Flame height - Revision history

Emma: Add 3 SVG illustrations from the level 3 Advanced visual plan

2026-11-02T06:29:35Z

Add 3 SVG illustrations from the level 3 Advanced visual plan

← Older revision		Revision as of 07:29, 2 November 2026
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	Intermittency describes the fraction of time that flame is present above a selected elevation. Within the lower flame, that fraction approaches unity. At sufficiently high elevations it approaches zero. The mean height corresponds to the intermediate value of 0.5, providing an operational definition that can be applied to observations over time.<ref name="H-1-2" />		Intermittency describes the fraction of time that flame is present above a selected elevation. Within the lower flame, that fraction approaches unity. At sufficiently high elevations it approaches zero. The mean height corresponds to the intermediate value of 0.5, providing an operational definition that can be applied to observations over time.<ref name="H-1-2" />
			[[File:fse-flame-height-v1.svg\|thumb\|upright=1.5\|alt=A changing flame outline is related to the height at which flame occurs half the time.\|Mean flame height is defined by an intermittency of 0.5. Based on Heskestad (2002), chapter 2-1, p. 2-2.]]

	The definition does not identify a rigid upper boundary to combustion. Flame tips can extend above the mean level, and the luminous region below it also changes. Visual estimates averaged by an observer tend to be slightly higher than measurements based on the stated intermittency criterion. Comparing reported heights therefore requires attention to how each measurement was obtained.<ref name="H-1-2" />		The definition does not identify a rigid upper boundary to combustion. Flame tips can extend above the mean level, and the luminous region below it also changes. Visual estimates averaged by an observer tend to be slightly higher than measurements based on the stated intermittency criterion. Comparing reported heights therefore requires attention to how each measurement was obtained.<ref name="H-1-2" />
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	The handbook example uses a circular methyl alcohol pool with a diameter of 1.5 m. Its heat release per burning area is 500 kW/m². The ambient temperature is 293 K, the air density is 1.20 kg/m³ and normal atmospheric pressure is assumed. These are stated conditions for an illustrative source, rather than a specification for all alcohol fires.<ref name="H-4" />		The handbook example uses a circular methyl alcohol pool with a diameter of 1.5 m. Its heat release per burning area is 500 kW/m². The ambient temperature is 293 K, the air density is 1.20 kg/m³ and normal atmospheric pressure is assumed. These are stated conditions for an illustrative source, rather than a specification for all alcohol fires.<ref name="H-4" />
			[[File:fse-flame-height-v2.svg\|thumb\|upright=1.5\|alt=A 1.5 m pool has a calculated mean flame height of 1.84 m above its fuel surface.\|The methyl alcohol example uses a fuel specific coefficient to calculate mean height. Based on Heskestad (2002), chapter 2-1, pp. 2-3–2-4.]]

	The circular area multiplied by the stated burning intensity gives a total heat release of 883.6 kW. The source uses a lower heat of combustion of 21,100 kJ/kg and an air to fuel ratio of 6.48. With a specific heat of 1.00 kJ/(kg·K) and gravity of 9.81 m/s², the coefficient is approximately 0.223.<ref name="H-4" />		The circular area multiplied by the stated burning intensity gives a total heat release of 883.6 kW. The source uses a lower heat of combustion of 21,100 kJ/kg and an air to fuel ratio of 6.48. With a specific heat of 1.00 kJ/(kg·K) and gravity of 9.81 m/s², the coefficient is approximately 0.223.<ref name="H-4" />
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	One handbook example considers wood pallets covering 1.07 m by 1.07 m and stacked 1.2 m high. Their total heat release is 2,600 kW. Converting the square footprint to an equivalent circular area gives a diameter of approximately 1.21 m. Using the representative coefficient gives a mean height of about 4.23 m above the base.<ref name="H-4" />		One handbook example considers wood pallets covering 1.07 m by 1.07 m and stacked 1.2 m high. Their total heat release is 2,600 kW. Converting the square footprint to an equivalent circular area gives a diameter of approximately 1.21 m. Using the representative coefficient gives a mean height of about 4.23 m above the base.<ref name="H-4" />
			[[File:fse-flame-height-v3.svg\|thumb\|upright=1.5\|alt=Flame height is 4.23 m above the pallet base and 3.03 m above the 1.2 m stack.\|The pallet example measures flame height from the base of the storage. Based on Heskestad (2002), chapter 2-1, p. 2-4.]]

