View source for Critical heat flux for ignition

'''Critical heat flux for ignition''' is the threshold heating intensity associated with forming an ignitable mixture above a heated material under specified conditions. Tewarson's SFPE treatment relates this threshold to the generation of combustible vapours from the exposed surface. Below the threshold, the represented heating cannot produce the mixture required for flaming [[Ignition|ignition]].<ref name="T-82">Tewarson (2002), chapter 3-4, p. 3-82.</ref>

The quantity is expressed as power per unit area, commonly kilowatts per square metre. It describes a threshold in [[Heat flux|heat flux]], rather than a temperature or a fixed ignition delay. A material exposed above that threshold still requires time to heat and generate the combustible mixture.<ref name="IS-64">Iqbal and Salley (2004), pp. 6-4–6-5.</ref>

An experimentally fitted critical heat flux is also a model parameter. NUREG-1805 distinguishes this extrapolated value from the minimum flux permitting ignition under practical test conditions. Its numerical value therefore belongs with the correlation, specimen and exposure conditions used to obtain it.<ref name="IS-65">Iqbal and Salley (2004), p. 6-5.</ref>

== Why a threshold exists ==

External heating supplies energy to a solid surface. Part of this energy moves into the material, while part returns to the surroundings through convection and radiation. The surface temperature follows the balance between these processes. Reaching conditions that generate enough combustible vapour requires sufficient heating as well as a suitable surrounding atmosphere.<ref name="IS-64" /><ref name="K-230">Kanury (2002), chapter 2-11, p. 2-230.</ref>

In the simplified steady-state account in NUREG-1805, incident heating is balanced by convection and radiation losses. The surface then ceases to become hotter. The threshold corresponds to heating sufficient to maintain the surface at the ignition condition. Increasing exposure duration cannot overcome an equilibrium temperature that remains below that condition within the model.<ref name="IS-64" />

The route to that equilibrium is a separate question. Conductivity, density and specific heat influence how quickly the surface temperature changes. A material can therefore have a particular threshold but respond slowly when exposed above it. Another material with a similar threshold can respond more quickly because its transient heating behaviour differs.<ref name="IS-64" />

Flaming ignition also requires a combustible gas mixture above the surface. Heating can decompose a solid and release vapours without immediately establishing a flame. Kanury separates the solid's thermal response, mixing with air and the gas-phase chemical reaction. This separation explains why a surface energy balance alone does not describe every ignition situation.<ref name="K-230" />

For piloted ignition, a small flame or spark initiates combustion in the prepared gas mixture. Without that pilot, the mixture must reach conditions allowing autoignition. The same target can consequently have different ignition behaviour under these two arrangements. A reported critical flux is incomplete if the ignition mode is not identified.<ref name="K-230" /><ref name="IS-62">Iqbal and Salley (2004), pp. 6-1–6-2.</ref>

== Practical minimum and fitted critical value ==

A practical ignition limit concerns what happens in an experiment under its stated conditions. A specimen is heated at a chosen intensity, and ignition is observed or not observed during the exposure. The result is tied to that specimen, the apparatus and the observation period. It is not an observation over unlimited time.<ref name="T-83">Tewarson (2002), chapter 3-4, pp. 3-83–3-84.</ref>

Tewarson describes a screening procedure using horizontal specimens exposed to several external heat fluxes. In that procedure, a flux is sought at which ignition does not occur for about 15 minutes. The description includes blackened specimen surfaces to control radiation absorption. This is a stated experimental procedure, rather than a universal definition of permanent non-ignition.<ref name="T-83" />

A fitted critical flux is obtained differently. Ignition times measured above the threshold are transformed and correlated against the applied flux. The fitted relation is extended to the condition corresponding to an indefinitely long ignition time. Its intercept provides an estimate of the critical flux within that mathematical description.<ref name="IS-65" />

NUREG-1805 explicitly distinguishes the practical minimum from this extrapolated estimate. Different correlations can represent the same experimental behaviour through different fitted parameters. The estimated threshold is therefore partly dependent on the selected model. Calling it a material property does not remove the need to specify how it was determined.<ref name="IS-65" /><ref name="IS-67">Iqbal and Salley (2004), p. 6-7.</ref>

The distinction becomes especially relevant near the threshold. Small changes in the difference between applied and critical flux can produce large changes in the predicted delay. A fitted curve may describe the tested region without establishing an exact boundary for every longer exposure. The source consequently describes fitting ignition data away from the critical value.<ref name="T-83" /><ref name="IS-65" />

== Relating flux to ignition time ==

NUREG-1805 presents a correlation for thermally thick materials under constant external radiant heating. It connects the [[Time to ignition|time to ignition]] to the excess of applied flux over the critical value. A thermal response parameter represents the material's resistance to the transient heating process. The equation below follows the report's particular parameter convention.<ref name="IS-65" />

<div class="fse-equation">t<sub>ig</sub> = (π / 4) [TRP / (q″<sub>e</sub> − CHF)]², for q″<sub>e</sub> &gt; CHF</div>

