Characterising entrainment in fountains and negatively buoyant jets

Abstract

Turbulent fountain flow consists of two distinct stages, the initial ‘negatively buoyant jet’ (NBJ) stage, and the fully developed ‘fountain’ stage. The present study investigates both stages of the flow using particle image velocimetry and planar laser-induced fluorescence, over a range of source Froude numbers, $10\lesssim Fr_o\lesssim 30$ , and Reynolds numbers, $5500\lesssim Re_o\lesssim 7700$ . While the velocity and buoyancy profiles in NBJs take similar Gaussian shapes over a wide range of axial locations, this was not observed in fountains. The changing profile shape is most evident in the outer flow (OF) region, while there is a degree of similarity in the inner flow (IF). Entrainment between IF and OF is shown to depend on the local Richardson number, $Ri$ . The fountains are found to have a negative entrainment coefficient, $\alpha <0$ , for the majority of their height, implying a net radial outflow of fluid from the IF to the OF. An alternative description of entrainment is considered, the ‘decomposed top-hat’ model, where the radial flow is separated into inflow and outflow components that are then estimated using the present experimental data. The inflow component was found to be proportional to the axial IF velocity, which is similar to the classical description of entrainment in pure jets/plumes, while the outflow depends on the local $Ri$ . Entrainment in NBJs may also be described by this framework, which, despite not having an OF, is still subject to an $Ri$ -dependent radial outflow.