EPA/600/A-97/092
For presentation at the American Meteorological Society
10th Joint Conference on the Applications of air Pollution
Meteorology with the AWM&, Phoenix, AZ Jan. 11 - 16, 1998
9B.3 RECENT EXPERIMENTS ON BUOYANT PLUME DISPERSION
IN A LABORATORY CONVECTION TANK
J.C. Weil
CIRES, University of Colorado
Boulder, Colorado
W.H. Snyder
Mechanical Engineering Department, University of Surrey
GuUdford, Surrey, England
R.E. Lawson, Jr.*
ASMD, ARL, National Oceanic and Atmospheric Administration
Research Triangle Park, North Carolina
M.S. Shipman
Geophex, Ltd.
Raleigh, North Carolina
1. INTRODUCTION
Buoyant plumes from tall stacks usually pro-
duce their highest ground-level concentrations
(GLCs) in a convective boundary layer (CBL),
where turbulent downdrafts bring elevated plume
sections to the surface. Our understanding of buoy-
ant plume dispersal has been significantly advanced
by Willis and Deardorff's (1983,1987) experiments
in a laboratory convection tank. Their studies
demonstrated the complex dispersion patterns and
the dependence of plume properties on the dimen-
sionless buoyancy flux F, = F&/(f7w!*2j), where F&
is the stack buoyancy flux, U is the mean wind
speed, u>. is the convective velocity scale, and «j
is the CBL depth. For F, = 0.03, the plume be-
haved similarly to a nonbuoyant plume after some
initial rise, but for F» = 0.11, the plume rose to the
CBL top, where it "lofted" or remained temporarily
and then gradually mixed downwards. Field obser-
vations around tall stacks suggested that the maxi-
mum hourly-averaged GLCs generally occur for the
lofting situation (e.g., Hanna and Paine, 1989).
In related experiments, Deardorff and Willis
(1984) investigated concentration fluctuations for
elevated sources and found large near-surface values
* On assignment to NERL, U.S. Environmental
Protection Agency.
Corresponding author address: J.C. Weil, NCAR,
P.O. Box 3000, Boulder, CO
of the fluctuation intensity ac/C (Le., > 1); here,
C is the ensemble-mean concentration and ac is the
root-mean-square (rms) concentration fluctuation.
The cre/C decreased significantly with increasing
distance along the plume centerline. Later exper-
iments provided much needed information on the
probability distribution of the concentration (Dear-
dorff and Willis, 1988).
While clearly revolutionary, these experiments
were limited by the measurement techniques and
the small sample sizes collected. For example,
in the highly-buoyant plume studies, only 4 to
9 repetitions of the concentration profiles were
obtained (Willis and Deardorff, 1987). This
resulted hi uncertainty in the (7 values near the
surface and underestimates of the lateral plume
spread av (see later discussion).
The above limitations were overcome in re-
cent convection tank experiments conducted at the
EPA Fluid Modeling Facility hi North Carolina.
The main experimental objective was to obtain
statistically-reliable dispersion characteristics in-
cluding C, ac, o-j,, etc. for highly-buoyant plumes,
F, > 0.1. Since the concentration fluctuations were
known to be large, a key design feature was a means
for obtaining a sufficiently large number of mea-
surements to ensure such reliability.
2. EXPERIMENT DESCRIPTION
The experimental arrangement was quite simi-
lar to that of Willis and Deardorff (1987). The con-
vection tank was about 124 cm on a side, was filled
-------
with water to a depth of 34 cm, and had an ini-
tial stratification aloft of l°C/cm. The convection
was driven by an electrically-heated bottom surface
that produced a z< ~ 20 cm and tw, = 0.74 cm/s at
the time of the measurements. A mean wind was
simulated by towing a model stack (height zt = 3
cm) along the tank floor at a speed U of 2.07 cm/s.
The stack emitted a water - ethanol mixture to sim-
ulate the buoyancy, and the mixture contained a
small amount of Rhodamine dye, which fluoresced
when excited by laser Eght,
In an approach different from that of Willis and
Deardorff, a laser was mounted on a movable table
alongside the tank and towed at the stack speed
in order to illuminate a y - z (crosswind, vertical)
plane at a fixed distance x downstream of the
stack. Pictures of the fluorescent dye were taken
from a camera viewing this plane end-on; the light
intensity was digitized, stored, and subsequently
converted to concentration in y and z intervals of
0.2 cm. In each tow, 59 cross-sectional images
were digitally recorded (at 0.8 s intervals) as the
stack traversed the tank. The tow was repeated
6-7 times for a total of 354 - 413 realizations of
each cross section. This is an unprecedented data
volume.
Four experiments were performed each with a
different F, but the same effluent speed, U, and
CBL variables; the F, values were 0, 0.1, 0.2 and
0.4, with F» = 0 serving as a reference case. In
each experiment, 8 downwind cross sections were
sampled.
