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Contents
  1. 1Definition and comparison with premixed flames
  2. 2Structure of a diffusion flame
  3. 3Laminar and turbulent diffusion flames
  4. 4Flame height and air entrainment
  5. 5Temperature, soot and radiation
  6. 6Stability, limits and extinction
  7. 7Use in fire safety engineering
  8. 8See also
  9. 9Notes
  10. 10References

A diffusion flame is a flame in which the fuel and the oxygen are not mixed in advance, but reach the reaction zone from opposite sides.[1] The fuel gas mixes with the surrounding air at the flame itself, either by molecular diffusion or by turbulence.[2] It is the counterpart of the premixed flame, in which fuel and air are mixed before ignition, as in a gas burner or a Bunsen burner.[2] A candle flame is the classic small example. A waste bin fire, a hydrocarbon pool fire and a forest fire all produce large, turbulent diffusion flames.[3]

Almost every unwanted fire burns as a diffusion flame, because no burner or other device is present to mix the fuel with air.[3] Solid and liquid fuels first release flammable vapours, and only these gases burn in the flame above the surface.[4][5] The rate of mixing of fuel and oxygen, rather than the rate of the chemical reactions, therefore controls how fast a real fire burns.[6] Most fire safety calculations describe the turbulent diffusion flame above a burning item and the buoyant plume that it creates.[3]

Definition and comparison with premixed flames

Flames are the visible part of combustion. In the flame body, gaseous fuel reacts with oxygen from the surrounding air. That fuel has either been premixed with air at the source, or it mixes with air at the flame by diffusion or turbulence.[2] The second case defines a diffusion flame. NUREG-1805 describes it as a flame in which the fuel and the oxygen are transported (diffused) from opposite sides of the reaction zone.[1] Diffusion is the movement of molecules through their random motion, which follows from their kinetic energy.[2]

Left: burner with fuel and air mixed in the tube and a cone flame. Right: fuel rising from a pool, air arriving from the sides, flame where they meet.
Premixed flame (left): fuel and air are mixed before they reach the flame. Diffusion flame (right): fuel and oxygen reach the reaction zone from opposite sides. Based on Van Rossum (2027), §4.3, and Iqbal and Salley (2004), p. 3-10.

The difference between the two flame types can also be expressed in time scales. In a diffusion flame, the time needed to bring fuel and oxygen together is much longer than the time needed for the chemical reaction.[7] In a premixed flame, fuel and oxygen are mixed before they reach the combustion zone, so the transport and reaction times are of similar size.[7] Fire scientists often describe a diffusion flame with the flame sheet approximation. It assumes that fuel and oxygen react almost instantly on contact, which gives an infinitely thin reaction zone. This simplification suits flames controlled by diffusion, such as a typical room fire.[7]

Premixed flames occur mostly in engineered combustion systems, such as boilers, furnaces, gas cookers, oxyacetylene torches and petrol engines.[3] Natural flaming processes, by contrast, produce diffusion flames.[3] The two types are still closely linked. Simmons notes that real fires are essentially diffusion flames, but that premixed burning is needed to understand several of their properties.[6] Even a Bunsen burner flame has an outer sheath that is essentially a diffusion flame when the gas mixture contains too little oxygen to burn all of the fuel.[8]

Structure of a diffusion flame

A burning candle shows the structure of a small diffusion flame. The heat of the match melts the wax, which rises up the wick and turns into vapour. The wax vapour combines with oxygen from the surrounding air and produces heat and light in the form of a flame.[9]

NUREG-1805 distinguishes three zones in this flame. The innermost zone is non-luminous and relatively cool, and contains a mixture of gas and air.[10] In the luminous zone, hydrogen and carbon monoxide from the decomposing wax react with oxygen at 590 to 680 °C, and free carbon particles glow before they are consumed. An outer zone, invisible to the eye, burns the remaining carbon monoxide and hydrogen.[10]

Candle flame cross-section with a dark inner zone, a yellow luminous zone with soot, and a thin invisible outer zone where oxygen arrives.
Zones of a candle flame, a laminar diffusion flame: the inner fuel-rich zone, the luminous soot zone and the outer zone where oxygen arrives and the burnout is completed. Based on Iqbal and Salley (2004), pp. 3-8 to 3-9, Simmons (2002), p. 1-151, and Van Rossum (2027), §4.3.

