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The influence of spanwise confinement on round fountains

Accepted version
Peer-reviewed

Type

Article

Change log

Authors

Debugne, ALR 
Hunt, GR 

Abstract

jats:pWe study experimentally the effects of spanwise confinement on turbulent miscible fountains issuing from a round source of radius jats:inline-formulajats:alternatives<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112018001945_inline1" />jats:tex-mathr0</jats:tex-math></jats:alternatives></jats:inline-formula>. A dense saline solution is ejected vertically upwards into a fresh-water environment between two parallel plates, separated by a gap of width jats:inline-formulajats:alternatives<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112018001945_inline2" />jats:tex-mathW</jats:tex-math></jats:alternatives></jats:inline-formula>, which provide restraint in the spanwise direction. The resulting fountain, if sufficiently forced, rapidly attaches to the side plates as it rises and is therefore ‘confined’. We report on experiments for five confinement ratios jats:inline-formulajats:alternatives<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112018001945_inline3" />jats:tex-mathW/r0</jats:tex-math></jats:alternatives></jats:inline-formula>, spanning from strongly confined (jats:inline-formulajats:alternatives<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112018001945_inline4" />jats:tex-mathW/r0→2</jats:tex-math></jats:alternatives></jats:inline-formula>) to weakly confined (jats:inline-formulajats:alternatives<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112018001945_inline5" />jats:tex-mathW/r0≈24</jats:tex-math></jats:alternatives></jats:inline-formula>), and for source Froude numbers jats:inline-formulajats:alternatives<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112018001945_inline6" />jats:tex-mathFr0</jats:tex-math></jats:alternatives></jats:inline-formula> ranging between jats:inline-formulajats:alternatives<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112018001945_inline7" />jats:tex-math0.5⩽Fr0⩽96</jats:tex-math></jats:alternatives></jats:inline-formula>. Four distinct flow regimes are observed across which the relative importance of confinement, as manifested by the formation and growth of quasi-two-dimensional structures, varies. The onset of each regime is established as a function of both jats:inline-formulajats:alternatives<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112018001945_inline8" />jats:tex-mathW/r0</jats:tex-math></jats:alternatives></jats:inline-formula> and jats:inline-formulajats:alternatives<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112018001945_inline9" />jats:tex-mathFr0</jats:tex-math></jats:alternatives></jats:inline-formula>. From our analysis of the time-averaged rise heights, we introduce a ‘confined’ Froude number jats:inline-formulajats:alternatives<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112018001945_inline10" />jats:tex-mathFrcFr0(W/r0)−5/4</jats:tex-math></jats:alternatives></jats:inline-formula>, which encompasses the effects of confinement and acts as the governing parameter for confined fountains. First-order statistics extracted from the flow visualisation, such as the time-averaged rise height and lateral excursions, lend further insight into the flow and support the proposed classification into regimes. For highly confined fountains, the flow becomes quasi-two-dimensional and, akin to quasi-two-dimensional jets and plumes, flaps (or meanders). The characteristic frequency of this flapping motion, identified through an ‘eddy counting’ approach, is non-dimensionalised to a Strouhal number of jats:inline-formulajats:alternatives<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112018001945_inline11" />jats:tex-mathSt=0.120.16</jats:tex-math></jats:alternatives></jats:inline-formula>, consistent with frequencies found in quasi-two-dimensional jets and plumes.</jats:p>

Description

Keywords

convection, plumes/thermals, wakes/jets

Journal Title

Journal of Fluid Mechanics

Conference Name

Journal ISSN

0022-1120
1469-7645

Volume Title

845

Publisher

Cambridge University Press (CUP)
Sponsorship
Engineering and Physical Sciences Research Council (EP/L504920/1)