Learning the concepts of air pollution dispersion for the first time can be quite challenging. Even if the qualitative portions of the topic are not so hard to grasp, the quantitative, formulaic parts can be downright intimidating. One method educators and trainers can use to break through such barriers is a physical modeling tool, labeled The SuperStack by the author, which realistically and safely demonstrates the dispersion of atmospheric contaminants using paper hole-punches to represent pollution particles. The artificial stack is 13 feet tall with a uniform 4-inch inside diameter, but can be used to provide practical, hands-on experience for stacks of a much grander scale.

Modeling theory

Before explaining how this practical equipment can be used to teach the fundamentals of air-pollution dispersion, it is important to understand basic dispersion modeling theory.

The three primary components of the air pollution system (elaborated on later) are emission sources, the atmosphere and receptors of contaminants. The unifying formula for the relationship among these components is:

Where:
C = concentration (g/m³), the impact of the source(s) on the receptor(s)
Q = emission rate (g/s), the contaminant quantity/time release into the atmosphere
S = stability (m-2), a critical weather condition related to the air’s mixing potential
U = wind speed (m/s), critical weather condition related to downwind transport of contaminants.
Scientists and engineers who study air pollution dispersion will frequently rely on a basic Gaussian plume equation, derived from empirical studies and statistical analysis, e.g. probability density function, to quantitatively estimate the concentration of atmospheric contaminants downwind of an emission source. A simplified version of the Gaussian plume equation follows:

Where:
Xi = contaminant concentration in the atmosphere (g/m³) at a specified downwind distance
q = uniform, continuous emission rate (g/s)
pi = 3.1416
mu = average wind speed (m/s) in the atmosphere downwind of the source
sigma_y = cross-wind dispersion parameter (m) at a specified downwind distance
sigma_z = vertical dispersion parameter (m) at a specified downwind distance
H = emission height (m).

(Note that “exp ” is typically designated as “e^x ” on calculators. Also note that in the equations and text that that follow, m = meters, m² = meters squared (area), m³ = meters cubed (volume), g = grams, mg/m³ = micrograms per cubic meter, and s = seconds.)

Basically, such equations are developed to approximate a downwind concentration (mass of a contaminant in a volume of air, typically in g/m³), given a known or estimated air release rate (contaminant loading per second, g/s), airflow (wind speed in distance per second, m/s) and atmospheric stability conditions across the impact area (in m²). As such, any formula that can simulate emission dispersal under specified weather and topographic conditions can be a valuable tool to an air quality scientist, engineer or emergency response personnel.

Modeling instruction and demonstration

A – Figure 1 shows the stack assembly with wooden base and support structure, along with a portable, two-speed blower motor coupled to the base of the stack. The stack is 13-feet tall with an I.D. of 4 inches. It can be separated to simulate shorter stack heights, while a two-speed blower can alter exit-gas velocities.

The stack simulator can be used to help students more fully comprehend the real world significance of the basic Gaussian plume equation. Furthermore, combining a physical model with a computational model such as the Gaussian plume equation can strengthen conceptual and quantitative understanding of the complex reality of chemical dispersion in air.

To combine these two models for more effective teaching/training, first, the instructor must introduce the general ideas of contaminant dispersion using the unifying formula presented above. Examples of sources and receptors, and key atmospheric dispersion components can be elicited from students. Alternatively, prior to revealing the unifying formula, students can be encouraged to construct a formula that represents the likely relationship among the three parts of the air pollution system.

To have students construct a formula, assign three variables to represent each system component, e.g., S (source strength), D (dispersion from wind and stability), and R (concentration at receptor). If necessary, students may be prompted by being reminded to consider the units of each variable. R = S / D is an appropriate solution. Once the importance of the unifying formula, along with the relationships among its variables, has been thoroughly explored, the instructor can move on to introduce the basic Gaussian plume equation, and then compare and contrast the formula with the plume equation. For instance, note that the primary similarity between the formula and the equation is that both use “q” in the numerator to represent emission rate in g/s and “u” in the denominator to represent wind speed in m/s. (The difference here of course is between capitalization/non-capitalization of the variables.)

One primary substantive difference between the formula and the equation is that the “S” stability term in the numerator of the formula is replaced by “pi, sigma_y, sigma_z” in the denominator of the plume equation. Another primary difference is the introduction of the expression “exp (- H2 / 2  sigma_z2 )” to account for additional dispersion of emissions released from an elevated source such as a smokestack. (The complete explanation of the importance of these differences is beyond the scope of this article, however, the similarity of the units of both sets of terms along with statistical theory can be employed to elaborate on the differences between the formula and equation.)

When students have grasped the crucial features of the formulaic models of air dispersion, instructors can then introduce the artificial stack and its real life application to the numerical models.

Now for the stack

Figure 2. The SuperStack is shown on the Geneva College campus with optional La Crosse Technology wind equipment (near stack top) and 1 m2 foam board for identifying particle concentrations downwind of the stack.

To begin, the source (smokestack) features can be examined. A hole punch is used to make multi-colored paper particles (the punched disks) that are inserted at the base of stack model. The known amount of “particulate loading” versus the time over which the particles are emitted out the stack provides the emission rate of the source, i.e., the particles-per-second rate. If students measure the mean mass of each paper particle, they can then determine the mass per second emission rate of particles exiting the stack.

Additional stack parameters essential to computing downwind particle emission impact should be identified and then measured. These parameters include stack height and diameter, and exhaust temperature and velocity.

The artificial stack stands 13 feet high from its base to its 4-inch exhaust opening. The stack can be separated to produce a 6.5-foot unit. The present unit consists of a two-speed blower for low- and high-speed flows that can be measured with, for example, a pitot tube anemometer through the stack’s sampling port. Using a simple liquid-in-glass thermometer, the stack gas temperature also can be measured through the port.

Atmospheric conditions such as wind speed and stability are key to air dispersion and can be identified via visual observations (like the Beaufort Scale for wind speed and cloud cover for stability estimates). Or better, a meteorological tower that extends anemometer equipment to the stack top can be constructed so that students can measure wind direction and speed (see Figure 2). Experience has shown that an approximately 15-mph sustained wind is needed to properly disperse the particles emitted from the stack. (Note that precipitation is usually not desirable during students’ first demonstrations, since paper particles will be washed out of the air. However, precipitation can show the real world effects of rain and heavy snowfall on particulate matter in subsequent sessions.)

Finally, the impact of the paper pollution particles on downwind receptors can be demonstrated by counting the portion of the total amount of particles that fall in a given area. To more readily accomplish this task, a 1-m² foam board has been fabricated (see Figure 2). One way in which this board can be used is to locate the area of the highest concentration of particles on the ground, then carefully lay the board over that area and trace out the board’s area using chalk or string.

Once the board is removed, the number of particles per square meter can be counted to yield the quantitative result of settled particles per square meter. Furthermore, if it is assumed that these particles represent all the particles that would also have impacted a 1-meter depth above the 1-m² area in which they settled, then the number of particles can now be equated to particles per cubic meter. Lastly, if the mean mass of each paper particle has been measured, the students can then determine the maximum mass per cubic meter concentration of particles that impacted the environment downwind of the stack.

Conclusion

What has been included here identifies some of the stack’s applications to assist students with their full comprehension of the characteristics of contaminant dispersion, and the meaning (including purpose, applicability and significance) of the air dispersion equations. PE

---

Acknowledgement
The author thanks Dr. James Gidley, Chair of the Engineering Department at Geneva College, for suggesting the title Super Stack. The author’s original title was Toxic Tower, which still may be used on occasion to attract interest in the equipment.