Steady and Transient Numerical Solutions for Turbulent Fountain Jet
Steady and unsteady numerical simulations of fountain jets covering several Froude numbers are performed using Computational Fluid Dynamic software. The physical model of the studied fountain is reproduced by dense fluid injected upwards in a less dense environment, while the mathematical model consists of the Navier-Stokes equations and a turbulence model. This model is solved numerically by using the finite volume method. Usually, a fountain jet reaches a maximum vertical penetration, then reverses, and folds into an annular region surrounding the jet. The final height of the jet is always lower than the one reached in the first moments of the jet’s lifetime. Thus, for a steady state situation, two parameters are of interest to predict, namely the maximum height and the final height of the jet. In a first step of this study, the attention has been devoted to the prediction of the final height of the fountain according to the Froude number. It has been found out that this height is correlated to the Froude number by three laws depending on the value of the Froude number. This finding fits well with previous theoretical and numerical studies. In a second step and for selected Richardson numbers, transient calculations highlighting the fountain behavior from the beginning to the final steady state have been conducted. The temporal variation of the fountain height is represented as well as the instantaneous figures highlighting the streamlines.
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