Opposed-flow flame spread - Revision history

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	The direction of the gas flow relative to the spread defines two classes. When the flame spreads upwind, against the flow, the process is called opposed-flow spread; when it spreads downwind, it is called wind-aided spread.<ref name="Q2247" /> The flow can come from an external wind or from the natural convection that the spreading flame, or another fire, sets up.<ref name="Q2247" /> Downward spread on a wall is a common case: the flame moves down while the air that feeds it rises, driven by buoyancy, at roughly 30 cm/s.<ref name="Q2250" /> Lateral spread across a vertical surface behaves in a similar way, and so does the outward spread from a small fire on a horizontal surface.<ref name="Q2250" />		The direction of the gas flow relative to the spread defines two classes. When the flame spreads upwind, against the flow, the process is called opposed-flow spread; when it spreads downwind, it is called wind-aided spread.<ref name="Q2247" /> The flow can come from an external wind or from the natural convection that the spreading flame, or another fire, sets up.<ref name="Q2247" /> Downward spread on a wall is a common case: the flame moves down while the air that feeds it rises, driven by buoyancy, at roughly 30 cm/s.<ref name="Q2250" /> Lateral spread across a vertical surface behaves in a similar way, and so does the outward spread from a small fire on a horizontal surface.<ref name="Q2250" />
			[[File:fse-opposed-flow-flame-spread-v1.svg\|thumb\|upright=1.5\|alt=Two vertical walls: left, a flame spreading downward against rising air with a tiny heated zone; right, a flame spreading upward with a long heated zone.\|Opposed-flow spread (left): the flame moves down against the rising air and heats only a strip of about 1 to 3 mm. Wind-aided spread (right): the flame moves up with the flow and heats the fuel over about its own length. Based on Quintiere (2002b), pp. 2-247 and 2-251.]]

	Quintiere summarises the process with the fundamental equation of flame spread. It considers the net heat that the flame transfers, per unit area and time, to the fuel ahead of it.<ref name="Q2247" /> For steady spread, this heat equals the heat needed to raise the fuel from its initial temperature to its ignition temperature:<ref name="Q2247" />		Quintiere summarises the process with the fundamental equation of flame spread. It considers the net heat that the flame transfers, per unit area and time, to the fuel ahead of it.<ref name="Q2247" /> For steady spread, this heat equals the heat needed to raise the fuel from its initial temperature to its ignition temperature:<ref name="Q2247" />
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	== Thermally thin fuels ==		== Thermally thin fuels ==
	A fuel is [[Thermally thin and thick materials\|thermally thin]] when it is so thin that its temperature is uniform across its thickness.<ref name="Q2248" /> For this case Quintiere writes an energy balance over the heated strip and expresses the flame heat flux as conduction through the gas. The result is nearly identical to the formula that de Ris derived more formally:<ref name="Q2248" />		A fuel is [[Thermally thin and thick materials\|thermally thin]] when it is so thin that its temperature is uniform across its thickness.<ref name="Q2248" /> For this case Quintiere writes an energy balance over the heated strip and expresses the flame heat flux as conduction through the gas. The result is nearly identical to the formula that de Ris derived more formally:<ref name="Q2248" />
			[[File:fse-opposed-flow-flame-spread-v2.svg\|thumb\|upright=1.5\|alt=Cross-section of a thin fuel layer with a flame above its pyrolysis region and a dashed control volume ahead of the flame.\|Energy balance for opposed-flow spread over a thin fuel: the gas flows towards the flame at speed Vg, and the flame heats the fuel over a length Δ from Ts to the ignition temperature Tig. Based on Quintiere (2002b), p. 2-248.]]

	<math display="block">V = \frac{\sqrt{2}\, k_\mathrm{g} \left( T_\mathrm{f} - T_\mathrm{s} \right)}{\rho c \delta \left( T_\mathrm{ig} - T_\mathrm{s} \right)}</math>		<math display="block">V = \frac{\sqrt{2}\, k_\mathrm{g} \left( T_\mathrm{f} - T_\mathrm{s} \right)}{\rho c \delta \left( T_\mathrm{ig} - T_\mathrm{s} \right)}</math>
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	Below 210 °C the flame cannot continue along this board, so an unheated board at room temperature does not support this mode of spread.<ref name="Q2250" /> Piloted ignition of the same material requires a heat flux of at least 16 kW/m².<ref name="IS610">Society of Fire Protection Engineers (2002), as cited in Iqbal and Salley (2004), p. 6-10.</ref> The steep rise in rate with surface temperature explains why far-field radiation and convection from the fire make the spread accelerate.<ref name="Q2247" />		Below 210 °C the flame cannot continue along this board, so an unheated board at room temperature does not support this mode of spread.<ref name="Q2250" /> Piloted ignition of the same material requires a heat flux of at least 16 kW/m².<ref name="IS610">Society of Fire Protection Engineers (2002), as cited in Iqbal and Salley (2004), p. 6-10.</ref> The steep rise in rate with surface temperature explains why far-field radiation and convection from the fire make the spread accelerate.<ref name="Q2247" />
			[[File:fse-opposed-flow-flame-spread-v3.svg\|thumb\|upright=1.5\|alt=Rising curve of spread rate against surface temperature for particleboard, from 0.46 mm/s at 210 °C to about 94 mm/s at 370 °C, on a log scale.\|Opposed-flow spread rate over 1.27 cm Douglas fir particleboard against the surface temperature ahead of the flame, from the LIFT formula and data. Below 210 °C spread does not continue; at 382 °C the surface ignites. Based on Quintiere (2002b), pp. 2-250 and 2-251.]]

