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Application of two-thirds law to plume rise from industrial-sized sources
APPLICATION OF TWO-THIRDS LAW TO PLUME RISE FROM INDLJSTRIALSIZED SOURCES*
While 1 agree with Rittmann’s conclusions regarding the increased susceptibility of small-source plumes to downwash, I find no support for the idea that the entrainment coefficient, B, is a function of source size. For buoyancy-dominated plumes known to be free of stack tip, building, or terraininduced effects, the rising part of their trajectories has always been observed to approximate the two-thirds law with fi = 0.6. If there were a trend towards larger values of/r with decreasing source size, it would certainly be apparent in laboratory-scale water-channel and wind-tunnel plumes. No such trend is evident in the extensive list of experimental values of the constant in the two-thirds law given by Briggs (1975, Table 3). Six laboratory studiesare cited; for all but the earliest experiment, p = 0.60 to 0.67. Bringfelt (1969) based his suggestion that fi decreases for larger source sizes largely on the values observed for the Tallawara and Lakeview power plants (two of the four b values listed in his Table 2). Both of these plants are near lakes; Briggs (1969) noted “much higher rise than comparable sources” for these two plants. The higher rises may be caused by lake breeze cell effects, rather than by anomalously low fl values. Bringfelt derived mean values of a from his own data set smaller than those Rittmann derives, probably because Bringfelt excluded most cases with w/u < 1.0. Bringfelt’s values were b = 0.53 for slightly stable or windy conditions and B = 0.57 for strongly stable or weak wind conditions. My second comment concerns Rittman’s Fig. 2. He assumes that Ah J x2,3, to extrapolate the cited observations to a standard distance, x = 250m. This is a considerable extrapolation for some of the measurements, such as those at the CEGB power plants, made at nearly six times this distance. This extrapolation would be valid if the plumes were definitely in the two-thirds law rise regime, but this probably is not the case for the two points representing the smaller of the CEGB plants, because this source was relatively weak. For these two points, at F = 57 and 175 m4 s 3, the model recommended in Briggs (I 969) gives 39 and 27 “,, less rise than does the two-thirds law, because of ambient turbulence. If these two points were corrected for this effect, or were simply left out, Fig. 2 would be entirely altered. It could not then be claimed that the “points that represented industrial-sized sources exhibited more scatter and fell at or below the predictions” (Rittmann, 1982). Rittman’s claim is based entirely on only two data points and these have been extrapolated from beyond the two-thirds law regime. As a minor complaint, it appears that three of Bringfelt’s runs are missing from Fig. 1 and that Fig. 4 shows three negative plume rise values at x = 250 m, while Bringfelt’s data tabulation has only one. As shown by the example above, both regression lines and physical conclusions can be influenced by even a few inappropriate or misplaced data points in such small data sets, so extra care is necessary. GARY A. BRIGGS 6.S. Enoironmental Protection Ayenc~ Meteorology and Assessment Division Research Triangle Park. NC 27711. C’.S.A.
* Rittmann 2575-2580.
B. E. (1982) Atmospheric
Enoironment
16,
Brlggs G A. (1969) Plume Rise, US. Atomic t.nergj Commission, TID-25075. Oak Ridge, TN. Briggs G. A. (1975) Plume rise predictions. In Lrcrurr, ,)tr lit Pollutwn and tkironmental Impact .-lnal.ysrs, pp. 39 I I I American MeteorologIcal Society. Boston, MA. Brmgfelt B. (1969) A study of buoyant chimmey plumes m neutral and stable atmospheres. ~Ifmo\phrrfc~ En~~rr~rt~nr~~r 3, 609 6’3.
