EPA-450/3-7 5-066
April 1975
LABORATORY SIMULATION
OF PLUME DISPERSION
FROM LEAD SMELTER
IN GLOVER, MISSOURI,
IN NEUTRAL AND STABLE
ATMOSPHERE
U.S. ENVIRONMENTAL PROTECTION AGENCY
Office of Air and Waste Management
Office of Air Quality Planning and Standards
Research Triangle Park, North Carolina 27711
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EPA-450/3-75-066
LABORATORY SIMULATION
OF PLUME DISPERSION
FROM LEAD SMELTER
IN GLOVER, MISSOURI,
IN NEUTRAL AND STABLE
ATMOSPHERE
by
Hsien-Ta Liu arid Jung-Tai Lin
Flow Research, Incorporated
1819 S. Central Avenue
Kent, Washington 98031
Contract No. 68-02-1294
Program Element No. 2AC129
EPA Project Officers: Edward Burt and Charles Whitmore
Prepared for
ENVIRONMENTAL PROTECTION AGENCY
Office of Air and Waste Management
Office of Air Quality Planning and Standards
Research Triangle Park, N. C. 27711
April 1975
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This report is issued by the Environmental Protection Agency to report
technical data of interest to a limited number of readers. Copies are
available free of charge to Federal employees, current contractors and
grantees, and nonprofit organizations - as supplies permit - from the
Air Pollution Technical Information Center, Environmental Protection
Agency, Research Triangle Park, North Carolina 27711; or for a fee,
from the National Technical Information Service, 5285 Port Royal Road,
Springfield, Virginia 22161.
This report was furnished to the Environmental Protection Agency by
Flow Research, Inc. , Kent, Washington 98031, in fulfillment of Contract
No. 68-02-1294. The contents of this report are reproduced herein as received
from Flow Research, Inc. The opinions, findings, and conclusions expressed
are those of the author and not necessarily those of the Environmental
Protection Agency. Mention of company or product names is not to be
considered as an endorsement by the Environmental Protection Agency.
Publication No. EPA-450/3-75-066
11
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Laboratory Simulation of Plume Dispersion from a Lead
Smelter in Glover, Missouri: Neutral and
Stable Atmosphere
by
Hsien-Ta Liu and Jung-Tai Lin
Flow Research, Inc., Kent, Washington 98031
Abstract
A series of laboratory experiments which simulated dispersion of
pollutants from a lead smelter in Glover, Missouri were conducted in a
stratified towing tank at Flow Research, Inc. Results of the experiments,
including flow visualization records in the form of still and moving pictures
and quantitative measurements with probes, were used here to determine the
locations where high ground concentrations were most likely to occur under the
simulated conditions.
In the laboratory, neutral and stable conditions corresponding to from
typical to adverse cases observed in the atmosphere were produced. Four
terrain models with a 1/2500 scale, simulating four wind directions, were
constructed. Under neutral conditions, the plumes were considerably diluted
within the simulated atmospheric boundary layer. Ground concentrations were
low everywhere on the four models. Under stable conditions, the plumes were
aloft upstream of the mountains, and ground concentrations were low. High
ground concentrations were measured in some cases downstream of the mountains
and at the locations where downslope winds occur. When the pollutants in the
plumes were brought by the downslope wind into direct contact with the leeward
ncuntain sl®pe, the mean ground concentrations were high.
Based on the results of this study, one of the most unfavorable situations
occurs when a strongly stable atmosphere is present. Therefore, it is recom-
mended that samplers be installed on top of and downstream of the mountains.
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Table of Contents
Page
Abstract i
Table of Contents ii
Nomenclature iv
1. Introduction 1
2. Simulation Considerations 3
2.1 Geometric Similarity 3
2.2 Kinematic Similarity 3
2.3 Dynamic Similarity 4
2.4 Boundary Conditions 8
2.5 Simulation Conditions 9
3. Laboratory Facilities and Experimental Methods 11
3.1 The Stratified Towing Tank 11
3.2 Terrain Models 11
3.3 Effluent Injection Device 12
3.4 Flow Visualization Techniques 13
3.5 Instrumentation 14
3.5.1 Density Measurement 14
3.5.2 Velocity Measurement 14
3.5.3 Concentration Measurement l4
4. Results of Flow Visualization 16
4.1 Neutral Conditions 16
4.2 Stable Conditions 17
4.2.1 Stratification Effect 17
4.2.2 Terrain Effect 18
5. Probe Measurements 19
5.1 Velocity Profiles 19
5.1.1 Neutral, High-Wind Conditions 19
5.1.2 Stable, Low-Wind Conditions 20
5.2 Ground Concentration Measurements 21
5.2.1 Neutral Conditions 21
5.2.2 Stable Conditions 22
6. Discussion and Recommendations 23
6.1 Neutral, High-Wind Conditions 23
6.2 Stable, Low-Wind Conditions 23
6.3 Recommendations 23
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Table of Contents (Cont'd)
Page
7. Conclusions 25
7.1 Neutral, High-Wind Conditions 25
7.2 Stable, Low-Wind Conditions 26
References 28
Tables 30
Figures 33
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Nomenclature
Symbol Description Dimension*
D stack diameter L
2 -1
D mass diffusivity of the ambient fluid L T
a
2 -1
D mass diffusivity of the stack effluent L T
s
d diameter of the plume L
/ O
F buoyancy flux of the plume L T
W
F stack Froude number,
F internal Froude number based on the stack
H U
height, ^
f frequency T
_2
g gravitational acceleration LT
H stack height L
h characteristic height, such as that of a L
mountain
K ratio of effluent velocity to free-stream -
