Streamline pattern induced by a turbulent plume in an emptying-filling box.

Abstract

The streamline pattern for the steady self-regulating stratified flow driven by a turbulent plume rising from the base of an ‘emptying-filling’ box is determined theoretically. Buoyant fluid that accumulates from the plume drives a flow out through openings at the top of the box and draws a flow of exterior fluid in through openings at the base. Whilst the bulk stratification and flow rates have received prior attention, the focus here is on predicting the streamline patterns in the regions below and above the horizontal density interface that characterises the stratification. These patterns have not been investigated previously for any configuration of openings. Motivation is provided by numerous practical applications of this problem, including to airflows in naturally ventilated buildings. Modelling the flow induced as a potential flow, analytic solutions are developed for the stream function which reveal stark differences between the pattern of motion above and below the interface. Below, streamlines fan outward from the base opening and are nearhorizontal adjacent to the plume perimeter. Above, the flow pattern is more intricate as buoyant fluid that spreads laterally outward on impinging with the top of the box divides to form two distinct regions: an inner region of flow recirculation adjacent to the plume; and an outer region where fluid flows toward the top opening. We explore the effect of the interface height on the flow structures identified before considering some of the implications for airflow control in thermally-stratified ventilated rooms. The model provides the first theoretical means for estimating the spatial distribution of the residence time. Using the residence time as a proxy for air quality we provide insight into the role of the room geometry and air exchange rates on occupant comfort.