{| class="wikitable"
! Symbol !! Description !! Unit
|-
| t<sub>ig</sub> || Predicted ignition time || s
|-
| q″<sub>e</sub> || Constant external radiant heat flux || kW/m²
|-
| CHF || Critical heat flux in the selected correlation || kW/m²
|-
| TRP || Thermal response parameter in the NUREG-1805 convention || kW·s<sup>1/2</sup>/m²
|}

The denominator is the applied flux minus the critical flux. It measures how far the imposed exposure lies above the model's threshold. A larger excess produces a shorter calculated delay when the response parameter remains fixed. Doubling that excess reduces the predicted time by a factor of four because the ratio is squared.<ref name="IS-65" />

The report relates its thermal response parameter to the temperature rise needed for ignition and the square root of [[Thermal inertia|thermal inertia]]. Here thermal inertia means the product of conductivity, density and specific heat. The response parameter therefore combines an ignition-temperature condition with the material's ability to absorb heat during the transient period.<ref name="IS-64" />

The following expression makes that combination explicit in the NUREG convention. The temperature difference is the ignition temperature minus the ambient temperature. Conductivity and specific heat use the report's kilowatt and kilojoule units, respectively. This produces the response-parameter unit used in the ignition correlation and its accompanying table.<ref name="IS-64" />

<div class="fse-equation">TRP = (T<sub>ig</sub> − T<sub>a</sub>) √(kρc)</div>

{| class="wikitable"
! Symbol !! Description !! Unit
|-
| T<sub>ig</sub> − T<sub>a</sub> || Ignition temperature rise above ambient || K
|-
| k || Thermal conductivity || kW/(m·K)
|-
| ρ || Density || kg/m³
|-
| c || Specific heat capacity || kJ/(kg·K)
|}

This expression helps distinguish threshold behaviour from the speed of heating. The temperature rise describes a condition that the exposed solid must reach in the simplified model. The property product describes how heat is distributed and stored during that approach. Neither part alone supplies the complete response parameter, and neither replaces the critical flux in the denominator.<ref name="IS-64" />

The treatment of material thickness also belongs with the correlation. NUREG-1805 identifies weight or thickness as significant for thin specimens, whereas its displayed correlation concerns thermally thick behaviour. A thin specimen cannot be assigned the thick-material response solely because both specimens have the same chemical name. Their different thermal response can require another representation.<ref name="IS-65" />

The same correlation can be rearranged into a straight-line form. Plotting the inverse square root of ignition time against external flux gives an intercept at CHF. In the NUREG convention, the slope also contains the factor √(4/π). This explains why both the slope and the intercept have a role in interpreting the experiment.<ref name="IS-65" />

<div class="fse-equation">1 / √t<sub>ig</sub> = √(4 / π) (q″<sub>e</sub> − CHF) / TRP</div>

Parameter conventions require attention because the SFPE chapter places a numerical factor inside its definition of TRP. Its printed equation therefore has a different appearance from the NUREG equation above. Values and equations must remain within a consistent convention. The worked example here uses the NUREG equation and its accompanying table together.<ref name="T-83" /><ref name="IS-64" />

== Worked example using red oak data ==

NUREG-1805 lists red oak with CHF = 10 kW/m² and TRP = 134 kW·s<sup>1/2</sup>/m². These are the tabulated values for the reported material, rather than universal values for every oak product. Consider an illustrative constant exposure of 20 kW/m². The imposed flux then exceeds the tabulated critical flux by 10 kW/m².<ref name="IS-66">Iqbal and Salley (2004), p. 6-6, Table 6-3.</ref><ref name="IS-65" />

Substituting those inputs into the NUREG correlation gives the calculation below. The unrounded result is about 141.026 seconds, or 141 seconds when rounded down. This is a calculated illustration of the model. It is not an additional ignition test or a prediction for an unspecified installed timber assembly.<ref name="IS-65" /><ref name="IS-66" />

<div class="fse-equation">t<sub>ig</sub> = (π / 4) [134 / (20 − 10)]² ≈ 141 s</div>

Now retain the same material parameters but select an exposure of 30 kW/m². The excess above the threshold becomes 20 kW/m², twice its previous value. The model then gives about 35.2565 seconds, reported as 35.2 seconds when rounded down. This is one quarter of the unrounded time at the lower exposure.<ref name="IS-65" /><ref name="IS-66" />

<div class="fse-equation">t<sub>ig</sub> = (π / 4) [134 / (30 − 10)]² ≈ 35.2 s</div>

The comparison concerns excess flux, rather than a simple ratio of total incident fluxes. Increasing the exposure from 20 to 30 kW/m² increases the total flux by half. It nevertheless doubles the amount above the 10 kW/m² threshold. The nonlinear time response follows directly from this difference in the denominator.<ref name="IS-65" /><ref name="IS-66" />

