Random-Walk Simulation of Gradient-Transfer Processes Applied to Dispersion of Stack Emission from Coal-Fired Power Plants

Abstract

A numerical solution to the three-dimensional advection-diffusion equation is developed and applied to the dispersion of power plant stack contaminants throughout the boundary layer. The method employs Lagrangian marker particles undergoing variable random-walk displacements to simulate a gradient-transfer process. The size of the particle displacements is directly related to the magnitude of the vertical and horizontal diffusivities which can be any functions of space and time. Using recent atmospheric turbulence data, empirical expressions for the eddy diffusivities are derived for the entire boundary layer in terms of common meteorologic parameters. Reasonable agreement is found between the numerical predictions and actual fly-ash data collected in the vicinity of a 500 MW coal-fired power station. The random-walk technique has a number of distinct advantages over both finite-difference and particle-in-a-cell methods. It is mathematically simple, computationally fast, and requires only modest amounts of computer memory. The accuracy of the method is evaluated by comparison with a series solution of the two-dimensional diffusion equation appropriate to the surface layer.