Oxygen can enter a laminar diffusion flame only slowly, because diffusion is a slow process. It therefore penetrates the flame only to a limited extent, and the outer part of a candle flame is the hottest.[2] Overall, the fuel and the oxygen react in stoichiometric proportions. Locally, however, the mixture ranges from very fuel-rich in the yellow carbon zone to excess oxygen in the hot blue zone on the air side.[6] On the fuel side, the lack of oxygen means that thermal decomposition of the fuel dominates. This leads to carbon formation and the characteristic yellow colour, while the maximum temperature is reached in the main reaction zone on the air side.[6]

The colours of a flame mainly come from hot soot particles that emit light because of their temperature.[2] Blue indicates almost complete combustion and yellow-orange indicates glowing soot. The pattern reflects local differences in oxygen, temperature and fuel vapour.[2] Fuels that produce little or no soot, such as alcohol, therefore burn with flames that are hard to see.[2] A pure hydrogen flame is almost invisible although its temperature is high, so the brightest flames are not always the hottest.[9]

The basic chemistry of a hydrocarbon diffusion flame is the same as in a premixed flame. The detailed mechanism, however, changes across the flame with the local conditions.[6] On the air side, the final burnout of carbon monoxide to carbon dioxide effectively stops once the temperature falls below 1,250 K, provided that a critical temperature gradient is also exceeded.[11] Chemical equilibrium exists only in a limited region of the flame. This lack of equilibrium is even more pronounced in turbulent diffusion flames.[11]

Laminar and turbulent diffusion flames

Introduction to Fire Safety Engineering divides diffusion flames into laminar and turbulent flames.[2] Laminar means that the streamlines of the flow are smooth and do not fluctuate significantly.[1] In a laminar diffusion flame, such as a candle, oxygen reaches the flame by diffusion alone. In a turbulent diffusion flame, turbulence supplies most of the oxygen and the flow pattern changes continuously.[2]

The book describes the turbulent flame as pushing and pulling at the surrounding air. When the flame receives enough oxygen, it becomes hotter, the gases expand and air is pushed away. When it receives too little, it cools, the gases contract and air is drawn back in.[2] The buoyant gas stream above a fire is generally turbulent, except when the fire source is very small.[5] Small fires often show a smooth, laminar flame sheet around the rim of the source before the flow becomes turbulent.[12]

The lower part of a turbulent fire flame looks fairly steady, while the upper part is intermittent. Vortex structures sometimes form near the base of the flame and are shed upwards.[13] Published measurements of the pulsation frequency cover burner and pool diameters from 0.03 to 20 m. The frequency falls as the fire becomes wider, from about 1.5 Hz for a source 1 m across to about 0.75 Hz for one 4 m across.[14] Measured frequencies for the same diameter differ by up to a factor of two.[14]

Releases of flammable gas under pressure form a separate group. Their flames are still diffusion flames, but the momentum of the release can become important.[5] At high release rates, the flame height stops increasing with the fuel flow and reaches several hundred times the source diameter.[13] In one of Heskestad's examples, hydrogen escapes from a 5 mm nozzle at 150 kPa above ambient pressure. The calculated flame height is 185 nozzle diameters, close to 0.9 m.[15]

Flame height and air entrainment

A turbulent diffusion flame takes its oxygen from ambient air that is drawn across the sharp, highly convoluted boundary of the buoyant flow. This process is called entrainment.[5] The flame height depends on the amount of air entrained, which in turn is linked to the heat release rate of the fire.[16] Much more air is entrained than the fuel strictly needs. At the mean flame height, the mass flow in the plume is about 13 times the stoichiometric air requirement of the fuel.[12]

