When a fire breaks out in a longitudinally ventilated tunnel, the basic question is this: will the smoke stay downstream of the evacuation direction, or will it spread back against the flow? The layer that spreads back is called backlayering, and the lowest longitudinal velocity that stops it is the critical velocity.
What critical velocity depends on
Critical velocity is not a fixed number; it is a function of the heat release rate (HRR), the tunnel cross-section and the gradient. The work of Wu and Bakar establishes the relationship between dimensionless heat release rate and dimensionless critical velocity using both full-scale and reduced-scale experiments, and proposes semi-empirical formulae based on Froude scaling [1].
The critical detail is this: the relationship is non-linear and saturates. At low HRR the critical velocity rises with heat release, but above a certain threshold it becomes nearly constant. The assumption "twice the fire, twice the velocity" is therefore wrong and leads to oversized fan selection.
NFPA 502 defines critical velocity and confinement velocity for road tunnels; the aim is a stable, stratified smoke layer with a tenable environment beneath it [2].
Too much velocity is also an error
Going significantly above the critical velocity is harmful: the smoke layer mixes, stratification breaks down, and visibility and temperature conditions downstream of the fire deteriorate rapidly. It also feeds the fire. The target of a ventilation design is not maximum velocity but a controlled velocity just above critical.
Modelling decisions
The problem is transient. The fire growth curve, the advance of the smoke front, the sequence in which fans start — all are functions of time. Steady state gives only the final condition, not what happens during evacuation. See the note on steady versus transient.
Buoyancy dominates. What holds the smoke layer up is the density difference; this is a natural convection problem, and the Boussinesq approximation is invalid here — the temperature difference is several hundred degrees, and density must be solved as a genuine function of temperature.
Radiation cannot be neglected. At fire temperatures radiation is the dominant mechanism, and smoke is a participating medium. See the radiation note.
Jet fans are modelled as thrust. Resolving the blades is unnecessary; the fan is represented as a volume delivering a defined thrust and exit velocity. What matters is the fan's distance from the ceiling and the spacing between fans — fans placed too close disturb each other's jets, and the total thrust comes out less than the sum of the individual thrusts.
Smoke density varies with temperature. Fan selection must be made for the hot condition; see the note on fan operating points.
References
- Wu, Y. & Bakar, M. Z. A. (2000). Control of smoke flow in tunnel fires using longitudinal ventilation systems — a study of the critical velocity. Fire Safety Journal, 35(4), 363–390. DOI: 10.1016/S0379-7112(00)00031-X
- National Fire Protection Association. NFPA 502 — Standard for Road Tunnels, Bridges, and Other Limited Access Highways. NFPA, Quincy, MA.