Asymmetry and penetration of transitional plane fountains in\ud stratified fluid

Fountains injected into stratified fluids are widely found in environmental and industrial settings. The onset of asymmetry and entrainment that occurs in transitional fountains is the key to understanding turbulence generation and entrainment mechanisms in fountains. In addition to the Reynolds number (Re) and the Froude number (Fr), the stratification of the ambient fluid, represented by the dimensionless temperature stratification parameter (s), also has a significant effect on the onset of asymmetry, unsteadiness, and entrainment in a fountain, and on the maximum height that the fountain penetrates in the ambient fluid. In this study, a series of three-dimensional direct numerical simulations (DNS) were carried out using ANSYS Fluent for transitional plane fountains in linearly-stratified fluids with Re and s in the ranges of 25 <= Re <= 300 and 0 <= s <= 0.5, all at Fr = 10. The transient behaviour of the fountains, in particular the effects of Re and s on the asymmetric transition and the maximum fountain penetration heights, is analysed and quantified using the DNS results. It is found that fountains are generally symmetric in the early developing stage, but become asymmetric and unsteady subsequently. The stratification of the ambient fluid is shown to stabilize the fountain flow and to reduce its asymmetry and unsteadiness. However, the effect of s on the asymmetric behaviour of a fountain is found to be weaker than that of Re. Empirical correlations were developed, using the numerical results, to quantify such effects on the time for the asymmetric transition. The effects of Re and s on the initial and time-averaged maximum fountain heights (zm,i and zm,a, respectively), and the time to attain zm,i are also analysed. Quantified correlations are developed using the DNS results, which demonstrate that both zm,i and zm,a increase with Re, but decrease with s, apparently due to the increasing negative buoyancy that the fountain must overcome to penetrate the ambient fluid. The results further show that the effect of s on zm,i and zm,a is much stronger than that of Re