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Smoke filling is the accumulation of smoke within an enclosure as a fire supplies heated combustion products and entrained air faster than they are removed. In a stratified enclosure, this accumulation forms and deepens an upper smoke layer, lowering its interface with the cooler gas below. The process depends on plume flow, gas temperature, enclosure geometry and ventilation, rather than the mass of combustion products alone.[1]
Smoke-filling calculations estimate how conditions change before or during operation of a smoke-management system. The predicted interface height is useful for assessing exposure, but it does not describe every hazard. Temperature, visibility and gas composition may also matter. Empirical correlations and zone models can predict different interface positions because they represent different definitions and assumptions about layer formation, mixing and the time required for smoke to reach the enclosure boundaries.[2]
Formation and descent of the upper layer
A fire plume carries hot gases upward from the burning fuel. Surrounding air enters the plume as it rises, increasing the mass flow and diluting the combustion products. When the rising flow reaches a ceiling, it spreads horizontally. A hot gas layer develops as this flow reaches the enclosure boundaries and accumulates beneath the ceiling.[3]
The accumulated mixture includes a substantial quantity of air. Entrainment therefore increases the amount of gas entering the upper layer while reducing its temperature and combustion-product concentrations. A calculation based only on fuel mass or soot production would omit most of the mixture responsible for layer growth. Smoke production in this context concerns the complete moving gas mixture.[4]
As the layer descends, the plume travels a shorter distance through the lower zone before entering it. The mass entering the layer consequently changes even if the fire's heat release remains steady. Milke relates the rapid initial descent of a layer in a tall space to the substantial entrainment over the initially long plume height. The descent subsequently slows as the clear height decreases.[5]
Layer depth is linked to the available enclosure volume. For a space with constant horizontal area, an added layer volume produces a corresponding change in interface height. In an enclosure whose area changes with height, that relationship is different at different elevations. A correlation developed for a uniform cross-section therefore cannot be applied unchanged merely because the total volume is similar.[6]
The calculation datum also matters. Milke defines plume clear height and ceiling height relative to the top of the fuel surface. A fire on an elevated platform has a different plume travel distance from a floor-level source beneath the same roof. Height inputs must follow the convention of the selected correlation rather than being taken automatically from the building's floor-to-ceiling dimension.[7]
Transport delay and interface definitions
Layer formation is not instantaneous in every enclosure. Smoke first rises to the ceiling and then spreads towards the bounding walls. Milke calls these intervals plume transport lag and ceiling-jet transport lag. They can be short in a small, low room but significant in a tall space with a large horizontal extent. Neglecting them can change the early part of a predicted smoke-filling history.[8]
Fire growth affects that transport. A small initial fire produces different velocities and temperatures from a steady fire at its eventual peak power. The chapter therefore distinguishes transport correlations for steady fires from those for growing fires. Treating the final heat release as present from ignition can obscure the period before the plume and ceiling flow establish an upper layer.[8]
Empirical and theoretical interface definitions also differ. In the experiments underlying the empirical correlations, smoke arrival was identified through observations or changes in measured temperature, gas concentration or optical density. A two-zone calculation instead divides the enclosure into idealised upper and lower zones. Its interface is the boundary between those uniform regions, rather than necessarily the first detectable trace of smoke.[9]
These definitions can lead to different reported heights for the same developing environment. The distinction should remain visible when comparing experimental data with a zone model. A disagreement does not automatically indicate an arithmetic error. It may reflect transport delay, the selected definition or the representation of the gradual transition between smoky and relatively clear gases.[9]
An empirical expression may yield a normalised interface height greater than one at an early time. That value is not a physical layer located above the ceiling. It indicates the initial period before the correlation predicts a descending layer within the enclosure. The result should be interpreted accordingly, rather than plotted as smoke occupying space above the roof.[10]
Mass, energy and volume balances