The mean flame height is defined through the flame intermittency, the fraction of time during which part of the flame lies above a given height. It is the height at which this fraction has fallen to 0.5.[13] This height marks the level where the combustion reactions are essentially complete and where the inert fire plume begins.[13] Flame heights averaged by the human eye agree fairly well with this definition, although the intermittency method tends to give slightly lower values.[13]

Several correlations for the mean flame height have been proposed.[13] For buoyant fires under normal atmospheric conditions, the correlation of Heskestad gives it from the heat release rate and the diameter of the fire.[17] Introduction to Fire Safety Engineering uses the same relation and calls the result the mean flame length:[18]

L=0.235Q˙2/5−1.02D

Symbols in the flame height correlation
Symbol Description Unit
L mean flame height, where the flame intermittency is 0.5 m
Q˙ total heat release rate of the fire kW
D diameter of the fire source, or the diameter of a circle with the same area for other shapes m

The coefficient 0.235 is a typical value. It reflects the fact that the heat released per unit mass of air entering the combustion reactions varies little between fuels. The typical value is adequate unless the actual fuel properties or the atmospheric conditions clearly indicate otherwise.[17]

For many gaseous and liquid fuels this quantity lies between 2,900 and 3,200 kJ/kg, which gives coefficients from 0.226 to 0.240. Hydrogen, with 0.211, and petrol, with 0.200, deviate more.[17] The correlation is based on liquid pool fires, other horizontal-surface fires and jet flames without high discharge momentum. It also fits large storage fires when the flames extend above the stored goods.[17] For very small heat release rates it gives negative flame heights, which have no physical meaning.[17]

A worked example in the SFPE Handbook considers a stack of wood pallets 1.2 m high, with a plan area of 1.07 by 1.07 m. The stack burns at 2,600 kW under normal atmospheric conditions.[19] A circle with the same area of 1.14 m² has a diameter of 1.21 m. The typical coefficient is used, because the incomplete combustion of wood makes the fuel properties hard to choose.[19] The calculation then runs as follows:

L=0.235×26002/5−1.02×1.21=5.46−1.23≈4.2 m

The mean flame height is therefore about 4.2 m above the base of the stack, or about 3.5 times its equivalent diameter.[19] The ambient conditions also matter. For a methanol pool fire 1.5 m across, the calculated flame height is 1.83 m under normal conditions. On a hot day in Denver, with lower air pressure and higher temperature, it rises to 2.23 m.[19] The book applies the relation to choose a plume model. If the mean flame length is smaller than the fire diameter, the Thomas plume is more reliable; otherwise the Heskestad plume is preferred.[18]

Line chart: mean flame height rising with heat release rate from 0 to 5,000 kW, for fire diameters 0.5 m, 1.21 m and 2.0 m.
Mean flame height from the Heskestad correlation for three fire diameters; the dot marks the pallet stack example (2,600 kW, 1.21 m, 4.2 m). Based on Heskestad (2002), pp. 2-3 to 2-4.

Walls and corners restrict the free entrainment of air. NUREG-1805 states that this lengthens the flames and makes the plume hotter at a given height than in the open.[16] McCaffrey's review of wall and corner experiments, however, reported generally small effects on the flame height itself.[14] Wind bends the flame away from the vertical. A deflection of about 25 degrees is expected when the wind speed is one tenth of the maximum gas velocity in the flame.[14]

Temperature, soot and radiation

Measured temperatures in turbulent diffusion flames lie well below the values from ideal calculations. McCaffrey studied non-premixed flames above gas burners and described three regions.[20] The continuous flame region starts slightly above the base and has a nearly constant temperature just below 900 °C. In the intermittent flame region above it, the temperature falls with height to about 320 °C at the visible flame tips. Above the tips lies the thermal plume, where no flames are visible.[20]

Side view of a pool fire: steady flame at the bottom, flickering flame above, smoke plume on top, with centreline temperatures of 900 °C and 320 °C.
Regions of a turbulent diffusion flame above a pool fire, with the mean flame height at 50 % intermittency and typical centreline temperatures. Based on McCaffrey (1979), as cited in Iqbal and Salley (2004), p. 3-14, and Heskestad (2002), pp. 2-1 to 2-2.

