What is the driving cause of the two directional airflow through a doorway during a fire

Movement of Fire Gases

OBJECTIVES

After studying this chapter, you should be able to:

• Describe the three zones of the plume of a fire burning in the open and calculate the air entrainment into the flame and the height of the luminous flame.

• List three reasons why the nature of the ceiling jet is important.

• Calculate the mass outflow from a room in which a steady-state fire is burning.

• Estimate the minimum rate of heat release that leads a room to flashover.

• List nine reasons why calculating the smoke flow through most buildings requires a computational fire model.

Introduction

A 2007 fire in a furniture store began outside an enclosed loading dock area and spread into the retail showroom. During the early stages of the fire, its spread was slowed by the limited supply of fresh air. This underventilation led to the generation of a large mass of pyrolyzed and only partially oxidized effluent. The combustible gases flowed above the suspended ceiling of the main retail showroom and into the showroom itself, forming a hot smoke layer below the suspended ceiling. The fire at the back of the main showroom and the gas mixture below the suspended ceiling were both still rich with fuel. When the front windows were broken, the inflow of additional air rapidly increased the heat release rate of the fire and added air to the hot upper layer, enabling the ignition of the unburned fuel/air mixture. The fire swept quickly from the rear to the front of the main showroom, trapping nine fire fighters [1].

The description of each stage of this fire involves the word “flow” or a synonym of it. This is not uncommon. The flows to and from the fire determine the magnitude and direction of fire growth, and the flow from a fire transports toxic gases, aerosols, and heat to locations where they can be detected or do harm.

This chapter applies the fluid flow, heat generation, and chemical concepts developed previously to the movement of the gases by a fire. The treatment begins with the local movement within the fire plume and progresses to movement throughout a building.

Structure of a Fire Plume in the Open

The fuel flow into a fire comes from gasification of the liquid or solid that is burning. When the molecular fragments leave the fuel surface, they have almost no momentum. They rise into the air above strictly due to buoyancy (see the Flow of Fluids chapter), entraining (drawing in) cool air along the perimeter as they burn. This air entrainment is distinctly more than the amount of air needed for combustion. In turn, even with exothermic reactions occurring wherever the gasified fuel and air mix within the flammability limits, the overall temperature of the fire plume begins to decrease with increasing height. At some height, the plume temperature (and thus the gas density) essentially matches the temperature of the surrounding air. The buoyant force, which depends on a temperature difference, drops to zero; and the smoke spreads outward rather than being directed upward.

The overall fire plume structure can be regarded as having the three zones Figure 12-1 [2]:

1. An always luminous flame zone. Because the flame temperature exceeds the temperature of the fuel surface, the gases accelerate upward.

2. An intermittently flaming zone. A movie of zone 2 would show fluctuating orange flames and transparent gases, with the lower part of the zone being orange more often, and the top of the zone being defined as the location where no orange is seen. The gas temperature, while fluctuating, has an average value that remains constant from the top to the bottom of this zone. Thus the upward velocity is essentially constant.

3. A buoyant plume. The plume is nonluminous. The temperature and the buoyant velocity decrease with height.

The height of the luminous flame, h (m), is the sum of the height of zone 1 and a fraction of the height of zone 2. The fraction of the zone 2 height that is included in h is the distance from the bottom of the zone to the point at which the frames would show a plume that is orange half the time and transparent half the time. The luminous flame height (m) has been shown experimentally to fit the following Equation 12-1 :

Figure 12-1 Three zones of a buoyant diffusion flame.

where d is the diameter of the base of the fire (m) and Qc is the convective heat release of the flame (kW) [3]. For ordinary combustible products, the convective fraction of the total heat release is typically in the range of 0.6 to 0.7 for nonaromatic fuels and in the range of 0.3 to 0.5 for aromatic fuels [4]. The remaining fraction is radiative.

Some solutions to this equation are plotted in Figure 12-2 . The ratio h/d can vary at least from 1 to 44. When conditions are such that h/d is less than 1, the flame breaks up into a number of small flamelets.

The turbulence intensity in zones 2 and 3 is quite high. The velocity fluctuations at the center can be on the order of 30 percent of the average velocity; the temperature fluctuations can be even greater. These fluctuations and the eventual decrease in plume temperature reflect the rate of air entrainment into the plume. Precise calculation of the rate of entrainment into a fire plume is not of practical value, because small ambient disturbances in the air near the plume can have substantial effects on the entrainment rate. A rough approximation of the air entrainment rate m′ (kg/s) for a turbulent plume of height z (m) and plume surface area A (m2) is given by

In most plumes, combustion occurs only in zones 1 and 2. At the top of zone 2, the mass of entrained air is roughly an order of magnitude greater than the mass needed for complete combustion.