3. RESULTS
We present salient features of the horizontal
scalar flux, plume spatial statistics, and concentra-
tion fields. We use convective scaling of disper-
sion wherein z« and w* are the relevant turbulence
length and velocity scales (Willis and Deardorff,
1987). An appropriate dimensionless distance Is
(I)
which is the ratio of travel time x/U to the
convective time scale Zi/w».
The horizontal scalar flux F in each sampled
cross section was determined from
= j f
c(x,y,z)Udydz
(2)
where c is the "instantaneous" concentration.
Figure la shows an example pseudo time-series
of the ratio T/Q, where Q is the source flux.
The above was constructed by arranging the
measurements from 7 tows in a time sequence
using the sampling interval (0.8 s). As can be
seen, there is a large variability in T/Q—from
0.1 to ~ 3, although on average, the mean flux
F = Q. We believe that the variability is
caused by longitudinal velocity fluctuations and
by the convergence/divergence of the flow at the
boundaries, i.e., the exchange of fluid and scalar
from updrafts to downdrafts and vice versa at z — 0
and £j. _
In each of the four experiments, the T averaged
over the 8 downwind distances was within 20% of
Q, As a correction to c, we multiplied the c in
all realizations by the inverse of the initial average
50 100 150 200 250 300 350
Time (a)
1.8
1.6 •
1.4-
1.2
1
OP
.8
.6 •
.4 •
2.
b)
A
a
o
o
V
PPA sales, F.=<3
PPH series, F.=0.1
PPC series, F.=0,2
PPM series, F.=0.4
PPO series, F.=0. W,/U=0
1 1.5
2 2.5
X
3.5
4,5
Fig. 1. a) Tune series of plume horizontal
scalar flux, and b) mean scalar flux as a function of
dimensionless distance X.
-------
1.1
1
.9
.8
.7 t
.5
.5 •
.4 •
.3 •
.2 -:
.1
0
A PPA series, F.=0
O PPH series, F,=<3.1
O ppc series, F,=0.2
O PPM series, F.=0.4
7 PPO series, F.=0, W./U-0
J
1,5
2 2.5
JT
3.5
4,5
PPA series, F.=0
Q PPH series, F.=0.1
O PPC series, F.=0.2
O PPM series, F.=0,4
V PPO series, Fv>0, V\yu=0
Fig. 2. Dimensionless mean plume height
versus X.
Fig, 3. Dimensionless crosswind dispersion as
a function of X.
flux ratio (F/Q) for each experiment. Figure Ib
presents the variation of the "corrected" T/Q with
X and demonstrates that it is within 10% of the
ideal value 1 at each X. The rms deviation (bars)
for F» = 0 (PPA series) shows that it is greatest
near the source and diminishes far downstream
due to the greater homogeruzation of the scalar; a
similar rms behavior is found for the other cases. In
contrast to the above, Willis and Deardorff (1987)
and Deardorff and Willis (1988) used a correction
to c that ranged from 1/3 to 3*
Figure 2 shows that the dimensionless mean
plume height "z/z* varies systematically with both
F, and X. Note that for F, = 0.1 and X < 2,
the buoyancy has a profound effect in increasing
~z relative to the nonbuoyant case (PPA), but for
X > 2, the J's for these two cases are quite
close. At X = 4, the "z/Zi for the two cases is
a 0.6 instead of the expected 0.5 for a unifonnly-
mixed plume below z\. Our result is consistent
with the vertical profile of the crosswind-integrated
concentration (CWIC) for F. = 0, which exhibits
a well-mixed distribution for z/Zi < 1.15. More
recent measurements show that the well-mixed
depth is perhaps 5 to 10% lower. Thus, there is
some uncertainty hi the final equilibrium 2 values,
and this is under investigation.
Figure 3 presents new measurements (open
symbols) of the dimensionless crosswind dispersion
ffy/Zi as a function of X and displays several
features: 1) the 0.1; Briggs, 1985). Briggs' expression
is ffy/Zi = o1F.1/3Jr2/'3 with oj = 1.6. The
tank data show that this functional dependence is
followed (dashed line) but that the coefficient 01
(= 0.47) is only 30% of the field value. This may
be partially explained by other effects (crosswind
shear, mesoscale variabilily, etc.) that are present
in the field but absent in the convection tank.
From the repeated cross section measurements,
we determined the spatial distributions of £7, &c,
and the CWIC (7» = ^C(x,y,z)dy. Figure
4 gives an example of the dimensionless CWIC
CyUzi/Q as a function of z/Zi and X for F» =
0.2. This clearly shows the maintenance of an
elevated maximum in Cv above 2j and the Cv
profile development within the mixed layer (2 < Zj)
over the range X < 3. For X > 3, the profile below
-------
PPCnrtM.F.-O.Z
1.4
1.2
1
jjO.8
"*•" 0.6
0.4
0.2
0
2 3
X
Fig. 4. Vertical profiles of CyUzi/Q versus X.