	== Role in fire growth ==		== Role in fire growth ==
	Quintiere's table of typical spread rates puts lateral or downward spread on thick solids at about 0.1 cm/s. Upward spread on thick solids reaches 1 to 100 cm/s, and smouldering only 0.001 to 0.01 cm/s.<ref name="Q2247" /> Opposed-flow spread is therefore much slower than [[upward flame spread]], in which the flame lies over the fuel ahead of it and preheats it over a long distance.<ref name="Q2251" /><ref name="VR43">Van Rossum (2027), §4.3.</ref> The fire dynamics tools of the U.S. Nuclear Regulatory Commission illustrate this with a window curtain. A pilot flame at the bottom causes rapid upward spread, while the same flame at the top gives much slower fire growth through slow downward spread.<ref name="IS63">Iqbal and Salley (2004), p. 6-3.</ref>		Quintiere's table of typical spread rates puts lateral or downward spread on thick solids at about 0.1 cm/s. Upward spread on thick solids reaches 1 to 100 cm/s, and smouldering only 0.001 to 0.01 cm/s.<ref name="Q2247" /> Opposed-flow spread is therefore much slower than [[upward flame spread]], in which the flame lies over the fuel ahead of it and preheats it over a long distance.<ref name="Q2251" /><ref name="VR43">Van Rossum (2027), §4.3.</ref> The fire dynamics tools of the U.S. Nuclear Regulatory Commission illustrate this with a window curtain. A pilot flame at the bottom causes rapid upward spread, while the same flame at the top gives much slower fire growth through slow downward spread.<ref name="IS63">Iqbal and Salley (2004), p. 6-3.</ref>
			[[File:fse-opposed-flow-flame-spread-v4.svg\|thumb\|upright=1.5\|alt=Range bars on a log scale from 0.001 cm/s for smouldering to 300,000 cm/s for detonation, with lateral or downward spread near 0.1 cm/s.\|Orders of magnitude of spread rates. Lateral or downward (opposed-flow) spread on thick solids is about 0.1 cm/s, far slower than upward spread. Based on Quintiere (2002b), p. 2-247.]]

	Even slow spread enlarges a fire quickly. In Quintiere's example, an ignited region 6 cm across on an upholstered chair spreads at about 1 mm/s and reaches 18 cm across within a minute. The burning area then grows nearly tenfold, which increases the heat release and the heat transfer to the fuel.<ref name="Q2246" /> Fire growth accelerates when the time for spread is short compared with the burning time. It can slow down and stop when the spread time is long compared with the burning time.<ref name="Q2246" />		Even slow spread enlarges a fire quickly. In Quintiere's example, an ignited region 6 cm across on an upholstered chair spreads at about 1 mm/s and reaches 18 cm across within a minute. The burning area then grows nearly tenfold, which increases the heat release and the heat transfer to the fuel.<ref name="Q2246" /> Fire growth accelerates when the time for spread is short compared with the burning time. It can slow down and stop when the spread time is long compared with the burning time.<ref name="Q2246" />

Mark: FSE wiki: corrections after independent fact-check (written by Claude Opus 5.5)

2026-11-01T23:23:08Z

FSE wiki: corrections after independent fact-check (written by Claude Opus 5.5)

Mark: New FSE wiki article: Opposed-flow flame spread (written by Claude Opus 5.5)

2026-11-01T22:15:19Z

New FSE wiki article: Opposed-flow flame spread (written by Claude Opus 5.5)

New page

'''Opposed-flow flame spread''' is the spread of a flame over the surface of a solid or liquid fuel in the direction opposite to the surrounding gas flow.<ref name="Q2247">Quintiere (2002b), p. 2-247.</ref> The flow can be an external wind or the air that the fire itself draws in, as in downward spread on a wall or sideways spread across a vertical panel.<ref name="Q2247" /><ref name="Q2250">Quintiere (2002b), p. 2-250.</ref> The flame heats the fuel ahead of it mainly by conduction through the gas, over a short strip of about 1 to 3 mm.<ref name="Q2248">Quintiere (2002b), p. 2-248.</ref><ref name="Q2251">Quintiere (2002b), p. 2-251.</ref> This form of [[flame spread]] is therefore slow: lateral or downward spread on thick solids has a typical rate of about 0.1 cm/s, against 1 to 100 cm/s for upward spread.<ref name="Q2247" />