W
velocity, ^
CO
2 -1
K thermal diffusivity of the ambient fluid L T
a
o _i
< thermal diffusivity of the stack effluent L T
O
k wave number L
k^ Kolmogoroff wave number L
L characteristic length L
$, geometric length L
m subscript referencing the model
*
L = length, T = time, T = temperature, M = mass
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Nomenclature (Cont'd)
Symbol
Brunt-Vaisala
Description
frequency, —
IS
/.£_ dP
K dz
*
Dimension
T-1
a constant
subscript referencing the prototype
W D
stack Reynolds number, —^-~
Reynolds number based on the ridge height,
u h
00
V
O 1
S(f) one-dimensional energy spectrum function L T
2
-1
U mean velocity component in the x direction LT
mean velocity j
i = 1, 2 and 3
2 _7
s stability parameter = (2?rN) T
U characteristic velocity LT
r1
U mean velocity in the i direction, LT
U free-stream velocity LT
u turbulent velocity LT
turbulent velo
i = 1, 2 and 3
u turbulent velocity in the i direction, LT
u velocity quantity LT
W stack effluent velocity LT
s
x,y,z Cartesian coordinate axes in longitudinal, L
lateral and vertical directions, respectively
Z height of the plume trajectory above the L
stack exit
Z height of the plume top above the stack exit L
6 turbulent boundary-layer thickness L
8 temperature deviation from the mean probe T
temperature
8 temperature T
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Nomenclature (Cont'd)
*
Symbol Description Dimension
9 effluent temperature T
s
2 -1
V kinematic viscosity of the ambient fluid L T
a.
2 -1
V kinematic viscosity of the effluent L T
S
-3
p density of the ambient fluid at the stack- ML
exit level
p stack effluent density ML
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1. Introduction
This report constitutes the primary results of a laboratory study that
investigated, through physical modeling, plume dispersion from a lead smelter
in Glover, Missouri under neutral and stable atmospheric conditions. The
objective of this study was to determine the optimum losations for the instal-
lation of pollutant sampling stations in the vicinity of the prototype smelter.
The experimental results also provided some of the data necessary for
the validation of existing and future numerical models.
The stack under study is located at the American Smelting and Refining
Company (ASARCO) sinter plant in Glover, Missouri. It is a custom smelter
with an annual production capacity of 90,000 tons of lead. Effluent gases
from the sinter machine, two clean-up conveyors, the sinter breaker, the
spiked roll, the pan conveyor, and the cooling drum are vented through a
water spray-chamber and a baghouse containing microtan synthetic bags. Before
passing through the baghouse, exhaust gases are cooled by introducing ambient
air through a vent. Then, the gases pass through the baghouse and are vented
through a 186-m concrete stack that is 3.66 m in diameter (Shea, 1973).
The smelter is located approximately .5 km SW of Glover, Missouri in the
valley of Big Creek. The surrounding terrain is quite rugged, being mostly
rolling hills and small creek valleys. The whole area is heavily forested,
with trees averaging from 5 to 10 m in height. Four mountains located
approximately 4-6 km from the stack (see fig. 1), contribute further complexity
to the terrain features. The four terrain models were constructed so that
the plumes were advected toward these mountains.
The effects of complex terrain on plume dispersion have been investigated
by Orgill, et al. (1971), Veenhuizen, et al. (1973) and Lin, et al. (1974).
In particular, under stable conditions, Lin, et al. (1974) demonstrated
that the plume dispersion phenomenon is complicated and that the associated
pollution problems are localized. Most importantly, previous studies have
demonstrated that many atmospheric flow phenomena in complex terrain under
stable conditions can be accurately reproduced in a stratified towing tank
(Lin, et al., 1974).
The present study investigated plume dispersion from the main stack
under both neutral and stable atmospheric conditions. Laboratory experiments
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using four 1/2500-scale terrain models which simulated four wind directions
were undertaken in the Flow Research stratified towing tank. Flow visual-
ization tests using a dyed plume were conducted. Quantitative measurements
of ground concentrations were made with thermistor probes, and velocity
profiles were measured with hot-film probes.
This report is divided into six sections. The simulation criteria
and conditions are discussed in section 2. In section 3, the laboratory
facilities and experimental methods used in this study are described. Results
of flow visualization and of probe measurements are presented and discussed
in sections 4 and 5, respectively. Further discussion and recommendations
for the installation of full-scale pollutant samplers are presented in
section 6. Finally, a few important conclusions derived from the study are
summarized in section 7.
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2. Simulation Considerations
In the simulation of flow phenomena in the laboratory, complete simi-
larity between the model and the prototype can be achieved only if they are
geometrically, kinematically, and dynamically similar (Sedov, 1959). For
plume dispersion in stratified flows over complex terrain, simulation para-
meters can be derived, through dimension analysis, from physical variables
which govern the flow field and the dispersion process (Lin, et al., 1974).
