Air Pollution Transport Teaching Modeling

Introduction

Understanding and predicting the impact of air emissions form various sources are essential components of a typical course on Air Pollution in an engineering curriculum. Air pollution teaching modules were developed to aid instructors and students with the basic ability to model convective-dispersive transport of air pollutants emitted from point and distributed sources. The modules rely on basic "Gaussian Models" and use site specific input parameters on topography and meteorological conditions such as wind speed and direction, atmospheric stability, ambient temperature, and stacks gas properties. 

Theory and Background

A very brief description of the basic "Gaussian Model" which is included in typical air pollution courses is outlined below. Atmospheric dispersion of air pollutants from a point source is typically depicted in Figure 1. This model predicts an average concentration under steady state condition.

Figure 1: Plume Boundary and Time Averaged Envelope.

The coordinate systems in all teaching modules described in this chapter use coordinate systems as shown in Figure 2. The shape of the plume undergoing dispersion is a function of the wind speed, vertical temperature profile and atmospheric stability. These functional relationships are discussed in details in most textbooks adopted for air pollution courses. For the sake of brevity and yet completeness of this chapter most of the common plume shapes are shown in Figure 3.

Figure 2: Plume Dispersion by Gaussian Distribution and Coordinate System.

Figure 3: Typical Velocity, Temperature Profile, and Plume Shapes.

 
The general equation to calculate the steady state concentration of an air contaminant in the ambient air resulting from a point source is given by:

where

     c(x,y,z) = contaminant concentration at the specified coordinate [ML-3], 
     x = downwind distance [L], 
     y = crosswind distance [L], 
     z = vertical distance above ground [L], 
     Q = contaminant emission rate [MT-1], 
     sy = lateral dispersion coefficient function [L], 
     sz = vertical dispersion coefficient function [L], 
     u = wind velocity in downwind direction [L T-1], 
     H = effective stack height [L]. 

The effective stack height, H, is equal to the physical stack height plus the plume rise. The plume rise under different conditions can be obtained by empirical equations derived by many researchers and the choice is based on the prevailing conditions at the site. Plume rise  calculations reported in this chapter primarily use Brigg's equation. 

In the above equation sy , the lateral dispersion coefficient function and sz , the vertical dispersion coefficient functions depend on the downwind distance and the atmospheric stability class. These coefficients in meters can be obtained from the equations utilized by the Industrial Source Complex (ISC) Dispersion Model developed by USEPA (1995):

sy = 465.11628 (x) tan(TH)

where

TH = 0.01745 [ c - (d) ln (x)]
sz = a xb

Table 1: Constants a,b,c,d depend on Pasquill Stability categories defined by Turner (1995).
Surface wind speed at 10 m (m/s) Day Night
Incoming Solar radiation Cloud Cover
Strong Moderate Slight Thinly Overcast Mostly Cloudy
< 2 A (s = 1) A-B B (s = 2)    
2-3 A-B B C (s = 3) E (s = 5) F (s = 6)
3-5 B B-C C D E
5-6 C C-D D (s = 4) D D
>6 C D D D D

The values for these constants for various stability classes are reported by USEPA. This concept is covered in most undergraduate classes on Air Pollution and students are expected to master this model. Teaching modules described in this chapter were developed on this concept and applications for different scenario were included.

Dispersion coefficients can also be obtained using Pasquill-Gifford-Turner estimates shown in the equations below.

 

 

where

s = an integer [1-6] representing the atmospheric stability shown in Table 1
kx,x = empirical constants, values for each of the stability class can be obtained from Green et al. (1960). 

Vertical and crosswind dispersion coefficients as functions of downwind distances for different stability classes are shown Figures 4 and 5.

Figure 4: Vertical Dispersion Coefficient as a Function of Downwind Distance from Source.
 

Figure 5: Horizontal Dispersion Coefficient as a Function of Downwind Distance from Source.

A Gaussian dispersion example is for both cases with/without reflection.

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