Direct simulation of fountains with intermediate Froude and Reynolds numbers

Abstract

Fountains with intermediate Froude and Reynolds numbers are of fundamental interest, especially for understanding the mechanism of turbulence and entrainment in turbulent fountains. However there has been little work done to investigate the behavior of these transitional fountains. In this work, the transient behavior of axisymmetric fountains with 1?Fr?8 and 200?Re?800 is studied by direct numerical simulation. It is found that when Re?200, there is little mixing between the downflow of the fountain and the ambient, even for Fr as high as 8; however, when Re?400, the mixing between the fountain downflow and the ambient becomes stronger, indicating that the entrainment and the turbulence are mainly due to Re and the contribution from Fr is much smaller; The maximum fountain penetration height z m fluctuates, even when the flow reaches the quasi-steady state, due to the interaction between the downflow and the bottom boundary and/or the entrainment between the downflow and the ambient; The averaged z m scales with FrRe 1/4 for 1?Fr?8 and 100?Re?800.