In this section, simulation parameters and their physical interpretations
that are relevant to this study are discussed.
2.1 Geometric Similarity
To satisfy the geometric similarity, the ratio of any geometric length
£ to a characteristic length L of the model must be identical to that
of the prototype; that is,
M- I — O i ">
- , I > \£' *-)
where the subscripts m and p refer to the model and the prototype, respectively.
In this study, the geometric scaling factor was selected to be 1/2500. The
geometric length includes not only the sizes of the stack and the terrain
features, but also the physical sizes of the flow field and the plume. For
the flow field, the thickness of the atmospheric boundary layer and the sizes
of the energy-containing eddies, which dominate the plume dispersion within
the boundary layer, must be modeled according to the same scaling factor.
For the plume, the plume trajectory, the width and height of the plume, and
the terminal rise of the plume in a stratified flow must be scaled by the
same factor.
2.2 Kinematic Similarity
Kinematic similarity requires the ratio of any velocity quantity M to a
characteristic velocity U of the model to be identical to that of the proto-
type, namely,
In I = In ' <2'2>
I U I m I U I p
W
g
In reference to the plume, the speed ratio ——, where W and U^ are,
u s
00
respectively, the effluent speed and the free-stream velocity, is the most
important kinematic criterion to be reproduced in the laboratory. When
simulating plume dispersion in the atmospheric boundary layer, however, one
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u
must consider the reproduction of
and
Uoo
where U. and
th
are, respectively, the mean velocities and turbulence intensity in the i
direction (i = 1, 2, and 3).
2.3 Dynamic Similarity
Once geometric and kinematic similarities are established, dynamic simi-
larity requires the following criteria be satisfied:
(i) the stack Froude number similarity must be:
D
w
m
W
gD
(2.3)
where F is the stack Froude number, g is the gravitational
acceleration, D
density, and p
is the stack diameter, p is the effluent
S
is the ambient fluid density;
(ii) the internal Froude number similarity must be:
H
W
NH
|W ]
Is
NH
L Jn
(2.4)
m L Jp
where F is the internal Froude number based on the stack
n
height H, and N is the Brunt-Vaisala frequency in Hz;
(iii) the stack Reynolds number similarity must be:
W D
s
V
IW D
s
*s
(2.5)
where R^ is the stack Reynolds number, and V is the
kinematic viscosity of the effluent;
(iv) the terrain Reynolds number similarity must be:
V
m
(2.6)
where R, is the terrain Reynolds number based on the
mountain peak height h, and V is the kinematic viscosity
3.
of the ambient fluid;
(v) the ambient-fluid Peclet number similarity must be:
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or
Pe =
a
m
Ucoh"
V
. a.
V
a
K
a_
"Ucoh"
V
a_
•n
V
a
K
a_
m
m
(2.7)
(vi)
or
where Pe is the ambient Peclet number,
3.
Pr
V /K
a a
1C
is the ambient Prandtl number and
a
diffusivity of the ambient fluid.
the stack Peclet number similarity must be:
is the thermal
Pe "=
s
"w D"
S
K
S
~W D~
s
K
S
)
~ m ~ ~ p
Pe =
s
W D"
s
V
s_
m
V
s
K
S_
=
Tn
"w D"
s
V
s_
r»
V
s
K
S_
(2.8a)
where Pe is the stack Peclet number, Pr = V /K
s s s s
is
K is the thermal diffusivity of
S
the Prandtl number and
the stack effluent.
(vii) the pollutant Peclet number similarity must be:
Pe
"w D"
s
V
s^
m
V
s
D
. P.
m
"w D"
s
V
s
•n
V
s
D
. P.
(2.8b)
where Pe is the pollutant Peclet number,
Sc = V /D
s s p
D is the mass
P
is the Schmidt number of the pollutant and
diffusivity of the pollutant.
The stack Froude number, which represents the ratio of the inertial
force to the buoyant force of the effluent, is an important parameter in the
simulation of the plume dispersion. For example, under neutral conditions,
the plume rise Z is solely determined by the dimensionless parameters F.
and K, the stack diameter D, and the distance downstream of the stack
x (Briggs, 1969; Lin, et al., 1974)
2/3
D
(S)
(2.9)
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The internal Froude number, which represents the ratio of the inertial
force to the buoyant force of the ambient fluid, affects the plume dispersion
in two ways. First, the stratification inhibits the vertical rise of the
plume. The terminal rise of the plume Z in a calm and stable fluid is
governed by the stratification and the buoyancy flux of the plume, F (Briggs,
1969; Lin, et al., 1974), as
Zt = 5F1/5s-3/8 . (2.10)
Secondly, the stratified flow interacts with distinctive terrain features,
such as mountains and valleys, which in turn govern the plume dispersion.
For example, the formation of mountain lee waves, which considerably alter
the flow patterns in the lee of a mountain, is governed by the internal
Froude number (Turner, 1973). Therefore, the plume dispersion in a rugged
terrain where lee waves are generated is also governed by the internal Froude
number.
In the FRI towing tank, experimental conditions can readily be selected
to match the stack Froude number and the internal Froude number usually
encountered in the atmosphere. The similarities of the stack Reynolds number
and the terrain Reynolds number, however, cannot be satisfied since the Reynolds
numbers in the laboratory are about 3 to 4 orders of magnitude smaller than
those in the field. The following discussions demonstrate that this lack of
similarity between R^ and R does not seriously impair the validity of
a realistic simulation.
