be influenced by the shape of the ceiling. For a smooth horizontal ceiling the flow will be the same in each radial direction. The hot gases in the ceiling jet will activate heat detectors or fire sprinkler heads located near the ceiling. As the fire continues to burn, the volume of smoke and hot gases in the hot upper layer increases, reducing the height of the interface between the two layers. The combustion products will start to flow out the door opening when the interface drops below the door soffit as shown in Figure 3.3. The hot layer thickness depends on the size and duration of the fire and the size of door or window openings. If there are insufficient ventilation openings, the fire will die down and may self‐extinguish because of lack of oxygen.
The nature of wall, floor and ceiling linings can have a significant influence on fire growth and development in a room. Combustible lining materials can drastically increase the rate of initial fire growth due to rapid flame spread up walls and across ceilings. Temperatures will be higher and fire growth more rapid in a well‐insulated room where less heat can be absorbed by the bounding elements. Computer models that predict fire growth including ignition and flame spread on combustible lining materials have been developed (Wade, 2004a, 2004b).
If an automatic sprinkler system is installed, it will operate early in the pre‐flashover fire period, and either extinguish the fire or prevent it from growing any larger after that time.
3.4.3 t‐Squared Fires
The growth rate of a design fire is often characterized by a parabolic curve known as a t‐squared fire such that the heat release rate is proportional to the time squared. The t‐squared fire can be thought of in terms of a burning object with a constant heat release rate per unit area, in which the fire is spreading in a circular pattern with a constant radial flame speed.
The t‐squared heat release rate is given by:
Q t k/ 2 (3.7)
where Q is the heat release rate (MW), t is the time (s) and k is a growth constant (s/√MW).
Values of k are given in Table 3.3 for slow, medium, fast and ultrafast fire growth, producing the heat release rates shown in Figure 3.5. The numerical value of k is the time for the fire to reach a size of 1.055 MW. The choice of growth constant depends on the type and geometry of the fuel. Values of k and peak heat release rate for many different burning objects are given Figure 3.4 Smoke damage following a pre‐flashover fire in a room, indicating the thickness of the hot upper layer during the fire
by Babrauskas (2008). An alternative formulation which gives identical results is to describe the heat release rate Q (MW) for a t‐squared fire by:
Q t2 (3.8)
where α is the fire intensity coefficient (MW/s2). Values of α are also given in Table 3.3.
Figure 3.6 shows the resulting heat release rates for furniture in an office fire with slow, medium and fast fire growth rates for a peak heat release rate of 9 MW. The furniture item weighs 160 kg with a calorific value of 20 MJ/kg, giving a total energy load of 3200 MJ, which is the area under each of the curves shown in Figure 3.6. The t‐squared fire can be used to construct pre‐flashover design fires, as input for calculating the initial fire growth in rooms.
Thin wood furniture such as wardrobes
100
Ultra fast Fast Medium
Slow 80
60 40 20 00
Heat output (MW)
10 20 30
Time (min)
40 50 60
Figure 3.5 Heat release rate for t‐squared fires
3.4.4 Fire Spread to Other Items
The fires described above are generally used to describe the heat release rate for burning of a single object. In the very early stages of a fire, before the upper layer gets very hot, fire may spread from the first burning object to a second object by flame contact if it is very close, or by radiant heat transfer. The time to ignition of a second object depends on the intensity of radiation from the flame and the distance between the objects. When the time to ignition of the second object has been calculated, the combined heat release rate can be added at any point in time to give the total heat release rate for these two and subsequent objects. This combined curve then becomes the input design fire for the room under consideration. There may be many more items involved, and the resulting combination may itself be approximated by a t‐squared fire for simplicity.
For example, Figure 3.7(a) shows the t‐squared heat release rate for two objects. The first burns with medium growth rate for 10 min, followed by 1 min of steady burning at its peak heat release rate of 4.0 MW. The second object ignites after 3 min, burning with fast growth rate for 4 min followed by steady burning at 2.5 MW for 2 min. Figure 3.7(b) shows the combined heat release rate curve for the two objects. The FREEBURN routine in the FPEtool computer package was used to calculate the time of ignition of the second object (Deal, 1993). There are now more sophisticated packages that can generate heat release rates from multiple fuel objects.
These are briefly discussed in the sections that follow.
3.4.5 Pre‐flashover Fire Calculations
In the fire engineering design process, much effort is expended in calculating the effects of pre‐flashover fires, because this stage of the fire has the most influence on life safety. In order to ensure safe egress of building occupants it is necessary for the designer to know the expected rate of fire growth, and the resulting depth and temperature of the hot upper layer in the fire room and adjacent corridors as the fire develops. It is also essential to know the activation time and resulting effects of automatic detection and suppression systems. These calculations
Fast Medium
Slow
Time (min) 10
8 6 4 2
00 5 10 15 20 25 30
Heat release rate (MW)
Figure 3.6 Heat release rates for a fire load of 3200 MJ
are most often made using computer models such as those described below. For hand calcula- tions of upper layer temperatures, Walton and Thomas (2008) describe equations derived by McCaffrey et al. (1981).
3.4.5.1 Zone Models
Zone models are relatively simple computer programs which can model the behaviour of a pre‐flashover fire such as that shown in Figure 3.3. Most are two‐zone models because they consider the room fire in terms of two homogeneous layers, or zones, and the connecting plume (Quintiere, 2008). Conservation equations for mass, momentum and energy are applied to each zone in a dynamic process that calculates the size, temperature and species concentration of each zone as the fire progresses, together with the flow of smoke and toxic products through openings in the walls and ceiling. Zone models do not calculate the growth of fire on objects
0
Time (min) 0
Heat output (MW)
6
4
2
0 5
3
1
2 4 6 8 10 12
0
Time (min)
2 4 6 8 10 12
(b)
Figure 3.7 Combined design fire for two burning objects
or surfaces, so they require input data such as a t‐squared fire. Typical output includes the layer height, temperatures and concentrations of gas species in both layers, floor and wall temperatures, and the heat flux at the floor level.
One of the most versatile and widely used zone models is CFAST (Peacock et al., 1993;
Portier et al., 1996) which can calculate the movement of smoke and hot gases in interconnected rooms. CFAST is available free of charge on the internet from the Building and Fire Research Laboratory of the National Institute of Standards and Technology (NIST). Wade (2004a, 2004b) has developed B‐RISK (formerly BRANZFIRE), which is an enclosure zone model with an optional fire growth model for combustible linings. It can calculate time‐dependent distribution of smoke and heat through a collection of connected compartments during a fire (Spearpoint, 2008).
3.4.5.2 Field Models
The assumption of two distinct layers of gases is a convenient way of describing and calcu- lating pre‐flashover fire behaviour in rooms, but in reality there is a gradual three‐dimensional transition of temperature, density and smoke between the layers, and this transition limits the accuracy of zone models. Field models are much more sophisticated computer programs which use Computational Fluid Dynamics (CFD) to model fires using a large number of dis- crete zones in a three‐dimensional grid. Field models are much more difficult to run and to interpret than zone models, so they are more often used as research tools rather than design tools. NIST has developed Fire Dynamics Simulator (FDS) (McGrattan et al., 2015a, 2015b), which simplifies the CFD modelling process to approximate forms of the Navier–Stokes equations for low‐speed, thermally driven flows to simulate the mixing and transport phenomenon of combustible products (Spearpoint, 2008). FDS is increasingly used by designers for modelling pre‐flashover fires, but neither zone models nor field models are suitable for accurately modelling post‐flashover fires.