The slow rate still matters, because even spread at about 1 mm/s enlarges a small burning area quickly and increases the heat transfer that drives further spread.<ref name="Q2246">Quintiere (2002b), p. 2-246.</ref> Simple energy balances give the spread rate for thermally thin fuels, such as paper, and for thermally thick fuels, such as boards and wall linings.<ref name="Q2249">Quintiere (2002b), p. 2-249.</ref> The lateral ignition and flame spread test (LIFT) provides the material data that these formulas need.<ref name="Q2250" /> Such data have shown promise in replacing older flammability indices with more meaningful measures, and they have been used to predict room-corner fire tests.<ref name="Q2247" /><ref name="Q2254">Quintiere (2002b), p. 2-254.</ref>

== Definition and terminology ==
Quintiere describes surface flame spread as the movement of a flame close to the condensed fuel that feeds it.<ref name="Q2246" /> Two fronts advance together: the flame in the gas phase and the edge of the vaporising or [[pyrolysis|pyrolysing]] region on the fuel surface. The flame spread velocity is defined as the speed of this pyrolysis front.<ref name="Q2246" />

The direction of the gas flow relative to the spread defines two classes. When the flame spreads upwind, against the flow, the process is called opposed-flow spread; when it spreads downwind, it is called wind-aided spread.<ref name="Q2247" /> The flow can come from an external wind or from the natural convection that the spreading flame, or another fire, sets up.<ref name="Q2247" /> Downward spread on a wall is a common case: the flame moves down while the air that feeds it rises, driven by buoyancy, at roughly 30 cm/s.<ref name="Q2250" /> Lateral spread across a vertical surface behaves in a similar way, and so does the outward spread from a small fire on a horizontal surface.<ref name="Q2250" />

Quintiere summarises the process with the fundamental equation of flame spread. It considers the net heat that the flame transfers, per unit area and time, to the fuel ahead of it.<ref name="Q2247" /> For steady spread, this heat equals the heat needed to raise the fuel from its initial temperature to its ignition temperature:<ref name="Q2247" />

<math display="block">\rho V \Delta h = \dot{q}'', \qquad \Delta h = c \left( T_\mathrm{ig} - T_\mathrm{s} \right)</math>

The ignition temperature in this balance is the surface temperature at which the fuel releases enough vapour to sustain piloted ignition. For liquids it is the fire point, and for solids it depends on the kinetics of thermal decomposition.<ref name="Q2247" /> The balance shows that the spread rate rises as the fuel density falls. It also grows without bound as the surface temperature ahead of the flame approaches the ignition temperature.<ref name="Q2247" />

{| class="wikitable"
! Symbol !! Description !! Unit
|-
| <math>V</math> || flame spread rate (speed of the pyrolysis front) || m/s
|-
| <math>\rho</math> || density of the fuel || kg/m³
|-
| <math>c</math> || specific heat capacity of the fuel || J/(kg·K)
|-
| <math>\Delta h</math> || heat needed per unit mass to raise the fuel from <math>T_\mathrm{s}</math> to <math>T_\mathrm{ig}</math> || J/kg
|-
| <math>\dot{q}''</math> || net heat flux from the flame to the fuel ahead of it || W/m²
|-
| <math>T_\mathrm{ig}</math> || ignition temperature of the fuel surface || K or °C
|-
| <math>T_\mathrm{s}</math> || surface temperature of the fuel ahead of the flame || K or °C
|-
| <math>T_\mathrm{f}</math> || flame temperature || K
|-
| <math>k_\mathrm{g}</math> || thermal conductivity of the gas || W/(m·K)
|-
| <math>\delta</math> || thickness of a thermally thin fuel || m
|-
| <math>V_\mathrm{g}</math> || speed of the opposed gas flow || m/s
|-
| <math>(k \rho c)_\mathrm{g}</math> || product of conductivity, density and specific heat of the gas || W²·s/(m⁴·K²)
|-
| <math>k \rho c</math> || thermal inertia of the fuel || kW²·s/(m⁴·K²)
|-
| <math>\Phi</math> || flame heating parameter of the LIFT method || kW²/m³
|-
| <math>T_\mathrm{s,min}</math> || minimum surface temperature for continued spread || °C
|}

== Heat transfer ahead of the flame ==
In opposed-flow spread, the flame heats the fuel ahead of it mainly by conduction through the gas.<ref name="Q2248" /> The heated length is short, about 1 to 3 mm. In wind-aided spread it is of the order of the flame length, 0.1 to 10 m.<ref name="Q2251" /> Measurements on polymethyl methacrylate (PMMA) by Ito and Kashiwagi show a maximum [[heat flux]] of about 70 kW/m² just ahead of the front in downward spread. Upward spread gives a nearly constant flux of about 25 kW/m², spread over a much longer distance.<ref name="Q2254" />

