Height And Stability Of Laminar Plane Fountains In A Homogeneous Fluid

摘要

The behaviour of plane fountains, resulting from the injection of a denser fluid upwards into a large body of a lighter homogeneous fluid, is investigated numerically. The transient behaviour of fountains with a uniform inlet velocity, Reynolds number Re = 100, Prandtl number Pr = 7, and Froude number 0.25 ≤ Fr ≤ 10.0 is studied numerically. In the present case, the density variation is as a result of temperature difference between the fountain and the ambient fluids. Three distinct regimes are identified; steady and symmetric fountains for 0.25 ≤ Fr ≤ 2.0, unsteady fountains with periodic lateral oscillation for 2.25 ≤ Fr ≤ 3.0, and unsteady fountains with aperiodic lateral oscillations for Fr ≥ 4.0. It is found empirically that the non-dimensional fountain height, z_m, scales differently with Froude number in each of these regimes; in the steady and symmetric region z_m ～Fr, in the unsteady and periodic lateral oscillation region z_m ～ Fr~(1.15) and in the unsteady and aperiodic lateral oscillation region z_m ～ Fr~(4/3). The results are compared with previous numerical and experimental results, where available and are consistent.