Natural ventilation driven by periodic gusting of wind

We investigate the mixing of a warm enclosed space by a series of discrete gusts of cold air from a high-level opening. Initially we examine the case of a series of gusts of identical size each modelled as a turbulent buoyant thermal. We develop a model of the filling box-like flow which develops in the space and identify the key parameter in the system as the ratio between the initial gust size and the product of the height of the room and the entrainment coefficient. We find an approximate analytic solution for the evolution of the density profile within the space which is in good agreement with a full numerical solution of the governing equations. We successfully test the predictions of the model with a series of new laboratory experiments. The experiments combined with the model also provide a new independent estimate for the entrainment coefficient of a thermal, epsilon = 0.37 +/- 0.02, based on the propagation speed of a filling box front. We then examine the mixing produced by a series of thermals of non-identical size which we characterize in terms of a mean size and coefficient of variation. We find that as the coefficient of variation increases, the density profile becomes progressively more stratified owing to the asymmetry of dilution through entrainment of large and small thermals. We discuss the implications of these results for the ventilation of a building subject to gusts of wind.