	Subtracting the stack height gives approximately 3.03 m above its top. This subtraction changes the reference level; it does not predict a second flame. The distinction matters when comparing the result with a ceiling, beam or detector elevation. Both dimensions must first be expressed relative to the same physical level.<ref name="H-4" />		Subtracting the stack height gives approximately 3.03 m above its top. This subtraction changes the reference level; it does not predict a second flame. The distinction matters when comparing the result with a ceiling, beam or detector elevation. Both dimensions must first be expressed relative to the same physical level.<ref name="H-4" />

Peter: New FSE wiki article: Flame height (written by GPT-6)

2026-11-01T22:20:16Z

New FSE wiki article: Flame height (written by GPT-6)

New page

'''Flame height''' is the vertical extent of the visible flaming region above a fire source. Because turbulent flames fluctuate, engineering correlations generally predict a mean height rather than the highest instantaneous tip. Heskestad defines the mean flame height as the level above which visible flame is present for half the observation time. This statistical definition separates a useful average dimension from the changing outline of the flame.<ref name="H-1-2">Heskestad (2002), chapter 2-1, pp. 2-1–2-2.</ref>

The mean height helps identify the transition between active combustion and the hot gas flow above it. It is used in calculations of plume behaviour, heating of structures and radiation to nearby objects. Fire power, source dimensions, fuel characteristics and surrounding conditions can all affect the result.<ref name="H-2-4">Heskestad (2002), chapter 2-1, pp. 2-2–2-4.</ref> A calculated height therefore has meaning only with its source geometry, reference level and correlation assumptions. In particular, a free burning pool, a fire beside a wall and a pressurised gas flame do not necessarily share the same height relationship.<ref name="N-19">Iqbal and Salley (2004), p. 3-19.</ref>

== Mean height and flame intermittency ==

A [[Diffusion flame|diffusion flame]] forms where combustible gases mix with surrounding oxidising air. The lower visible region can appear comparatively continuous, while the upper region repeatedly appears and disappears. The flame tip moves as mixing and combustion fluctuate. A single photograph therefore records one state within that changing behaviour, rather than directly measuring the mean flame height.<ref name="H-1-2" />

Intermittency describes the fraction of time that flame is present above a selected elevation. Within the lower flame, that fraction approaches unity. At sufficiently high elevations it approaches zero. The mean height corresponds to the intermediate value of 0.5, providing an operational definition that can be applied to observations over time.<ref name="H-1-2" />

The definition does not identify a rigid upper boundary to combustion. Flame tips can extend above the mean level, and the luminous region below it also changes. Visual estimates averaged by an observer tend to be slightly higher than measurements based on the stated intermittency criterion. Comparing reported heights therefore requires attention to how each measurement was obtained.<ref name="H-1-2" />

Nor does the mean flame height mark the end of the [[Fire plume|fire plume]]. Hot combustion products and entrained air continue to rise beyond the visible flames. Their temperature and velocity change with height as further surrounding air enters. Objects above the flame can consequently experience hot gas exposure even when direct flame contact is intermittent or absent.<ref name="H-1-2" /><ref name="N-16">Iqbal and Salley (2004), p. 3-16.</ref>

Temperature and velocity do not reach their maxima at identical positions within the flame. Heskestad describes a nearly constant centreline temperature in the lower part of a relatively tall flame. Temperatures then decrease through its intermittent upper portion as reactions diminish and entrained air cools the flow. The centreline velocity generally reaches its maximum slightly below the mean flame height.<ref name="H-1-2" />

This profile explains why a geometric flame boundary is insufficient to specify a complete exposure. An object can move between regions with different fluctuations and gas velocities even within the visible flame. The average height remains useful as a reference for those regions. It does not replace the separate temperature and heat transfer information needed for a thermal assessment.<ref name="H-1-2" /><ref name="N-16" />

== What controls the height ==

For buoyant fires, the balance between fuel release and mixing with air influences how far combustion extends above the source. Increasing the total [[Heat release rate|heat release rate]] tends to increase the height predicted by the common Heskestad correlation. Increasing source diameter at unchanged heat release changes that relationship. A broad fire and a compact fire can therefore have different mean heights despite producing equal power.<ref name="H-3">Heskestad (2002), chapter 2-1, p. 2-3.</ref>

The [[Dimensionless heat release rate|dimensionless heat release rate]] combines fire power with source size and ambient properties for comparison between fires. Heskestad discusses this scaling alongside a parameter that explicitly includes fuel characteristics. Such comparisons help organise experimental observations across different source sizes. They do not remove the distinction between a buoyant fire and a flame dominated by release momentum.<ref name="H-2-4" />

Fuel properties enter through the relationship between released heat and the air required for combustion. Heskestad gives a representative coefficient for many fuels under normal atmospheric conditions, together with exceptions. A coefficient suitable for a general estimate is therefore not an exact universal material constant. Known fuel properties can justify a different value within the same dimensional relationship.<ref name="H-3" />