NUREG-1805 concludes that flame tip temperatures of turbulent diffusion flames are about 320 to 400 °C. Fires smaller than about 1 m across have continuous flame temperatures of about 900 °C, while large pool fires can reach 1,100 to 1,200 °C.[21] Average flame temperatures of common fuels lie between about 920 and 1,200 °C.[22] Petrol and wood flames have almost the same temperature, which NUREG-1805 explains by the different radiation properties of the two flames.[3] A larger oxygen supply, for example from wind or an oxygen-enriched atmosphere, raises the flame temperature.[10]

Average flame temperatures of selected fuels[22]
Fuel Flame temperature (°C)
Benzene 921
Gasoline (petrol) 1,026
JP-4 (jet fuel) 927
Kerosene 990
Methanol 1,200
Wood 1,027

Soot forms in the fuel-rich regions of a diffusion flame. The particles grow through reactions between gas and solid and are then partly burnt out to carbon monoxide and carbon dioxide.[23] The time available for soot formation is a few milliseconds. In all flames, whatever the fuel, the first soot particles appear on the centreline where the temperature reaches 1,350 K.[23]

The diffusion-controlled flame ends where fuel and oxidant are in stoichiometric proportion on the flame axis. A soot burnout zone follows, which covers 10 to 50 % of the visible flame length as the soot concentration rises.[23] Smoke escapes when the soot in this zone cools below about 1,300 K, through radiation losses and mixing with cold air.[23]

The tendency of a fuel to form soot is expressed by its smoke point. This is the smallest height of a laminar diffusion flame at which smoke just escapes from the flame tip.[23] A low smoke point means a strong tendency to form soot. For hydrocarbons, this tendency decreases from aromatics to alkynes, alkenes and alkanes.[23] The highest measured smoke point is 0.240 m, for ethane.[24] For well-ventilated fires, Introduction to Fire Safety Engineering lists soot yields from 0.015 kg/kg for wood to 0.23 kg/kg for polyurethane.[25]

Diffusion flames radiate heat to their surroundings, and this radiation comes mainly from the soot particles inside the flame.[26] At high soot concentrations, the emissivity of the flame approaches unity.[23] As a rule of thumb, a fire releases about 70 % of its energy by convection and 30 % by radiation, although the ratio differs from fire to fire.[2] For pool fires and other horizontal-surface fires, the convective fraction is rarely measured below 60 to 70 % of the total heat release rate.[13]

Stability, limits and extinction

A diffusion flame needs a place where it can anchor. For a jet of fuel gas burning in air, the stability of the flame depends on a pocket of premixed gas at its base.[6] Just above the burner rim, the gas velocity is low and fuel and air mix. The burning velocity of this mixture, compared with the local gas velocity, decides whether the flame stays attached or is blown off.[6] A recirculation zone behind an obstruction in a gas stream can also hold a diffusion flame. Such flames can be very stable, which matters when a fire behind an obstacle has to be extinguished.[6]

Diffusion flames also have limits of flammability. Simmons and Wolfhard measured how far the oxidant stream must be diluted to prevent a diffusion flame from stabilising. The oxygen mole fraction at that point is called the limiting oxygen index, or simply the oxygen index.[27] The adiabatic flame temperature at the oxygen index equals that of a stoichiometric premixed mixture at its limit. It lies about 150 K above the value at the lower flammable limit in air.[27] The flammability of a diffusion flame can therefore be judged from a premixed stoichiometric mixture of the same fuel and oxidant.[27]

