Numerical analysis of scalar dispersion in a turbulent boundary layer

Abstract

Most reliable and convenient computational models for the third-order scalar diffusive transport terms, $\overline{u_iu_jθ}$ and $\overline{u_iθ^2}$, which play important roles in spatially dispersing pollutants, pollen, plant disease spores, etc., in the environmental atmosphere, are sought and then they are applied to predict a practical scalar dispersion problem in a turbulent boundary layer. At first, a comparative assessment of several computational turbulence models for $\overline{u_iu_jθ}$ and $\overline{u_iθ^2}$ has been carried out by applying the models to various non-isothermal turbulent flows. The second-order quantities appearing in the models are adopted from directly measured values. The models tested in the present study are; conventional simple gradient model, eddy-damped quasi-normal approximation models and Weinstock``s theoretical model which is derived by formally integrating the Navier-Stokes equation [J. Fluid Mech., 202, 319-338, 1989]. It is rather a surprise to find that the simple gradient model which is modified to include the bouyancy effect performs almost equally or even better than the other more complicated ones. It is found that the computational model for the scalar flux diffusion, $\overline{u_iu_jθ}$ must include the shear-gradient contribution in addition to the simple gradient term of the quantity transferred. And, secondly, the experiment of Raupach and Legg[J.Fluid Mech., 136, 111-137, 1983] to investigate the scalar dispersion phenomena in a turbulent boundary layer over a rough surface has been simulated by a four-equation turbulence model with the third-order transport models selected in this study. The profiles of all properties except the streamwise heat flux are predicted with fairly good accuracy. The predicted peak mean temperature, dispersion and the wall temperature expressed by the Lagrangian scales are successfully compared with the experimental correlations of Dupont et al. [Int. J.Heat Mass Transfer, 38(4),...