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A phenomenological model for fountain-top entrainment

Debugne, ALR and Hunt, GR (2016) A phenomenological model for fountain-top entrainment. Journal of Fluid Mechanics, 796. pp. 195-210. ISSN 0022-1120

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Abstract

© 2016 Cambridge University Press. In theoretical treatments of turbulent fountains, the entrainment of ambient fluid into the top of the fountain, hereinafter fountain-top entrainment Q top (m 3 s -1 ), has been neglected until now. This neglect, which modifies the energetic balance in a fountain, compromises the predictive ability of existing models. Our aim is to quantify Q top by shedding light on the physical processes that are responsible for fountain-top entrainment. First, estimates for Q top are obtained by applying, in turn, an entrainment closure in the vein of Morton et al. (Proc. R. Soc. Lond., vol. 234, 1956, pp. 1-23) and then of Shrinivas & Hunt (J. Fluid Mech., vol. 757, 2014, pp. 573-598) to the time-averaged fountain top. Unravelling the assumptions that underlie these approaches, we argue that neither capture the dynamical behaviour of the flow observed at the fountain top; the top being characterised by quasi-periodic fluctuations, during which large-scale eddies reverse and engulf parcels of ambient fluid into the fountain. Therefore, shifting our mindset to a periodical framework, we develop a new phenomenological model in which we emphasise the role of the fluctuations in entraining external fluid. Our model suggests that Q top is similar in magnitude to the volume flux supplied to the fountain top by the upflow (Q u ), i.e. Q top ∼ Q u , in agreement with experimental evidence. We conclude by providing guidance on how to implement fountain-top entrainment in existing models of turbulent fountains.

Item Type: Article
Subjects: UNSPECIFIED
Divisions: Div A > Fluid Mechanics
Depositing User: Cron Job
Date Deposited: 17 Jul 2017 19:39
Last Modified: 03 Aug 2017 03:11
DOI: