Gaussian Model-Pasquill Condition-lecture 6

7/28/2019 Gaussian Model-Pasquill Condition-lecture 6

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Pakistan Institute of Engineering and Applied Sciences

Radiation Safety and Radioactive Waste Management Course(Lecture 6)

DISPERSION MODELLING (PASQUILL CONDITIONS)

The Gaussian Plume Equation predicts a plume that is symmetrical with respect to y and with respect to x-axis.

Symmetrical does not mean that the cross-section is circular. Usually the two dispersion coefficients y and z are not

necessarily equal for all the distances x and are different in majority of the cases. Different y and z means that

spreading in vertical and horizontal direction are not equal. Most often y > z , so that a contour of constant

concentration is like an ellipse, with long axis horizontal. To use Gaussian Plume equation one must know the

appropriate values ofy and z . From the previous equations 11 and 12 it is expected that they have the values like:

However, if the value of Ks in the above equation is considered, it can be seen that they are assigned an arbitrarystatistical value, independent to atmospheric behavior. It seems reasonable to assume that they would depend on wind

speed and on the degree of atmospheric turbulence, which is a function of wind speed and degree of solar heating

(insolation) etc. It is also reasonable to assume that for any given degree of insolation the value of K will be linearly

proportional to the wind speed i.e. Ky / v and Kz / v are constant. Thus according to the equations 11 and 12, which

relate statistically the dispersion coefficient with diffusion coefficient, for any specified meteorological condition, both

standard deviation y and z should increase as square root of the downwind distance x .

Experimental evidence does not agree well with this prediction. The available data have been correlated and presented

in the form of plots on log-log scale fory and z as a function of x . Experimental data show that the dispersion

coefficients increase much more rapidly with distance [Figure 11.1 and 11.2]. This means that the diffusion model for

atmospheric dispersion is not an exact description of the phenomenon. The experimental data disagree with the

diffusion theory because the equation assumed for atmospheric mixing is much too simple to account for all the

complicated things that actually go in the atmosphere, even on days with simple wind patterns, which are the only

ones on which experimental tests are attempted. Thus it can be seen that the preceding derivation shows a way to

obtain a logical material balance for dispersion of a pollutant from a point source in the atmosphere, subject to some

strong simplifying assumptions. However, the values of dispersion coefficients y and z cannot yet be computed from

theory as theory cannot accommodate meteorological features. Now if the values of dispersion coefficients given in

figure 11.1 and 11.2 may be accepted as adequate representations of experimental results, they can be used along with

the equation 14 to make prediction of concentrations downwind from a point source.

Lecture delivered by Dr. Naseem Irfan

)12&11(.........2

................2

Eqsv

Kxand

v

Kx zz

y

y ==

)14(2

)(

2exp

2

)(

2exp

22

2

2

2

2

2

2

2

EqHzyHzy

v

Q

zyzyzy

++

++=


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This is currently the most widely used method for routine calculations of air pollutant dispersion from point sources.

The experimental data on which figures 11.1 and 11.2 are based are limited and not necessarily directly applicable to



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cities. Most of the experimental data is taken were taken for steady flow of winds over grasslands ( the Salisbury Plain

in England and the grasslands of Nebraska). It can be used for cities because nothing better is available. These plots

are based on measurements for all downwind distances less than or equal to on kilometer. The values beyond that

distance are extrapolations. However, comparison with experiments shows that advanced versions of this model

predict observed concentration fairly well. Thus It has become a standard practice, therefore, to use experimental

values of dispersion coefficients in the main dispersion equation (14) to calculate effluent concentration. The label A

to F on the lines in the figure 11.1 to 11.2 corresponds to different levels of atmospheric stability conditions which is a

direct indications that these functions depends on atmospheric conditions. Thus, z, which relates to the dispersion in

the vertical direction, can be expected to increase more rapidly with distance under unstable conditions than under

stable conditions.