AUTHOR’S
REPLY
1 thank Dr. Briggs for his Discussion, which, along with this reply, should help to clarify better the impact of source size on plume rise and the application of the two-thirds law. The first few sentences of the Discussion strike at the fundamental issue. Evidence and theory indicate that smaller sources are more susceptible to effects of the stack wake. buildings, terrain and ambient turbulence. Therefore. the overall entrainment coefficient is likely larger than the 0.6 value obtained when the stack, building, terrain and ambientturbulence can be suppressed in water channels or wind tunnels. Although B for the vertical rise of bent-over plume may be fairly constant for all source sizes, the other effects are not. In the two-thirds law (Equation 10 in the original paper). the only variable available to adjust for phenomena that change plume rise is @. Therefore, the only realistic way to apply the two-thirds law to field sources is to consider that [j includes all significant factors that affect entrainment or otherwise affect the rise. For example, when the plume interacts with the stack wake, the overall entrainment rate increases, and rise is reduced. The practical application of the two-thirds law cannot afford to include only one phenomenon when others are also important, since plume rise will be over predicted. Dr. Briggs notes that Bringfelt calculated lower /j values than I did for the same data. The inain reason is that Bringfelt used u values at maximum plume height, while I corrected to utlp, the wind speed at the stack tip. My method is consistent with the current modeling practice to use utlpand, therefore, estimates a fi value that is accurate when subsequently applied for plume-rise prediction. Dr. Briggs objects to the use of x = 250 m on Fig. 2. Use of 250 m was a convenience to make Fig. 2 consistent with the other figures. Since data were available for only one distance for each source and since these distances were all different. some convention was necessary to compare the data graphically. Dr. Briggs may be correct that the two smallest sources had terminated or reduced rise because of ambient turbulence. If so, these data reinforce the conclusion that smaller sources are more affected by phenomena that reduce rise. Unfortunately, the model to which Dr. Briggs refers for considering ambient turbulence is not normally applied in airquality models. Finally, Dr. Briggs complains about inaccuracies in Figs I and 4. First, all appropriate points are included in Fig. 1 and the statistical analysis used to generate the regression line. Second, the text clearly states that the solid symbols represent the three cases in which negative plume rise was observed, even if it was not negative at 250 m. If the rise was not positive at 250 m, Ah = + I m was arbitrarily assigned. Perhaps Dr. Briggs was reading an early draft in which this point was not stated clearly. Department of’ Civil Engineering University of’ Illinois at Urbana-Champaign l_irbana, IL 61801, U.S.A.
BRUCE E. RITTMANN
While 1 agree with Rittmann’s conclusions regarding the increased susceptibility of small-source plumes to downwash, I find no support for the idea that the entrainment coefficient, B, is a function of source size. For buoyancy-dominated plumes known to be free of stack tip, building, or terraininduced effects, the rising part of their trajectories has always been observed to approximate the two-thirds law with fi = 0.6. If there were a trend towards larger values of/r with decreasing source size, it would certainly be apparent in laboratory-scale water-channel and wind-tunnel plumes. No such trend is evident in the extensive list of experimental values of the constant in the two-thirds law given by Briggs (1975, Table 3). Six laboratory studiesare cited; for all but the earliest experiment, p = 0.60 to 0.67. Bringfelt (1969) based his suggestion that fi decreases for larger source sizes largely on the values observed for the Tallawara and Lakeview power plants (two of the four b values listed in his Table 2). Both of these plants are near lakes; Briggs (1969) noted “much higher rise than comparable sources” for these two plants. The higher rises may be caused by lake breeze cell effects, rather than by anomalously low fl values. Bringfelt derived mean values of a from his own data set smaller than those Rittmann derives, probably because Bringfelt excluded most cases with w/u < 1.0. Bringfelt’s values were b = 0.53 for slightly stable or windy conditions and B = 0.57 for strongly stable or weak wind conditions. My second comment concerns Rittman’s Fig. 2. He assumes that Ah J x2,3, to extrapolate the cited observations to a standard distance, x = 250m. This is a considerable extrapolation for some of the measurements, such as those at the CEGB power plants, made at nearly six times this distance. This extrapolation would be valid if the plumes were definitely in the two-thirds law rise regime, but this probably is not the case for the two points representing the smaller of the CEGB plants, because this source was relatively weak. For these two points, at F = 57 and 175 m4 s 3, the model recommended in Briggs (I 969) gives 39 and 27 “,, less rise than does the two-thirds law, because of ambient turbulence. If these two points were corrected for this effect, or were simply left out, Fig. 2 would be entirely altered. It could not then be claimed that the “points that represented industrial-sized sources exhibited more scatter and fell at or below the predictions” (Rittmann, 1982). Rittman’s claim is based entirely on only two data points and these have been extrapolated from beyond the two-thirds law regime. As a minor complaint, it appears that three of Bringfelt’s runs are missing from Fig. 1 and that Fig. 4 shows three negative plume rise values at x = 250 m, while Bringfelt’s data tabulation has only one. As shown by the example above, both regression lines and physical conclusions can be influenced by even a few inappropriate or misplaced data points in such small data sets, so extra care is necessary. GARY A. BRIGGS 6.S. Enoironmental Protection Ayenc~ Meteorology and Assessment Division Research Triangle Park. NC 27711. C’.S.A.