In zone 3, the combustion has ceased and the height is large compared to the width of the base of the plume. The average midline temperature (relative to the ambient temperature) decreases at a rate inversely proportional to the 5/3 power of the height. The average midline velocity decreases more slowly, at a rate inversely proportional to the 1/3 power of the height. The diameter of the plume increases at a rate directly proportional to the height [2].

Fire Plume under a Ceiling

For a fire in a building, the plume will impinge on the ceiling, unless the fire is very small or the ceiling is very high. When this happens, the hot gases make a 90-degree turn and spread out radially under the ceiling, forming a ceiling jet Figure 12-3 . This ceiling jet is important for at least two reasons:

• Devices to detect the fire, including automatic sprinklers and residential smoke alarms, are generally mounted at heights just below the ceiling, and knowledge of the time of arrival and properties of the ceiling jet are crucial for predicting the point of actuation for a detection device.

Figure 12-2 Calculated flame height of turbulent diffusion flames versus the convective heat-release rate for two fire sizes.

Figure 12-3 A turbulent ceiling jet under an unconfined ceiling with walls remote from the fire. “X” marks a distance along a ceiling jet radius that is equal to the distance between the base of the fire and the height of the ceiling.

• The downward thermal radiation from the ceiling jet, and, a little later, from the hot ceiling itself, affects the rate of fire spread. It is also a major factor in preheating and igniting combustible items not yet involved in the fire.

If the fire is burning at steady state and if the fire centerline is far from the nearest wall (e.g., the fire is near the center of a large room), the maxima of ceiling jet velocity and temperature exist at a distance below the ceiling equal to about 1 percent of the distance from the base of the fire to the ceiling. The radial velocity of the jet progressively decreases as it moves farther away from the fire centerline.

Note

The decrease in the radial velocity of the ceiling jet occurs for three reasons:

1. The leading edge of the flow is a circle of increasing circumference, while the mass flow is unchanged.

2. The ceiling jet is generally turbulent, and mixing occurs between the jet and the air below. This entrainment slows down the jet and reduces its temperature.

3. The jet transfers heat to the ceiling, which reduces the temperature of the jet. According to the ideal gas law, the volume of the jet decreases proportionately. The mass flow is unchanged, so the velocity decreases.

Texture: Eky Studio/ShutterStock, Inc.; Steel: © Sharpshot/Dreamstime.com

Formulas have been developed for calculating the temperature and velocity distribution in such a ceiling jet [5]. For example, focus on the location marked by “X” in Figure 12-3. At this location, the calculated maximum velocity in the jet will have dropped to half the value near the fire centerline. The difference between the jet temperature and the ambient temperature will have dropped to approximately 40 percent of the value near the fire centerline. If the walls are much farther away than the fire-to-ceiling distance, the temperature and velocity of the ceiling jet will decay to negligibly low values before the jet encounters the nearest wall.

Filling of a Fire Compartment by Smoke

If a fire is ignited in a compartment without openings, one of two things will happen:

• The release of heat causes an increase in the pressure and temperature of the gases in the compartment, according to the ideal gas law. Ordinary construction materials can withstand a substantial increase in pressure if the pressure is applied evenly and gradually. However, windows can break in a fire because of stresses created when the viewable area of the glass is heated and expands more than the area shaded by the frame. In case of a prolonged fire, gypsum wallboard panels can crack, but typically large gaps do not open up until the cooling phase after the fire.

• If no rupture occurs, the oxygen in the compartment becomes depleted to the point that the combustion ceases.

In either case, as long as the compartment does not contain an opening, a hot layer forms near the ceiling. This upper layer becomes deeper as the burning continues. As the bottom of the smoke layer approaches the flames, the luminous flame height decreases, because the flame is attempting to extend into a region characterized by severe oxygen depletion. Meanwhile, the fire has set up a convective flow pattern, with the gas rising above the fire, traveling along the ceiling and down along the walls, and finally being re-entrained into the flames. This pattern produces two results. First, the upper and lower layers in the compartment are mixed, so the environment becomes more uniform throughout the compartment. Second, the fire entrains air that is increasingly depleted of oxygen (vitiated), and the burning rate decreases accordingly.

Smoke Flow from a Compartment with an Opening

A more common case is that of a compartment with an opening, either by design or due to a window rupture. Figure 12-4 depicts a fire in a compartment with an open doorway. The ceiling jet has reached the walls, and a hot, smoky gas layer has formed near the ceiling. Continued burning has increased the (top-to-bottom) thickness of the layer until it extends below the top of the door opening; in addition, the hot, smoke-laden gases are flowing into the next compartment. The interface between the hot upper layer and the cool lower layer composes a somewhat wrinkled horizontal plane, called the neutral plane . (No such plane would form if the burning item were close to the doorway.)