Pasquill obtained a set of curves by working on experimental data, for six different atmospheric conditions. The

following relations may approximate a seventh stability condition, type G which is extremely stable:

z (G) = 3/5 z (F) and y (G) = 2/3 y (F) -------------- Eq. (11.1 & 11.2)

As can be observed from the figures 11.1 and 11.2, the less stable conditions have higher values of both

y ,

z thanstable conditions, at all distances from the source. It is possible to estimate the stability conditions in the lower

atmosphere by simply measuring the temperature at two or more heights on a meteorological tower. The slope of the

temperature profile can be computed by dividing the temperature difference T by the difference in height Z of the

measurements. The relationship between the Pasquill stability categories and the observed T/Z is given in the table

11.1. The United States , the Nuclear Regulatory Commission (USNRC) requires the temperature ( as well as wind

speed and direction) to be continually monitored at two points, usually at 10m and 60m, on a tower or mst near every

operating nuclear plant.

The Pasquill conditions can also be determined by monitoring the fluctuations in the angle of wind vane. On days

when the atmosphere is unstable, a wind vane tends to fluctuate more widely than on days when the atmosphere is



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stable. The correlation between the standard deviation of the angle of the vane, , to the various Pasquill categories

is shown in table 11.1. A further elaboration for these categories classification given by Turner is given in Table

11.2. Although the instrumentation to measure directly has been installed at a number of nuclear power plants, this

method is generally considered to be less reliable- interpretations of the data is more difficult than the simple

temperature measurements just described. For instance if one wants to estimate y and z at a point 0.5 km downwind

from a pollutant source on a bright summer day with a wind speed greater than 6 m/s. The table 11.2 may be used to

conclude that for a bright summer day the incoming solar radiation is strong thus stability category will be C.

Now, using Figures 11.1 and 11.2 the values of the dispersion coefficients at a downwind distance of half a kilometer

will be 56 m and 32 m fory and z respectively. Equation 14 is correct for ground level or any elevation above it.

For large values of z , the contribution of ( z + H ) 2 term becomes negligible and the result is practically identical

with the equation with no ground effect.

For conditions of y = 0 and z = 0, which corresponds to the line on the ground directly under the centerline of the

plume, the exponential term in y drops out of the equation 14. Now further multiplying both sides by v / Q gives:

The function on the right depends only on effective stack height and atmospheric stability conditions through

dispersion coefficients. Now if for any specific stability condition a downwind distance x and stability conditions are

provided then one could make up a plot of [ c v / Q ] or (concentration multiplied by a constant number) for any

effective stack height can be calculated. Turner has done this for six stability conditions one of which is shown in

figure 11.3 for a stability condition C. The figure shows the relation of effective stack height with the quantity and

location of maximum pollutant concentrations. One may conclude that as the effective stack height is increased the

quantity of maximum concentration decreases and occurs at a greater distance from the stack.


=

zy

H

Q

v

z

22

1exp

1 2


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Figure 11.3 Ground level [c v / Q ] values, directly under the plume center-line, as a function of downwind

distance from the source and effective stack height H, in meters, for C stability conditions.

As the plume flows downwind, it will eventually grow until it is completely mixed below the mixing height L alsoshown in the figure 11.4 As discussed in daily variation of prevalent lapse rate due to warming and cooling of earth

surface, after mid afternoon, there will exist extremely unstable conditions. This will lead to vigorous vertical mixing

from the ground up to that height and due to presence of standard lapse rate above there will be negligible vertical

mixing. The rising air columns that provide good vertical mixing induce large-scale turbulence in the atmosphere

[Figure 11.5]. This turbulence is three-dimensional, so it provides good horizontal mixing as well. Pollutants released

at ground level will be mixed almost uniformly up to mixing height, but not above it. Thus the mixing height sets the

upper limit to dispersion of atmospheric pollutants. In the morning, when inversion conditions exist quite close to the

Earth surface, the mixing height is much lower and it grows during the day. Similarly mixing heights are larger in

the summer than the winter [Table 11.2]. In order to locate these mixing height from naked eye, one may differentiate

the air clear and blue region above the mixing height and hazy and brown or gray below the mixing height. Another

feature for recognition of mixing height is the clouds themselves. The tops of clouds are not perfectly uniform, but

they are all at practically the same height, which corresponds to mixing height Figure 11.5]. Up to the mixing height

rising, unstable air brings moisture up from below to form the clouds. Above the mixing height there is no

corresponding upward flow.


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Gaussian Model-Pasquill Condition-lecture 6