Morehart, Zukoski and Kubota extinguished pool fire flames by diluting the air with combustion products. The flames went out at oxygen concentrations of 12.4 to 14.3 %, the lower value for a 50 cm burner and the higher for a 9 cm burner.[28] In water mist tests in obstructed machinery spaces, the average oxygen concentration at extinction was 14.5 % for heptane spray fires and 13.5 % for pool fires.[28] These results apply to quiet conditions, because higher strain rates in the flow raise the oxygen concentration at extinction.[28] For United States nuclear power plants, NUREG-1805 states that carbon dioxide systems work by reducing the oxygen content below the 15 % required for a diffusion flame.[29]

The oxygen index of solids, measured with a candle-type test, is a different quantity. Its result can also be governed by effects in the solid, so it should not be used to calculate gas-phase diffusion flame limits.[30] Beyler also notes that much less research has been done on limits of diffusion flames than on limits of premixed flames.[31]

Use in fire safety engineering

Most fire protection engineering applications deal with the buoyant plume that a turbulent diffusion flame creates above the burning fuel.[3] The properties of these plumes matter for fire detection, the heating of building structures, smoke filling rates, venting and the design of suppression systems.[5] When the flame reaches an unconfined ceiling, the unburnt gases spread out radially, entrain air and form a flame under the ceiling.[3] A flame that directly strikes a surface generally transfers large quantities of heat to it.[3]

Computer fire models usually treat the diffusion flame as controlled by mixing. The Fire Dynamics Simulator (FDS) technical guide states that a simple eddy dissipation model is sufficient when fuel and oxidiser are initially unmixed and the chemistry is fast compared with mixing.[32] By default, FDS assumes that fuel and oxygen always react, regardless of local temperature or concentration. This is usually adequate for large, well-ventilated fires, but not for under-ventilated compartments or fires exposed to water mist or carbon dioxide.[33] For such cases FDS predicts local extinction with a critical flame temperature. The guide illustrates the idea with a candle that goes out under an inverted jar.[33]

Several limits apply when diffusion flame relations are used in design. The chemistry inside turbulent diffusion flames is far from equilibrium, which makes modelling from first principles difficult.[11] For a turbulent methane flame, an equilibrium model predicted a peak carbon monoxide fraction about 2.5 times the measured value, while a laminar flamelet model came within 10 %.[11] Small disturbances of the ambient air increased measured plume mass flows by 20 to 50 % in laboratory tests.[12] The combustion efficiency also differs between fuels. It is close to unity for methanol and heptane pools, but about 45 % for polystyrene and 63 % for a burning stack of wood pallets.[13]

See also

Notes

  1. ↑ 1.0 1.1 1.2 Iqbal and Salley (2004), p. 3-10.
  2. ↑ 2.00 2.01 2.02 2.03 2.04 2.05 2.06 2.07 2.08 2.09 2.10 2.11 Van Rossum (2027), §4.3.
  3. ↑ 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 Iqbal and Salley (2004), p. 3-12.
  4. ↑ Van Rossum (2027), §4.1.
  5. ↑ 5.0 5.1 5.2 5.3 5.4 Heskestad (2002), p. 2-1.
  6. ↑ 6.0 6.1 6.2 6.3 6.4 6.5 6.6 6.7 Simmons (2002), p. 1-151.
  7. ↑ 7.0 7.1 7.2 Tien et al. (2002), p. 1-86.
  8. ↑ Simmons (2002), p. 1-144.
  9. ↑ 9.0 9.1 Iqbal and Salley (2004), p. 3-8.
  10. ↑ 10.0 10.1 10.2 Iqbal and Salley (2004), p. 3-9.
  11. ↑ 11.0 11.1 11.2 11.3 Simmons (2002), p. 1-152.
  12. ↑ 12.0 12.1 12.2 Heskestad (2002), p. 2-12.
  13. ↑ 13.0 13.1 13.2 13.3 13.4 13.5 13.6 13.7 Heskestad (2002), p. 2-2.
  14. ↑ 14.0 14.1 14.2 14.3 Heskestad (2002), p. 2-15.
  15. ↑ Heskestad (2002), p. 2-5.
  16. ↑ 16.0 16.1 Iqbal and Salley (2004), p. 4-1.
  17. ↑ 17.0 17.1 17.2 17.3 17.4 Heskestad (2002), p. 2-3.
  18. ↑ 18.0 18.1 Van Rossum (2027), §6.7.
  19. ↑ 19.0 19.1 19.2 19.3 Heskestad (2002), p. 2-4.
  20. ↑ 20.0 20.1 McCaffrey (1979), as cited in Iqbal and Salley (2004), p. 3-14.
  21. ↑ Iqbal and Salley (2004), p. 3-14.
  22. ↑ 22.0 22.1 Iqbal and Salley (2004), p. 3-13.
  23. ↑ 23.0 23.1 23.2 23.3 23.4 23.5 23.6 Tewarson (2002), p. 3-131.
  24. ↑ Tewarson (2002), p. 3-132.
  25. ↑ Van Rossum (2027), §6.2.
  26. ↑ Nowlen et al. (2005b), p. 8-3.
  27. ↑ 27.0 27.1 27.2 Beyler (2002b), p. 2-183.
  28. ↑ 28.0 28.1 28.2 Beyler (2002b), p. 2-184.
  29. ↑ Iqbal and Salley (2004), p. B-46.
  30. ↑ Beyler (2002b), p. 2-186.
  31. ↑ Beyler (2002b), p. 2-172.
  32. ↑ McGrattan et al. (2026), p. 54.
  33. ↑ 33.0 33.1 McGrattan et al. (2026), p. 62.