The upper-layer mass changes through plume inflow and through any flows entering or leaving the layer at openings. With no exhaust, the rate of mass accumulation equals the incoming plume mass flow in the simplified balance. When extraction operates, its mass flow must be subtracted. This accounting concerns mass, which remains conserved even while the gas heats, cools or expands.[11]
An energy balance determines the thermal state of the accumulated gas. Convective energy arrives from the fire, while heat transfers to the enclosure boundaries and energy leaves with outgoing gases. The density then depends on the resulting temperature. Van Rossum explains the sequence from layer mass and energy to temperature, density and volume, before converting volume into layer thickness.[12]
This sequence prevents a common confusion between mass flow and volume flow. The same mass of hot gas occupies more volume than cooler gas under comparable pressure. Layer descent can therefore reflect thermal expansion as well as incoming mass. Cooling reduces that expansion, but its effects on stratification and mixing may require more than a simple density correction.[11][13]
A Heskestad plume relation can provide the mass flow reaching the layer interface when its assumptions apply. The relevant height is the distance from the source to that interface. Continuing to calculate entrainment up to the ceiling after a deep layer has formed would use the wrong available height for the lower-zone plume. The plume relation and layer calculation must therefore be updated consistently.[14]
A stationary layer is a possible later outcome when inflow and effective removal balance under suitable thermal conditions. It is not the assumption underlying an unvented filling calculation. Conversely, merely specifying an exhaust volume does not show that its mass removal balances the plume supply. The operating gas density and the layer actually feeding the outlet affect that comparison.[12][15]
Empirical filling correlations
Milke presents correlations for steady fires and fires with quadratic growth in large enclosures. They describe a central fire away from walls, a constant horizontal cross-sectional area and filling without smoke extraction. Wind, stack effects and interacting ventilation systems are excluded from the simplified representation. The supporting experiments cover enclosure shape factors A/H² between 0.9 and 14.[10]
For a steady fire, the normalised layer height is expressed as follows. The logarithm is natural, and the numerical coefficient requires the stated metre, second and kilowatt units.[16]
For the growing-fire case, the corresponding expression uses the specified growth time tg. The growth-time convention must match the fire curve used with the source correlation.[17]
| Symbol | Meaning | Unit |
|---|---|---|
| z | Height of the smoke interface above the fuel datum | m |
| H | Ceiling height above the same datum | m |
| A | Constant horizontal cross-sectional area | m² |
| t | Time from ignition | s |
| Q̇ | Total heat release rate for the steady fire | kW |
| tg | Growth time defining the quadratic fire curve | s |
The steady correlation uses total heat release, whereas a plume mass-flow expression may use only its convective portion. These inputs should not be interchanged simply because both are expressed in kilowatts. Milke explicitly distinguishes them when deriving the theoretical filling approximation. A consistent calculation identifies where the convective fraction has already been included in a correlation coefficient.[18]
The lower stated limit is z/H = 0.2. That limit reflects the experimental range and does not authorise continuation of the curve down to the floor. The interface correlation also does not provide temperature, optical density or toxic-gas concentration. Those outputs need additional calculations or a model that tracks them. A single height curve must therefore be used within its defined purpose.[10][2]
The correlations include the initial delay implicitly through their early-time behaviour. A theoretical filling model may instead start with a layer at the ceiling at ignition and add transport lag separately. Combining an empirical expression with an additional arbitrary delay can count the same effect twice. Comparisons should establish how each method handles formation before interpreting differences in predicted height.[8][18]
Worked example for a growing fire
The SFPE example uses an atrium with a horizontal area of 800 m² and a height of 20 m above the fire datum. The selected fast quadratic fire has a growth time of 150 s. Its enclosure shape factor is 2.0, within the stated range of the correlation. The example concerns the filling period before smoke exhaust operates.[19]
At 120 s, substitution into the growing-fire expression gives z/H = 0.9494. The interface height is therefore approximately 18.99 m, leaving a relatively shallow upper layer. At 140 s, the calculated height is approximately 15.18 m. Solving the same expression for an interface height of 15.00 m gives 141.19 s, consistent with the source's rounded result of about 140 s.[19]
