Diffusion and convection of gaseous and fine particulate from a chimney

Abstract

Particle dispersion from a high chimney is considered and an expression for the subsequent concentration of the particulate deposited on the ground is derived. We consider the general case wherein the effects of both diffusion and convection on the steady state ground concentration of particulate are incorporated. Two key parameters emerge from this analysis: α, the ratio of diffusion to convection, and λ, the nondimensionalised surface mass transfer rate. We also solve the inverse problem of recovering these two parameters given the boundary concentration profile and provide an estimate of the concentration flux above the chimney stack.

The Mathematics of Atmospheric Dispersion Modeling

“…2 ) x, y = y/H, z = z/H, and C = (uH 2 /Q) C (a similar rescaling of variables is used in other studies such as [25] and [31]). Compare the relative sizes of terms in the equation for typical values of the parameters given in Table 3.1, and consequently show that neglecting the diffusion term in the x-direction is a reasonable approximation.…”

“…Llewelyn [22] solved a time-dependent version of the atmospheric dispersion problem and showed that his solution reduces asymptotically to Ermak's at steady state. An alternative derivation using complex variable techniques was used by MacKay, McKee, and Mulholland [25] for the problem with deposition but no settling. Interestingly, similar solutions have been derived for other problems arising, for example, in diffusion of ligand molecules in a protein matrix [27].…”

An inverse Gaussian plume approach for estimating atmospheric pollutant emissions from multiple point sources

“…The heights of the four contaminant sources, corrected for plume rise, are H s = [15,35,15,15] while the nine receptors are located at heights h r = [0, 10,10,1,15,2,3,12,12]. The dustfall jars are glass containers in the shape of circular cylinders having a diameter of 0.162 m, and so the area parameter used in the deposition calculation in Eq.…”

“…Another related stream of research has focused on solving the corresponding inverse problem, whereby measurements of particulate concentrations or ground-level depositions are given and the aim is to determine information about the location or efflux rate of contaminant sources. Inverse methods based on Gaussian plume type solutions have been developed by a number of authors in this context including Jeong et al [13] and Hogan et al [14], while MacKay et al [15] developed an alternate solution approach using complex variable theory. Other researchers have applied a more direct computational approach by solving the nonlinear governing equations using methods based on Kalman filtering [16], Lagrangian particles [17], Bayesian techniques [18,19], or by integrating the equations backward in time [17,20].…”

“…The algorithm should be capable of generating reliable estimates of emissions rates given a relatively small number of deposition measurements. The novelty of this work stems from a combination of factors: -We make use of real (noisy) meteorological and deposition data, in contrast with some other studies that use synthetic data [14,15]. -Deposition measurements are relatively small in number and represent time-averaged accumulations.…”