School of Engineering, The University of Queensland
Abstract
The behaviour of plane fountains, resulting from the injection of dense fluid upwards into a large container of homogeneous fluid of lower density, is investigated. The transient behaviour of fountains with parabolic inlet velocity profile and Reynolds numbers, 50 ≤ Re ≤ 150, Prandtl numbers, Pr=7, 300 and 700, and Froude numbers, Fr = 0.25 to 10.0 are studied numerically. The fountain behaviour falls into three distinct regimes; steady and symmetric; unsteady and periodic flapping; unsteady and aperiodic. The analytical scaling of nondimensional fountain height, zm, with Fr and Re is zm ∼ Fr4/3−2γ/3Re−γ. The constant γ is found empirically for each of the regimes. The fountain height decreases with increase in Reynolds number in the steady region but increases with Reynolds number in the unsteady regimes. However, the fountain height increases with Froude number in all regimes. Numerical results and the analytical scaling show that zm is independent of Prandtl number in the range considered. The fountain exhibits periodic lateral oscillations, i.e., periodic flapping for intermediate Froude numbers ranging from 1.25 ≤ Fr ≤ 2.25