The sharp early descent is a result of the chosen correlation and geometry. It does not mean that a deep layer existed from ignition. The calculated ratio exceeds one at sufficiently early times, representing the formation delay. For these inputs, the ratio first reaches one at approximately 115.8 s. That value is a calculated feature of the expression rather than a measured arrival time in a real atrium.[10][19]
Continuing the calculation gives interface heights of approximately 10.55 m at 180 s and 6.95 m at 240 s. These remain above the lower validity boundary of 4 m for this 20 m enclosure. The calculation reaches that boundary at approximately 351.3 s. Results below it would extend beyond the stated experimental range and are not justified by the correlation alone.[10][17]
The example separates three quantities that can otherwise be confused: the interface height, the time since ignition and the duration after layer formation. Reporting only the height without the fire-growth definition would make the result difficult to reproduce. Reporting the calculated early-time values as physical heights above the ceiling would misrepresent the model. The interpretation is as important as the numerical substitution.[8][19]
Use in a fire-safety assessment
Layer descent can contribute to estimating available safe egress time, but the interface is only one description of the environment. Milke identifies temperature, toxic-gas exposure and reduced visibility as additional hazards. Van Rossum similarly treats layer height, temperature and optical density as distinct model outputs. The selected acceptance condition should identify which exposure is being assessed and at what location.[20]
An interface-only criterion may treat any immersion in smoke as unacceptable. That can be useful for a stated assessment, but it does not mean that every smoke layer has identical physiological effects. Conversely, a layer remaining above occupants does not by itself eliminate radiant exposure from hot gases. The height history must be interpreted alongside the thermal and smoke conditions relevant to the scenario.[20]
A filling result can also be used to examine the interval before an exhaust system becomes effective. Milke distinguishes this initial period from the later vented period, during which smoke removal can arrest descent. The two phases require different balances. Continuing an unvented curve after substantial removal starts would represent a different ventilation scenario from the one actually being assessed.[15]
Uniform-zone assumptions deserve particular attention in large or complex spaces. Milke identifies strong horizontal variation, temperature stratification that prevents smoke reaching the ceiling, and sprinkler-induced cooling and mixing as examples requiring care. A detailed spatial model or a different assessment method may be needed when local conditions govern the result. Greater enclosure volume alone does not establish the validity of a two-zone representation.[13]
Smoke from an adjoining room also follows a different route from a central fire directly within the large enclosure. It can pass through an opening and spill beneath a balcony before entering the main space. Van Rossum explains that these additional entrainment stages can materially increase the smoke flow. The central-fire filling correlations should not silently replace that different source and plume arrangement.[21]
The calculation record should therefore state fire location, growth history, enclosure shape, height datum, interface definition and ventilation state. It should also identify the correlation's range or the zone model's assumptions. These details establish what the predicted layer history represents and what additional information is needed before it can support a complete assessment of smoke exposure.[6][9][20]
See also
Notes
- ↑ Milke (2002), pp. 4-292–4-298; Van Rossum (2027), §§9.1–9.3.
- ↑ 2.0 2.1 Milke (2002), pp. 4-293–4-297.
- ↑ Milke (2002), pp. 4-292–4-296.
- ↑ Milke (2002), pp. 4-292–4-293.
- ↑ Milke (2002), pp. 4-296–4-298.
- ↑ 6.0 6.1 Milke (2002), pp. 4-294–4-297.
- ↑ Milke (2002), pp. 4-293, 4-308.
- ↑ 8.0 8.1 8.2 8.3 Milke (2002), pp. 4-295–4-296.
- ↑ 9.0 9.1 9.2 Milke (2002), pp. 4-296–4-297.
- ↑ 10.0 10.1 10.2 10.3 10.4 Milke (2002), p. 4-297.
- ↑ 11.0 11.1 Milke (2002), p. 4-298; Van Rossum (2027), §9.3.
- ↑ 12.0 12.1 Van Rossum (2027), §9.3.
- ↑ 13.0 13.1 Milke (2002), pp. 4-295–4-298.
- ↑ Milke (2002), p. 4-298; Van Rossum (2027), §§6.7, 9.3.
- ↑ 15.0 15.1 Milke (2002), pp. 4-294, 4-298.
- ↑ Milke (2002), p. 4-297, equation 13.
- ↑ 17.0 17.1 Milke (2002), p. 4-297, equation 14.
- ↑ 18.0 18.1 Milke (2002), pp. 4-297–4-298.
- ↑ 19.0 19.1 19.2 19.3 Milke (2002), pp. 4-297–4-298, Examples 2–3.
- ↑ 20.0 20.1 20.2 Milke (2002), pp. 4-293–4-294; Van Rossum (2027), §9.3.
- ↑ Van Rossum (2027), §§6.7, 9.3; Milke (2002), p. 4-295.
References
- Milke, J. A. (2002). Smoke management in covered malls and atria. In P. J. DiNenno (Ed.), SFPE handbook of fire protection engineering (3rd ed., pp. 4-292–4-310). National Fire Protection Association.
- Van Rossum, E. (2027). Introduction to Fire Safety Engineering.