Experimental data (Hoult and Weil, 1972 and Lin, et al., 1974) have
shown that the plume rise, under neutral and stable conditions, is independent
of the stack Reynolds number R as long as the plume is fully turbulent at
the exit of the stack. A turbulent plume can be achieved by installing a
tripping device a short distance upstream of the stack exit (see section 3.3).
Remarkable correlation of the plume rise in calm and stable fluids has
been obtained for plumes of vastly different sizes (section 4.2.1). Many
investigators (e.g., Schlichting, 1968) have shown that flow phenomena are
only weakly dependent on the Reynolds number R^ when Ri is sufficiently
large and the flow is fully turbulent. Under neutral conditions, the region
of most concern is the turbulent boundary layer (TBL), in which advection and
mixing of pollutants in the plume occur. The turbulent motion must be simulated
such that the turbulent energy and its distribution among the energy-
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containlng eddies, which effectively disperse the pollutants in the plume,
are scaled according to the scaling factors of length and velocity. In the
laboratory, atmospheric turbulent boundary layers can be realistically simulated
(Plate, 1971). Various tripping methods have been successfully employed to
provide a thick TBL with a realistic turbulent structure (Counihan, 1969;
Yu and Lin, 1975). The TBL in this study was tripped, and the turbulent
structure of this tripped TBL was in good agreement with field data (section
5).
Under stable conditions, however, the TBL is usually thin and the
turbulent intensity in the TBL is usually low (Slade, 1969). Field observations
(Schiermeier and Niemeyer, 1968, figs. 11 and 12) show that a plume released
from a tall stack usually rises above the thin TBL and levels off in the form
of a suspended thin ribbon in the laminar-like environment. Such behaviors
of the plume have been realistically reproduced in a stratified towing tank
(Lin, et al., 1974). The trajectories of the simulated plumes are in good
agreement with field data (Briggs, 1969). The internal Froude number F
H
is therefore more important than the terrain Reynolds number R, in simu-
lating plume dispersion under stable conditions. Over a complex terrain,
the mean flow field is influenced by the stratification and the terrain
features, or by definition, by the internal Froude number (based on the
characteristic height of the terrain). In a laminar-like flow region, the
plume dispersion is mainly governed by the mean flow field and, therefore,
by the internal Froude number.
The similarities of the Peclet numbers described in eqs. (2.7) and
(2.8) are discussed in the following. In the case where the same, fluid is
used in the laboratory and in the field, similarity of the ambient Peclet
number and the stack Peclet number cannot be satisfied because the Peclet
numbers in the laboratory are approximately three to four orders of mag-
nitude smaller than those in the field. Hence, following the argument on
the similarity of the Reynolds number, the similarity of the Peclet number
is not critical if the flow is turbulent. For the present investigation,
salt water was the working fluid. Because the Schmidt number Sc = V /D
a a a
or Sc = V /D of salt water has a value of approximately 700 and
s s s
because the Prandtl number of air for the field situation is about 0.7,
the Peclet number in the laboratory is the same order of magnitude as that
in the field. The advantage of using salt water instead of air as the
working medium is therefore quite clear. Note that this argument: is valid
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for the motion of energy-containing eddies, which is our basic concern
here. This argument is not valid, however, for the motions of small-scale
eddies, which have a scale of approximately the order of the Kolmogorov
length (Hinze, 1959) because the spectrum contains a k region for the
scalar quantity of a high Schmidt or Prandtl number but not for those of a
low Schmidt or Prandtl number.
The similarity of the pollutant Peclet number requires further considera-
tion. To simulate the pollutant concentration for the present study, we
used the temperature excess of a heated plume as the tracer. Because the
Prandtl number of water is about 7 and the Schmidt number of the pollutant
in the field is approximately the order of unity, we therefore estimate
the pollutant Peclet number in the laboratory to be about two or three orders
of magnitude smaller than that in the field. Two conditions are considered
concerning the similarity of the pollutant Peclet number. First, in a
neutral atmosphere, the boundary layer flow over the terrain is turbulent,
and thus, the plume dispersion is governed by the turbulent motion in the
TBL and in the plume. Therefore, we can follow the argument for the
Reynolds number and expect that the Peclet number does not need to be
critically simulated. Secondly, in an extremely stable atmosphere, the
background flow is laminar-like, but the plume in the laboratory remains
turbulent for about 2000 diameters downstream of the stack. For the present
study, the plumes traveled less than 2000 diameters (7.2 km) downstream of
the stack before they were broken up by the downslope wind (section 4.2).
Again, in the turbulent region of the plume, the similarity of the Peclet
number is not a critical requirement.
2.4 Boundary Conditions
The laboratory simulation was conducted in a towing tank (section 3.1).
The side and bottom walls of the tank could impose some effects on the plume
dispersion. For the present study, the maximum plume spread was about 30
cm in width and depth, which is only one-third of the tank width and depth.
Therefore, the effects of the side walls were expected to be insignificant.
To simulate an absorptive upper boundary for the stable cases, layers of
nylon netting were installed on the bottom of the tank because the model was
towed upside down.
