Overturning in a filling box

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.