On turbulent particle fountains
Journal of Fluid Mechanics
Cambridge University Press
R1 (12 pages)
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Mingotti, N., & Woods, A. (2016). On turbulent particle fountains. Journal of Fluid Mechanics, 793 (R1 (12 pages))https://doi.org/10.1017/jfm.2016.167
We describe new experiments in which particle-laden turbulent fountains with source Froude numbers 20 > Fr₀ > 6 are produced when particle-laden fresh water is injected upwards into a reservoir filled with fresh water. We find that the ratio U of the particle fall speed to the characteristic speed of the fountain determines whether the flow is analogous to a single-phase fountain (U ≪ 1) or becomes a fully separated flow (U ≥ 1). In the single-phase limit, a fountain with momentum flux M and buoyancy flux B oscillates about the mean height, h_m = (1.56±0.04)M^(3/4)B^(-1/2), as fluid periodically cascades from the maximum height, h_t = h_m +∆h, to the base of the tank. Experimental measurements of the speed u and radius r of the fountain at the mean height h_m, combined with the conservation of buoyancy, suggest that F r(h_m) = u(g'r)^(−1/2) ≈ 1. Using these values, we find that the classical scaling for the frequency of the oscillations, ω ∼ BM⁻¹ is equivalent to the scaling u(h_m)/r(h_m) for a fountain supplied at z = h_m with Fr = 1 (Burridge & Hunt 2013). This suggests that the oscillations are controlled in the upper part of the fountain where Fr ≤ 1, and that they may be understood in terms of a balance between the upward supply of a growing dense particle cloud, at the height where Fr = 1, and the downward flow of this cloud. In contrast, in the separated flow regime, we find that particles do not reach the height at which Fr = 1: instead, they are transported to the level at which the upward speed of the fountain fluid equals their fall speed. The particles then continuously sediment while the particle-free fountain fluid continues to rise slowly above the height of particle fallout, carried by its momentum.
particles, fountains, suspensions
This work has been funded through the BP Institute, EPSRC and Hughes Hall, Cambridge. We gratefully acknowledge the technical assistance of A. Pluck, and the constructive comments of three anonymous referees.
External DOI: https://doi.org/10.1017/jfm.2016.167
This record's URL: https://www.repository.cam.ac.uk/handle/1810/253844
Attribution-NonCommercial 2.0 UK: England & Wales
Licence URL: http://creativecommons.org/licenses/by-nc/2.0/uk/
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