The boundary conditions on the terrain model surface are the nonslip
of the velocity and the nontransport of heat and mass through the surface.
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The latter condition was maintained by the use of polyurethane foams, an
insulation material, to construct the terrain models.
2.5 Simulation Conditions
As stated in section 1, the primary objective of the present investi-
gation was to determine, through laboratory simulation, the optimum locations
for the installation of air-quality sampling stations at the Glover site.
In designing the experiment, one of the critical steps was to select a length
scale according to the capacity of the laboratory facility such that the
above-mentioned similarities were satisfied. As shown in the contour map of
the vicinity surrounding the Glover ASARCO plant (fig. 1), the area of
interest is about 12 km x 8 km. The towing tank used for the experiment has
a width of 1.2 m, and thus, if the entire area of interest were modeled, a
scaling factor of 1/10,000 would be required. With this scaling factor, the
stack model would have a height of about 2 cm and an exit diameter of about
0.4 mm, and the Ketcherside Mountain, which is the highest mountain in this area,
would be about 5 cm high. According to previous experiments (Veenhuizen, et al.,
1973), the diameter of this stack model is probably too small to produce a
turbulent plume at the stack exit; and therefore, if a turbulent plume is
desired, the stack diameter ought to be exaggerated; this would violate the
geometrical similarity and is undesirable. Instead of modeling the entire
12 km x 8 km area, four separate terrain models (1/2500 scale), which
correspond to the four rectangular areas marked in fig. 1, were constructed
to simulate four wind directions. In each wind direction, one of the four
major mountains is located directly downstream of the stack. It was speculated
that the ground concentrations in the vicinity of the mountains would be
high under these simulated wind directions.
The present investigation attempted to simulate both neutral, high-wind
and stable, low-wind conditions in the Flow Research stratified towing tank.
The physical data and the effluents for the main stack of the Glover ASARCO
plant were provided by the Environmental Protection Agency, Research Triangle
Park, North Carolina, and they are listed in table 1. Also, the atmospheric
conditions, such as the wind speed and the lapse rate, which are expected to
be from typical to extreme in the area of Glover, Missouri, are provided and
tabulated in table 2.
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The dimensionless parameters K, F and F calculated for the field
H D
case were reproduced in our experiments. For all experiments, we selected
the scaling factor of length to be 1/2500. Under neutral conditions, we
selected the scaling factor of velocity to be 1/64, and therefore, the scaling
factor of time was 1/40. In other words, the flow phenomenon observed for
one second in those experiments has the corresponding time scale of 40 seconds
in the full-scale case. Under stable conditions, the scaling factor of
velocity was 1/83, and therefore, the scaling factor of time was 1/30.
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3. Laboratory Facilities and Experimental Methods
3.1 The Stratified Towing Tank
Experiments were performed in a stratified towing tank, 18.3 m long,
1.2 m wide and .9 m deep. A detailed description of this facility has been
given in a previous FRI report (Pao, et al., 1971). Special features of the
towing tank system that are pertinent to the present investigation are described
briefly in the following: (1) It has a specially designed filling system,
which facilitates the preparation of a stratified fluid with any desired stable
stratification. (2) It has a smooth, oil-lubricated carriage with a noise
level that is approximately 0.6% of the towing speed. These features allow
accurate measurements of the velocity, temperature, and salinity fluctuations
with hot-film probes, thin-film and/or thermistor probes, and single-electrode,
conductivity probes. (3) It has transparent side and bottom walls, which
allow flow visualization experiments from several directions. (4) It has a
minicomputer system for direct on-line multiple-channel data acquisition and
subsequent statistical data analysis.
3.2 Terrain Models
Four terrain models of 1/2500 scale were constructed to simulate four
wind directions (see fig. 1). First, enlarged prints of 1/2500 scale were
made photographically on mylar sheets (Technical Service Department, the
Boeing Company) from the USGS 1%-minute topographic maps. The models, 3.7 m long
3
and 1.1 m wide, were made of polyurethane foams (approximately 9.6 Kg/m ),
according to the enlarged mylar contour maps, with a router. The model surfaces
were intentionally constructed to be stepped with vertical increments of .24
cm corresponding to 6.1-m contour intervals in the prototype. The stepwise
feature of the model realistically represents the roughness condition of the
prototype terrain, on which trees from 5 m to 10 m in height were forested. A
4.9-m-long platform, made of a 1-cm-thick acrylic sheet reinforced with aluminum
angles, was built to support the terrain models. It was designed so that
individual terrain models could be interchanged with each other in the towing
tank. Two-dimensional fences made of .3-cm acrylic sheets, with a maximum-
height of 2 cm and a spacing of 2.5 cm, were installed in the upstream 1.3-m
portion of the platform to serve as a turbulent-boundary-layer tripping device.
The fences were also designed to conform with the general features of the proto-
type terrain.
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The most pronounced features of Model I, the Vickery Mountain (elev. 488
m) and the valleys of Carver Creek and of Big Creek, are primarily two-
dimensional (fig. 1). The Vickery Mountain spans almost the entire width of
the model. The terrain features of Models II and III are essentially three-
dimensional. The horseshoe-shaped Hogan Mountain (elev. 512 m) in Model II
is situated such that the vertical cross-section along the centerline of the
model shows two humps. The Ketcherside Mountain (elev. 518 m) in Model III
has a single peak and is the highest of the four mountains. The valley of
Big Creek extends over both models II and III and makes a small angle with
the centerlines of the models. Model IV has features similar to those of
Model I, with another mountain (no name) and the valley of Big Creek as the
outstanding landmarks. The mountain (elev. 485 m), which is about the same
size as the Vickery Mountain, also spans a large portion of the model width.