The flame temperature that drives this heat transfer depends mainly on the oxygen concentration of the surrounding air. The reason is that the heat released per unit mass of oxygen is nearly constant for most hydrocarbons, at about 13 kJ/g.<ref name="Q2248" /> Spread under a ceiling, where the oxygen concentration has fallen through [[oxygen depletion]], is therefore expected to slow down.<ref name="Q2248" /> The heat of combustion, the heat of gasification and the specific heat of the gas also enter the full expression for the flame temperature.<ref name="Q2248" />

The simple theory makes the spread rate independent of the speed of the opposed flow. That holds only while the chemical reactions in the flame are fast compared with the time the gas takes to pass through it.<ref name="Q2248" /> The ratio of these two times is the Damköhler number, which varies with the inverse square of the flow speed. When the flow is too fast, the reactions are incomplete and the flame weakens.<ref name="Q2248" /> Below a critical value of the Damköhler number no further spread is possible, and the flame is extinguished.<ref name="Q2249" />

== Thermally thin fuels ==
A fuel is [[Thermally thin and thick materials|thermally thin]] when it is so thin that its temperature is uniform across its thickness.<ref name="Q2248" /> For this case Quintiere writes an energy balance over the heated strip and expresses the flame heat flux as conduction through the gas. The result is nearly identical to the formula that de Ris derived more formally:<ref name="Q2248" />

<math display="block">V = \frac{\sqrt{2}\, k_\mathrm{g} \left( T_\mathrm{f} - T_\mathrm{s} \right)}{\rho c \delta \left( T_\mathrm{ig} - T_\mathrm{s} \right)}</math>

The spread rate is inversely proportional to the thickness, density and specific heat of the fuel, so thinner and lighter sheets spread faster.<ref name="Q2248" /> The flame temperature should ideally be the adiabatic stoichiometric value, but heat losses and chemical kinetic effects lower it in practice.<ref name="Q2248" /> Measured rates on thin paper fall as the opposed flow speed increases, in line with the effect of the Damköhler number.<ref name="Q2249" />

For common combustible solids, Quintiere reasons that the thin analysis holds up to a thickness of about 1 mm.<ref name="Q2249" /> For downward spread on PMMA, Fernandez-Pello and Hirano found thin behaviour below 2 mm and thick behaviour above 2 cm, with a non-uniform temperature in between.<ref name="Q2249" /> Apart from items such as paper, garments and draperies, most solids behave as thermally thick under flame spread conditions.<ref name="Q2249" />

== Thermally thick fuels ==
In a thick fuel, only a surface layer is heated while the flame passes. Its depth follows from heat conduction theory as the square root of the thermal diffusivity multiplied by the heating time.<ref name="Q2249" /> The heated length in the gas follows from a balance between conduction and convection. Combining these steps gives the thick-fuel result, again identical to that of de Ris:<ref name="Q2249" />

<math display="block">V = \frac{V_\mathrm{g}\, (k \rho c)_\mathrm{g} \left( T_\mathrm{f} - T_\mathrm{ig} \right)^2}{k \rho c \left( T_\mathrm{ig} - T_\mathrm{s} \right)^2}</math>

The spread rate now depends on the [[thermal inertia]] <math>k \rho c</math> of the fuel and falls with the square of the gap between the ignition temperature and the surface temperature.<ref name="Q2249" /> Unlike in the thin case, the ideal rate grows with the speed of the opposed flow. Chemical kinetics act against this, so the actual rate may rise or fall with flow speed, depending on the oxygen concentration.<ref name="Q2250" />

For PMMA in normal air, with an oxygen mass fraction of 0.233, the rate is insensitive to flow speeds up to about 30 cm/s and falls at higher speeds.<ref name="Q2250" /> The buoyancy-induced flow in downward spread on a wall is roughly 30 cm/s. Under normal fire conditions the spread rate therefore depends mainly on the oxygen concentration, at least for PMMA.<ref name="Q2250" /> In turbulent opposed flow, the rate on thin paper fell as the turbulence intensity rose, whereas thick PMMA showed a maximum at a flow speed of about 0.5 m/s.<ref name="Q2250" /> Quintiere suggests that, for engineering purposes, solids thicker than about 1 mm may be regarded as thermally thick. Up to a thickness of 1 to 2 cm, the spread rate can still depend on the thickness and on the material behind the fuel.<ref name="Q2249" />

== Measurement and material data ==
The cone calorimeter and the lateral ignition and flame spread test have provided the basis for the material data that flame spread calculations need.<ref name="Q2247" /> Quintiere and Harkleroad developed a practical test procedure that yields the parameters for opposed-flow spread on thick materials burning in air under natural convection.<ref name="Q2250" /> The thick-fuel result is rewritten with a single flame heating parameter <math>\Phi</math>, which depends on the flow speed and the oxygen concentration:<ref name="Q2250" />

