Fire plume

A fire plume is the buoyant flow of combustion products, entrained air and any flames above a localised fire. It rises because hot gases are less dense than the surrounding air, and it transports heat and smoke into the upper part of an enclosure or the outdoor atmosphere. Most fire plumes are turbulent except when the source is very small.

The plume links fuel combustion with smoke filling, detector response, structural heating and venting. Its properties depend on heat release rate, fire geometry, air entrainment and surrounding boundaries. A free axisymmetric plume is only one configuration among several encountered in buildings.

A plume is not simply the visible flame. The visible reacting region can occupy only its lower part, while the broader buoyant flow continues upwards with diluted combustion products and entrained air. Temperature, velocity and composition all change with height.

Buoyancy and plume formation

Buoyancy results from density differences between hot fire gases and cooler surrounding air. At approximately constant pressure, heating reduces gas density and produces an upward force. This force drives the rising plume and draws cooler air into the fire region.

The combustion source can be solid, liquid or gaseous. Heat feedback releases volatiles from solids and evaporates liquids, while pressurised gas can supply fuel directly. High-pressure releases can add source momentum, changing the simple buoyancy-driven picture.

The rising flow includes both combustion products and surrounding air. Turbulent motion mixes these streams and produces a highly convoluted instantaneous boundary. A time-averaged description is therefore often more useful than treating the edge as a smooth fixed surface.

Buoyancy is a driving force, while convection is heat transfer associated with the moving gas. The plume uses both: buoyant motion creates convective transport of energy and combustion products. Wind and mechanical systems can alter or oppose that movement.

Entrainment and dilution

Entrainment is the inflow of surrounding air into the plume. It increases the total mass flow as the plume rises and dilutes its temperature and combustion-product concentrations. The plume consequently becomes broader and contains a greater proportion of air.

The 2005 International Fire Engineering Guidelines note that entrained air usually greatly exceeds burned-fuel mass flow. Some smoke-development methods therefore neglect the fuel mass term in comparison. Heat release from the fuel still drives the flow and cannot be neglected as an energy input.

Entrainment explains why a small combustion source can generate a large smoke flow. Smoke filling is not determined only by the mass of fuel burned. Plume height, heat release rate and the perimeter available for air entrainment all influence the delivered volume.

Air entering from all sides supports an axisymmetric model. Walls, corners and other restrictions reduce the available entrainment perimeter and change the plume shape. Applying a free-plume relationship without adjusting for these conditions can misestimate mass flow.

Flame region and mean flame height

The lower part of a plume can contain a diffusion flame in which fuel vapour and oxygen mix and react. Lower luminosity often appears comparatively steady, while the upper flame is intermittent. Vortex structures can form near the base and move upwards.

Flame height describes the vertical extent of this reacting region. Heskestad presents an objective mean height based on intermittency: the level where flame is present half the time. This definition gives consistent measurements and is reasonably consistent with, although slightly lower than, averages made by human observation.

Centreline temperature can remain nearly constant in the lower flame and then decay as reactions trail off and entrained air cools the flow. Velocity tends to reach a maximum near or slightly below mean flame height and then declines. These profiles make a single plume temperature or velocity unrepresentative of all heights.

Temperature and velocity change through a fire plume. Based on Heskestad (2002), p. 2-2.

Mean flame height is also used to distinguish the reacting region from the overlying approximately inert plume. Its value depends on heat release rate and source diameter or related scaling, rather than being a fixed multiple for every fire. Different source regimes can produce different flame behaviour.

Estimating mean flame height

Van Rossum presents the empirical mean-flame-height relation below. It combines total heat release rate with the equivalent circular diameter of the fire. The coefficient applies when power is entered in kilowatts and both lengths are expressed in metres. $$L=0.235{\dot{Q}}^{2/5}-1.02D,D=\sqrt{\frac{4A}{\pi }}$$

Symbol	Description	Unit
$L$	Mean flame height above the fuel surface	m
$\dot{Q}$	Total heat release rate	kW
$D$	Equivalent circular source diameter	m
$A$	Horizontal fire-source area	m²

For illustration, Van Rossum's 1 MW fire-area example gives a burning area of 4 m². Treating that area as circular gives D = 2.26 m. Entering 1,000 kW in the relation gives a mean flame height of approximately 1.42 m.

