Behaviour of laminar plane fountains with a parabolic inlet velocity profile in a homogeneous fluid

The behaviour of plane laminar fountains with parabolic velocity inlet profile is studied using numerical simulation over the parametric range 0.25 ≤ Fr ≤ 10.0, 50 ≤ Re ≤ 150 and Pr = 7, 300, 700. The behaviour of the flow is most strongly affected by the Froude number and to a lesser extent by the Reynolds number, particularly for weak fountains at low Reynolds numbers. Behaviour is independent of the Prandtl number over the parametric range investigated. Three distinct regimes are observed: a steady symmetric pattern at low Froude numbers (Fr < 1.25), an unsteady periodic flapping characterised by lateral oscillations at intermediate Froude numbers (1.25 ≤ Fr ≤ 2.25) and an unsteady aperiodic flapping at higher Froude numbers. Based on dimensional analysis, the rise height of the fountain is shown to follow the correlation zm∼Fr4/3−2/3(c+d)Re−(c+d)Pr−d. The constants c and d are determined from numerical results for each regime.

► Numerical simulation of plane laminar fountains with parabolic velocity profile. ► Three distinct regimes are identified. ► As Froude number increases the dependence of the fountain height on Re decreases. ► Fountain height increases with Fr in all regimes with different scaling relations. ► Behaviour is independent of Prandtl number over the parametric range investigated.