A mathematical approach to submerged horizontal buoyant jet trajectory and a criterion for jet flow patterns

This paper focused on the trajectory and flow patterns of submerged horizontal gas jet in stagnant ambient liquid. A rigorous mathematical model for the jet trajectory was developed based on geometric analysis, mass conservation, and momentum. Additional, multiple N2-Water experiments employing binary image processing were designed and performed. The experimental procedures and mathematical derivations are presented here in details. To assess the ability of the mathematical model to predict the jet trajectory, extensive experimental results were extracted for comparison with the mathematical results. The mathematical results were found to be in good agreement with the experimental results. Furthermore, a dimensionless jet spreading angle model was proposed and fitted to the experiment results. A flow pattern transition criterion based on the penetration depth of the buoyant jet in the water was also discussed, distinguishing the gas buoyant jet form bubbly or transitional flow patterns.