Figure 2 shows enlarged contour maps of the individual models. In these maps,
the stack, denoted by a solid circle, is located on the right-hand side. The
locations of the thermistor probes used for the pollutant measurement are
indicated by solid stars, and the numbers nearby denote the probe numbers.
During the experiment, terrain models and the stack were mounted upside
down on an oil-lubricated carriage in the stratified towing tank. To simulate
a buoyant plume in the atmosphere, a heavy plume was injected from an inverted
stack into the ambient fluid.
3.3 Effluent Injection Device
A concentrated dye solution (brilliant-blue food dye) with p =1.17
24 s
Kgfs m was used as the effluent. The injection device consisted of a heated
flask containing the effluent fluid, a temperature controller (YSI Model 72),
a veristaltic pump (Manostat Model 72-895-05) using insulated tygon tubing, an
accumulator, and a heated hose (Technical Heaters, Inc., Model 352) connected
to the stack. First, the dye solution was preheated to 80 C in the flask. The
dye solution was then pumped through the heated hose, where the temperature
was controlled at 90 ± 2°C, and finally, it was forced out the stack into the
ambient fluid. The heat contained in the plume served as a tracer, and the
ground concentrations were then measured with thermistor probes. Because a
low concentration level was expected, the variation of the temperature of the
fluid in the towing tank had to be small. To maintain the temperature variation
along the tank to within ±.01 C, the side walls of the tank and the water
surface were insulated with sheets of polyurethane foam, and a grid with vertical
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-13-
rods (1.3 cm in diameter) was towed in the tank at least one hour before each
experiment. For a heated plume at 90 C and the ambient fluid at 20°C, the
thermal noise level (6-0 )/(0 -6), corresponding to .01 C, was therefore
_, a s a
1.4 x 10 .
The injection device included a tripping device that ensured the plume
was turbulent at the stack exit. This tripping device was made of a sapphire
nozzle, .018 cm in diameter, which was installed about .5 cm upstream of the
stack exit. For an untripped plume, the flow was laminar when the stack
Reynolds number was about 200. When the plume was tripped, the Reynolds number
at the nozzle was increased to about 1600, which is much higher than the
critical Reynolds number. The distance between the nozzle and the exit of the
stack was found to be critical. If the distance was smaller than required,
the flow at the stack exit would be governed by the nozzle instead of the
stack. On the other hand, if the distance was significantly larger than required,
the flow tripped by the nozzle would relaminarize before it reached the stack
exit. After a series of tests, a distance of 0.5 cm between the nozzle and
the stack exit was found to be satisfactory.
3.4 Flow Visualization Techniques
The tracer effluent used in the experiments was a mixture of salt water
and a brilliant-blue food dye. The plume was photographed with still and
movie cameras, as follows:
One 35-mm still picture camera was towed with the terrain model to
record the side view of the plume, and one 35-mm still picture camera
stationary to the tank was used to record the plan view.
Two 16-mm movie cameras were towed to record the side arid angle views.
- Two 35-mm still picture cameras carried by photographers were used
to record plume dispersion from various angles.
The back diffusive lighting, used for flow visualization, was provided by three
fluorescent light panels, each of which was 61 cm wide and 122 cm long,
suspended from the towed carriage. The light was diffused by inserting
translucent, acrylic sheets, which were .32 cm thick and transmitted 53% of
the incident light, between the light panels and the towing tank. The visuali-
zation records have been summarized in still pictures and in a movie film
(Liu, et al., 1975), which constitutes an essential portion of the final report.
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-14-
3.5 Instrumentation
3.5.1 Density Measurement
A conductivity gauge (Model 1Q10) manufactured by Flow Research, Inc.,
was used to measure the density profile in the tank. This gauge has a frequency
response from DC to 1 KHz. The sensor was a single-electrode conductivity
probe, which was a .025-mm stainless-steel tip platinized with platinum black
solution. The sensitivity of the conductivity gauge was about 1 volt per 0.025 gm/
3
cm . The probe was calibrated in jars of salt solution of known density. Then,
the calibration data were least-square fitted with a second-degree polynomial.
Figure 3 is a typical density profile (Run IVb) measured in the towing tank.
The Brunt-Vaisala frequencies calculated from the density profiles for individ-
ual runs are tabulated in table 2.
3.5.2 Velocity Measurement
The mean and turbulent velocities of the incoming flow near the stack
were measured with two 10-channel constant-temperature anemometers (1053-B,
Thermo-Systems, Inc.) and thirteen conical, and one cylindrical, hot-film sensors
(TSI Models 1230S and 1290 AK). For use in salt water, the sensors are coated
with quartz. The anemometer has a frequency response of up to 1000 Hz. The
hot-film sensors were mounted on a vertical strut covering a vertical distance
of 30 cm, with the spacing between sensors decreasing toward the terrain surface.
