Turbulent Diffusion in Thermally Stratified Turbulent Boundary Layers (Wind-tunnel experiment)

Abstract

   Fundamental experiments on turbulent diffusion in thermally stratified turbulent boundary layers in the wind tunnel were carried out in order to make clear the mechanism of turbulent diffusion.
   The wind velocity for this study was 1.6 m/sec and turbulent boundary layer was made by setting an L-shaped metallic bar, whose side length was 19 mm, at the leading edge of a flat plate (Fig. 1). In this boundary layer, temperature profiles were made in nearly straight lines in temperature gradient (1.5K/cm in the case of stable condition and -1.8K/cm in the case of unstable condition on the average; see Fig. 2).
   Pure propane gas was emitted from a point source at several heights (h_s=0.1∼9 cm) which was set at x=100 cm, and the concentration distributions were measured three-dimentionally.
   Statistic quantities of turbulence were measured by temperature-compensated hot-wire anemometers (single hot-wire, V-meter and X-meter, Pt-plated tungsten wire of 2 mm in length and 5 μm in diameter) and cold wire (same material as the anemometer, 2 mm and 5 μm) (Figs. 2, 5, 6, 7, 9).
   Turbulent diffusion is obviously affected by the thermally stratified layers (Figs. 10 and 12).
   It is clear that the concentration distribution in lateral direction is normal distribution (Fig. 11), then, the concentration of the case of a line source for each source height can be calculated from eq. (4). The distributions of the synthetic concentration are shown in Figs. 13(a)∼(d). by the series of symbol Ο. The two-dimentional diffusion equation in stationary state is u (∂C_L/∂x) = ∂/∂z (K_z (∂C_L/∂z)), where K_z is the vertical diffusion coefficient and C_L the concentration from a line source. Integrating the equation with z, the vertical diffusion coefficient K_z can be calculated from the concentration distribution for the line source and wind velocity (eq. (6)).
   The profiles of K_z for each condition are shown in Figs. 14(a)∼(c). It is evident that K_z is proportional to height z; K_z=k·z, where k is a proportional constant. The values of constant k for each source height and each condition are shown in Table 3.
   On the other hand, Sakagami (1954) solved the diffusion equation in which K_z was assumed to be proportional to height z (K_z=k_s·z). Sakagami's solution for the line source is given in eq. (8). The concentration distributions for each source height are obtained by choosing suitable parameter B and shown by solid lines in Figs. 13(a)∼(d).
   The values of k_s (proportional constant for the vertical diffusion coefficient in Sakagami's solution) are calculated from eq. (10) and shown in Table 4(b). The mean values of k_s in the region of x=120∼150 cm agree well with the experimental ones except the case of the source height h_s=0.1 cm (Table 3 and Table 4(b)).