Thermal stratification produced by plumes and jets in enclosed spaces

The air.ow and thermal strati"cation produced by a localised heat source located at .oor level in a closed room is of considerable practical interest and is commonly referred to as a ‘"lling box’. In rooms with low aspect ratios H=R.1 (room height H to characteristic horizontal dimension R) the thermal plume spreads laterally on reaching the ceiling and a descending horizontal ‘front’ forms separating a stably strati"ed, warm upper region from cooler air below. The strati"cation is well predicted for H=R.1 by the original "lling box model of Baines and Turner (J. Fluid. Mech. 37 (1968) 51). This model represents a somewhat idealised situation of a plume rising from a point source of buoyancy alone—in particular the momentum .ux at the source is zero. In practical situations, real sources of heating and cooling in a ventilation system often include initial .uxes of both buoyancy and momentum, e.g. where a heating system vents warm air into a space. This paper describes laboratory experiments to determine the dependence of the ‘front’ formation and strati"cation on the source momentum and buoyancy .uxes of a single source, and on the location and relative strengths of two sources from which momentum and buoyancy .uxes were supplied separately. For a single source with a non-zero input of momentum, the rate of descent of the front is more rapid than for the case of zero source momentum .ux and increases with increasing momentum input. Increasing the source momentum .ux e;ectively increases the height of the enclosure, and leads to enhanced overturning motions and "nally to complete mixing for highly momentum-driven .ows. Strati"ed .ows may be maintained by reducing the aspect ratio of the enclosure. At these low aspect ratios di;erent long-time behaviour is observed depending on the nature of the heat input. A constant heat .ux always produces a strati"ed interior at large times. On the other hand, a constant temperature supply ultimately produces a well-mixed space at the supply temperature. For separate sources of momentum and buoyancy, the developing strati"cation is shown to be strongly dependent on the separation of the sources and their relative strengths. Even at small separation distances the strati"cation initially exhibits horizontal inhomogeneity with localised regions of warm .uid (from the buoyancy source) and cool .uid. This inhomogeneity is less pronounced as the strength of one source is increased relative to the other. Regardless of the strengths of the sources, a constant buoyancy .ux source dominates after su?ciently large times, although the strength of the momentum source determines whether the enclosure is initially well mixed (strong momentum source) or stably strati"ed (weak momentum source). c