Flame extinction

Flame extinction is the point at which a flame can no longer sustain itself and goes out. A flame survives only while its reactions produce heat faster than the flame loses it. When the losses win, the flame cannot propagate any further. For diffusion flames, the type of flame found in real fires, this happens when the flame temperature drops below a limiting value of about 1,600 K (1,326 °C). Fires can be brought to that point in four ways: separating the fuel from the flame, removing or diluting the oxygen, cooling the fuel or the flame, or adding chemicals that disturb the reactions.

Extinguishing agents work through one or more of these routes. Water acts mainly by removing heat, nitrogen and carbon dioxide mainly by lowering the oxygen fraction, and halons mainly by stopping the chemical reactions. Flames in still air have been observed to go out at oxygen concentrations of 12.4 to 14.3 %. The physics of flame extinction underlies the design of water mist and gaseous extinguishing systems, inerting and the extinction models in computer fire simulations.

Physical basis

A flame is a balance between heat production and heat loss. The lower flammability limit of a fuel and air mixture can be explained by assuming that the heat lost from the flame, mainly by radiation, exceeds the heat produced within it. Beyond this point the flame cannot sustain itself. Calculations show that mixtures at this limit share a nearly constant adiabatic flame temperature, the temperature that the products would reach without any heat loss. For most hydrocarbons it lies at about 1,600 ± 100 K.

As cooling or dilution removes more heat, the flame temperature falls; below a limit of about 1,600 K the flame can no longer sustain itself. Based on Drysdale (2002), p. 1-97 and Mawhinney and Back (2002), p. 4-313.

A similar limiting temperature governs the extinction of diffusion flames by cooling. If enough heat is removed from the flame and the hot gases to bring the flame temperature below this critical value, the flame goes out. Only enough heat has to be absorbed to reach the limiting temperature. The gases do not have to be cooled to ambient temperature. Inert gases act in a similar way. Nitrogen, argon and carbon dioxide lower the final flame temperature, and if the burning velocity falls far enough, the flame is extinguished.

Premixed flames can also go out for flow reasons. A flat premixed flame is stable only when the gas flows towards it at exactly its burning velocity. If the flow is too fast, the flame is blown off, and if it is too slow, the flame moves back into the supply. A flame that tries to pass through a gap that is too narrow is quenched. This is probably due to a combination of heat loss to the walls and the removal of reactive free radicals. Flame traps use this quenching effect.

Extinguishing mechanisms

The fire triangle shows that fuel, oxygen and a heat source must be present at the same place and time. If one of the three is removed, combustion will not be sustained. As the oxygen level falls, a fire stops spreading and may eventually go out, depending on the exact oxygen concentration. The triangle covers most situations, but it does not explain extinguishment by dry chemicals and halons. Fire service guidance also uses the fire tetrahedron, which adds the chemical chain reaction to fuel, heat and oxygen.

The fire triangle and the fire tetrahedron, with the extinguishing mechanism that acts on each element. Based on Iqbal and Salley (2004), pp. 1-5 and B-15 and Van der Graaf et al. (2021/2023), p. 63.

NUREG-1805 lists four extinguishing mechanisms: physically separating the fuel from the flame, removing or diluting the oxygen supply, lowering the temperature of the fuel or the flame, and adding chemicals that change the combustion chemistry. In practice several mechanisms usually act together. When water is applied to a burning solid, the solid is cooled and produces less fuel vapour. The flame is cooled and sends less heat back to the fuel, steam may keep oxygen away in a confined space, and a fog of droplets blocks radiation. Dry chemical powders interact chemically with the flame, coat the fuel surface, cool the flame and block radiant heat. The relative importance of each contribution varies with the circumstances.

Chemical inhibition works differently from cooling. Bromine compounds reduce the burning velocity of a premixed flame even in trace amounts. When enough is added to extinguish a stoichiometric hydrocarbon and air flame, the adiabatic flame temperature of the mixture is only slightly lower than without the additive. The bromine and iodine species scavenge the flame radicals that carry the chain reaction. Most halon replacement compounds have little of this chemical effect and act mainly by extracting heat from the reaction zone, so they need higher concentrations than Halon 1301.

Oxygen depletion and dilution

A fire in a closed or poorly ventilated room can put itself out through oxygen depletion. A diffusion flame in a vitiated atmosphere goes out before it has consumed all the available oxygen, as a candle under an inverted jar shows. Morehart and co-workers diluted the air around pool fires with combustion products and found that the flames went out at oxygen concentrations of 12.4 to 14.3 %. In compartment tests with diesel pool fires, the oxygen concentration could not be brought below 14 % while the pools were burning. In water mist tests in obstructed machinery spaces, the oxygen concentration at extinction averaged 14.5 % for heptane spray fires and 13.5 % for pool fires.

