Transition behaviour of weak turbulent fountains

Abstract

Numerical simulations of fully turbulent weak fountain flow are used to provide direct evidence for the scaling behaviour of fountain flow over the Froude number range Fr = 0.1–2.1 and Reynolds number range Re = 20–3494. For very weak flow at Fr < 0.4, the flow mean penetration height, Zm, scales with Zm/R0 = A1Fr2/3 + A2Fr2/3 where R0 is the source radius. A1 and A2 are constants which quantify the separate effects of the radial acceleration of fountain fluid from the source (A1) and the backpressure from the surrounding intrusion, if present, on the upflow (A2). The evidence presented in this work suggests that the mechanisms for the two parts in the scaling of Zm scale with Fr2/3. The intrusion behaviour varies with the Reynolds number (Re) but there is no Re affect on the fountain penetration height. For Re < 250 the radial intrusion flow is subcritical and has different behaviour. For Fr between 0.4 and 2.1 the effect of source momentum flux increases and the flow structure changes to one where there is a coherent upflow and a cap region where the flow stagnates and then reverses. The two regions have separate scaling behaviour such that the overall height, through this transition range of Froude numbers, can be described by Zm/R=C1Fr2/3 + C2Fr2, where C1 and C2 are constants. Over this transition range the effect of source velocity profile is more significant than the Reynolds number effects and the effect of inlet turbulence is minor.