A Simple Model for the Movement of Fire Smoke in a Confined Tunnel

Fires in tunnels are unfortunately frequent occurrences often with tragic outcomes. A recent example is the fire on the funicular train at the ski resort in Kaprun (Austria), which caused nearly 160 deaths. Design engineers and risk analysts require knowledge of the fluid dynamics of the fire and smoke movement to answer questions such as how much oxygen can access and feed the fire, and what concentration of smoke will the people be exposed to. As an example in the Austrian accident the geometry was a long tunnel with fire doors closed at one end, and with a fire initiated near the closed (lower) end. The hot smoke from the fire is a source of buoyancy; the smoke reaches the ceiling of the tunnel, and then develops along the ceiling as a wall-bounded plume. The motion of the smoke is driven by a buoyancy force, but at the same time, mechanisms of turbulent heat and mass transfer act as a brake to this motion. In this paper we present how a generic model describing a semi-enclosed buoyancy-driven flow can be interpreted and used in the modelling of fire smoke movement in a confined tunnel. A consideration of the net pollutant volume flux through the tunnel leads to predictions for the variation of concentrations along the tunnel. The smoke concentrations near the fire smoke source scale linearly with the length of the tunnel, with higher concentrations at the lower section of the tunnel, as could be expected. Similarly the concentration of oxygen making its way through to the fire source decreases linearly with the length of the tunnel. A lower bound estimate of the smoke residence time can be obtained based on smoke concentration predictions from the model.