Fireball

Fireball is a rapidly developing burning cloud that forms when a substantial release of volatile fuel ignites. The burning gases can expand and rise as surrounding air mixes into them. Engineering models commonly represent the cloud by an equivalent sphere, although real fireballs rarely maintain a spherical shape. Their changing dimensions and short lifetime distinguish their thermal exposure from a steady fire.

A fireball can accompany the failure of a pressurised vessel containing a flammable liquefied gas. The vessel failure, release and subsequent combustion are related parts of the event, with different consequences. Radiation from the burning cloud is assessed separately from the pressure effects and fragments associated with vessel rupture. Estimating the thermal exposure requires the participating fuel mass, fireball geometry, burning duration and radiative properties. The position and orientation of the exposed object also influence the radiation it receives.

Formation and the release sequence

A pressurised liquid can partly vaporise when its container fails and the pressure falls. The resulting release can include vapour and entrained liquid. Rapid ignition can produce a large burning cloud before the material disperses over a wider area. The quantity participating in this process strongly influences the size of the resulting fireball.

The release geometry helps determine the fire that follows. Immediate ignition of a substantial sudden release can produce a fireball. A continuing release through a relatively small opening can instead sustain a jet fire. The same stored substance can therefore produce different flame shapes and exposure histories under different failure conditions.

The release and ignition sequence influence the form of the fire. Based on Beyler (2002), pp. 3-268–3-269.

Delayed ignition changes the sequence again. Vapour can travel downwind and mix with surrounding air before finding an ignition source. The flame can then propagate through the cloud towards the release location. Beyler describes this moving cloud fire separately from the rapid burning sphere used in the fireball model.

Burning can continue after the initial cloud has been consumed. A flame returning towards the release can ignite a remaining pool or a continuing jet. The short fireball or cloud-fire duration therefore does not necessarily describe the complete incident duration. A consequence assessment can require several successive fire exposures within one release scenario.

A BLEVE concerns the failure and rapid expansion of a vessel containing liquid above its atmospheric boiling temperature. A fireball describes combustion of released fuel. NUREG-1805 discusses their combined consequences for flammable contents, including radiant exposure and the container becoming a projectile. A radiation calculation alone does not evaluate those mechanical consequences.

The broader term explosion consequently does not identify the geometry of a fireball or quantify its radiation. Vessel failure can arise through impact, deterioration or weakening under heat, as discussed in the nuclear inspection guidance. Identifying the failure mechanism and ignition sequence precedes selection of a thermal model. A visible burning cloud is only one part of that scenario description.

Growth, buoyancy and burning duration

The fireball initially develops through the interaction of fuel release, combustion and mixing with air. Release momentum can dominate its early development. In the momentum-dominated description, the diameter grows rapidly and then changes relatively little during much of the burning period. The handbook illustrates this behaviour using a small LPG cylinder release.

Buoyancy provides another influence because the hot gases are less dense than their surroundings. In a buoyancy-dominated fireball, air entrainment governs growth while the burning cloud rises. The fireball can lift away from the ground before combustion ends. A fixed sphere touching the ground therefore represents only one simplified geometric condition.

These regimes have different time histories even when their predicted maximum diameters are similar. Beyler describes initial diameter growth proportional to the fourth root of time for momentum-dominated releases. The buoyancy-dominated description instead has initial growth proportional to time squared. Those relationships describe the cited idealisations, rather than every stage of an actual irregular flame.

The distinction also affects the choice of a representative source position. The average height of the fireball centre is used in simplified radiation geometry. The maximum elevation reached by the burning cloud is a different quantity. Substituting that maximum height for the mean centre would change the distance and angle used to calculate exposure.

For buoyancy-dominated fireballs, the handbook gives a separate estimate of the time to lift off. It scales with the same mass exponent as the buoyant burning duration and is approximately 40% of that duration. This connection helps describe the sequence of growth and rise. It does not establish a period during which nearby objects are protected from radiation.

Estimating diameter and duration

The maximum equivalent diameter is primarily related to the mass of released fuel participating in the fireball. Beyler presents the following empirical relationship, with diameter in metres and fuel mass in kilograms. Its numerical coefficient belongs to those units. The equivalent spherical volume simplifies the geometry without asserting that the visible envelope is exactly spherical.

