Time-dependent displacement ventilation caused by variations in internal heat gains: application to a lecture theatre.

We examine transient displacement flows in naturally ventilated spaces that are subject to an increase in internal heat gains as in, for example, an empty lecture theatre which is then occupied by an audience. Heat gains create a layer of warm air at the ceiling which initially increases in depth and temperature, and descends towards the occupied regions. A theoretical model is developed to predict the time-dependent movement of the interface that separates the warm upper and cool lower layers of air, and comparisons are made with the results of laboratory experiments. The time scale for the flow to reach a steady state is found to depend upon the height and cross-sectional area of the space, the opening areas and the strength of the heat gains. We estimate that this time scale is of the order of an hour for a typical lecture theatre. An interesting feature of these flows is that the interface descends below or 'overshoots' the steadystate interface position during the transient period, thus potentially exposing the occupants to the higher air temperatures and pollutant levels of the upper layer. We predict that the initial transient ventilation flow rates are significantly less than those established in the steady state. As a consequence, ventilation designs based upon steady-state flow conditions may fail to provide adequate ventilation if the time scale for the development of the flow is comparable with the time the space is occupied.