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Overturning in a filling box

Published online by Cambridge University Press:  28 March 2007

N. B. KAYE  and
G. R. HUNT
N. B. KAYE
Affiliation:
Department of Civil and Environmental Engineering, Imperial College London, Imperial College Road, London, SW7 2AZ, UK
G. R. HUNT
Affiliation:
Department of Civil and Environmental Engineering, Imperial College London, Imperial College Road, London, SW7 2AZ, UK
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Abstract

Overturning in a cylindrical filling box driven by a turbulent plume is examined theoretically and experimentally. We establish the initial penetration depth (h) of the buoyant flow that intrudes vertically up the sidewall as a function of the box radius (R) and height (H). Dimensional arguments reduce the problem to finding η = h/H as a function of the aspect ratio Φ = R/H. The flow is modelled in two parts, the radial outflow from the plume along the base of the box and the flow up the sidewall. The outflow is modelled as a forced radial gravity current with constant buoyancy flux while the sidewall flow is modelled as a line fountain. Two regimes were found: first, when the plume outflow is adjusting toward a pure gravity current on impact with the vertical wall and the rise height is given by η ∼ Φ−1/3; secondly, when the outflow is fully developed on, or before, impact and the rise height is given by η ∼ Const. Experimental results show good agreement with these scalings and allow the constants of proportionality to be established.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 576 , 10 April 2007 , pp. 297 - 323
Copyright
Copyright © Cambridge University Press 2007

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