O- 1
New Data
PPA series, F.=0
PPH series, F.=0.1
PPC series, F.-O2
PPM series, F.-Q.4
PPO series, F.=0
D & W (1984)
W k D (1987)
F. = 0.11
F. = 0.28
=0.54
0 .5 1 1.5 2 2.5 3 3.5 4 4.5
Fig. 5. Surface value of CvUzi/Q as a function
of X.
Zi is essentially uniform but with a magnitude less
than the well-mixed value, CvUzi/Q = 1. For
X > 4, we expect that the elevated maximum Cy
would diminish and the CWIC in the mixed layer
would increase due to entrainment of the plume
aloft. The maintenance of the elevated maximum
near its initial height (z/Zj s 1.1) differs from
the Willis and Deardorff (1987) observations, which
PPA series, F.=0
PPH series, F.=ai
PPC series, F.=0.2
PPM seiios, F.=0,4
PPO series, F.=0,
.5
Fig. 6. Dimensionless ground-level concentra-
tion versus X.
showed the maximum Cy first to overshoot z< and
then to remain at or below zi as X increased.
The dimensionless CWIC near the surface (Fig.
5) shows that the addition of buoyancy significantly
reduces the CWIC near the source (X < 2) by
comparison to the nonbuoyant case (PPA). For
X > 2, the moderately-buoyant case (F» = 0.1,
PPH) follows the nonbuoyant case rather well as
also found for z/Zj. Further systematic reductions
in the CWIC result as Ff increases from 0.1 to
0.4, a trend also found by Willis and Deardorff
(W & D, 1987). However, as seen in Fig. 5, their
results are lower than ours, especially for F, > 0.1.
TMs may be due to insufficient repetitions in their
experiments as suggested by their paper.
For dispersion applications, the quantity of
most interest is the surface concentration which
is displayed in dimensionless form in Fig. 6;
the concentration is along y = 0 and z/Zi =
0.05. Again, we observe that the buoyancy
has a dramatic effect in reducing the near-source
concentrations. The concentrations for Fm = 0 and
0.1 are approximately the same for X > 2.5 due to
the plume becoming vertically well-mixed and to
the similarity in their
-------
7
5
4
3
1
A PPA series, F.=0
D PPH series, F.=0.1
O PPC series, F.=O2
O PPM series, F.=0.4
PPO series, F.=0, W,/U=0
1.5
Lab. z./zi = 0.15, F. = 0.1
Field z./z; = 0.11 - 0.15, F. = 0.068 - 0.12
0 .5 1 1.5 2 2.5 3 3.5 4 4.5
X
Fig. 7. Concentration fluctuation intensity at
the surface versus X.
attained. This behavior is due to the increasingly
elevated plume centerlines for the more buoyant
releases (Fig. 2), and hence to a more intermittent
plume at the surface. Although there is a significant
variation with F. at short range, the <7C/C exhibits
a more gradual variation with X for X > 1.5 and
collapses to a nearly universal distribution. This
is attributed to the greater homogenization of the
plume within the mixed layer as X increases.
To test the laboratory results, we compared
the centerline GLCs (i.e., along y = 0) with
field observations downwind of the Kincaid power
plant. The plant had a 187-m stack and emitted
an SF6 tracer during an intensive field program
(Hanna and Paine, 1989). The data used here are
the maximum 1-hr SFe GLCs on crosswind arcs,
which ranged from 1.2 to 30 km downwind. The
meteorological variables had the following values:
1124 m < Zi < 1750 m, 2.4 m/s < U < 4.5 m/s,
and 2.0 m/s < wf < 2.6 m/s.
Figure 8 compares the dimensionless GLC
CUz?/Q from the laboratory and field, where
the field values of za/Zi and Ff are close to
their laboratory counterparts of 0.15 and 0.1,
respectively. We believe that the agreement
between the two data sets is quite good considering
the vast difference in scale and the absence of
extraneous effects (mesoscale variability, etc.) in
the convection tank. Figure 8 also presents a
O
="
O
0.5
C ± trc
• Field
— — Model; well-mixed
10
Fig. 8. Dimensionless ground-level concentra-
tion distribution for laboratory and field data.
model result based on a vertically well-mixed scalar
distribution with CUz?/Q = l/[(27r)1/2crff/zi]; we
have adopted 5. Note that for X < 4,
nearly all of the field observations are within ± 0.1,
2) surface C and ac/C variation with X, and 3)
agreement between the centerline GLC distribution
and field observations. This new experimental data
base will be of considerable value in future model
development efforts. Further experiments over a
greater range of za/Zi and for other Ff values also
would be of much benefit.
