OF   PLU MES

                 OF PLUMES
                 Francis Pooler, Jr.
          U.S. Weather Bureau Research Station
        Robert A. Taft Sanitary Engineering Center
                 Public Health Service
               Division of Air Pollution
                  Cincinnati, Ohio


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       Public Health Service Publication No.  999-AP-16

                              GPO 822-190-2

    Expected ground-level concentrations resulting from emissions
from large power plants are discussed for three meteorological
situations considered to be most likely to result in significant air
pollution concentrations.  These situations are (1) high wind;  (Z)  in-
version breakup; and (3) limited mixing layer with a light wind.
Effects of increasing stack height are discussed for each situation.
Numerical examples based on calculations included as an appendix
are shown.

      Dispersion of effluent from large power-generating plants must be
considered on the basis of individual plants.  Although diffusion formulae
for comparatively small  sources have been at least partially checked
against actual dispersion,  similar extrapolations from existing data
probably cannot be applied to estimates of pollutant emissions from plants
in the range of 1000- to 5000-megawatts capacity.  Plants of such sizes
emit heat at a rate equivalent to the  net heating by the sun over an area
many hundreds or  thousands  of meters in  diameter; it is evident that
such a source will set up its own circulation pattern in the air, at least
in the immediate vicinity of the plant.  Most of the time the effluent plume
will rise far above the ground, and its only influence on air quality will
be  to increase the surface  concentrations  of pollutants in the air mass
downwind by some rather small amount. If significant background pol-
lution  levels exist,  however,  even  a small addition to the background
concentration could introduce a pollution problem.
      It is assumed that any new plant -will be designed to meet two en-
gineering criteria to prevent pollution  in the immediate vicinity of the
plant.   First, the  stacks will be tall  enough to prevent  aerodynamic
downwash caused by large obstacles  to the air flow.  This criterion can
be met by following the "2-1/2" rule, which states that a stack should be
at least 2-1/2 times the height of any nearby obstacles to the flow. Be-
cause a large power plant requires a large  building,  the minimum stack
height  imposed by this criterion alone will be several hundred feet. Sec-
ond, the exit speed of gases from the stack  and designof the chimney top
should be adequate to prevent entrainment  of effluent  into the turbulent
wake of the  stack. Generally, an exit speed in excess  of the wind  speed
will minimize this problem. Since both criteria evolve from aerodynamic:
considerations,  the adequacy of the  plant design  can be tested by -wind-
tunnel  models.
      If it is assumed that these engineering criteria are  met, then es-
timating potential pollution from large plants narrows to a consideration
of relatively infrequent weather conditions (conditions  that do occur,
however) that can bringabout ground-level fumigations: high winds, in-
version breakup, and a  limited mixing layer with light winds.  The fre-
quency of these adverse  conditions will determine the  magnitude and
frequency of the potential pollution.

     The following discuss ion of  these threetypesof fumigation is illus-
trated  numerically in Figures 1 through 3. The calculations on which
these figures are based  are  included  as  an appendix.  The models of
plume  dispersion used  werp based  on  the  experience of and data col-
lected  by TVA personnel  (.Gartrellet al. 1964), as well  as on the author' s
personal observationof the behavior of plumes .from large heat sources.
These  models were first used in conjunction with climatological data


of the Oak Ridge, Tennessee, area (Holland,  1953) as an informal cross-
check  on calculations  then being made by TVA personnel to determine
the stack height required  for a proposed new generating plant  (Thomas
et al. ,  1963).  The  conclusions  regarding required stack height were
the same for both methods of calculation.  The  exact assumptions used
to obtain the numerical values shown by the figures are not critical in
this discussion; the principal purpose here is to suggest the meteorolog-
ical factors that influence dispersion and should be  considered in loca-
tion and design of  large power plants.