Atmospheric conditions also influence the calculation. The chapter presents a methyl alcohol example under normal conditions and then recalculates it for lower pressure and higher ambient temperature. The resulting flame height increases even though the source geometry and burning intensity are retained. This illustrates why a numerical coefficient carries assumptions about the surrounding atmosphere.<ref name="H-4">Heskestad (2002), chapter 2-1, p. 2-4.</ref>

The handbook gives a heat release per unit mass of reacting air between 2,900 and 3,200 kJ/kg for many gaseous and liquid fuels. Under normal conditions, that range corresponds to coefficients between 0.240 and 0.226. The limited variation helps explain why a representative coefficient can be useful. It does not mean that fuel identity has disappeared from the underlying physical relationship.<ref name="H-3" />

Examples outside that representative range include hydrogen and gasoline, for which the chapter lists coefficients of 0.211 and 0.200 respectively. These values refer to the coefficient in the stated correlation, with its dimensional units and source assumptions. They are not measured flame heights or radiative fractions. Their use still requires a compatible heat release rate and source diameter.<ref name="H-3" />

== The Heskestad height correlation ==

For a buoyancy dominated source, the correlation subtracts a diameter term from a power dependent term. With a representative coefficient under normal atmospheric conditions, it takes the following form. Heat release must be supplied in kilowatts, and both the diameter and calculated height are in metres.<ref name="H-3" />

<div class="fse-equation">L = 0.235 Q̇<sup>2/5</sup> − 1.02 D</div>

For a noncircular source, Heskestad defines an equivalent diameter from a circle with the same burning area. This definition preserves area in the height calculation. It does not preserve the actual perimeter of an elongated source, which may matter in other plume relationships.<ref name="H-3" />

<div class="fse-equation">D = √(4 A<sub>f</sub>/π)</div>

The more general dimensional form replaces 0.235 with a coefficient determined from fuel and environmental properties. Heskestad expresses that coefficient using the actual heat of combustion and air requirement. This form explains the origin of the representative coefficient and supports the methyl alcohol example below.<ref name="H-3" />

<div class="fse-equation">L = a Q̇<sup>2/5</sup> − 1.02 D</div>
<div class="fse-equation">a = 15.6 [c<sub>p</sub>T<sub>∞</sub> / {gρ<sub>∞</sub><sup>2</sup>(H<sub>c</sub>/r)<sup>3</sup>}]<sup>1/5</sup></div>

{| class="wikitable"
! Symbol !! Description !! Unit
|-
| L || Mean flame height above the defined source level || m
|-
| Q̇ || Actual total heat release rate || kW
|-
| D || Source diameter or equivalent area diameter || m
|-
| A<sub>f</sub> || Burning area || m²
|-
| a || Dimensional flame height coefficient || m·kW<sup>−2/5</sup>
|-
| c<sub>p</sub> || Specific heat of ambient air || kJ/(kg·K)
|-
| T<sub>∞</sub> || Ambient absolute temperature || K
|-
| ρ<sub>∞</sub> || Ambient air density || kg/m³
|-
| g || Acceleration of gravity || m/s²
|-
| H<sub>c</sub> || Actual lower heat of combustion || kJ/kg
|-
| r || Actual stoichiometric air to fuel mass ratio || kg/kg
|}

The heat release input concerns energy actually released, rather than an assumed complete combustion potential. Heskestad distinguishes actual heat release from the theoretical value obtained using complete combustion. For some fuels these are close; for others the difference is substantial. Substituting inconsistent fuel and heat release information can therefore undermine an otherwise correct numerical calculation.<ref name="H-1-2" />

== A methyl alcohol pool example ==

The handbook example uses a circular methyl alcohol pool with a diameter of 1.5 m. Its heat release per burning area is 500 kW/m². The ambient temperature is 293 K, the air density is 1.20 kg/m³ and normal atmospheric pressure is assumed. These are stated conditions for an illustrative source, rather than a specification for all alcohol fires.<ref name="H-4" />

The circular area multiplied by the stated burning intensity gives a total heat release of 883.6 kW. The source uses a lower heat of combustion of 21,100 kJ/kg and an air to fuel ratio of 6.48. With a specific heat of 1.00 kJ/(kg·K) and gravity of 9.81 m/s², the coefficient is approximately 0.223.<ref name="H-4" />

Using the unrounded coefficient and heat release gives a mean flame height of 1.838 m, or about 1.84 m. The handbook prints approximately 1.83 m using its rounded intermediate values. The small numerical difference follows from rounding, rather than a change in the physical model. Both results describe the same example under the specified conditions.<ref name="H-4" />

Using the representative coefficient of 0.235 instead gives about 2.01 m for the same source. This comparison shows the effect of retaining the general coefficient when fuel information is available. It does not establish an experimental error band or a probability distribution. The two values are outputs from alternative coefficient choices within the published relationship.<ref name="H-3" /><ref name="H-4" />

