Velocity and density measurements in forced fountains with negative buoyancy

Abstract

In fluid mechanics, fountains take place when a source fluid is driven by its own momentum into a surrounding ambient fluid, and it is counterbalanced by buoyancy. These phenomena are largely encountered in nature and human activities. Despite the numerous studies on the subject, few experimental data are available about the internal structure of turbulent fountains. Here, we present a set of laboratory experiments with the aim to (i) get direct velocity and density measurements of fountains in a controlled environment and (ii) obtain insights about the basic physics of the phenomenon. The results concern the characteristics of the mean and turbulent flow: we report the analysis of the turbulent kinetic energy, the velocity skewness, and the Reynolds stresses, including a quadrant analysis of the fluctuating velocities. For some tests, the correlation between density and vertical velocity is investigated for both mean and fluctuating values. We have quantified the momentum transport, which is mainly out-downward at the nozzle axis with peaks at the mean rise height, where also maximum levels of the buoyancy and mass fluxes are present. The ability of acoustic Doppler current profilers to identify the rise height of the fountain and to measure the velocity field is also discussed.

Entrainment and dilution in a fountain top

“…A similar finding has been reported by Addona et al. (2021), who analysed the turbulent kinetic energy, the velocity skewness and the Reynolds stresses of the fluctuating velocity in a turbulent forced fountain. They found that the turbulent kinetic energy is maximum at (where is the steady height of the fountain), suggesting that the maximum production of turbulence takes place near the base of the fountain top, where the inner flow meets the pulsating fountain top.…”

“…They also presented a statistical description of a turbulent fountain as consisting of a potential core surrounded by a growing shear region; a cap region of large-scale pulsating flow where generation of turbulence due to buoyancy is significant; and finally an annular counterflow region that is akin to a buoyant plume. A similar finding has been reported by Addona et al (2021), who analysed the turbulent kinetic energy, the velocity skewness and the Reynolds stresses of the fluctuating velocity in a turbulent forced fountain. They found that the turbulent kinetic energy is maximum at z/z ss ∼ 1 (where z ss is the steady height of the fountain), suggesting that the maximum production of turbulence takes place near the base of the fountain top, where the inner flow meets the pulsating fountain top.…”

“…There are other studies in the literature that used point-based measurements of velocity and temperature/density in a turbulent fountain to understand velocity-temperature/density Ambient Cap region correlations, Reynolds stresses and the balance of mean momentum and turbulent kinetic energy equations (Cresswell & Szczepura 1993;Addona, Chiapponi & Archetti 2021). For instance, Cresswell & Szczepura (1993) reported that the effect of negative buoyancy is mainly seen in the mean flow gradients, thereby altering the turbulence field indirectly.…”