<math display="block">V = \frac{\Phi}{k \rho c \left( T_\mathrm{ig} - T_\mathrm{s} \right)^2}</math>

In the test, the flame spreads sideways along a vertical sample that is exposed to an external radiant heat flux. The parameters <math>\Phi</math>, <math>k \rho c</math> and <math>T_\mathrm{ig}</math> are deduced from the measurements, and the procedure is standardised as the LIFT test.<ref name="Q2250" /> A wide range of tests gave ignition temperatures from 280 °C for PMMA to 570 °C for paper on gypsum wallboard. Values of <math>\Phi</math> ranged from about 1 to 15 kW²/m³.<ref name="Q2250" />

Each material also has a minimum surface temperature below which continued spread is not possible.<ref name="Q2250" /> The minimum irradiance that allows piloted ignition marks a critical condition for spread. Results from the lateral test were similar to those for downward spread, except for materials that melt and drip heavily.<ref name="Q2250" /> The table lists selected values, which are significant to two places only.<ref name="Q2251" />

{| class="wikitable"
! Material !! <math>T_\mathrm{ig}</math> (°C) !! <math>k \rho c</math> (kW²·s/(m⁴·K²)) !! <math>\Phi</math> (kW²/m³) !! <math>T_\mathrm{s,min}</math> (°C)
|-
| PMMA Polycast (1.59 mm) || 278 || 0.73 || 5.4 || 120
|-
| PMMA type g (1.27 cm) || 378 || 1.02 || 14.4 || 90
|-
| Douglas fir particleboard (1.27 cm) || 382 || 0.94 || 12.7 || 210
|-
| Plywood, plain (1.27 cm) || 390 || 0.54 || 12.9 || 120
|-
| Flexible foam (2.54 cm) || 390 || 0.32 || 11.7 || 120
|-
| Gypsum board, common || 565 || 0.45 || 14.4 || 425
|-
| Polystyrene (5.08 cm) || 630 || 0.38 || not measurable || 630
|}

A second test arrangement, the fire propagation apparatus of standard ASTM E2058 of the American Society for Testing and Materials, measures downward propagation against an imposed airflow.<ref name="T389">Tewarson (2002), p. 3-89.</ref> For a vertical PMMA slab 25 mm thick, with an airflow of 0.09 m/s, the pyrolysis front and the heat release rate grew linearly with time.<ref name="T389" /><ref name="T390">Tewarson (2002), p. 3-90.</ref> Upward propagation in the same apparatus was much faster and accelerated with time.<ref name="T389" />

=== Worked example ===
A vertical lining of Douglas fir particleboard, 1.27 cm thick, is heated by radiation from a fire elsewhere in the room. The LIFT data give an ignition temperature of 382 °C, a thermal inertia of 0.94 kW²·s/(m⁴·K²), <math>\Phi = 12.7</math> kW²/m³ and a minimum spread temperature of 210 °C.<ref name="Q2251" /> The example estimates how fast a flame spreads downward or sideways over the board for several surface temperatures ahead of the flame. At the minimum spread temperature of 210 °C, the spread rate is:<ref name="Q2250" />

<math display="block">V = \frac{12.7}{0.94 \times (382 - 210)^2} \approx 4.6 \times 10^{-4}\ \mathrm{m/s} = 0.46\ \mathrm{mm/s}</math>

At surface temperatures of 250 °C, 300 °C and 350 °C, the same formula gives 0.78 mm/s, 2.0 mm/s and 13 mm/s.<ref name="Q2250" /><ref name="Q2251" /> Crossing 0.1 m of board then takes about 210 s at 210 °C, but only about 7 s at 350 °C. Raising the surface temperature from 210 °C to 300 °C multiplies the spread rate by about 4.4.

Below 210 °C the flame cannot continue along this board, so an unheated board at room temperature does not support this mode of spread.<ref name="Q2250" /> Piloted ignition of the same material requires a heat flux of at least 16 kW/m².<ref name="IS610">Society of Fire Protection Engineers (2002), as cited in Iqbal and Salley (2004), p. 6-10.</ref> The steep rise in rate with surface temperature explains why far-field radiation and convection from the fire make the spread accelerate.<ref name="Q2247" />

== Role in fire growth ==
Quintiere's table of typical spread rates puts lateral or downward spread on thick solids at about 0.1 cm/s. Upward spread on thick solids reaches 1 to 100 cm/s, and smouldering only 0.001 to 0.01 cm/s.<ref name="Q2247" /> Opposed-flow spread is therefore much slower than [[upward flame spread]], in which the flame lies over the fuel ahead of it and preheats it over a long distance.<ref name="Q2251" /><ref name="VR43">Van Rossum (2027), §4.3.</ref> The fire dynamics tools of the U.S. Nuclear Regulatory Commission illustrate this with a window curtain. A pilot flame at the bottom causes rapid upward spread, while the same flame at the top gives much slower fire growth through slow downward spread.<ref name="IS63">Iqbal and Salley (2004), p. 6-3.</ref>

