Plume rise

For completeness we also give ay in this form in Table 18.3 for the PG correlations. The three sets of coefficients in Table 18.3 are based on different data. In choosing a set for a particular application, one should attempt to use that set most representative of the conditions of interest [see Gifford (1976), Weber (1976), AMS Workshop (1977), Doran et al. (1978), Sedefian and Bennett (1980), and Hanna et al. (1982)]. 

The behavior of a plume is affected by a number of parameters, including the initial source conditions (exit velocity and difference between the plume temperature and that of the air), the stratification of the atmosphere, and the wind speed. Based on the initial source conditions, plumes can be categorized in the following manner  

We shall deal here with buoyant and forced plumes only. Our interest is in predicting the rise of both buoyant and forced plumes in calm and windy, thermally stratified atmospheres. 

Chracterization of plume rise in terms of the exhaust gas properties and the ambient atmospheric state is a complex problem. The most detailed approach involves solving the coupled mass, momentum, and energy conservation equations. This approach is generally not used in routine calculations because of its complexity. An alternate approach, introduced by Morton et al. (1956), is to consider the integrated form of the conservation equations across a section normal to the plume trajectory [e.g., see Fisher et al. (1979) and Schatzmann (1979)]. 

Initial buoyancy initial momentum Initial buoyancy initial momentum Initial buoyancy initial momentum 

Buoyant plume Initial buoyancy initial momentum 

TABLE 18.3 Summary of Several Plume Rise Formulas Expressed in the Form A/i = 

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G. A. Briggs, "Plume Rise," USAEC Critical Review Series TID-25075, NTIS, Springfield, Va., 1969. 

Effective Stack Height Plume Rise, US EPA Air Pollution Training Institute Pub. SP.406, with Chapts. D, E, and G by G. A. Briggs and Chapt. H by D. 

G. A. Briggs, Plume Rise Predictions, Eectures on Air Pollution andEnvironmental Impact Analyses, American Meteorological Society, Boston, Mass., 1975. 

D. B. Hoult, J. A. Fay, and L. J. Forney, Theory of Plume Rise Compared with Field Observations Fluid Mechanics Laboratory Publication No. 68-2, Massachusetts Institute of Technology, Department of Mechanical Engiaeeriag, Cambridge, Mass., 1968. 

The effective stack height (equivalent to the effective height of the emission) is the sum of the actual stack height, the plume rise due to the exhaust velocity (momentum) of the issuing gases, and the buoyancy rise, which is a function of the temperature of the gases being emitted and the atmospheric conditions. 

Some of the more common plume-rise equations have been summarized by Buonicore and Theodore (Industrial Control Equipment for Gaseous Pollutants, vol. 2, CRC Press, Boca Raton, Florida, 1975) and include ... 

Briggs, Plume Rise, AEG Critical Review ser., U.S. Atomic Energy Commission, Div. Tech. Inf. 

Briggs, G. A., Plume Rise Predications Lectures on Air Pollution and Environmental Impact Analyses, Workshop Proceedings, American Meteorological Society, Boston, Massachusetts, 1975, pp. 59-111. 

Banderson, Darryl (ed.), Plume Rise and Bouyancy Ejfects, Atmospheric Science and Power Production, DOE Beport DOE/TIC-27601, 1981. 

In addition to short-term emission estimates, normally for hourly periods, the meteorological data include hourly wind direction, wind speed, and Pasquill stability class. Although of secondary importance, the hourly data also include temperature (only important if buoyant plume rise needs to be calculated from any sources) and mixing height. 

Wind speed also affects the travel time from source to receptor halving of the wind speed will double the travel time. For buoyant sources, plume rise is affected by wind speed the stronger the wind, the lower the plume. Specific equations for estimating plume rise are presented in Chapter 20. 

At a downwind distance of 800 m from a 75-m source having an 180-m plume rise, cr, is estimated as 84 m and cr is estimated as 50 m. If one considers buoyancy-induced dispersion as suggested by PasquUl, by how much is the plume centerline concentration reduced at this distance ... 

For most plume rise estimates, the value of the buoyancy flux parameter F in m s is needed. 

The final effective plume height H, in m, is stack height plus plume rise. Where buoyancy dominates, the horizontal distance Xf from the stack to where the final plume rise occurs is assumed to be at 3.5 , where x is the horizontal distance, in km, at which atmospheric turbulence begins to dominate entrainment. 

Plume rise for distances closer to the source than the distance to the final rise can be estimated from... 

If the stack gas temperature is below or only slightly above the ambient temperature, the plume rise due to momentum will be greater than that due to buoyancy. For unstable and neutral situations ... 

This equation is most applicable when vju exceeds 4. Since momentum plume rise occurs quite close to the source, the horizontal distance to the final plume rise is considered to be zero. 

Briggs, G. A., "Plume Rise." United States Atomic Energy Commission Critical Review Series, TlD-25075. National Technical Information Service, Springfield, VA, 1969,... 

Briggs, G. A., Some recent analyses of plume rise observation, in "Proceedings of the Second International Clean Air Congress" (H. M. Englund and W. T. Beery, eds.). Academic Press, New York, 1971, pp. 1029-1032. 

Assuming that the buoyancy flux parameter F is greater than 55 in both situations, what is the proportional final plume rise for stack A compared to stack B if A has an inside diameter three times that of B ... 

Vertical temperature gradient The lapse rate (rate of decrease in temperature with increases in height) must be taken into account because it affects the final height to which a buoyant plume rises. 

One major item remains before we can apply the dispersion methodology to elevated emission sources, namely plume height elevation or rise. Once the plume rise has been determined, diffusion analyses based on the classical Gaussian diffusion model may be used to determine the ground-level concentration of the pollutant. Comparison with the applicable standards may then be made to demonstrate compliance with a legal discharge standard. 

A particularly difficult aspect of the problem of diffusion of atmospheric pollution is the determination of the height to which a buoyant plume with an initial exit velocity will rise. Plume rise, which is defined as the distance between the top of the stack and the axis of the centroid of the pollutant distribution, has been found to depend on ... 

Thus, based on the above, it is not surprising that even under the best conditions an uncertainty factor of approximately 2 is likely in estimates of the plume rise. Despite this somewhat pessimistic introduction, estimations of plume rise are worthwhile and an integral part of the dispersion analysis. Table 2 presents some of the well-known plume rise formulas used in different model approaches. The two major controlling variables which appear in many, if not all, of the plume rise formulas surveyed are ... 

Multiple regression techniques have been applied by investigators to determine the coefficients in a plume rise equation containing both of the above terms ... 

Plume rise observations based on single-stack operation were regressed into the above expression and empirically fitted to the following expression, which incorporates atmospheric stability classes into the coefficients ... 

Table 2. Examples of Plume Rise Formulas Reported in the Literature...

Holland Ah = (1.5V,d -H 0.04QJ/U where Ah — plume rise (m), Vj = stack exit velocity (m/s), d = stack diameter (m), = heat emission rate (kcal/s), U = stack top wind speed (m/s) Highly empirical. Requires stack testing confirmation on case-bycase basis... 

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