Knowledge about this hot upper layer is crucial to assessment of life safety in a building fire. The layer thickness, temperature, and optical density all affect the intensity of downward thermal radiation incident on people and combustibles in the lower part of the compartment. The rate of outflow of the hot layer influences life safety in and fire spread to the adjacent space(s).

The layer temperature and optical density are determined by the heat release from the fire, the heat losses to the ceiling and walls, the fraction of the burned fuel converted to soot, and the volume of air into which the heat and soot are dispersed. Continuing with the compartment geometry depicted in Figure 12-4, assume that the burn rate has reached a steady state. Air enters the compartment through the lower part of the doorway, is entrained into the fire plume, and buoyantly flows upward into the hot gas layer. Hot gas escapes from the compartment through the upper part of the doorway.

Figure 12-4 Smoke layer from a fire in a compartment with an open doorway.

These inward and outward doorway flows are driven by pressure differences. From the Flow of Fluids chapter, recall that the difference in pressure between the top and bottom of a column of gas of height h is equal to gρh, where ρ is the gas density. The gas in the hot layer has a substantially lower density than the air in the lower part of the room or the air outside. Figure 12-5 shows the resulting pressure variations with height. In the doorway, there is a height at which the inside and outside pressures are the same; it corresponds to the intersection of the neutral plane with the doorway opening. Above this height, the pressure is higher inside, causing an outflow. Below the neutral point, the reverse is true, and an inflow occurs.

The driver for this two-directional air flow at the doorway is the rate of air entrainment into the fire plume. This rate is proportional to the burning rate of the fire and the vertical distance between the base of the plume (the top surface of whatever is burning) and the neutral plane (the bottom of the hot layer). The greater the entrainment rate, the lower the bottom of the hot layer. The mass rate of outflow is slightly greater than the mass rate of air inflow because of the added mass of the gasified combustible(s).

The “drag” on this outflow is the heat loss from the hot layer to the ceiling and the upper portion of the walls. This heat loss depends on the factors discussed in the Heat Transfer chapter, including the thermal inertia of the walls, the heat capacity of the upper-layer gas (air plus combustion products), and the degree of turbulence in the upper layer.

Knowing all these input values, fire scientists routinely use computational fire models (discussed in the Computational Modeling of Fires chapter) to calculate the height of the neutral plane and the flows in and out of the compartment. The pertinent equations were developed from and confirmed by numerous laboratory experiments.

In such an experiment, the researcher measures the top-to-bottom temperature and pressure profiles in the doorway. The height at which the pressure differential changes from higher in the room to lower in the room locates the plane separating the inflow and outflow. The temperatures enable calculation of the gas density in each flow. An estimate of each mass flow is obtained using the square root of the average pressure differential, the gas density, the ideal gas law, and the partial area of the doorway through which that flow passes. The (unmeasured) degree of heat loss is estimated from the measured temperatures, which are lower than they would be if no heat losses occurred.

Figure 12-5 Pressure gradients at the doorway, caused by the relative densities of cold air and hot gases.

Early in the fire, the smoke mainly fills the upper layer of the room. The flow of smoke from the room might suffice to activate a smoke alarm in the next compartment, but does not put people or property in that room at risk. This situation changes when the bottom of the upper layer becomes lower than the door soffit. Smoke begins to billow out the doorway. If the fire does not run out of fuel, the fire grows quickly and the room rapidly reaches a flashover condition, perhaps within tens of seconds. At this time, the burning intensity is at a steady state.

Based on observations from numerous experiments, fire engineers have arrived at an approximate, two-stage portrayal of the smoke outflow from the room: no outflow before flashover, steady outflow after flashover. From these experiments, they also evolved a simple equation for estimating the steady inflow or outflow of hot gases through a door or window in the fire room. If the opening is of height H (m) and area A (m2), then the mass flow out of the opening, (kg/s), is given by

The value of C is generally taken as 0.5 kg/s·m5/2 [6].

Using this relationship, several engineers have developed equations for the minimum heat release rate that leads to flashover. These equations differ slightly due to differences in the assumptions regarding the thermal physics of the combustion and the heat losses. For reasonable compartment sizes and openings, they agree within approximately ±20 percent. The simplest such equation is

where is given in units of kW. For a compartment with a common doorway size (0.6 m × 2.0 m), is approximately 1.3 MW. It is a common practice to use a mnemonic of 1 MW to characterize the approximate heat-release rate that threatens a typical residential room reaching flashover.

Calculation of the flows requires one of the computational fire models discussed in the Fire and Smoke Hazards chapter in the following cases:

• The fire is not at or near a steady state.

• The combustible is located near the opening (and thus the boundary between the layers is not flat).

• The calculation focuses on a hypothetical fire rather than one that has been measured.