5. ACKNOWLEDGMENTS
We are grateful to Jie Lu for assistance in
the experimental design and to David Miller and
G. Leonard Marsh for help in the data collec-
-------
tion and analysis. This work was supported by
the DOD/DOE Strategic Environmental Research
and Development Program through a Cooperative
Agreement between the U.S. EPA and The Penn-
sylvania State University with a subcontract to the
University of Colorado.
6. DISCLAIMER
TMs paper has been reviewed in accordance
with the U.S. Environmental Protection Agency's
peer and administrative review policies and ap-
proved for presentation and publication. Mention
of trade names or commercial products does not
constitute endorsement or recommendation for use.
7. REFERENCES
Briggs, G.A., 1985: Analytical parameterizations
of diffusion: the convective boundary layer. J.
Climate Appl. Meteor., 24,1167-1186.
Deardorff, J.W., and G.E. Willis, 1984: Ground-
level concentration fluctuations from a buoyant
and a non-buoyant source within a laboratory
convectively mixed layer. Atmos. Environ., 18,
1297-1309.
Deardorff, J.W., and G.E. Willis, 1988: Concen-
tration fluctuations within a laboratory convec-
tively mixed layer. Lectures on Air Pollution
Modeling, A. Venkatram and J.C. Wyngaard,
Eds., Amer. Meteor. Soc., Boston, 357-384.
Eanna, S.R., and RJ, Paine, 1989: Hybrid plume
dispersion model (HPDM) development and
evaluation. J. Appl. Meteor., 28, 206-224.
Weil, J.C., and L.A, Corio, 1985: Dispersion formu-
lations leased on convective scaling. Maryland
Power Plant Siting Program, Maryland Dept.
of Natural Resources, Annapolis, MD, Rept.
No. PPSP-MP-60.
Willis, G.E., and J,W. Deardorff, 1983: On plume
rise within the convective boundary layer.
Atmos. Environ., 17, 2435-2447.
Willis, G.E., and J.W. Deardorff, 1987: Buoyant
plume dispersion and inversion entrapment in
and above a laboratory mixed layer. Atmos.
Environ., 21, 1725-1735.
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TECHNICAL REPORT DATA
1. REPORT NO. 2.
EPA/60Q/A-97/092
4. TITLE AND SUBTITLE
Recent Experiments on Buoyant Plume Dispersion in a Laboratory Convection
Tank
7, AUTHOR(S)
'Weil, 1C., 2W.H. Snyder, JR.E. Lawson, Jr., and "M.S. Shipman
9. PERFORMING ORGANIZATION NAME AND ADDRESS
'ORES, University of Colorado
Boulder, CO
2Mechanical Engineering Depaartment, University of Surrey
Guilford, Surrey, England
'Same as Block 12
"Geophex, Ltd.
Raleigh, NC
12. SPONSORING AGENCY NAME AND ADDRESS
National Exposure Research Laboratory
Office of Research and Development
U.S. Environmental Protection Agency
Research Triangle Park, NC 277 1 1
5.REPORTDATE
6.PERFORMTNG ORGANIZATION CODE
8,PERFORMINa ORGANIZATION REPORT NO.
10.PROGRAM ELEMENT NO,
11. CONTRACT/GRANT NO.
13.TYPE OF REPORT AND PERIOD COVERED
14. SPONSORING AGENCY CODE
EPA/600/9
15. SUPPLEMENTARY NOTES
16. ABSTRACT
Buoyant plumes from tall stacks usually produce their highest ground-level concentrations (GLCs) in a convective boundary layer
(CBL), where turbulent downdrafts bring elevated plume sections to the surface. Our understanding of buoyant plume dispersal
has been significantly advanced by Willis and Deardorff s ( 1 983, 1 987) experiments in a laboratory convection tank. Their
studies demonstrated the complex dispersion patterns and the dependence of plume properties on the dimensionless buoyancy flux
=Ft/(Uwf , where Fb is the stack buoyancy flux, C/is the mean wind speed, w. is the convective velocity scale, and 2, is the
CBL depth. For F. = 0.03, the plume behaved similarly to a nonbuoyant plume after some initial rise, but for F. = 0. 1 1 , the plume
rose to the CBL top, where it "lofted" or remained temporarily and then gradually mixed downwards. Field observations around
tall stacks suggested that the maximum hourly-averaged GLCs generally occur for the lofting situation (e.g., Hanna and Paine,
1989).
17. KEY WORDS AND DOCUMENT ANALYSIS
a. DESCRIPTORS b.IDENTIFIERS/ OPEN ENDED TERMS o.COSATI
1 8. DISTRIBUTION STATEMENT 19. SECURITY CLASS (This Report) 21 .NO. OF PAGES
20. SECURITY CLASS (This Page) 22. PRICE
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