The equation does not provide a valid finite ignition time at or below CHF. At the threshold, its denominator tends to zero. Below the threshold, blindly squaring the negative difference would produce a positive number without a valid physical interpretation in this model. The correlation's stated heating regime remains part of the calculation.<ref name="IS-64" /><ref name="IS-65" />

== What tests and tabulated values represent ==

The [[Cone calorimeter|cone calorimeter]] and the fire propagation apparatus can both provide ignition observations under controlled heating. Tewarson describes their use in deriving ignition parameters and compares their test arrangements. The SFPE discussion refers to historical test editions, including ASTM E1354-90 for the cone calorimeter. It does not establish the requirements of a later edition.<ref name="T-85">Tewarson (2002), chapter 3-4, pp. 3-84–3-85.</ref>

The apparatus comparison also identifies differences in the ignition source and specimen arrangement. The listed cone calorimeter uses a spark igniter, while the listed fire propagation apparatus uses a pilot flame. Their horizontal specimen dimensions are both listed as 100 mm by 100 mm. Similar dimensions therefore do not establish that the complete exposure and ignition arrangements are identical.<ref name="T-85" />

The reported measurements include ignition time as well as quantities associated with subsequent burning. An ignition observation establishes when the specified event begins under that exposure. Heat release and material gasification measurements describe other aspects of the specimen's fire behaviour. A single critical-flux value consequently does not replace the other measurements obtained from the apparatus.<ref name="T-85" />

Surface treatment can change the measured response. Tewarson reports thermal response parameters of 274 and 383 kW·s<sup>1/2</sup>/m² for blackened and non-blackened polymethylmethacrylate surfaces, respectively. The chapter relates the difference to radiation absorption. These values illustrate why apparently similar material names do not guarantee interchangeable ignition parameters.<ref name="T-83" />

The NUREG table also separates threshold and response behaviour. Its ordinary Douglas fir and fire-retardant Douglas fir entries both have CHF = 10 kW/m². Their listed response parameters are 138 and 251 kW·s<sup>1/2</sup>/m², respectively. Equal critical fluxes therefore do not imply equal calculated ignition times under the same exposure.<ref name="IS-66" />

Other entries demonstrate the range within the particular data collection. The report lists polypropylene at 15 kW/m² and polymethylmethacrylate at 11 kW/m². Polycarbonate is listed at 15 kW/m², while a separate polycarbonate-panel entry has 16 kW/m². These historical entries describe their source specimens and do not classify all products made from those polymers.<ref name="IS-66" />

The response parameter and threshold also depend on how the ignition observations are correlated. NUREG-1805 discusses several methods with their own associated parameter sets. A coefficient fitted for one method is not automatically a physical constant suitable for another. Retaining the original method and its data preserves the meaning of the calculated result.<ref name="IS-67" />

== Engineering use and limits ==

Critical flux supports assessment of whether a heated target can reach an ignition condition within a represented scenario. NUREG-1805 discusses this as part of predicting secondary ignition and subsequent fire development. The report was prepared for the United States Nuclear Regulatory Commission's nuclear power plant fire protection inspection programme. Its data and methods are not universal regulatory acceptance limits.<ref name="IS-61">Iqbal and Salley (2004), title page and p. 6-1.</ref>

The constant-flux, thermally thick correlation addresses a particular heating problem. Changes in thickness, exposure history and gas conditions can require a different treatment. Kanury also distinguishes a transient flame from flaming that persists after external heating is removed. A threshold for one observed event cannot automatically establish the conditions for the other.<ref name="IS-65" /><ref name="K-230" />

Gas conditions can limit flaming even when a solid becomes hot and decomposes. Kanury describes hot, oxygen-depleted gases that can produce pyrolytic damage without ignition. The heating intensity alone does not describe that situation. The surrounding oxygen supply and the gas-phase reaction remain relevant alongside the solid's thermal response.<ref name="K-239">Kanury (2002), chapter 2-11, p. 2-239.</ref>

Ignition temperature is likewise not an invariant substitute for a flux threshold. NUREG-1805 notes that this temperature can vary with the heating rate. It also explains why a decomposing solid does not have a unique bulk flash point equivalent to that of a liquid. The surface, released vapours and applied heating history must remain distinguishable in interpreting the result.<ref name="IS-62" />

More detailed ignition treatments also associate threshold behaviour with target dimensions and gas-phase chemistry. Kanury discusses effects of slab height and thickness, reaction kinetics and radiation losses. Those dependencies limit the interpretation of a single threshold detached from its test arrangement. They also explain why a fitted critical value should retain its source and stated conditions.<ref name="K-240">Kanury (2002), chapter 2-11, p. 2-240.</ref>

== See also ==
* [[Autoignition temperature]]

== 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.
* Kanury, A. M. (2002). Flaming ignition of solid fuels. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., chapter 2-11). National Fire Protection Association.
* Tewarson, A. (2002). Generation of heat and chemical compounds in fires. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., chapter 3-4, pp. 3-82–3-161). National Fire Protection Association.

[[Category:Ignition & Flame Spread]]