D = 5.8 m^1/3

The corresponding duration expressions distinguish momentum-dominated and buoyancy-dominated behaviour. Each gives time in seconds when mass is in kilograms. They are alternative regime descriptions, rather than two consecutive periods that should be added together.

The duration correlations use different mass exponents for two release regimes. Based on Beyler (2002), pp. 3-306–3-307.

t_m = 0.45 m^1/3

t_b = 2.6 m^1/6

Symbol	Description	Unit
D	Maximum equivalent fireball diameter	m
m	Participating fuel mass	kg
tm	Momentum-dominated duration estimate	s
tb	Buoyancy-dominated duration estimate	s

The diameter relationship does not contain storage pressure explicitly. Its stated independence from pressure assumes that the release conditions are sufficient to vaporise the relevant fuel. It therefore does not establish that pressure has no influence on the event. Pressure affects release dynamics and appears in the chapter's separate correlations for radiative behaviour.

For sufficiently large masses, the momentum expression gives a longer duration than the buoyancy expression. Beyler argues that buoyancy remains present and limits the appropriate duration. The chapter consequently uses the buoyancy expression for very large releases, described approximately as above 30,000 kg. Extending the momentum expression indefinitely would ignore this stated limitation.

Mass and diameter are not proportional. Doubling the participating mass increases the calculated diameter by the cube root of two, approximately 1.26. This follows directly from the diameter correlation. The result concerns maximum equivalent size; it does not establish that radiation at a particular target also increases by exactly the same factor.

Representing thermal radiation

Flame radiation transfers energy from the burning cloud to exposed surroundings. The handbook presents point-source and spherical-source representations. Both simplify the changing fireball, but they describe its radiative output in different ways. The selected representation needs compatible geometry and radiative properties to produce a meaningful estimate at a target.

The point-source treatment places the radiative output at a representative centre. Its calculation depends on radiant power, the distance from that centre and the orientation of the target. Heat release is commonly averaged by dividing the available combustion energy by the selected fireball duration. This averaging replaces a changing energy-release history with a constant equivalent rate.

Only a fraction of the combustion energy is represented as radiation. Beyler reports radiative fractions generally between 0.1 and 0.4 in this treatment. The chapter also presents a pressure-dependent fit whose original data cover 0.2–1.4 MPa. Such a fitted range is part of the model evidence, rather than permission to extrapolate to arbitrary storage conditions.

The spherical-source treatment instead assigns an average surface emissive power to an equivalent sphere. Emissive power is energy leaving each unit of emitting surface per unit time. The incident flux follows by multiplying it by a geometric view factor and atmospheric transmissivity. These factors distinguish source emission from energy arriving at the receiving surface.

q″ = τ E F

F = (r/L)² cos θ, when the complete sphere is visible to the target

Symbol	Description	Unit
q″	Incident radiant heat flux	kW/m²
τ	Atmospheric transmissivity	Dimensionless
E	Average surface emissive power	kW/m²
F	Geometric view factor	Dimensionless
r	Equivalent sphere radius	m
L	Distance from target to sphere centre	m
θ	Angle between target normal and line to centre	rad

The simple view factor requires the sphere to lie wholly within the receiving surface's field of view. When the surface orientation permits only a portion to be seen, the handbook supplies a different expression. A target facing directly towards the centre has zero angle in the formula above. The surface normal, rather than the surface plane, defines that angle.

Beyler reports measured fireball surface emissive powers between 100 and 450 kW/m². The chapter notes that 350 kW/m² is widely used for the described large-scale releases. This value is a modelling choice supported by that experimental context. It is not the incident heat flux at every object outside the fireball.

An illustrative spherical-source calculation

Consider a selected participating mass of 1,000 kg. This is an illustrative input within the scale of releases discussed in the handbook, rather than a reconstruction of a particular experiment. The diameter correlation gives 58 m. The momentum and buoyancy duration expressions give approximately 4.5 s and 8.2 s respectively.

