Correlations for maximum penetration heights of transitional plane fountains in linearly stratified fluids

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 the Reynolds number (Re), Froude number (Fr) and dimensionless temperature stratification parameter (s) over 28 ≤ Re ≤ 300, 3 ≤ Fr ≤ 10, and 0.1 ≤ s ≤ 0.5, to study and quantify the effects of these governing parameters on the maximum fountain penetration height, including the initial one during the early developing stage and the time-averaged one at the quasi-steady state, as well as the time to reach the initial maximum penetration height. The results show that both the initial and time-averaged maximum fountain heights as well as the time to attain the initial maximum fountain height increase with Fr but decrease with s, whereas the effect of Re is negligible, and the fluctuations of the maximum fountain penetration height at some specific locations at the quasi-steady state also follow the similar trends. Empirical correlations to quantify the effects of Fr, s and Re on these bulk fountain behavior parameters were obtained from the DNS results over the ranges of Fr, s and Re considered.