Even slow spread enlarges a fire quickly. In Quintiere's example, an ignited region 6 cm across on an upholstered chair spreads at about 1 mm/s and reaches 18 cm across within a minute. The burning area then grows nearly tenfold, which increases the heat release and the heat transfer to the fuel.<ref name="Q2246" /> Fire growth accelerates when the time for spread is short compared with the burning time. It can slow down and stop when the spread time is long compared with the burning time.<ref name="Q2246" />

In an enclosure, heat from the fire and its hot combustion gases accumulates and reaches other combustible objects by radiation.<ref name="VR43" /> The surface temperature ahead of a spreading flame then rises, and the spread accelerates.<ref name="Q2247" /> Orientation and geometry can also change the mode of spread. In the London King's Cross fire, flames spread up a wooden escalator, and the sidewalls of the escalator caused the flames to hug the steps.<ref name="Q2254" /> An experimental study of that fire, listed by Quintiere, refers to it as the [[trench effect]].<ref name="Q2257">Quintiere (2002b), p. 2-257.</ref>

== Limits and uncertainty ==
The formulas are heuristic. They come from energy balances with simple assumptions, and their results are consistent with more formal analyses but remain approximate.<ref name="Q2246" /><ref name="Q2248" /> The ignition temperature is assumed constant for each material.<ref name="Q2250" /> Kanury stresses that the surface temperature at ignition is an effect rather than a cause, and that it depends on the conditions of the experiment.<ref name="K2242">Kanury (2002a), p. 2-242.</ref>

Computing the flame heat flux from first principles is a complex problem that has limited the ability to predict flame spread.<ref name="Q2247" /> Data from the lateral test do not apply to materials that melt and drip heavily. Some materials, such as fire-retardant plywood and polystyrene, gave no measurable spread at all.<ref name="Q2250" /><ref name="Q2251" />

Where conditions are simple, the theory performs well. For filter paper burning in microgravity at 50 % oxygen in still gas, a measured spread rate of 0.44 cm/s compared with a predicted 0.42 cm/s, once gas-phase radiation was included.<ref name="Q2256">Quintiere (2002b), p. 2-256.</ref> A complete numerical simulation by Di Blasi and co-workers, including solid- and gas-phase kinetics, reached qualitative success.<ref name="Q2250" />

Quintiere concludes that flame spread depends on the heat transfer at the flame front, which in turn depends on the fuel, its configuration and orientation, and the surrounding conditions.<ref name="Q2256" /> Flame spread in enclosures, mines, ducts and buildings adds a further complex array of conditions. Flame spread on materials therefore has to be evaluated in the context of their use, with data that suit the assessment.<ref name="Q2256" />

== See also ==
* [[Critical heat flux for ignition]]
* [[Time to ignition]]
* [[Fire spread]]
* [[Ignition]]

== Notes ==
<references />

== References ==
* 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.
* Kanury, A. M. (2002a). Flaming ignition of solid fuels. 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. 2-229–2-245). National Fire Protection Association; Society of Fire Protection Engineers.
* Quintiere, J. G. (2002b). Surface flame spread. 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. 2-246–2-257). 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.
* Van Rossum, E. (2027). ''Introduction to Fire Safety Engineering''. Fire Safety Academy.

[[Category:Ignition & Flame Spread]]

← Older revision		Revision as of 00:23, 2 November 2026
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	'''Opposed-flow flame spread''' is the spread of a flame over the surface of a solid or liquid fuel in the direction opposite to the surrounding gas flow.<ref name="Q2247">Quintiere (2002b), p. 2-247.</ref> The flow can be an external wind or the air that the fire itself draws in, as in downward spread on a wall or sideways spread across a vertical panel.<ref name="Q2247" /><ref name="Q2250">Quintiere (2002b), p. 2-250.</ref> The flame heats the fuel ahead of it mainly by conduction through the gas, over a short strip of about 1 to 3 mm.<ref name="Q2248">Quintiere (2002b), p. 2-248.</ref><ref name="Q2251">Quintiere (2002b), p. 2-251.</ref> This form of [[flame spread]] is therefore slow: lateral or downward spread on thick solids has a typical rate of about 0.1 cm/s, against 1 to 100 cm/s for upward spread.<ref name="Q2247" />		'''Opposed-flow flame spread''' is the spread of a flame over the surface of a solid or liquid fuel in the direction opposite to the surrounding gas flow.<ref name="Q2247">Quintiere (2002b), p. 2-247.</ref> The flow can be an external wind or the air that the fire itself draws in, as in downward spread on a wall or sideways spread across a vertical panel.<ref name="Q2247" /><ref name="Q2250">Quintiere (2002b), p. 2-250.</ref> The flame heats the fuel ahead of it mainly by conduction through the gas, over a short strip of about 1 to 3 mm.<ref name="Q2248">Quintiere (2002b), p. 2-248.</ref><ref name="Q2251">Quintiere (2002b), p. 2-251.</ref> This form of [[flame spread]] is therefore slow: lateral or downward spread on thick solids has a typical rate of about 0.1 cm/s, against 1 to 100 cm/s for upward spread.<ref name="Q2247" />