For a simplified momentum-dominated geometry, place the average centre at half the diameter above ground, giving 29 m. Select a ground-level target 100 m horizontally from the release. The distance to the centre is then approximately 104 m, obtained from the horizontal and vertical separations. It is this sloping distance that enters the view-factor calculation.

The target distance is measured to the equivalent fireball centre. Based on Beyler (2002), pp. 3-306–3-308.

Assume that the target faces the centre and can see the complete sphere. Its angle is zero, and the calculated view factor is approximately 0.0776. Select the source's 350 kW/m² emissive power and set transmissivity to unity for this illustration. The resulting incident flux is approximately 27 kW/m², calculated without intermediate rounding.

The unity transmissivity assumption represents no atmospheric attenuation along the path. The example therefore isolates the chosen source and geometric factors. A calculation using a different transmissivity would give a different incident value. The result does not establish that the actual atmosphere, flame shape or target orientation matches these assumptions.

Holding that average flux constant for the selected 4.5 s momentum duration gives approximately 122 kJ/m² of incident radiant energy. This is the time integral of the illustrative constant flux. It is not an absorbed skin dose, a prediction of injury severity or a structural temperature. Those outcomes require their own response models and exposure assumptions.

Observations and the limits of simple shapes

Accident observations illustrate how several consequences can develop within one event. Beyler describes a derailment at Oneonta involving multiple propane tank cars. An initial fireball was associated with a tank splitting open. Its thermal exposure then heated other tanks, followed by further vessel failures. The sequence demonstrates how a short initial release can contribute to continuing escalation.

The same chapter describes the Crescent City derailment, where impact between tank cars opened a propane container. The escaping gas produced an initial fireball, followed by further events over several hours. Such accounts support considering the surrounding inventory and subsequent fires. They do not mean that the first fireball itself burned for the entire incident duration.

Experiments provide a more controlled view of the changing geometry. The handbook's illustrated 7.5 kg LPG release has rapid early growth, a period with relatively little diameter change and later cooling with liftoff. Brightness also changes during this sequence. Representing the complete event by one diameter and one emissive power therefore averages physically different stages.

The assumed shape also needs evidence for the particular release. Beyler reviews an early model that represented unconfined vapour-cloud burning as a fireball, drawing on very small gas releases. Later cold-propane and LNG experiments did not universally exhibit that form. The chapter uses these observations to distinguish fireball calculations from the treatment of propagating cloud flames.

These different observations have different evidential roles. A documented accident establishes that a sequence can occur, while a controlled experiment can support a particular correlation. Neither automatically provides every input needed for another release. The source's event-tree approach therefore begins with the actual failure and ignition conditions before choosing a geometric model.

Consequences and interpretation

The effects of heat on people depend on both radiation intensity and exposure duration. The fireball's brief lifetime does not remove its potential to cause severe thermal exposure. Equally, a maximum emissive power does not specify what a person receives at a particular position. Distance, orientation and atmospheric transmission intervene between the flame and the exposed surface.

Property exposure also depends on the receiving object. NUREG-1805 identifies the participating fuel mass, diameter, duration and emissive power as principal fireball inputs. A consequence calculation then relates those inputs to the object being assessed. A single calculated radiation value is an exposure description, rather than a complete prediction of ignition or damage.

The thermal calculation must also remain separate from the vessel's mechanical hazards. Fragments and pressure effects require information beyond the equivalent radiating sphere. Neither the calculated diameter nor the duration supplies a fragment trajectory or blast pressure. Combining these consequences in an assessment requires identifying each mechanism explicitly.

Finally, these relationships are empirical engineering models. The participating mass, degree of vaporisation, release regime and representative geometry all influence their applicability. Beyler stresses that consequence methods require judgement about the actual scenario. Accurate arithmetic cannot compensate for assuming a fireball when the release instead produces a travelling cloud, a continuing jet or another fire configuration.

See also

• Boilover

References

• Beyler, C. L. (2002). Fire hazard calculations for large, open hydrocarbon fires. In P. J. DiNenno (Ed.), SFPE handbook of fire protection engineering (3rd ed., Chapter 3-11, pp. 3-268–3-314). 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.