Smoke filling time for a room due to a small fire: The effect of ceiling height to floor width aspect ratio

We consider the filling of a room with smoke from a small, centrally located floor fire. We present theoretical arguments for the behaviour of the filling time relative to the idealised ‘filling box time’ [Baines WD, Turner JS. Turbulent buoyant convection from a source in a confined region. J Fluid Mech 1969;37:51–80] as a function of the room height to width aspect ratio. Initially, the rate at which the smoke layer deepens is shown to be more rapid for relatively wide rooms (large aspect ratio). However, at larger times, relatively tall rooms (small aspect ratio) fill more rapidly due to large scale overturning and engulfing of ambient fluid. A series of experiments were performed to verify these results and showed good qualitative agreement with our theoretical predictions. The experiments were also used to evaluate the extent of deviation of the actual smoke front position from the idealised filling box model as a function of the aspect ratio.