Fire Plume Simulator: Heskestad Axisymmetric Plume Correlations

simulator intermediate ~10 min
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ΔT ≈ 115°C at ceiling from 1 MW plume

A 1 MW fire with 1 m diameter produces a flame height of approximately 1.3 m. At a 5 m ceiling, the plume centerline temperature rise is about 115°C above ambient, with a centerline velocity of 4.5 m/s.

Formula

L = 0.235 Q̇^(2/5) − 1.02D (flame height, m)
ΔT₀ = 9.1(T∞/(gc²ρ²))^(1/3) Q̇_c^(2/3) (z−z₀)^(-5/3)
ṁ = 0.071 Q_c^(1/3) z^(5/3) + 0.0018 Q_c (mass flow, kg/s)

Buoyancy-Driven Flow

Fire generates a buoyant column of hot combustion products that rises due to density differences with the surrounding air. This fire plume is the primary mechanism for transporting heat, smoke, and toxic gases from the fire source to the upper regions of a compartment. Understanding plume behavior is essential for designing smoke control systems, positioning detectors, and predicting the thermal environment that occupants and structures will experience.

Heskestad's Correlations

Gunnar Heskestad developed widely-used empirical correlations that describe the axisymmetric plume above a fire. His model divides the plume into three regions: a persistent flame zone near the fire, an intermittent flame zone where flames appear and disappear, and a buoyant plume region above the flames. The correlations predict centerline temperature rise, velocity, and mass entrainment rate as functions of height, heat release rate, and fire diameter.

Entrainment and Dilution

As the plume rises, it entrains ambient air at a rate proportional to the plume's perimeter and velocity. This entrainment is crucial: it determines how quickly the hot gases are diluted and cooled. At the ceiling level, the plume may contain 10-100 times more entrained air than combustion products. Higher ceilings mean more entrainment, lower temperatures, and lower concentrations of toxic gases — one reason tall atriums provide better smoke management.

Engineering Applications

Plume models are the foundation of performance-based fire design. They determine the required capacity of smoke exhaust systems, predict sprinkler activation times, establish detector placement criteria, and inform structural fire resistance requirements. The Heskestad model is embedded in design guides worldwide, including NFPA 92 for smoke management and BS 7346 for smoke ventilation design.

FAQ

What is a fire plume?

A fire plume is the column of hot gases rising above a fire due to buoyancy. As the hot gases rise, they entrain cooler ambient air, which dilutes and cools the plume. The plume structure determines smoke detector activation, sprinkler response, and smoke layer formation in compartments.

What is the Heskestad plume model?

The Heskestad model (1984) provides empirical correlations for axisymmetric buoyant plumes above pool fires. It predicts centerline temperature, velocity, and mass flow rate as functions of height and heat release rate. It is one of the most widely used plume models in fire protection engineering.

How is heat release rate measured?

Heat release rate (HRR) is measured using oxygen consumption calorimetry, based on the principle that approximately 13.1 MJ of heat is released per kilogram of oxygen consumed. Large-scale calorimeters like the cone calorimeter and furniture calorimeter are standard tools in fire testing.

What determines flame height?

Heskestad's correlation gives mean flame height as L = 0.235Q̇^(2/5) − 1.02D, where Q̇ is in kW and D is fire diameter in meters. Flame height increases with heat release rate but decreases with fire diameter because wider fires entrain air more efficiently.

Sources

Embed

<iframe src="https://homo-deus.com/lab/fire-engineering/fire-plume/embed" width="100%" height="400" frameborder="0"></iframe>
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