Direct simulation of transitional axisymmetric fountains in a homogeneous environment

Fountain flows are common in heat transfer and environmental settings. The transient behavior of transitional fountains with intermediate values of Froude number (Fr) and Reynolds number (Re) is of fundamental interest to fluid mechanics and heat transfer as it is the key to understand the onset of entrainment and turbulence present in turbulent fountains. In this work, the transient behavior of axisymmetric fountains with 1≤Fr≤8 and 100≤Re≤800 is studied by direct numerical simulation (DNS). It is found that at Re≤200, there is little entrainment present at the upflow-downflow interface and at the downflow-ambient interface, even for Fr as high as 8; however, at Re>200, entrainment is present at these interfaces and the extent of the entraining regions increases with Re, which clearly demonstrates that the entrainment is mainly due to the effect of Re whereas the contribution from the Fr effect is relatively much smaller. The DNS results also show that the maximum fountain penetration height fluctuates, even when the flow reaches full development, due to the entrainment at the upflow-downflow and the downflow-ambient interfaces, and its time-averaged value scales with Fr3/2Re1/4 for 1