Numerical simulation of scalar dispersion downstream of a square obstacle using gradient-transport type models

We present a numerical study of scalar transport released from a line source downstream of a square obstacle to investigate the capabilities and limitations of gradient-transport modeling in predicting atmospheric dispersion. The standard k–ɛ and k–ω models and a Reynolds Stress Transport closure are employed and compared to predict the time-averaged turbulent flow field, while a standard gradient–diffusion model is initially adopted to relate the scalar flux to mean gradients of the concentration field. The analysis of two algebraic closures for turbulent scalar fluxes based on the generalized-gradient–diffusion hypothesis and its quadratic extension is also presented. In spite of the rather simple flow setup, where both the flow and the scalar fields can be assumed homogeneous in the spanwise direction, the analysis clarifies several critical issues concerning gradient-transport type models. We established the dominant role of predicted turbulent kinetic energy on scalar dispersion when a scalar diffusivity is employed, irrespectively of the Reynolds stress closure adopted for the averaged momentum equation. Moreover, the standard gradient–diffusion hypothesis failed to predict the streamwise component of the scalar flux, which is characterized by a counter-gradient-transport mechanism. Although the resulting contribution in the averaged scalar transport equation is small in the present flow configuration, this limitation can become severe for strongly inhomogeneous flows in the presence of point sources, where the spread of the scalar plume is essentially three-dimensional. The predictive capabilities of gradient-transport type modeling are found clearly improved using algebraic closures, which appear to represent a promising tool for predicting atmospheric dispersion in complex flows when unsteady transport mechanisms are not dominant.