* Rittmann 2575-2580.
B. E. (1982) Atmospheric
Enoironment
16,
Brlggs G A. (1969) Plume Rise, US. Atomic t.nergj Commission, TID-25075. Oak Ridge, TN. Briggs G. A. (1975) Plume rise predictions. In Lrcrurr, ,)tr lit Pollutwn and tkironmental Impact .-lnal.ysrs, pp. 39 I I I American MeteorologIcal Society. Boston, MA. Brmgfelt B. (1969) A study of buoyant chimmey plumes m neutral and stable atmospheres. ~Ifmo\phrrfc~ En~~rr~rt~nr~~r 3, 609 6’3.
AUTHOR’S
REPLY
1 thank Dr. Briggs for his Discussion, which, along with this reply, should help to clarify better the impact of source size on plume rise and the application of the two-thirds law. The first few sentences of the Discussion strike at the fundamental issue. Evidence and theory indicate that smaller sources are more susceptible to effects of the stack wake. buildings, terrain and ambient turbulence. Therefore. the overall entrainment coefficient is likely larger than the 0.6 value obtained when the stack, building, terrain and ambientturbulence can be suppressed in water channels or wind tunnels. Although B for the vertical rise of bent-over plume may be fairly constant for all source sizes, the other effects are not. In the two-thirds law (Equation 10 in the original paper). the only variable available to adjust for phenomena that change plume rise is @. Therefore, the only realistic way to apply the two-thirds law to field sources is to consider that [j includes all significant factors that affect entrainment or otherwise affect the rise. For example, when the plume interacts with the stack wake, the overall entrainment rate increases, and rise is reduced. The practical application of the two-thirds law cannot afford to include only one phenomenon when others are also important, since plume rise will be over predicted. Dr. Briggs notes that Bringfelt calculated lower /j values than I did for the same data. The inain reason is that Bringfelt used u values at maximum plume height, while I corrected to utlp, the wind speed at the stack tip. My method is consistent with the current modeling practice to use utlpand, therefore, estimates a fi value that is accurate when subsequently applied for plume-rise prediction. Dr. Briggs objects to the use of x = 250 m on Fig. 2. Use of 250 m was a convenience to make Fig. 2 consistent with the other figures. Since data were available for only one distance for each source and since these distances were all different. some convention was necessary to compare the data graphically. Dr. Briggs may be correct that the two smallest sources had terminated or reduced rise because of ambient turbulence. If so, these data reinforce the conclusion that smaller sources are more affected by phenomena that reduce rise. Unfortunately, the model to which Dr. Briggs refers for considering ambient turbulence is not normally applied in airquality models. Finally, Dr. Briggs complains about inaccuracies in Figs I and 4. First, all appropriate points are included in Fig. 1 and the statistical analysis used to generate the regression line. Second, the text clearly states that the solid symbols represent the three cases in which negative plume rise was observed, even if it was not negative at 250 m. If the rise was not positive at 250 m, Ah = + I m was arbitrarily assigned. Perhaps Dr. Briggs was reading an early draft in which this point was not stated clearly. Department of’ Civil Engineering University of’ Illinois at Urbana-Champaign l_irbana, IL 61801, U.S.A.
BRUCE E. RITTMANN