	The slow rate still matters, because even spread at about 1 mm/s enlarges a small burning area quickly and increases the heat transfer that drives further spread.<ref name="Q2246">Quintiere (2002b), p. 2-246.</ref> Simple energy balances give the spread rate for thermally thin fuels, such as paper, and for thermally thick fuels, such as boards and wall linings.<ref name="Q2249">Quintiere (2002b), p. 2-249.</ref> The lateral ignition and flame spread test (LIFT) provides the material data that these formulas need.<ref name="Q2250" /> ~~Such data~~ have ~~shown~~ promise in replacing older flammability indices with ~~more meaningful measures, and they~~ have been used to predict room-corner fire tests.~~<ref name="Q2247" />~~<ref name="Q2254">Quintiere (2002b), p. 2-254.</ref>		The slow rate still matters, because even spread at about 1 mm/s enlarges a small burning area quickly and increases the heat transfer that drives further spread.<ref name="Q2246">Quintiere (2002b), p. 2-246.</ref> Simple energy balances give the spread rate for thermally thin fuels, such as paper, and for thermally thick fuels, such as boards and wall linings.<ref name="Q2249">Quintiere (2002b), p. 2-249.</ref> The lateral ignition and flame spread test (LIFT) provides the material data that these formulas need.<ref name="Q2250" /> Attempts to include configuration effects, such as spread in corners and on ceilings, have not yet led to fully established methods but show promise in replacing older flammability indices.<ref name="Q2247" /> Flame spread equations combined with cone calorimeter data have also been used to predict room-corner fire tests.<ref name="Q2254">Quintiere (2002b), p. 2-254.</ref>

	== Definition and terminology ==		== Definition and terminology ==
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	The spread rate is inversely proportional to the thickness, density and specific heat of the fuel, so thinner and lighter sheets spread faster.<ref name="Q2248" /> The flame temperature should ideally be the adiabatic stoichiometric value, but heat losses and chemical kinetic effects lower it in practice.<ref name="Q2248" /> Measured rates on thin paper fall as the opposed flow speed increases, in line with the effect of the Damköhler number.<ref name="Q2249" />		The spread rate is inversely proportional to the thickness, density and specific heat of the fuel, so thinner and lighter sheets spread faster.<ref name="Q2248" /> The flame temperature should ideally be the adiabatic stoichiometric value, but heat losses and chemical kinetic effects lower it in practice.<ref name="Q2248" /> Measured rates on thin paper fall as the opposed flow speed increases, in line with the effect of the Damköhler number.<ref name="Q2249" />

	For common combustible solids, ~~Quintiere reasons~~ that the thin analysis holds up to a thickness of about 1 mm.<ref name="Q2249" /> For downward spread on PMMA, Fernandez-Pello and Hirano found thin behaviour below 2 mm and thick behaviour above 2 cm, with a non-uniform temperature in between.<ref name="Q2249" /> Apart from items such as paper, garments and draperies, most solids behave as thermally thick under flame spread conditions.<ref name="Q2249" />		For common combustible solids, it has been reasoned that the thin analysis holds up to a thickness of about 1 mm.<ref name="Q2249" /> For downward spread on PMMA, Fernandez-Pello and Hirano found thin behaviour below 2 mm and thick behaviour above 2 cm, with a non-uniform temperature in between.<ref name="Q2249" /> Apart from items such as paper, garments and draperies, most solids behave as thermally thick under flame spread conditions.<ref name="Q2249" />

	== Thermally thick fuels ==		== Thermally thick fuels ==
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	A second test arrangement, the fire propagation apparatus of standard ASTM E2058 of the American Society for Testing and Materials, measures downward propagation against an imposed airflow.<ref name="T389">Tewarson (2002), p. 3-89.</ref> For a vertical PMMA slab 25 mm thick, with an airflow of 0.09 m/s, the pyrolysis front ~~and the heat release rate grew~~ linearly with time.~~<ref name="T389" />~~<ref name="T390">Tewarson (2002), p. 3-90.</ref> Upward propagation in the same apparatus was much faster and accelerated with time.<ref name="T389" />		A second test arrangement, the fire propagation apparatus of standard ASTM E2058 of the American Society for Testing and Materials, measures downward propagation against an imposed airflow.<ref name="T389">Tewarson (2002), p. 3-89.</ref> For a vertical PMMA slab 25 mm thick in oxygen-enriched air, with an oxygen mass fraction of 0.334 and an airflow of 0.09 m/s, the pyrolysis front advanced linearly with time.<ref name="T390">Tewarson (2002), p. 3-90.</ref> The heat release rate during downward propagation also grew linearly with time.<ref name="T389" /> Upward propagation in the same apparatus, in a test in normal air with an oxygen mass fraction of 0.233, was much faster and accelerated with time.<ref name="T389" /><ref name="T390" />

