Flow regimes in emptying–filling boxes with two buoyancy sources of differing strengths and elevations

Abstract

Emptying–filling boxes have been studied in a wide range of configurations for decades, but the flow created in the box by two plumes rising from sources of arbitrary strength and elevation was previously unsolved. Guided by experiments and simplified analytical modelling, we reveal a rich array of two- and three-layer stratifications across seven possible flow regimes. The governing equations for these regimes show how the prevailing regime and stratification properties vary with three key parameters: the relative strength of the plumes, the height difference between their sources and a parameter characterising the resistance of the box to emptying. We observe and explain new behaviours not described in previous studies that are crucial to understanding emptying–filling boxes with multiple plumes. In particular, we demonstrate that the oft-assumed premise that $n$ plumes leads to a stratification with $n+1$ layers is not necessarily true, even in the absence of mixing. Two emptying–filling box models are developed: an analytical model addressing all combinations of the governing parameters and an extended model for three-layer stratifications that incorporates two mixing processes observed in the experiments. The predictions of these two models are in generally excellent agreement with measurements from the experimental campaign covering 69 combinations of the governing parameters. This study improves our understanding of emptying–filling boxes and could facilitate improvements to natural ventilation building design, as demonstrated by an example scenario in which occupants feel cooler upon the addition of a second source of heat.