The vertical strut and the terrain model were towed with the same carriage
system. For calibration, the strut was moved to a distance of about 30 cm
lower than the position during the velocity measurement. This allowed the
probes to be free from disturbances induced by the terrain model. This arrange-
ment introduced, however, a small error in measuring velocity in a stratified
fluid because the probes were not calibrated in the same fluid as that in which
the measurement was conducted. For the experiments conducted, the fluid density
varies by a factor of 3% for a vertical distance of 30 cm, and by referring
to the appendix described in Flow Research Report 57 (Liu and Lin, 1975), we
estimated the errors involved in the measurements of the mean and turbulent
velocity to be about 5% and 4%, respectively. Note, however, that this type
of error would not occur for the case of a non-stratified fluid.
3.5.3 Concentration Measurement
Using temperature as a tracer, we measured ground concentrations with
thermistor probes (Fenwal Electronics GC32SM2). The thermistor probes have a
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-15-
nominal resistance of 2000ft and a temperature coefficient of -3.4%/°C at room
temperature. The probe tip is 0.076 cm in diameter, and the time constant
(3db point) of the thermistor probe in still water is about .07 sec. A
10-channel gauge with the thermistor probe as one arm of the wheatstone bridge
was used to measure temperature in the fluid. The sensitivity of the system
is typically 10 V/ C, and the noise level is about 3 mV peak-to-peak. The
thermistor probe has a long-term stability, and a typical drift is .01 C/year.
The probes were first calibrated against a precision thermometer with
an accuracy of .01 C (Brooklyn Thermometer Company, Inc.). in a constant-
temperature bath which was equipped with a temperature controller (YSI Model 72)
with an accuracy of .01 C. In the range of temperature differences of interest
(0~.5 C), the pre-calibration curves appear to be linear (fig. 4). To obtain
the in-situ calibrations for the probe located in the tank, we followed the
procedure described below. First, the temperature of the fluid in the tank
and the voltage output of the thermistor probe were measured. These measurements
provided one data point for the in-situ calibration, and the curve was then
obtained by extrapolating this data point using the known slope of the pre-
calibrated curve. For ground concentration measurements, the probe tips were
located about 2 mm above the surface of the terrain model. The locations of
the probes, in reference to the stack, are indicated by solid stars in fig. 2.
-------
4. Results of Flow Visualization
The visualization results are illustrated in still pictures (figs. 5
through 8) and are discussed in this section. In addition, a 16-mm color film
(Liu, et al., 1975) containing the essential visualization results is included
as an important supplement to the report. Frequent reference to this movie
is made in this context to aid in interpretation of the results.
Figures 5 through 8 are photographs that show the side and plan views
of the dispersing plume over the terrain models. The plan views were photo-
graphed with a camera that was stationary to the towing tank. These photographs
show the evolution of a section of the plume with time as the models were towed
by. An overall picture of the plume on the horizontal plane was obtained by
splicing the slightly overlapping frames together in sequence. The side view
of the plume was photographed through the viewing sections of the towing tank
with a camera mounted on the carriage and towed along with the individual models.
These photographs not only provide the overall picture of the plume, but also
help interpret the ground concentration measurements by pinpointing the regions
of high ground concentrations.
4.1 Neutral Conditions
Under neutral conditions, a simulated turbulent boundary layer was
generated for all the terrain models. The side views of the plume dispersion
are seen in figs. 5a, 6a, 7a and 8a. In the near region, say within a few
hundred stack-diameters downstream of the stack, the plume trajectory appears
to fluctuate with time, in contrast with that observed in a laminar background
flow. Farther downstream, the plume is broken up and no coherent trajectory
is observed. The plume disperses in a patchy manner; this dispersion pattern
indicates the motion of large eddies in the boundary layer. Occasional touch-
down of pollutant "pockets" on the ground was observed for short periods. The
ground concentrations, however, are expected to be low since pollutants are
diluted considerably inside the turbulent boundary layer. The plan views of
the plume (figs. 5c, 6d, 7d and 8d) show that the plume axes are nearly parallel
to the wind direction and that the local topography does not cause any appreci-
able distortion of the plume axes.
The TBL's over the terrain models were tripped to render realistic
simulation of the atmospheric boundary layer in which plume dispersion is
studied. The characteristics of the tripped TBL are discussed in section 5.1.
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-17-
To emphasize the importance of establishing a realistically simulated TBL when
modeling plume dispersion under neutral conditions, fig. 9 shows a side view
of the plume in Run IVa. This view was photographed shortly after the terrain
model was towed and after it had reached a constant speed, but before the TBL
was fully developed. Note that the only mixing of the plume was introduced
by the turbulent motion inside the plume. The striking difference between
fig. 8a and fig. 9 is evident.
4.2 Stable Conditions
Under stable, low-wind conditions, the plumes over individual models
display many interesting features, several of which are common to all models
and others which are distinctively unique. These differences indicate that the
interaction of stratified flows and topography appears to significantly in-
fluence the flow field in the vicinity of the terrain, which in turn affects
the dispersion patterns of the plume. Two stability conditions, which corres-
pond to typical cases observed in the atmosphere, were simulated for each model
except Model I (see table 2).