                HIGH-WIND FUMIGATION  (Figure 1)
      High-wind fumigation occurs when the dilution of effluent by mo-
tions  in the air--longitudinal  dilution  due  directly  to  wind speed,  and
transverse dilution  by eddies, the  magnitude of which is a function of
wind  speed--is sufficient  to overcome the tendency for a heated plume
to accelerate upward as the  result of buoyancy forces.  With sufficiently
rapid dilution, the plume continuously decelerates  vertically, and an ef-
fective plume rise can be computed.  The  larger  the  source,  the greater
the wind  speed necessary  to cause this vertical deceleration throughout
the entire plume volume.  Although a precise relationship between plant
                                                   5000-Mw PLANT

                                              0.06  0.08    .0.10
                                               059   '0.100   0132  X 0.157
                                              0. 62 /   0115  / 0 161   /O 201

      0|0   0.20 0.30 0.40

                                             I   0.10  I'015
            5      10     15      20
            WIND SPEED, meters/sec
                                       0      5      10      15     20
                                             WIND SPEED, meters/sec
 Figure 1,
          Estimated ground-level SC>2 concentrations (ppm) in high-wind, neutral
          stability conditions.  (Sulfur content of coal  is assumed to be 1%; for
          other sulfur contents, value would be changed proportionately.  Values
          represent 1/2 hour averages. To approximate 3-minute average, multi-
          ply by 2.5; to approximate 2-hour average,  multiply by 0.5.)
                                POTENTIAL DISPERSION OF PLUMES

capacity and this "critical" wind speed is not known,  it is probable that
the critical speed for a  1000-Mw plant would be about  25 mph (13
meters/sec), and for a  5000-Mw plant, about 40 mph (20 meters/sec),
if  all emissions  are  assumed to come from a single stack.  At wind
speeds  less  than critical, an increasing proportion of the plume should
rise at  a. rate determined principally by buoyancy forces; the dilution
of this part  of the plume is determined by its upward motion as much
as by ambient turbulence.  Plume rise with such a divergent plume
is difficult to define,  and the concept of a coherent plume should
probably be  discarded in favor of a formulation in which the stabilized
portion of  the plume is considered,  rather than the rising portion.
The  particular f o r mu la t i o n s  for  "plume rise" and plume dispersion
were selected  only because they are widely used; the numerical
results probably  do show  reasonable  trends, even though they should
be valid, if at all,  only for wind  speeds in excess of  "critical. " The
implicationis that for plants of large enough capacity,  the concentrations
in a high-wind fumigation probably depend only on stack height and emis-
sion conditions, and thus maximum concentrations froma 5000-Mw plant
would be only slightly above those from a.  1000-Mw plant (with all emis-
sions from a single  stack).

      Although inversion-breakup fumigation is likely to produce the
highest concentrations at ground level, the area fumigated is likely to
be_.a long, narrow ribbon-like  formation  with  its closest  point a num-
ber  of  miles away; therefore,  the  chances of detecting fumigations of
this  type are very slight unless the  same  area is  fumigated repeatedly
because of topographic restraints.  This type of fumigation occurs when
effluent is emitted into a stable layer so that the plume moves off as an
elevated flat ribbon.  A  surface-based mixing layer subsequently de-
velops, builds up to include the plume,  and stirs  the effluent  down to
ground level.  The resultant ground-level concentration is inversely
proportional to plume height, horizontal spread, and wind speed at plume
height.  The plume rise above  the top of the stack is determined by the
wind speed and the degree of stability in the inversion layer. Since wind
speed generally increases through this layer while intensity of the inver-
sion decreases, these factors tend to counteract each  other so thatplume
rise is not strongly dependent on stack height; thus increasing the stack
height  increases height of the plume above the ground by a like  amount.
With a taller stack, the plume is likely to be transported away by a strong-
er flow, and the  horizontal spread of the plume will be greater  because
a longer time is required for the mixing layer to develop to plume height.
Thus, tall stacks are fully as important for minimizing this  kind of fumi-
gation  as for a high-wind fumigation. In addition,  since the plume from
a sufficiently tall stack may rise above the top of a nocturnal inversion,
the frequency of inversion-breakup fumigations is reduced with taller
stacks. Under inversion conditions  an increase of plant size will result
ina proportionately smaller increase of plume rise than under high-wind
conditions; thus, the maximum concentrations  should increase  as plant
capacity is increased, but at a  less than  linear rate.



