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Investigating Invalidity of Air Dispersion Gaussian Plume models using Three Dimensional Finite Element Model

Abstract

Youssef Hafez*

Although deficiencies in air dispersion Gaussian plume models have been well known, yet quantification of their negligence of some mechanisms like the longitudinal diffusion has not been yet made. This is done in this study using a three dimensional unsteady finite element model, Suite-3D (Solving Unsteady Incompressible Transport Equation in Three Dimensions, 3D). The model is developed to solve the advection-diffusion transport equation with decay and source terms. Suite-3D uses the standard Galerkin’s method without upwinding. Difference schemes are used (central, backward, forward) for the time integration. The elements are 8-node cubic brick elements (hexahedrons). Eight Gaussian quadrature points are used for the numerical integration of the element matrices. Suite-3D is validated against exact solutions of two problems; one has only advection and diffusion terms while the other has advection-diffusion-decay-source terms. The total percentage relative error for the first case was less than 0.61% while it reached 1.0% in the second case. The model is applied to study air pollution dispersion due to a point source. Special treatment is applied to allow comparing Suite-3D with the steady Gaussian
plume model. It is noted that neglecting the x-diffusion term in Gaussian plume model under calm wind conditions (velocity=0.2 m/s) results in discrepancies up to 81% at 180 m downstream of the source compared to prediction by the Gaussian plume model. In this zone Gaussian plume models can be considered to be not valid.