Smoke Movement in Buildings

If a building consists of just a series of compartments, all on the same level and all connected by open doorways, you can estimate the flows using initially zero. As the smoke moves down the corridor, it becomes diluted by the air in the corridor and is cooled both by that air and by heat loss to the ceiling and walls. At some distance from the fire room, the smoke flow essentially reaches the ambient temperature, and no demarcation between a hot layer and a cool layer is apparent. Only after a large volume of smoke has heated the corridor from the ceiling down to the height of the soffits will the uniform layer depth be realized.

1. At the beginning of the fire, some doors might be closed and some windows might be open; also, during the fire people might open or close doors or windows, or the fire might break a window. The previously described calculation methods might still be applicable if the number of changes is small and one change does not affect another. (Interacting changes might, for example, lead to cross-ventilation in a compartment.) If the effect of each change may not be independent, it is prudent to use a computation fire model.

2. If the building contains long corridors, the assumption of a corridor filling uniformly from the top down is not realistic. As the smoke leaves the fire room, the height of the smoke layer is determined by the height of the neutral plane in that doorway. In the corridor, the depth of the smoke layer is initially zero. As the smoke moves down the corridor, it becomes diluted by the air in the corridor and is cooled both by that air and by heat loss to the ceiling and walls. At some distance from the fire room, the smoke flow essentially reaches the ambient temperature, and no demarcation between a hot layer and a cool layer is apparent. Only after a large volume of smoke has heated the corridor from the ceiling down to the height of the soffits will the uniform layer depth be realized.

3. A multistory building contains stairwells, elevator and ventilation shafts, and possibly atria. These areas serve as both pathways for vertical smoke movement and repositories for large masses of smoke.

4. The building might have a sloping ceiling or a ceiling supported by beams, both of which would modify the behavior of the ceiling jet.

5. The presence of wind outside a building influences air movement within the building, if any doors or windows are open.

6. An operating heating, ventilation, or air-conditioning system has a profound effect on smoke movement in a building. Even if the system is shut down, hot gases might still move through the ducts due to buoyancy or expansion due to the fire’s heat release.

7. In a tall building, a stack effect might arise depending on the weather. The pressure difference between the top of the building and the bottom of the building is given by the equation ΔP = ρgh. On a cold day in winter, the temperature within the building is higher than the temperature outside, so the ideal gas law says that the indoor density, ρi, is proportionately lower than the outdoor density, ρo. The height of the building and the gravitational constant are the same outdoors and indoors. Therefore, the pressure difference indoors, ΔPi, is lower than the pressure difference outdoors, ΔPo. As a result, air would leak into the building at the lower levels and leak out at the upper levels, prior to the occurrence of a fire. The resulting upward flow inside the building would help carry smoke upward. On a hot day in summer, this effect is reversed if the building is air conditioned. In such a case, the air density is higher indoors, and the pressure difference is accordingly higher indoors. As a result, air would leak out of the building at the lower levels and leak in at the upper levels. The hot, buoyant smoke would then be flowing against the downward flow from the stack effect.

8 The force of the flow from an activated fire suppression system would change the nature of the air patterns within the fire room.

9. The hazard potential of the smoke changes through processes other than dilution with fresh air. Larger aerosol particles and droplets are removed from the upper layer, either by sticking to walls or by falling due to gravity. Hydrogen chloride and hydrogen bromide stick to some surfaces.

Lest this all seem overwhelming, the physics behind items 1 through 8 has been incorporated by experts into widely available computational fire models. For item 9, relatively few data are available regarding the kinetics of the generation and evolution of smoke aerosols and even fewer data on the loss of gases on realistic surfaces. Therefore, the yields of the smoke components serve as input data to the models, and the models simply transport and dilute the components as they flow throughout the building.

WRAP-UP

Chapter Summary

• The plume of a fire burning in the open can be depicted as containing three zones. The lowest zone is luminous, and the gases accelerate upward. The flames in the middle zone are intermittent; the average gas temperature and upward velocity are constant. The upper zone is a nonluminous buoyant plume, whose temperature and velocity decrease with height.

• When a fire plume hits a ceiling, it spreads horizontally. The ceiling jet activates automatic sprinklers and smoke alarms and radiates thermal energy onto combustibles, accelerating fire growth.

• In a fire in a compartment, the ceiling jet forms a hot, smoky upper layer, which becomes hotter, more optically thick, and deeper as the fire progresses.

• A two-way flow occurs through the doorway of a fire room. The inflow through the lower portion of the opening is driven by air entrainment into the flames. The mass outflow through the upper portion of the opening is slightly higher due to the added mass of the combustion products.

• Calculation of the smoke flow from large fires in most buildings requires the use of a computational fire model. The ventilation pattern can change during a fire, for example, and the geometry of building is rarely as simple as needed for hand calculations to be accurate.