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Upward versus downward non-Boussinesq turbulent fountains

Published online by Cambridge University Press:  21 March 2019

Samuel Vaux Open the ORCID record for Samuel Vaux [Opens in a new window] ,
Rabah Mehaddi ,
Olivier Vauquelin Open the ORCID record for Olivier Vauquelin [Opens in a new window]  and
Fabien Candelier
Samuel Vaux*
Affiliation:
Institut de Radioprotection et de Sûreté Nucléaire (IRSN), PSN-RES, SA2I, LIE, Cadarache, 13115 St Paul-lez-Durance, France
Rabah Mehaddi
Affiliation:
Université de Lorraine, CNRS, LEMTA UMR 7563, 54518 Vandoeuvre-lès-Nancy, France
Olivier Vauquelin
Affiliation:
Aix-Marseille Université, CNRS, IUSTI UMR 7343, 13013 Marseille, France
Fabien Candelier
Affiliation:
Aix-Marseille Université, CNRS, IUSTI UMR 7343, 13013 Marseille, France
*
†Email address for correspondence: samuel.vaux@irsn.fr
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Abstract

Turbulent miscible fountains discharged vertically from a round source into quiescent uniform unbounded environments of density $\unicode[STIX]{x1D70C}_{0}$ are investigated numerically using large-eddy simulations. Both upward and downward fountains are considered. The numerical simulations cover a wide range of the density ratio $\unicode[STIX]{x1D70C}_{i}/\unicode[STIX]{x1D70C}_{0}$, where $\unicode[STIX]{x1D70C}_{i}$ is the source density of the released fluid. These simulations are used to evaluate how the initial maximum height $H_{i}$ and the steady state height $H_{ss}$ of the fountains are affected by large density contrasts, i.e. in the general non-Boussinesq case. For both upward and downward non-Boussinesq fountains, the ratio $\unicode[STIX]{x1D706}=H_{i}/H_{ss}$ remains close to $1.45$, as usually observed for Boussinesq fountains. However the Froude (linear) scaling originally introduced by Turner (J. Fluid Mech., vol. 26 (4), 1966, pp. 779–792) for Boussinesq fountains is no longer valid to determine the steady fountain height. The ratio between $H_{ss}$ and the height predicted by the Turner’s relation turns out to be proportional to $(\unicode[STIX]{x1D70C}_{i}/\unicode[STIX]{x1D70C}_{0})^{n}$. Remarkably, it is found that the power exponent $n$ differs following the direction in which the buoyant fluid is released ($n=1/2$ for downward fountains and $n=3/4$ for upward fountains). This new result demonstrates that for non-Boussinesq turbulent fountains the configurations heavy/light and light/heavy are not equivalent. Finally, scalings are proposed for fountains, regardless of the direction (upwards and downwards) and of the density difference (Boussinesq and non-Boussinesq).

JFM classification

Convection: Plumes/thermals
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 867 , 25 May 2019 , pp. 374 - 391
Copyright
© 2019 Cambridge University Press 

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