Fire Thermal Fluid Simulation
Theory: growth and limits of compartment fires
Overview
I ran a room fire in FDS. How can I tell whether the results are right?
Start with hand formulas to get rough values and check the order of magnitude. Fire results are governed mostly by how the fire size is specified, often as a t² fire growing with time squared. The hot layer under the ceiling can be estimated with the MQH correlation; at a rise of about 500 K flashover occurs — the whole room ignites at once. And fire size caps out at what the air through the doorway can sustain. Let's calculate all three for a standard-size room.
t-squared fire
A fire whose heat release grows with time squared. The coefficients $\alpha$ are defined so that 1 MW is reached in about 600, 300, 150 and 75 s respectively.
Hot-layer temperature (MQH)
$A_o\sqrt{H_o}$ is the opening ventilation factor, $A_T$ the internal surface area excluding openings, $h_k$ the wall heat-loss coefficient. For thick walls $h_k$ falls over time, so the hot layer keeps warming even for a constant fire.
Ventilation limit
The MQH correlation and t² fires
The MQH correlation was built in 1981 by McCaffrey, Quintiere and Harkleroad at the US National Bureau of Standards (now NIST) from many compartment fire tests, and is named for their initials. The t² fire concept spread around the same time as a simple way to express fire growth. Both are simple, yet they remain yardsticks for checking FDS and similar results. FDS itself was developed by NIST and released in 2000.
Worked example: a 3.6×2.4×2.4 m room
Doorway 0.8 m wide and 2.0 m high; walls and ceiling of gypsum board (0.48 W/mK, 1440 kg/m³, 840 J/kgK). Internal surface area excluding openings 44.5 m², ventilation factor 2.26 m^2.5.
Time to flashover
| Growth rate | Time to flashover | Heat release then |
|---|---|---|
| Slow | 612 s | 1.10 MW |
| Medium | 331 s | 1.28 MW |
| Fast | 178 s | 1.49 MW |
| Ultrafast | 96 s | 1.75 MW |
The ventilation-limited heat release is 3.4 MW; Thomas's flashover estimate is 1.2 MW.
Hot layer for a steady 300 kW fire
| Elapsed time | Hot-layer rise |
|---|---|
| 1 min | 143 K |
| 5 min | 187 K |
| 10 min | 210 K |
| 20 min | 236 K |
A fast fire reaches flashover in under three minutes — at a size not very different from a slow fire's.
The fire size needed for flashover is set roughly by room size and openings, falling within 1–2 MW. What differs is the time to get there. A fast fire meets walls that are still cold and absorb heat well, so it needs a somewhat larger fire — yet still under three minutes. Evacuation and firefighting plans hinge on that time, and the flammability of furnishings and linings sets the growth rate. In CFD, results are governed by how heat release is specified, so always state which t² rate you chose and check the order of magnitude against hand calculations.
How to run the CFD
- Specify heat release from test data or a t² curve, and record the basis.
- Make cells fine relative to the characteristic fire diameter D* (D*/δx of 4 to 16 as a guide).
- Include wall materials and thicknesses and solve heat loss to walls; it strongly affects hot-layer temperature.
- Specify openings and exterior conditions correctly; ventilation governs fire size.
- Compare with MQH, plume and ceiling-jet correlations for order-of-magnitude agreement.
“The window broke and the fire grew”
In one fire reconstruction, modelling only the doorway as an opening made the fire ventilation-limited and smaller than the actual damage suggested. Site investigation showed a window had cracked from the heat mid-fire, admitting a large amount of air. Re-running with the window failure time reproduced the sudden jump in heat release. In compartment fires, openings changing mid-fire change fire size, so glass breakage and door states must be considered as conditions.
Common mistakes
Mistakes and fixes
| Mistake | Effect | Fix |
|---|---|---|
| Unjustified heat release | Results meaningless | Use t² or test data |
| Ignoring ventilation limit | Fire too large | Check limit from openings |
| Adiabatic walls | Hot layer too hot | Solve wall conduction |
| Coarse grid | Plume wrong | Use D*/δx |
| Fixed openings | Growth misjudged | Include breakage and doors |
I'd like to learn related topics.
Try the structural fire tool and sprinkler coverage tool. Related pages include thermal plumes, thermal stratification, conjugate heat transfer and thermal stress analysis.
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