These values depend on the gas that dilutes the air. With nitrogen as diluent, the limiting oxygen concentration below which a premixed mixture cannot burn is generally 10 to 12 %. With carbon dioxide it is 2 to 3 percentage points higher, because carbon dioxide has a higher molar heat capacity. The limiting oxygen concentration of premixed mixtures and the oxygen index of diffusion flames correspond closely. Water vapour has a molar heat capacity between those of nitrogen and carbon dioxide, so its extinction limits are expected to lie between theirs.

Inert gas agents work on the same principle. They reduce the flame temperature below the level needed to sustain the reactions, both by lowering the oxygen concentration and by raising the heat capacity of the atmosphere. Adding enough inert gas to bring the oxygen concentration below 12 % extinguishes flaming fires. The small-scale test for such agents is the cup burner. A small laminar flame burns above a cup of fuel, and the agent is mixed into the air flowing past it until the flame goes out. That agent fraction is the minimum extinguishing concentration.

Cup burner: a small flame burns above a cup of fuel while air mixed with the agent flows past it; the agent fraction at which the flame goes out is the minimum extinguishing concentration. Based on DiNenno (2002), pp. 4-174 and 4-175.

Worked example: oxygen left at extinction

For n-heptane cup burner flames, the agent fractions at extinction are about 32 % for nitrogen, 41 % for argon and 23 % for carbon dioxide by volume. The bromine compound Halon 1301 (CF₃Br) needs only 3.1 %. Air contains 21 % oxygen by volume. When an agent makes up a fraction $x$ of the mixture, the remaining oxygen fraction is therefore:

$$X_{{\mathrm{O}}_{\mathrm{2}}}=0.21(1-x)$$

Oxygen left in the air flow at extinction of n-heptane cup burner flames

Agent	Agent fraction at extinction (vol %)	Oxygen remaining (vol %)
Argon	41	12.4
Nitrogen	32	14.3
Carbon dioxide	23	16.2
Halon 1301	3.1	20.3

Symbols

Symbol	Description	Unit
$X_{{\mathrm{O}}_{\mathrm{2}}}$	volume fraction of oxygen in the diluted air	–
$x$	volume fraction of the extinguishing agent	–

The results show two separate effects. Among the inert gases, carbon dioxide extinguishes the flame while the most oxygen remains, which fits its high heat capacity. Halon 1301 extinguishes the flame although the air keeps more than 20 % oxygen, which shows that it does not act by depleting oxygen but by chemical inhibition.

Agent concentration at extinction of n-heptane cup burner flames and the oxygen left in the air flow. Based on DiNenno (2002), p. 4-175.

Cooling by water and water mist

Water works mainly by removing heat from the burning surface as it evaporates. Heating liquid water from 298 K to 373 K takes 0.32 kJ/g, and evaporating it takes another 2.26 kJ/g, so each gram that turns into steam absorbs about 2.58 kJ. A water mist system breaks the water into many fine droplets, which evaporate faster and therefore extract heat from the flame more effectively. Mawhinney and Back distinguish three primary mechanisms: cooling of the gas phase, oxygen depletion and dilution of the fuel vapour, and wetting and cooling of the fuel surface. Attenuation of radiation and effects on the reaction kinetics act as secondary mechanisms.

Wighus defined the spray heat absorption ratio as the rate at which evaporating water absorbs heat divided by the heat release rate of the fire. For an unconfined propane flame under optimum conditions, a ratio as low as 0.3 was enough for extinction. In more realistic machinery space conditions, values around 0.6 were found, because small flames can survive in shielded corners. Experiments on the mist concentration needed around a diffusion flame gave 100 to 200 g/m³, and as little as 50 g/m³ for heptane flames.

Worked example: water needed to cool a pool fire

NUREG-1824 describes an oil spill fire in a pump room with a heat release rate of 7,416 kW. With a spray heat absorption ratio of 0.3, the evaporating water must absorb 0.3 × 7,416 = 2,225 kW. At 2.58 kJ/g, that requires 2,225/2.58 ≈ 862 g/s, or about 0.87 kg/s of evaporated water. With the more realistic ratio of 0.6, the requirement doubles to about 1.73 kg/s. These amounts count only the water that actually evaporates in the flame. Delivery of mist into the flame is almost unpredictable in real systems, and its efficiency is far below 100 % in full-scale compartment fires.