The predicted height is above the fuel surface. It represents the mean luminous extent, so an object at that elevation would not experience a perfectly steady boundary between flame and clear air. Its thermal exposure would depend on fluctuating gases, radiation and duration. Flame height alone therefore does not determine the object's temperature or ignition time.<ref name="N-16" />

== Source levels and stacked fuels ==

A reference level becomes especially important when fuel occupies a substantial height. Heskestad reports that the correlation can represent certain deep storage fires when flames extend above the storage. For these cases, the height is measured from the base of the fire. Treating the result as a distance above the top would overstate the total vertical extent.<ref name="H-3" />

One handbook example considers wood pallets covering 1.07 m by 1.07 m and stacked 1.2 m high. Their total heat release is 2,600 kW. Converting the square footprint to an equivalent circular area gives a diameter of approximately 1.21 m. Using the representative coefficient gives a mean height of about 4.23 m above the base.<ref name="H-4" />

Subtracting the stack height gives approximately 3.03 m above its top. This subtraction changes the reference level; it does not predict a second flame. The distinction matters when comparing the result with a ceiling, beam or detector elevation. Both dimensions must first be expressed relative to the same physical level.<ref name="H-4" />

The [[Virtual origin|virtual origin]] used in a plume model is another height, with a different meaning. It represents an equivalent source position for the gas flow above the flames. It can be calculated from mean flame height and convective heat release for appropriate storage configurations. It is neither the top of the fuel nor the highest visible flame tip.<ref name="H-9-10">Heskestad (2002), chapter 2-1, pp. 2-9–2-10.</ref>

== Engineering uses ==

The [[Heskestad plume]] method uses the mean flame height to distinguish calculation regions. Relations for temperature and velocity above the flames cease to apply when extended into the reacting region. Entrainment within flames also follows different behaviour from entrainment farther above them. Establishing the flame height therefore precedes selecting the relevant plume relationship.<ref name="H-6-12">Heskestad (2002), chapter 2-1, pp. 2-6–2-12.</ref>

Van Rossum also uses the relationship between mean flame length and fire diameter when discussing plume model selection. Relatively short flames over a broad source favour the Thomas representation in the described approach. Taller flames favour the Heskestad representation. This is a rough selection method described through the introductory text, rather than a universal boundary between physical fire types.<ref name="VR-6.7">Van Rossum (2027), §6.7.</ref>

Flame height helps describe the extent of heating during [[Upward flame spread|upward flame spread]] along a surface. The US nuclear inspection guidance discusses flame contact with walls and the associated distribution of heat transfer. It treats wall, line and corner configurations separately from an unobstructed pool. These distinctions matter when the receiving surface also becomes involved in combustion.<ref name="N-4">Iqbal and Salley (2004), pp. 4-1–4-5.</ref>

For nearby targets, flame dimensions can inform radiation geometry and the possibility of direct flame exposure. However, the target does not instantly acquire the flame temperature. Its heating depends on the heat transfer and its own thermal properties over time. The US guidance explicitly separates the flame's thermal state from the temperature reached by an exposed object.<ref name="N-16" />

== Limits and uncertainty ==

The representative correlation can return a negative height at sufficiently low heat release relative to source diameter. Heskestad identifies that result as unphysical and outside the correlation's validity. It must not be interpreted as a real flame below the surface. Such conditions may involve a breakdown of a single flaming area into separate burning regions.<ref name="H-3" /><ref name="H-4" />

High momentum releases also require separate treatment. A pressurised gas jet carries momentum from its source, in addition to buoyancy generated by combustion. Heskestad distinguishes this regime from the buoyancy controlled relationship. Extending the simple power law into every jet fire would ignore that physical distinction.<ref name="H-2-4" />

Wind can bend flames away from the vertical and alter their observed dimensions. The chapter discusses flame deflection and trailing in wind experiments. A vertical flame height and a distance measured along an inclined flame are consequently different geometric quantities. The still air correlation does not by itself establish the target exposure in a wind affected arrangement.<ref name="H-15">Heskestad (2002), chapter 2-1, p. 2-15.</ref>

Finally, a calculated mean height retains uncertainty in fire power, burning area and the selected model. The US guidance presents its pool calculations as idealised scenarios with defined assumptions, including a circular or nearly circular burning area. Wall and corner cases require corresponding configurations. Agreement in arithmetic cannot compensate for a source geometry that the selected correlation does not represent.<ref name="N-19" /><ref name="N-4" />

== See also ==
* [[Flame]]

== Notes ==
<references />

== References ==
* Heskestad, G. (2002). Fire plumes, flame height, and air entrainment. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 2-1–2-17). National Fire Protection Association.
* 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.
* Van Rossum, E. (2027). ''Introduction to Fire Safety Engineering''. Fire Safety Academy.

[[Category:Fire Dynamics]]