Abstract
Maximum and steady-state terminal penetration heights of vertical plane fountains have been studied in laboratory experiments using shadowgraph and planar, laser-induced fluorescence (PLIF) techniques. The initial Froude numbers of the flow were in the range 20 to 130 and Reynolds numbers 180 to about 700. The normalized, terminal rise height was computed numerically from the equations of motion and found congruent to findings of earlier and present measurements. The entrainment coefficient function used in modeling is derived from analytical, closed-form solutions regarding the momentum and mass flux of plane buoyant jets, and is expressed as a function of the local Richardson number and a jet width parameter proposed by List and Imberger J Hydraul Div 99:1461–1474 (1973).
Article Highlights
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Flow visualization via shadowgraph and PLIF experiments of vertical plane fountains were conducted.
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Normalized maximum penetration and terminal rise height of plane fountains have been considered.
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An entrainment function derived from analytical solution of vertical buoyant jets is introduced.
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Data Availability
All the experimental data of this investigation are included in Table 2.
Code Availability
Matlab codes used to extract the terminal height from video frames and Visual Basic code for computing the terminal rise height are available upon reasonable request.
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Acknowledgments
The assistance of Dr. P. Dimitriadis for the PLIF arrangement and technician Mr. Y. Patselis is gratefully acknowledged. An initial version of the paper has been included in the e-Proceedings of the “15th International Conference on Protection and Restoration of the Environment”, 2021, Patras, Greece, ISBN 978-618-82337-2-0.
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Panos N. Papanicolaou: Conceptualization, Methodology, Formal analysis and investigation, Validation, Supervision, Writing - original draft preparation; Panagiotis Minos: Formal analysis and investigation, Hardware design, Implementation of experiments, Software, Validation, Visualization; Final approval.
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Minos, P., Papanicolaou, P.N. Mixing of Vertical Plane Fountains in a Calm Uniform Ambient. Environ. Process. 9, 23 (2022). https://doi.org/10.1007/s40710-022-00580-0
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DOI: https://doi.org/10.1007/s40710-022-00580-0