	=== Worked example ===		=== Worked example ===
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	<math display="block">V = \frac{12.7}{0.94 \times (382 - 210)^2} \approx 4.6 \times 10^{-4}\ \mathrm{m/s} = 0.46\ \mathrm{mm/s}</math>		<math display="block">V = \frac{12.7}{0.94 \times (382 - 210)^2} \approx 4.6 \times 10^{-4}\ \mathrm{m/s} = 0.46\ \mathrm{mm/s}</math>

	At surface temperatures of 250 °C, 300 °C and 350 °C, the same formula gives 0.78 mm/s, 2.0 mm/s and 13 mm/s.<ref name="Q2250" /><ref name="Q2251" /> Crossing 0.1 m of board then takes about 210 s at 210 °C, but only about 7 s at 350 °C. Raising the surface temperature from 210 °C to 300 °C multiplies the spread rate by about 4.4.		At surface temperatures of 250 °C, 300 °C and 350 °C, the same formula gives 0.78 mm/s, 2.0 mm/s and 13 mm/s.<ref name="Q2250" /><ref name="Q2251" /> Crossing 0.1 m of board then takes about 210 s at 210 °C, but only about 7.5 s at 350 °C, with both times rounded down to the safe side. Raising the surface temperature from 210 °C to 300 °C multiplies the spread rate by about 4.4.

	Below 210 °C the flame cannot continue along this board, so an unheated board at room temperature does not support this mode of spread.<ref name="Q2250" /> Piloted ignition of the same material requires a heat flux of at least 16 kW/m².<ref name="IS610">Society of Fire Protection Engineers (2002), as cited in Iqbal and Salley (2004), p. 6-10.</ref> The steep rise in rate with surface temperature explains why far-field radiation and convection from the fire make the spread accelerate.<ref name="Q2247" />		Below 210 °C the flame cannot continue along this board, so an unheated board at room temperature does not support this mode of spread.<ref name="Q2250" /> Piloted ignition of the same material requires a heat flux of at least 16 kW/m².<ref name="IS610">Society of Fire Protection Engineers (2002), as cited in Iqbal and Salley (2004), p. 6-10.</ref> The steep rise in rate with surface temperature explains why far-field radiation and convection from the fire make the spread accelerate.<ref name="Q2247" />
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	The formulas are heuristic. They come from energy balances with simple assumptions, and their results are consistent with more formal analyses but remain approximate.<ref name="Q2246" /><ref name="Q2248" /> The ignition temperature is assumed constant for each material.<ref name="Q2250" /> Kanury stresses that the surface temperature at ignition is an effect rather than a cause, and that it depends on the conditions of the experiment.<ref name="K2242">Kanury (2002a), p. 2-242.</ref>		The formulas are heuristic. They come from energy balances with simple assumptions, and their results are consistent with more formal analyses but remain approximate.<ref name="Q2246" /><ref name="Q2248" /> The ignition temperature is assumed constant for each material.<ref name="Q2250" /> Kanury stresses that the surface temperature at ignition is an effect rather than a cause, and that it depends on the conditions of the experiment.<ref name="K2242">Kanury (2002a), p. 2-242.</ref>

	Computing the flame heat flux from first principles is a complex problem that has limited the ability to predict flame spread.<ref name="Q2247" /> ~~Data from the lateral test do not apply to~~ materials that melt and drip heavily. Some materials, such as fire-retardant plywood and polystyrene, gave no measurable spread at all.<ref name="Q2250" /><ref name="Q2251" />		Computing the flame heat flux from first principles is a complex problem that has limited the ability to predict flame spread.<ref name="Q2247" /> For materials that melt and drip heavily, results from the lateral test may not represent downward spread. Some materials, such as fire-retardant plywood and polystyrene, gave no measurable spread at all.<ref name="Q2250" /><ref name="Q2251" />

	Where conditions are simple, the theory performs well. For filter paper burning in microgravity at 50 % oxygen in still gas, a measured spread rate of 0.44 cm/s compared with a predicted 0.42 cm/s, once gas-phase radiation was included.<ref name="Q2256">Quintiere (2002b), p. 2-256.</ref> A complete numerical simulation by Di Blasi and co-workers, including solid- and gas-phase kinetics, reached qualitative success.<ref name="Q2250" />		Where conditions are simple, the theory performs well. For filter paper burning in microgravity at 50 % oxygen in still gas, a measured spread rate of 0.44 cm/s compared with a predicted 0.42 cm/s, once gas-phase radiation was included.<ref name="Q2256">Quintiere (2002b), p. 2-256.</ref> A complete numerical simulation by Di Blasi and co-workers, including solid- and gas-phase kinetics, reached qualitative success.<ref name="Q2250" />