< 400
         0 50 040 0.30
     0     25    50    7.5     100    [25
           WIND SPEED,  meters/sec
WIND SPEED, meters/sec
 Figure 2.  Estimated ground-level  SC>2 concentrations ( ppm) in inversion-breakup
          fumigation.  (Sulfur content of coal is assumed to be 1%; for other sul-
          fur contents, values would be changed  proportionately.  Values repre-
          sent 1/2- to 1-hour averages.)
                    WITH LIGHT WINDS   (Figure 3)

      Fumigation in. a limited mixing layer with light winds  occurs when
effluent is contained within too small a mixing volume. Under these cir-
cumstances, the plume will  rise to the top of the surface-based mixing
layer (up to the base of the inversion),  which may be up to  thousands of
feet deep, and then diffuse and  subside to ground level at a rate  deter-
mined bythe rate of convective overturning brought about by solar heat-
ing of the ground.   Stack height  has essentially no effect  on fumigations
of this  kind.   The  ground-level  concentration after some  time will be
given by emission  rate  divided,  by the product of mixing height,  mean
wind  speed,  and cross-wind spread.  The time after  which such a com-
putation becomes meaningful  is that required for  the effluent to mix and
subside to ground level.  With a relatively small plant, this subsidence
begins almost  immediately after the plume has risen to the  top of the
mixing, layer; with increasing plant size,  a greater fraction of the plume
will still be warmer and therefore less  dense than the air through which
it rose,  and thus  will stabilize at some short distance above the mixing
                                POTENTIAL DISPERSION OF PLUMES


                    2500 -

                            1          I
                          1000 -Mw PLANT
0.30 \\  \\
  \  .0227   X.O.C
                                              ~      0.70
                           ^.0.362    +0226    ^.0.159
                               V                   0.15
                                                                    _I.Op9 \  \+0.480    \0.305
                                                                 n635\    10.416
                                                                  \  >     '

                                                      1.40 |VDO '80 O-60 "0.50
                                                       I	I
                            2         3        4
                      WIND SPEED, meters/sec
                                                          WIND SPEED,  meters/sec
                        'Figure'3.   Estimated gr o u n d-l e v e I SC>2 concentrations ( ppm) in lightrwind, limited-mixing-
                                    depth conditions.  (Sulfur content of coal is assumed to be 1%; for other sulfur con-
                                    tents, values would be changed proportionately.  Values represent 1/2- to  1-hour
                                    averages.  To approximate 3-minute average, multiply by  1.75; to approximate 2- to
                                    3-hour average, multiply by 0,75.)

layer or within the capping stable layer. The plume will be released in-
to the mixing layer as that layer develops greater depth, thus introducing
a time-delay factor, which increases with increasing plant size. Incon-
sequence,  the maximum ground-level  concentration with  this kind of
fumigation increases with plant  size at a less than linear rate, but the
area fumigated increases in direct proportion to plant size.

      The experience of the TVA with their many steam-generating
plants illustrates some of these  situations. As plants of increasingly
larger capacity have been built,  -with correspondingly taller  stacks, the
fumigations have  shifted from the high-wind type, with which many people
are most familiar,  to  the light-wind type.   Although tall stacks can be
built to minimize the high-wind and inversion-breakup fumigations, the
total  pollution discharge of the larger plants becomes a problem  when
the limited capacity of the mixing layer prevents adequate dilution. Thus,
the other element that determines concentrations, the pollutant source
strength, must be controlled if such large plants are  to be built in parts
of the country where this type of  fumigation  occurs with any appreciable
frequency. Although conditions of this type are most frequent in Southern
California,  no section of the country can consider itself immune  from
such problems if the pollution sources are present.

