3.6 Post‐flashover Fires
3.6.3 Fire Temperatures
Estimation of temperatures in post‐flashover fires is an essential part of structural design for fire safety. Unfortunately this cannot be done precisely. This section describes measured and predicted temperatures from various studies, and a range of methods for estimating tempera- tures for design purposes. Temperatures in post‐flashover fires are usually of the order of about 1000 °C. The temperature at any time depends on the balance between the heat released within the room and all the heat losses; through openings by radiation and convection, and by conduction into the walls, floor and ceiling.
3.6.3.1 Measured Temperatures
Several experimental studies have measured temperatures in post‐flashover fires. There is considerable scatter between the results of different studies. Figure 3.11 shows the shapes of typical time temperature curves, starting at flashover, measured by Butcher et al.
(1966) in real rooms with door or window openings and well distributed fuel load.
Figure 3.11 also shows the ISO 834 standard curve used for fire resistance testing, as described in Section 3.7.2.
Figure 3.12 shows the maximum recorded temperature during the steady burning period for a large number of wood crib fires in small‐scale compartments reported by Thomas and Heselden (1972). The recorded temperature was the average of a number of thermocouple readings within each compartment. An empirical equation for the line in Figure 3.12 has been developed by Law (1983), summarized by Walton and Thomas (2008). The maximum temperature Tmax (°C) is given by:
Tmax 6000 1 e0 1. / (3.19)
where
A A A H
t v
v v
The maximum temperature in Equation 3.19 may not be reached if the fuel load is small.
For low fuel loads it can be reduced according to:
T Tmax 1 e0 05. (3.20)
200
00 10 20 30
Time (min)
40 50 60
30(½) 15(¼) 15(½)
Figure 3.11 Experimental time temperature curves. Reproduced from Butcher et al. (1966) under the terms of the Open Government Licence
Ventilation factor Av Hv/At(m½)
Opening factor At/Av Hv(m–½) 0.10
Fuel controlled
Ventilation controlled 1000
Temperature (°C)
500
00 10
Large openings Small openings
20 30 40
0.05 0.033 0.025
Figure 3.12 Maximum temperature in the burning period of experimental fires. Reproduced from Thomas and Heselden (1972) by permission of Building Research Establishment Ltd
where
L A Av t Av
and L is the fire load (kg, wood equivalent).
3.6.3.2 Swedish Curves
The most widely referenced time–temperature curves for real fire exposure are those of Magnusson and Thelandersson (1970), shown in Figure 3.13. These are often referred to as the ‘Swedish’ fire curves. They are derived from heat balance calculations, using Kawagoe’s equation (Equation 3.8) for the burning rate of ventilation controlled fires. Each group of curves is for a different ventilation factor, with fuel load as marked. Note that the units of fuel load are megajoules per square metre of total surface area (not MJ/m2 floor area, which is more often used in design calculations). The rising branch of the curve for ventilation factor of 0.04 is very similar to the standard time–temperature curve (described in Section 3.7.2).
To show the effects of changing fuel load and ventilation more clearly, some of the curves in Figure 3.13 have been redrawn in Figure 3.14 and Figure 3.15. Figure 3.14 shows the effect of varying the size of the ventilation openings, for a constant fuel load. Well ventilated
1000 800 600 400 200
00 1 2 3 4 5 6 0 1 2 3 4 5 6
0 1 2 3 4 5 6 0 1 2 3 4 5 6
50 25
100
12.5 37.5 150
200250
50 75 25
100 200
300 400500 Fv= 0.02
Fv= 0.08
Fv= 0.04
Fv= 0.12
Temperature (°C)
Time (h) 1200
1000 800 600 400 200 0
50 200 150 100
400 800 600
1000
Time (h) 900
600 300 225 150 75
1500
1200 Fuel load
(MJ/m2 total area)
Temperature (°C)
Figure 3.13 Time–temperature curves for different ventilation factors and fuel loads (MJ/m2 total sur- face area). Reproduced from Magnusson and Thelandersson (1970) by permission of Fire Safety Engineering Department, Lund University
fires burn faster than poorly ventilated fires, so they burn at higher temperatures, but for a shorter duration.
Figure 3.15 shows the effect of varying the fuel load for a constant size of ventilation opening.
The rate of burning is the same in all cases because it is controlled by the window size, but increasing the fuel load leads to longer and hotter fires before the decay period begins.
3.6.3.3 Rate of Temperature Decay
The rate of temperature decay in a post‐flashover fire is not easy to predict. The decay rate depends mainly on the shape and material of the fuel, the size of the ventilation openings and the thermal properties of the lining materials. If all the fuel is liquid or molten material in a
0 1 2 3 4 5 6
Time (h) 0
Figure 3.14 Time–temperature curves for varying ventilation and constant fuel load (MJ/m2 total surface area)
0 1 2 3 4 5 6
Time (h) 1200
1000 = 0.04
800 600 400
50 100
200 300
500
200 0
Temperature (°C)
Fv= Av Hv At Fuel load
(MJ/m2)
Figure 3.15 Time–temperature curves for varying fuel load (MJ/m2 total surface area) and constant ventilation
pool, the burning period will end suddenly when all the fuel has been consumed. On the other hand, solid materials like wood will burn at a predictable rate, leading to long decay periods depending on the thickness of the fuel items. The burning rate will be controlled by limited ventilation as long as the area of burning surfaces remains large. After the burning surface area reduces to a certain level, the fire will become fuel controlled and the decay rate will depend on the volume and thickness of the remaining items of fuel. If the fuel has a small ratio of surface area to volume, the fuel controlled burning in the later stages of the fire will lead to a long slow decay rate.
The rate of temperature decay depends on the ventilation openings because large openings will allow rapid heat loss from the compartment by both convection and radiation, whereas small openings will allow the heat to be trapped for much longer. The effect of thermal prop- erties of the construction materials is not easy to quantify. On one hand, materials of low thermal inertia will store less heat and hence transfer less heat back into the compartment after the fire is out, leading to a rapid rate of decay. On the other hand, such materials (which also have low thermal conductivity) will insulate the compartment and result in higher tempera- tures if any residual burning occurs in the decay period. Of these two contradictory effects, the first is likely to predominate, so that materials of low thermal inertia will likely lead to more rapid decay rates.