Ventilation Controlled Burning

3.6 Post‐flashover Fires

3.6.1 Ventilation Controlled Burning

In typical rooms, post‐flashover fires are ventilation controlled, so the rate of combustion depends on the size and shape of ventilation openings. It is usually assumed that all window glass (other than wired glass or fire resistant glass) will break and fall out at the time of flash- over, as a result of the rapid rise in temperature. If the glass does not fall out the fire will burn for a longer time at a lower rate of heat release. This can be detrimental for massive structural elements (or protected elements) as slow heating causes increased thermal exposure. In a ventilation controlled fire, there is insufficient air in the room to allow all the combustible gases to burn inside the room, so the flames extend out the windows and additional combustion takes place where the hot unburned gaseous fuels mix with outside air (Figure 3.8).

3.6.1.1 Rate of Burning

When the fire is ventilation controlled, the rate of combustion is limited by the volume of cold air that can enter and the volume of hot gases that can leave the room. For a room with a single opening, Kawagoe (1958) used many experiments to show that the rate of burning of wood fuel m (kg/s) can be approximated by:



m 0 092. A H_{v v} (3.11)

where A_v is the area of the window opening (m²) and H_v is the height of the window opening (m).

In many references the burning rate m is given as 5 5 . A H_{v v} kg/min or 330 A H_{v v} kg/h, which are the same as Equation 3.11 in different units of time. Note that A H_{v v} can be rewritten as BH_v^1.5 where B is the breadth of the window opening. This shows that the burning rate is largely dependent on the area of the window opening, but more so on its height.

If the total mass of fuel in the room is known, the duration of the burning period t_b (s) can be calculated using:

t_b M m_f/ (3.12)

Figure 3.8 Post‐flashover fire on the top floor of a multi‐storey office building. The flames coming out of the windows indicate that this fire is ventilation controlled

Q_vent m H _c (3.13) where ΔH_c is the heat of combustion of the fuel (MJ/kg).

If the total amount of fuel is known in energy units (MJ), the duration of the burning period t_b (s) can be calculated from:

t_b E Q/ _vent (3.14)

where E is the energy content of fuel available for combustion (MJ).

These calculations all depend on the approximate relationship for burning rate given by Equation 3.11 which is widely used, but not always accurate. Even if the burning rate is known precisely, the calculation of heat release rate is not accurate because an unknown proportion of the pyrolysis products burn as flames outside the window rather than inside the compartment.

Other sources of uncertainty arise because some proportion of the fuel may not be available for combustion, and the fire may change from ventilation control to a fuel controlled fire after some time.

Drysdale (2011) shows how Equation 3.11 can be derived by considering the flows of air and combustion products through an opening as shown in Figure 3.9. In a ventilation controlled fire there are very complex interactions between the radiant heat flux on the fuel, the rate of pyrolysis (or evaporation) of the fuel, the rate of burning of the gaseous products, the inflow of air to support the combustion, and the outflow of combustion gases and unburned fuel through openings. The interactions depend on the shape of the fuel (cribs or lining materials), the fuel itself (wood or plastic or liquid fuel) and the ventilation openings.

The empirical dependence of the ventilation controlled burning rate on the term A H_{v v} has been observed in many studies, but some tests have shown departures from Kawagoe’s equation. Following a large number of small‐scale compartment fires with wood cribs reported by Thomas and Heselden (1972), Law (1983) proposed a slightly more refined equation for burning rate, finding that the burning rate is not directly proportional to A H_{v v} but also depends on the floor shape of the compartment. Law’s equation is:



m A H W

D e

v v

0 18. 1 ^{0 036.} (3.15)

where

A A A H

t v

v v

W is the length of the long side of the compartment width (m), D is the length of the short side of the compartment (m), and A_t is the total area of the internal surfaces of the compartment (m²). In the calculation above, it is assumed that the opening is in the long side of the compartment.

Equation 3.15 gives approximately the same burning rate as Equation 3.11 for square com- partments with a ventilation factor of A H A_{v v}/ _t 0 05. (Ω = 20). The burning rate is greater than Equation 3.11 for smaller openings and wider shallower compartments. Equation 3.15 only applies directly to compartments with windows in one wall because it is not easy to dif- ferentiate the terms W and D if there are windows in two or more walls. Equation 3.15 is used in the Eurocode 1 Part 1.2 (CEN, 2002b) for calculating the rate of burning when assessing the flame height from compartment windows.

Thomas and Bennetts (1999) have cast considerable doubt on the applicability of Kawagoe’s equation, showing that the burning rate also depends heavily on the shape of the room and the width of the window in proportion to the wall in which it is located. If the width of the window is less than the full width of the wall, the burning rate is seen to be much higher than predicted by Equation 3.11 because of increased turbulent flow at the edges of the window. Despite these recent findings, Kawagoe’s equation is the basis of most post‐flashover fire calculations, until further research is conducted.

3.6.1.2 Ventilation Factor

The amount of ventilation in a fire compartment is often described by the ventilation factor F_v (m^0.5) given by:

F_v A H A_{v v}/ (3.16)_t

where A_v is the area of the window opening (m²), H_v is the height of the window opening (m) and A_t is the total internal area of the bounding surfaces (including openings) (m²). The ven- tilation factor F_v has units of m^0.5 which has little intuitive meaning. However, if the acceleration of gravity g is introduced, the term A gH A_{v v}/ has units of metres per second, _t which is related to the velocity of gas flow through the openings. Considering only a single opening, the term A gH_{v v} has units of cubic metres per second, which is related to the volumetric flow of gases through the opening.

3.6.1.3 Multiple Openings

Equation 3.8, Equation 3.11 and Equation 3.15 have been written for a single window opening in one wall of the compartment. If there is more than one opening, the same equations can be used, with A_v being the total area of all the openings and H_v being the weighted average height of all the window and door openings. Openings can be on several walls, which implies an

The terms B_i and H_i are the breadth and height of the windows, respectively, l₁ and l₂ are the floor plan dimensions, and H_r is the room height.