Passive scalar dispersion in a turbulent boundary layer from a line source at the wall and downstream of an obstacle

Abstract

Simultaneous measurements of the velocity and scalar concentration fields have been made in the plume emitting from a two-dimensional line source at the wall. The source is one obstacle height, h , downstream of a two-dimensional square obstacle located on the wall of a turbulent boundary layer. These measurements were made in two fluid media: water and air. In both media particle image velocimetry (PIV) was used for the velocity field measurements. For the scalar concentration measurements laser-induced uorescence (LIF) was used for the water flow and Mie scattering diffusion (MSD) for the air flow. Profiles of the mean and root-mean-square streamwise and wall-normal velocity components, Reynolds shear stress and mean and root-mean-square scalar concentration were determined at x = 4 h and 6 h downstream of the obstacle in the recirculation region and above it in the mixing region. At these streamwise stations the scalar fluxes, uc and vc , were also determined from the simultaneous velocity and scalar concentration field data. Both of these fluxes change sign from negative to positive with increasing distance from the wall in the recirculating region at 4 h . A conditional analysis of the data was carried out by sorting them into the eight categories (octants) given by the sign combinations of the three variables: ± u , ± v and ± c . The octants with combinations of these three variables that correspond to types of scalar concentration flux motions that can be approximated by mean gradient scalar transport models are the octants that make the dominant contributions to uc and vc . However, in the recirculating zone, counter-gradient transport type motions also make significant contributions. Based on this conditional analysis, second-order mean gradient models of the scalar and the momentum uxes were constructed; they compare well to the measured values at 4 h and 6 h , particularly for the streamwise scalar flux, uc . Additional measurements of the velocity and concentration fields were made further downstream of the reattachment location in the wake region of the air flow. The mean velocity deficit profile determined from these measurements at x = 20 h compares quite well to a similarity solution profile obtained by Counihan, Hunt & Jackson (1974). Their analysis was extended in the present investigation to the concentration field. The similarity solution obtained for the mean concentration compares well to profiles measured at x = 12 h , 15 h , and 20 h , up to about three obstacle heights above the wall.