Measurements of interacting turbulent shear layers in a duct

Abstract

Measurements have been made of the turbulent flow in a rectangular duct of aspect ratio 12:1 at a Reynolds number $\overline{U}h/\nu = 10^5$ (based on duct height h) using conditional-sampling techniques. The lower boundary layer was heated in the entry region, and the fluctuating output of a resistance thermometer was used to distinguish ‘hot’ and ‘cold’ fluid. Thus separate velocity-fluctuation statistics could be obtained for fluid from the upper and lower boundary layers, even after the two layers had merged. The measurements suggest that the interaction region near the centre-line consists of a continuously contorting interface between the ‘hot’ and ‘cold’ layers, shaped by the eruption of large eddies across the centre-line from either side of the duct and surprisingly little affected by the inevitable fine-scale mixing.

In the mean, this time-sharing between ‘hot’ and ‘cold’ fluid gives the impression of two superposed turbulence fields whose mean-square intensities add to give the total intensity. Exact superposition (which cannot take place in a nonlinear system) would imply that one layer had the same turbulent intensity profiles as an isolated boundary layer spreading into a non-turbulent free stream with the same mean velocity profile as the duct flow. The centre-line interaction grows in strength with increasing distance downstream until a steady rate of mutual eddy intrusion and fine-scale mixing is achieved, when the flow is commonly called ‘fully developed’. It is concluded that superposition (timesharing) is a physically reasonable first approximation for use in turbulence models for interacting shear layers: it is argued that better approximations could be obtained if necessary by correlating departures from superposition (i.e. changes in turbulence structure) by means of one or more interaction parameters.