Experiments and a model of turbulent exchange flow in a vertical pipe

In this paper we present experimental measurements of buoyancy driven turbulent exchange flow in a vertical pipe (L/d ratios of 9–12). The flow is driven by an unstable density difference across the ends of the pipe, created using brine and distilled water. Away from either end, a fully developed region of turbulence exists with a linear density gradient. Using a mixing length model that accounts for the end effects, we obtain the turbulent scales and flux. The Nusselt number scales like the square root of the Rayleigh number (Nu ∼ Ra1/2). We give an empirical relation to quantify the end effects and hence calculate the flux of the salt (NaCl) given the aspect ratio of the pipe and the overall density difference across it.