Modelling
We aim to model the concentration of pollutants in air (3D space) using the Gaussian Plume Model.
Pre Requisite Knowledge
The Gaussian plume model is a (relatively) simple mathematical model that is typically applied to point source emitters, such as coal-burning electricity-producing plants. Occassionally, this model will be applied to non-point source emitters, such as exhaust from automobiles in an urban area.
Air pollution is represented by an idealized plume coming from the top of a stack of some height and diameter. One of the primary calculations is the effective stack height. As the gases are heated in the plant (from the burning of coal or other materials), the hot plume will be thrust upward some distance above the top …show more content…
Plume is infinite with no plume history(each hour being modeled is independent of the previous hour)
6. The pollutants are non- reactive gases or aerosols that remain suspended in the following the turbulent movement of the atmosphere.
7. The plume is reflected at the surface with no deposition or reaction with the surface.
8. The dispersion in the crosswind(y direction) and vertical(z direction) take the form of Gaussian
Gaussian plume model:
The most general form of the Gaussian plume dispersion equation is where:
1. C(x,y,z) is the concentration of the emission (in grams per cubic meter) at any point x meters downwind of the source, y meters laterally from the centerline of the plume, and z meters above ground level.
2. Q is the quantity or mass of the emission (in grams) per unit of time (seconds)
3. u is the wind speed (in meters per second)
4. h is the effective stack height (in meters)
5. and are the standard deviations of a statistically normal plume in the lateral and vertical dimensions, respectively
For ground level concentration C(x, y, 0, h), the above equation gets reduced to: If only concentrations at ground level on the centerline of the plume are required then the equation is simplified further and it …show more content…
Night is defined as the period from one hour before sunset to ine hour after sunrise.
The stability class of the atmosphere for the set of given condition may be determined from the above two tables.
Detemination of diffusion coefficients:
= c xd
= a xb
where x is the downwind distance from the stack in meters.
The values for a, b, c and d can be calculated from the table
Power Law Exponents and coefficients for
Atmospheric Downwind Distance (m) Downwind Distance (m) Downwind Distance (m)
Stability class 100< X < 500 500< X < 5000 5000 < X a b a b a b
A=1 0.0383 1.281 0.0002539 2.089 0.0002539 2.089
B=2 0.1393 0.9467 0.04936 1.114 0.4936 1.114
C=3 0.1120 0.91 0.1014 0.926 0.1154 0.9109
DD=4 0.0856 0.865 0.2591 0.6869 0.7368 0.5642
DN=5 0.0818 0.8155 0.2527 0.6341 1.297 0.4421
E=6 0.1094 0.7657 0.2452 0.6358 0.9204 0.4805
F=7 0.06646 0.8050 0.1930 0.6072 1.505 0.3662
Power Law Exponents and coefficients
We aim to model the concentration of pollutants in air (3D space) using the Gaussian Plume Model.
Pre Requisite Knowledge
The Gaussian plume model is a (relatively) simple mathematical model that is typically applied to point source emitters, such as coal-burning electricity-producing plants. Occassionally, this model will be applied to non-point source emitters, such as exhaust from automobiles in an urban area.
Air pollution is represented by an idealized plume coming from the top of a stack of some height and diameter. One of the primary calculations is the effective stack height. As the gases are heated in the plant (from the burning of coal or other materials), the hot plume will be thrust upward some distance above the top …show more content…
Plume is infinite with no plume history(each hour being modeled is independent of the previous hour)
6. The pollutants are non- reactive gases or aerosols that remain suspended in the following the turbulent movement of the atmosphere.
7. The plume is reflected at the surface with no deposition or reaction with the surface.
8. The dispersion in the crosswind(y direction) and vertical(z direction) take the form of Gaussian
Gaussian plume model:
The most general form of the Gaussian plume dispersion equation is where:
1. C(x,y,z) is the concentration of the emission (in grams per cubic meter) at any point x meters downwind of the source, y meters laterally from the centerline of the plume, and z meters above ground level.
2. Q is the quantity or mass of the emission (in grams) per unit of time (seconds)
3. u is the wind speed (in meters per second)
4. h is the effective stack height (in meters)
5. and are the standard deviations of a statistically normal plume in the lateral and vertical dimensions, respectively
For ground level concentration C(x, y, 0, h), the above equation gets reduced to: If only concentrations at ground level on the centerline of the plume are required then the equation is simplified further and it …show more content…
Night is defined as the period from one hour before sunset to ine hour after sunrise.
The stability class of the atmosphere for the set of given condition may be determined from the above two tables.
Detemination of diffusion coefficients:
= c xd
= a xb
where x is the downwind distance from the stack in meters.
The values for a, b, c and d can be calculated from the table
Power Law Exponents and coefficients for
Atmospheric Downwind Distance (m) Downwind Distance (m) Downwind Distance (m)
Stability class 100< X < 500 500< X < 5000 5000 < X a b a b a b
A=1 0.0383 1.281 0.0002539 2.089 0.0002539 2.089
B=2 0.1393 0.9467 0.04936 1.114 0.4936 1.114
C=3 0.1120 0.91 0.1014 0.926 0.1154 0.9109
DD=4 0.0856 0.865 0.2591 0.6869 0.7368 0.5642
DN=5 0.0818 0.8155 0.2527 0.6341 1.297 0.4421
E=6 0.1094 0.7657 0.2452 0.6358 0.9204 0.4805
F=7 0.06646 0.8050 0.1930 0.6072 1.505 0.3662
Power Law Exponents and coefficients