                         LOCAL EFFECTS
      Local factors may exert some influence on each of these types  of
fumigation.  Since  large power  plants are  built adjacent to sources  of
cooling water, there are invariably some topographic complications that
must  be considered. With both high-wind and inversion-breakup fumiga-
tions,  the  more  elevated points  in the areas affected will experience
higher concentrations than would be found  over flat  terrain.   For the
high-wind  fumigation comparatively large-scale  topographic  features,
such  as  a small  mountain upwind or an extensive water s.urface down-
wind, can create a mean downflow that lowers  the  plume as  it moves
downwind. For the inversion-breakup fumigation, large-scale channel-
ling such as found with the Trail, B.C., smelter (Hewsonand Gill,  1944)
may confine the plume to a selected path and  lead to repeated  local fumi-
gations.   In other areas a stable layer may flow over a much warmer
region, e.g., from water to  land in the summer or from the  outskirts
of a large city  over the city itself,  and lead to an inversion-breakup
fumigation because  of  a spatial  transition of the  flow.  For the light-
wind fumigation a. large,  cool surface, such as a lake, will always be a
favored region for subsidence, so that the downwind  shore may  experi-
ence more frequent and severe fumigations  than any surrounding areas.
      The dispersionpotential fora large power plant must be calculated
from  a consideration of the  locale into which the plant is to be fitted,
and thus the details of location and design must be treated individually.
Meteorological control of plant operations may be required when poten-
tial pollution cannot be minimized by any  other methods.
                               POTENTIAL DISPERSION OF PLUMES


                 Formulae and Numerical Values  Used

          in Calculating Maximum Ground-Level Concentrations

 (All symbols and numerical values are listed and defined in Table Al. )

      Atmospheric pressure of  1000 mb and temperature of 15C were
 assumed for all calculations.   The emission rate of heat to the atmos-
 phere was assumed to be  15 percent of the plant  generating capacity,
 with an emission temperature of 140C and a stack efflux  speed of 20
 meters per second.   From mass continuity with these assumptions, the
 stack diameter for a 1000-Mw plant is 9.565 meters.  With an assumed
 coal  consumption rate of  3,83  tons per hour for  a  1000-Mw plant,  with
 full conversion of the sulfur to  SO2 and its emission to the atmosphere,
 the SO2  emission rate is 1. 932 x 10^ p grams per second. For  a 5000-
 Mw plant, the heat and SO2 emission rates were multiplied by 5,  and
 the stack diameter  by 5l/2  2.236. All calculations were for p  1  per-
 cent; the concentrations shown in Figures 1,  2,  and 3 should be multi-
 plied by p for other sulfur  contents.

      Plume rise was calculated from Holland's formula,

                1. 5Vsds + 0.409 x 10"4QH
 and the maximum ground-level concentration from  Button's equation,

           Xm~'reuh2 "so2

 Calculations were  made for four -wind speeds   5, 10, 15, and 20
 meters  per  second;  and for three stack heights   200,  400,   and 600
 feet.  Concentrations at  intermediate  values  were obtained by  graphi-
 cal interpolation.

      A formula for plume rise was developed from  dimensional  consid-
erations :
jApgdj vsTa

4p3. T- u(u + vs)
      It was assumed that the effluent plume rises some distance through
the inversion layer and becomes stabilized with the .plume centerline a
distance Ah above the top of the stack.  Thereafter, as the plume  moves
downwind,  it widens with  downwind travel but the depth is constant.  It
was assumed that the maximum ground-level concentration occurs when
the plume elements emitted at the time that a surface-based mixing layer.

has developed just to stack-top level are later mixed to ground level as
the mixing layer builds up to plume level, resulting in the minimum time
after emission  for plume travel within the inversion layer.  It was as-
sumed that the mixing layer would have to develop to the top of the plume,
defined here as 2az above the plume centerline (see Figure Al).  The
                                   'i;VU- PLUME" CENTERLINE'.;
             (A) Temperature profile at time of emission, (t = o)
             (B) Temperature profile at time of fumigation, (t = tm)

                                Figure Al.

net amount of heating of  the mixing  layer required (proportional to the
area enclosed between curves A and  B) is given by

where xv =
         at t   0.  Values of C
                                  0. 05'657 m
and n = 0.. 25
were assumed.  Initial plume widths were represented by assuming 
stabilization above the inversion base of any plume element will be pro-
portional to the excess temperature of the element, and inversely pro-
portional to the stability of the layer. The maximum penetration AH will
thus be given by
The effluent will be uniformly distributed in the layer from H to (H + AH).

