Abstract

Results are presented based on data from high-fidelity DNS simulations of a turbulent forced fountain (Re0 = 1,667, Fr0 = 21). Within a quiescent environment, of uniform density, a steady flow of relatively dense fluid is forced vertically upwards (from a circular source). These flows rise up as a negatively buoyant jet, and after some distance the buoyancy reverses the flow causing it to fall back and form a downflow. For sufficiently long observations, the flow is statistically steady, and the fountain is characterised by the downflow enshrouding the dense upflowing jet-like core, atop of which sits a highly periodic unstable region of flow that forms the fountain cap. Consideration of the physics identifies that these fountains exhibit entrainment (herein the transfer of mass, momentum, buoyancy or other scalars by either mean or turbulent flow processes) across at least three physically meaningful interfaces. At the fountain outer boundary, entrainment occurs across a turbulent/non-turbulent interface. Internally the flow can be divided, based on the loci of points of zero mean vertical velocity, into an upflow and a downflow; or into an inner and outer flow, based on the loci of point of zero mean mass transport, i.e. a separatrix. Both of these internal boundaries are turbulent/turbulent interfaces, at which entrainment driven by turbulent flow processes dominates the classical mean flow entrainment. Reynolds averaging the data, we show that existing models of fountains fail to capture these important internal entrainment processes; conditionally averaging the data shows great promise for accurately capturing these dynamics over much of the fountain height. Understanding and modelling the fountain cap region remains an outstanding challenge.