At larger scales, the oxygen effect grows. Evaporating water expands by more than three orders of magnitude, which can disrupt the flow of air into the flame. In a closed room, the steam also lowers the oxygen concentration. If fire and steam together reduce the oxygen concentration below about 13 %, the limiting value for most hydrocarbon fuels, the fire goes out. For solid fuels and liquids with a flash point above room temperature, wetting and cooling of the fuel surface is often the dominant mechanism. It reduces the release of fuel vapour until the mixture above the surface falls below the lower flammability limit.

Tewarson describes this surface process with the fire point theory. A flame on a burning surface goes out when the mass loss rate falls to a critical value, which is similar to the critical mass loss rate at ignition. Critical mass loss rates measured at ignition, which approximate those at extinction, include 3.2 g/(m²·s) for PMMA, 2.5 g/(m²·s) for polyethylene and 2.7 g/(m²·s) for polypropylene. For these materials, the corresponding critical chemical heat release rates are 77 to 104 kW/m². Tewarson concludes that this critical value depends only weakly on the chemical nature of the material.

Extinction, inerting and design

A flame extinguishing concentration is not the same as an inerting concentration. The extinguishing concentration of an agent applies to diffusion flames, in which pure fuel vapour burns while oxygen diffuses into the flame from outside. It is not effective against premixed flames or explosive mixtures of fuel vapour and air. Inerting requires a concentration that stops flame propagation even at the most flammable, stoichiometric mixture, so that no fuel and air mixture in the room can burn. For most fuels, this concentration is about 30 to 40 % higher than the flame extinguishing value.

For Halon 1301, the minimum design concentrations for flame extinguishment are 5.0 % for methane and n-heptane and 5.2 % for propane. The inerting concentrations are 7.7 %, 6.9 % and 6.7 % respectively, including a safety factor of 10 %. If a reflash or explosion is possible after the fire, the extinguishing concentration is not sufficient and the inerting concentration is used. This choice between extinguishing and inerting concentrations is a basic step in the design of a gaseous extinguishing system with Halon 1301.

The flow around the flame also matters. The cup burner represents flames at low strain, comparable to typical natural fires with a strain rate of about 25 s⁻¹. At high strain rates, flames are extinguished at lower agent concentrations. Expressed in oxygen terms, the oxygen concentration at extinction rises as the strain rate increases.

Extinction in fire models

Fire models need explicit rules for extinction, because simple combustion models let fuel and oxygen react whenever they meet. The Fire Dynamics Simulator therefore checks each grid cell for local extinction, for example in under-ventilated rooms or when a suppression agent is present. Both of its options rest on the concept of a critical flame temperature. The first option uses a limiting oxygen volume fraction that falls with the cell temperature, starting at 0.135 at 20 °C, in line with the measurements of Morehart and co-workers. The second option suppresses combustion when the heat released could not raise the cell above the critical flame temperature. Both rules are empirical and ignore the strain of the flow.

Zone models use simpler criteria. CFAST limits the burning rate in a layer through a lower oxygen limit, with a default limiting oxygen mass fraction of 0.15. This value does not depend on the temperature. When oxygen limits the combustion, CFAST keeps the pyrolysis rate unchanged and lets only part of the fuel burn, while the unburnt fuel is carried into the upper layer.

Limitations and misconceptions

Extinction values are not universal constants. The oxygen concentration at extinction depends on the fuel, the diluent, the temperature of the surroundings and the strain of the flow. In jet fires, high-pressure sprays and engine nacelles with high flow rates, the strain rate changes the conditions for extinction substantially. Water mist data are particularly sensitive to how much mist actually reaches the flame, which designers can hardly predict or control in a real machinery space.

The extinction of a flame does not always end the fire. Diffusion flames anchored behind an obstruction, where a recirculation zone keeps the gas velocity low, can be highly stable and difficult to extinguish. Water mist may even make a flame flare up briefly on first contact. A flammable mixture left behind after extinction can reignite or explode. Where that risk exists, the higher inerting concentration is used instead of the extinguishing concentration.

The fire triangle is also a simplification. It describes extinction by cooling, smothering and fuel removal well, but it does not cover agents that act on the chemical chain reaction, such as halons and dry chemical powders. Some agents classed as inert are not harmless either. Carbon dioxide is physiologically active and toxic at concentrations of about 9 %, well below its extinguishing concentration.

See also

• Oxygen reduction system
• Equivalence ratio
• Diffusion flame
• Premixed flame
• Flammability limits

References

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