      For the plume elements at (H + AH) to become re-incorporated into
the mixing layer, the mixing layer must increase in depth by an amount
AH, or  the temperature of the mixing layer must be increased by  Tm.
If AH  is small compared to H, the required heating per unit area of sur-
face is  given by

            q  = HpacpATm                                        (9)

Also q = Rt .  Hence,
                      R         7T3uHR
It was further assumed that, once released, the plume elements  subside
and mix back to ground level according to a vertical velocity distribution
dt   0.5+0. 00 Iz.  Integrating,  the subsidence time tg  is given by

            ts    1000 ln(l  + 0. 002H)                              (11)

      The maximum ground-level concentration -when the total plume is
stirred back to ground level is given by
                    ["i  Z-n
      u(tr + ts) + xvj   2 ;  values of Cy- 1.00m1'4, n= 0. 50

were  assumed,  whence xv    ("-u)1'^

      Calculations of Xm were made for -wind speeds of 1,  2,  3,  and 4
meters per second,  and mixing  layer  depths of 500, 1000, 1500, and
2000  meters.  Concentrations at intermediate values "were  obtained  by
graphical interpolation.

      The maximum (centerline) ground-level concentrationXj. for a time
of travel t other than (tr + tg) as a fraction of the maximum concentra-
tion is given by
Xt  = (t-tg)   U(tr + tg) + Xy

Xm     tr   [    Ut + Xy    J

Xt      U(tr + tg) + Xy    "

Xm    L    ut + xv    J
                                          0. 75
                                               for ts  (tr + ts)  (13b)
           Xt   0                             for t < ts         (13c)

10                             POTENTIAL DISPERSION OF PLUMES

            These equations could also be expressedinterms of distance
through the equality x  ut. Togetherwith Equation (12), these equations
show that for a given set of meteorological conditions (u, H, and R), the
ground-level concentration initially increases with travel  time  t at the
same rate for all plant sizes; however, the larger the plant, the longer
the travel time over which ground-level  concentration increases, and
hence the higher the maximum concentration.


Cp    specific heat of air at constant pressure, 0.240 cal g  K"  .
Cy   horizontal diffusion coefficient,  (meters)2.

ds    stack diameter, meters.

e     base of natural logarithms,  2.71828....
g     acceleration of gravity,  9. 806 m sec  .

h     (=hs + Ah) plume height above ground, meters.
hg    stack height,  meters.

Ah   plume rise, meters.
H     depth of mixing layer, meters.
AH   increase in depth of mixing layer,  meters.
n     dimensionless exponent related to distance-dependence of diffusion
p     percentage sulfur in coal.
q     net heating of an air  column, cal m   .

Q     emission rate  of SO2, g sec"  .

QTT   emission rate  of heat, cal sec.
R     net rate of sensible heating of an air column by solar radiation,
      assumed constant equal  to  0.4 Langleys min     66.67 cal m"^
      sec"  .
t      travel time,  seconds.
tm   time required for mixing layer to develop to top of plume,  seconds
      (for inversion breakup).
tr     time required for mixing layer to develop to topof plume,  seconds
      (for light wind).
ts     time  required for  plume  elements to descendfromtop of  mixing
      layer to the surface, seconds  (for  light wind).

Ta   ambient air temperature,  assumed constant  at 15C  = 288. 16K.

ATm maximum temperature difference b et w e e n plume elements and
      surroundings,  C  (for light wind).

u     wind speed, m sec"  .
vs    stack exit speed, m sec   .