References

  • Beyler, C. L. (2002b). Flammability limits of premixed and diffusion flames. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), SFPE handbook of fire protection engineering (3rd ed., pp. 2-172–2-187). National Fire Protection Association; Society of Fire Protection Engineers.
  • Heskestad, G. (2002). Fire plumes, flame height, and air entrainment. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), SFPE handbook of fire protection engineering (3rd ed., pp. 2-1–2-17). National Fire Protection Association; Society of Fire Protection Engineers.
  • Iqbal, N., & Salley, M. H. (2004). Fire Dynamics Tools (FDTs): Quantitative fire hazard analysis methods for the U.S. Nuclear Regulatory Commission Fire Protection Inspection Program (NUREG-1805). U.S. Nuclear Regulatory Commission, Office of Nuclear Reactor Regulation.
  • McGrattan, K., Hostikka, S., Floyd, J., McDermott, R., Vanella, M., Mueller, E., & Paul, C. (2026). Fire Dynamics Simulator technical reference guide: Vol. 1. Mathematical model (6th ed., NIST Special Publication 1018-1). National Institute of Standards and Technology. https://doi.org/10.6028/NIST.SP.1018
  • Nowlen, S. P., Najafi, B., Wyant, F. J., Forester, J., Kazarians, M., Kolaczkowski, A., Joglar, F., Funk, D., Hannaman, G., & Anoba, R. (2005b). EPRI/NRC-RES fire PRA methodology for nuclear power facilities: Vol. 2. Detailed methodology (NUREG/CR-6850; EPRI 1011989). Electric Power Research Institute; U.S. Nuclear Regulatory Commission, Office of Nuclear Regulatory Research.
  • Simmons, R. F. (2002). Premixed burning. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), SFPE handbook of fire protection engineering (3rd ed., pp. 1-144–1-154). National Fire Protection Association; Society of Fire Protection Engineers.
  • Tewarson, A. (2002). Generation of heat and chemical compounds in fires. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), SFPE handbook of fire protection engineering (3rd ed., pp. 3-82–3-161). National Fire Protection Association; Society of Fire Protection Engineers.
  • Tien, C. L., Lee, K. Y., & Stretton, A. J. (2002). Radiation heat transfer. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), SFPE handbook of fire protection engineering (3rd ed., pp. 1-73–1-89). National Fire Protection Association; Society of Fire Protection Engineers.
  • Van Rossum, E. (2027). Introduction to Fire Safety Engineering. Fire Safety Academy.
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