Vertical Round Buoyant Jets and Fountains in a Linearly, Density-Stratified Fluid

Panos N Papanicolaou,George C Stamoulis

doi:10.3390/fluids5040232

Panos N Papanicolaou, George C Stamoulis

Open Access

https://doi.org/10.3390/fluids5040232

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Abstract

Turbulent round buoyant jets and fountains issuing vertically into a linearly density-stratified calm ambient have been investigated in a series of laboratory experiments. The terminal (steady-state) height of rise and the mean elevation of subsequent horizontal spreading have been measured in positively buoyant jets (at source level), including pure momentum jets and plumes, as well in momentum-driven negatively buoyant jets (fountains). The results from experiments confirmed the asymptotic analysis that was based on dimensional arguments. The normalized terminal height and spreading elevation with respect to the elevation of injection of momentum-driven (positively) buoyant jets and fountains attained the same asymptotic values. The numerical results from the solution of entrainment equations, using an improved entrainment coefficient function, confirmed the results related to buoyancy dominant flows (plumes), while their predictions in momentum-driven flows were quite low if compared to measurements.

Highlights

A round buoyant jet is the flow out of a pipe or circular nozzle that discharges into a quiescent or moving volume of fluid of different density
A vertical jet is positively buoyant if the direction of flow initially is that of the effective gravity, due to the density difference between jet and ambient fluid at the elevation of discharge; otherwise, it is called a negatively buoyant jet or fountain
The terminal height of rise and spreading height normalized with Lj are plotted in Figure 4a,b, respectively, versus the dimensionless parameter MN/B

Summary

Introduction

A round buoyant jet is the flow out of a pipe or circular nozzle that discharges into a quiescent or moving volume of fluid of different density. A vertical jet is positively buoyant if the direction of flow initially is that of the effective gravity, due to the density difference between jet and ambient fluid at the elevation of discharge; otherwise, it is called a negatively buoyant jet or fountain. In a density-stratified, stable, calm ambient, a vertical jet that is positively buoyant at the elevation of injection entrains and mixes with the surrounding fluid up to an elevation where the average jet density is equal to that of the ambient fluid (neutral buoyancy). The jet flow reverses and returns to the elevation of neutral buoyancy, where it spreads horizontally. A vertical fountain (jet negatively buoyant at injection elevation) in a stable, density-stratified ambient will rise and mix with ambient up to the elevation where its kinematic momentum flux vanishes, under the influence of reverse buoyancy. The maximum steady-state elevation attained by a Fluids 2020, 5, 232; doi:10.3390/fluids5040232 www.mdpi.com/journal/fluids

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