FROM LARGE POWER PLANTS                                   11

x     travel distance, meters.

xv    virtual travel distance to represent initial plume spread, meters.
6_6    vertical potential temperature gradient, C m; assumed constant
6z    at 1. 96 x 10~2 C m"1 for inversion breakup.
TT     constant, 3. 14159. . . .

"a    ambient  air density,  assumed constant at 1.209 x 10  g m  .
p    density difference between stack effluent and ambient air, assumed
      constant at 0. 3658 x  103 g m"3.

*SO  density of SC>2 at ambient conditions, assumed constant at  2. 671 x
      10"3 g cm"3.
jj    vertical  and crosswind standard deviations of  plume distribution
      at height H, meters (for light wind).
*y    crosswind standard deviation of plume distribution, meters.

TZ    vertical  standard  deviation of plume distribution, meters.

\rn  maximum ground  level concentration,  ppm (vol).
Xt    centerline ground level concentration at travel  time t, ppm (vol).

Gartrell,  F. E. ,  Thomas, F. W. ,  Carpenter,  S.B.,  Pooler,  F. Jr.,
      Turner,  D. B. , and Leavitt, J.M. (1964) Full-Scale Study of Dis -
      persion of Stack Gases  A Summary Report.  Tennessee Valley
      Authority,  Chattanooga, Tennessee.
Hewson, E. W. ,  and Gill, G. C. (1944).  Meteorological Investigations
      in Columbia River Valley near Trail. Part II of Report Submitted
      to the  Trail Smelter Arbitral Tribunal,  U. S. Bureau of Mines
      Bulletin  453.  Government  Printing Office, "Washington.

Holland, J. Z.  (1953)  A Meteorological Survey of the Oak  Ridge Area,
      ORO-99.  U.S.  Atomic Energy Commission, OakRidge, Tennes-
Thomas,  F.  W. , Carpenter,  S. B. , and Gartrell, F. E. (1963)  Stacks-
      How High?  Journal of the Air Pollution Control Association  13:
    GPO 8221903                  13

 BIBLIOGRAPHIC: Pooler,  Francis Jr.   Potential dis-
      persion of plumes from large power plants.
      PHS Publ. No.  999-AP-16.   1965.  ,13pp.

 ABSTRACT:  Expected ground-level concentrations re-
      sulting from emissions from large  power plants
      are discussed for three meteorological situations
      considered to be most likely to result in signifi-
      cant concentrations.  These situations are (1) high
      wind; (2) inversion breakup; and (3) limited mixing
      layer with a. light wind.  Effects of  increasing
      stack height are discussed for each situation.
      Numerical examples based on calculations included
      as an appendix are shown.
BIBLIOGRAPHIC:  Pooler, Francis Jr.  Potential dis-
      persion of plumes from large power plants.
      PHS Publ. No. 999-AP-16.   1965.  13 pp.

ABSTRACT:  Expected ground-level concentrations re-
      sulting from emissions from large power plants
      are discussed for three meteorological situations
      considered to be most likely to result in signifi-
      cant concentrations.  These situations are  (1) high
      wind; (2) inversion breakup; and (3) limited mixing
      layer with a light wind.  Effects of increasing
      stack height are discussed for each situation.
      Numerical examples  based on calculations  included
      as an appendix are shown.
BIBLIOGRAPHIC:  Pooler, Francis Jr.  Potential dis-
      persion of plumes from large power plants.
      PHS Publ. No. 999-AP-16.  1965.  13pp.

ABSTRACT:  Expected ground-level concentrations  re-
      sulting from emissions from large power plants
      are discussed for three meteorological situations
      considered to be  most likely to  result in  signifi-
      cant concentrations.  These situations are  (1) high
      wind; (2) inversion breakup; and (3) limited mixing
      layer with a light wind.  Effects of increasing
      stack height are discussed for each situation.
      Numerical examples based on calculations  included
      as an appendix are shown.
                                                              ACCESSION NO.