This is the mean height of the reacting region, not the total height reached by hot smoke. The plume continues above the flame, and instantaneous flame tips fluctuate around the statistical height. Heskestad defines the mean flame height by the level at which flame is present half the time.

In this example the estimated flame is shorter than the equivalent source diameter. It therefore falls on the broad-fire side of Van Rossum's approximate Heskestad-versus-Thomas model-selection convention. This comparison selects a suitable description of entrainment; it does not turn either model into a universal expression for every fire geometry.

The free-plume treatment concerns buoyancy-dominated turbulent flow into an approximately uniform surrounding atmosphere. A high-momentum jet, a nearby wall or an existing upper smoke layer changes those conditions. The equation consequently cannot establish ceiling exposure or smoke-layer behaviour without the corresponding flow model.

Heskestad and Thomas plume models

The Heskestad plume model uses heat release rate, source geometry and a virtual origin to estimate plume properties. The virtual origin is a calculated point on the plume axis that can lie above or below the fuel surface. It allows the model to represent the effective source location for entrainment.

Heskestad's relations address flame height, plume temperature, velocity, virtual origin and entrainment. Their application assumes an axisymmetric turbulent plume in otherwise uncontaminated, uniform air unless a specific stratified treatment is included. The relations cease to apply where the plume enters a smoke layer.

The Thomas plume relates mass flow primarily to fire-source perimeter and rise height. Van Rossum explains that this makes the estimate comparatively simple and, within its stated basis, less directly dependent on fire power than other models. Perimeter and height still have to be defined consistently with the scenario.

Van Rossum describes a rough selection in which Heskestad is more suitable for relatively small fires and Thomas for relatively large fires, based on the relationship between mean flame length and hydraulic fire diameter. This is a model-selection convention from the cited Dutch guidance, not a universal physical boundary.

Heskestad and Thomas plume models use different input emphases. Based on Van Rossum (2027), §6.7 and Heskestad (2002), p. 2-1.

Ceiling jets and upper layers

A Ceiling jet forms when the rising plume reaches a ceiling and turns horizontally. Hot gases then spread beneath the surface and transfer heat to it and to nearby devices. This changes both the flow direction and the relevant heat-transfer problem.

The jet interacts with walls, openings and the developing upper layer. It can feed a hot gas layer above a cooler lower layer, creating thermal stratification. Plume entrainment then becomes a mass and energy source for that layer.

Free-plume relations should not simply be continued into this layer. Heskestad explicitly limits them at elevations where the plume enters smoke. A zone or ceiling-jet treatment is needed instead, depending on the required result.

Upper-layer smoke includes substantial entrained air as well as combustion products. Its temperature, volume and composition therefore reflect the whole plume history rather than only fuel chemistry. This influences smoke filling and the conditions at vents.

Line plumes and boundary effects

A Line plume idealises a source distributed along a length rather than around a single central axis. Van Rossum discusses this geometry for smoke spilling from an adjacent space beneath a ceiling edge. That spill configuration entrains air differently from an isolated circular source, so a free axisymmetric plume relation cannot represent it without modification.

Walls reduce the region from which air can be entrained. A plume immediately against a wall or in a corner therefore has different mass flow from a free plume. Simple half- or quarter-air approximations can illustrate the restriction, but the actual geometry and burner arrangement matter.

Boundary position changes plume entrainment. Based on Van Rossum (2027), §6.7.

Van Rossum also describes the mirror-fire approach for particular wall and corner configurations. A wall-attached half-round burner can be represented as half of an equivalent full plume with doubled heat release, while a corner arrangement uses a corresponding fourfold source concept. These are model-specific constructions, not instructions for every fire.

Heat release and plume properties

Heat release rate drives plume buoyancy and energy transport. Heskestad divides total heat release into convective and radiative parts, with convective flux carried by the plume and radiation emitted in other directions. In the discussed sources, convective flux is rarely less than 60% to 70% of the total.

The often-used 70% convection and 30% radiation split is an approximation. Actual proportions vary with fuel, scale and combustion conditions, and the split becomes less reliable in developed compartment fires. A model should state the value used and its limitations.

Combustion efficiency also affects the energy input. Theoretical complete-combustion power based on mass loss and heat of combustion can overestimate actual heat release when incomplete products remain. Heskestad cites efficiencies from near unity for some pools to substantially lower values for polystyrene and wood-pallet stacks.

Fire area and intensity influence both flame height and entrainment geometry. A small intense source and a larger distributed source with the same total power can produce different plume shapes and air entrainment. Total megawatts alone do not define the plume.

Experimental evaluation can use collection hoods, temperature and velocity measurements, and observations of flame intermittency. Each technique addresses a different plume property. A flame-height observation should not be substituted for mass entrainment, and a centreline temperature should not be presented as the whole plume average.

Heskestad's mean flame height based on 50% intermittency illustrates the value of an explicit measurement definition. It reduces reliance on subjective selection of a visible edge, although it remains slightly lower than the human-eye average in the cited comparisons. The method and averaging basis should accompany the value.

Mass-flow measurements require a clear boundary as well. Zukoski's collection-hood approach described by Van Rossum balances exhaust extraction with plume flow entering a maintained smoke layer. That arrangement provides a different measurement from a point velocity reading within an unconfined plume.

Model evaluation should then compare like with like. Source diameter, heat-release partition, virtual origin, measurement height and wall position can all change the result. Agreement in one configuration does not validate unrestricted use in another.

A plume result should finally be checked against conservation and physical plausibility. Mass flow should be consistent with the chosen entrainment path and layer accumulation, while convective energy should remain consistent with the heat-release input. These checks can reveal an inappropriate model before its output is used for design.

Plume models estimate smoke production and mass flow for smoke-management design. They support estimates of layer filling, vent flow and the dilution of combustion products. Their inputs must match the fire location and the height at which the result is needed.

Detection analysis uses plume and ceiling-jet transport to estimate when heat or smoke reaches a device. Structural analysis uses the same flow to determine convective heating of ceilings and members. Radiative exposure requires a separate treatment rather than being inferred from convective plume power alone.

Zone models use the plume as a pump carrying mass from a lower zone to an upper zone. Quintiere notes that many such models neglect plume volume and transport time relative to the layers. These assumptions simplify the equations but can matter in large spaces or rapidly changing fires.

Stationary models evaluate plume properties at a selected time, while dynamic models update them as heat release changes. A stationary choice can be conservative in some assessments, but it does not show the sequence by which those conditions were reached.

Limits and uncertainty

A plume is not a fixed chimney of combustion products. Its boundary, temperature and composition fluctuate with turbulence, source behaviour and surroundings. Time-averaged properties should be identified as such rather than interpreted as instantaneous uniform values.

Free-plume assumptions fail or need modification near walls, ceilings, smoke layers and obstructions. Different models address different configurations, and choosing one by name alone is not enough. Geometry and application range must be checked.

Dilution does not necessarily make smoke harmless. Entrained air lowers concentration and temperature but increases total mass flow, so substantial energy and combustion products can still be transported. Hazard depends on the resulting conditions and exposure time at the receiver.

Height is another required reference. Plume properties above a fuel surface, at mean flame height and at the underside of a smoke layer describe different stages of transport. Reporting only a vertical distance without its reference point can make otherwise correct model results impossible to compare.

See also

• Convection
• Fire dynamics
• Diffusion flame
• Smoke filling

References

• Australian Building Codes Board, National Research Council of Canada, International Code Council, & Department of Building and Housing New Zealand. (2005). International fire engineering guidelines (2005 ed.). Australian Building Codes Board.
• Heskestad, G. (2002). Fire plumes, flame height, and air entrainment. In P. J. DiNenno (Ed.), SFPE handbook of fire protection engineering (3rd ed.). National Fire Protection Association.
• Quintiere, J. G. (2002). Compartment fire modeling. In P. J. DiNenno (Ed.), SFPE handbook of fire protection engineering (3rd ed.). National Fire Protection Association.
• Van Rossum, E. (2027). Introduction to Fire Safety Engineering. Fire Safety Academy.