4.2.1 Stratification Effect
As shown in figs. 5 through 8, a plume over complex terrain under stable
conditions is markedly different from a plume under neutral conditions. Under
stable conditions, both the rise and the vertical spread of the plume are
limited. For small internal Froude numbers, overshooting of the plume from
its terminal height is noticeable. The striking resemblence among the plumes
shown in figs. 5 through 8 and the TVA Keystone plume under a stable atmosphere
(Schiermeier and Niemeyer, 1968) indicate that the simulation is indeed realistic.
Note that the same TBL tripping device used in the neutral cases was employed
in the stable cases. Apparently, the mechanical turbulence generated by the
tripping device and the downstream rugged terrain surface is considerably
damped by stratification. The well-defined plume edges indicate that the
turbulence intensity at the plume level is very low. This observation coincides
with field data (Slade, 1969), which show that the TBL in a stable atmosphere
is thin and has a low turbulence intensity. The top of the plumes for the low
Froude-number cases are measured from the side views of the plumes, and the
results are plotted vs. 5F s in fig. 10. Other results available from
Briggs (1969) and laboratory measurements by Lin, et al. (1974) are also plotted.
The empirical equation, expressed in eq. (2.10) and drawn as a solid line in
-------
fig. 10, correlates all the data very well. This finding shows that, despite
the low stack (R ~200, untripped) Reynolds number encountered in the present
investigation, the plume has been successfully tripped to be turbulent, and
the plume dispersion has been properly simulated.
4.2.2 Terrain Effect
Upstream of the mountains, the plumes are aloft, and the terrain effect
on plume dispersion is insignificant, except for the case, F = 5.4, shown
H
in fig. 6b. The shape of the plume in fig. 6b appears to conform closely to
the two humps of the Hogan Mountain. This, the only observed terrain effect,
lessens considerably as the internal Fourde number is reduced by a factor of
two (F = 2.7), as shown in fig. 6c. Concerning the lateral spreading, no
significant meandering is observed for any of the four models.
The terrain effect on plume dispersion is, however, observed just down-
stream of the mountaintops. There is strong downslope wind downstream of the
mountaintops, and this flow carries the plume toward the leeward mountain
slope. In all the visualization results, only the plumes shown in figs. 5b
and 7c could have direct contact with the leeward mountain slopes. Figure
5b corresponds to Run Ib, which has the lowest internal Froude number (F = 2.2),
rl
and fig. 7c corresponds to Run IIIc (F = 2.7), which has the highest mountain
n
of all the four models.
As the downslope wind carries the plume closer to the leeward mountain
slope, the terrain effect on plume dispersion becomes stronger. The plumes
shown in figs. 7f, 8e and 8f tend to divert from the ambient wind direction.
Closer examination of the terrain features indicates that the plume is either
carried around the mountain peak (fig. 7f) or is forced to follow a valley
along the leeward mountain slope (figs. 8e and 8f). When the plume is aloft,
however, no appreciable meandering is observed, and the plume axis is parallel
to the ambient wind direction (fig. 7e).
The generation of lee waves is demonstrated by several traces of the
plumes, which are shown in figs. 6b, 6c, 8b and 8c. The wavelength of the lee
waves traced by the plumes decreases as the internal Froude number decreases.
The vertical spread of the plume appears to thicken downstream of the first
wave trough (figs. 6b and 8b). For a few low internal-Froude-number cases
(figs, 6c, 7c and 8c), the waves are actually broken up. The lateral spreads
(figs. 5a and 7f) corresponding to the low internal-Froude-number cases
(F = 2.2 and 2.7, respectively) tend to increase abruptly at locations where
n
the waves are broken up, and therefore, a strong turbulent region is indicated.
-------
-19-
5. Probe Measurements
5.1 Velocity Profiles
5.1.1 Neutral, High Wind Conditions
The vertical profiles of mean and turbulent velocities were measured
in the vicinity of the stack for the four terrain models. The profiles provided
the basic information on the turbulent motion in the boundary layer. The
results are presented in figs, lla through lid. In these figures , the origin
of the coordinate system (x,y,z) refers to the coordinates of the stack base.
For all the four runs, the towing speed of the terrain model or the free-
stream velocity U was 12.6 cm/sec. The thickness of the boundary layer &,
defined as the vertical distance at which the mean velocity U is equal to
0.99U , ranges from 22 cm to 27 cm for the four models.
The mean velocity profiles are replotted as U/U vs. z/6 in fig. 12.
For a major portion of the profile, the mean velocity can be approximated by
a power law
U
CO
The mean value of n for the four models is about 3. It has been reported
that n = 7 for turbulent flows over a smooth or rough flat plate (Schlichting,
1968) and n « 6 to 4 for flows over wind-generated water waves (Liu and
Karaki, 1973). The smaller value of n for the present case is believed to
result from the rugged surface boundary; Plate (1971) has shown that the value
of n tends to decrease with an increase in surface roughness.
The vertical profile of the longitudinal turbulent velocity shown in
figs, lla through lid is also different from the profile of the turbulent
velocity observed in a turbulent boundary layer over a smooth or rough plate
(Hinze, 1959). For the present case, the profile appears to have a thick
region z/6 < 0.5, in which the turbulent intensity is as high as 10 to 12%
of the free-stream velocity. Note that, in the experiments, the plume was
released at a level z = 7.4 cm, and its trajectory was influenced by the
turbulent motion even in the region immediately downstream of the stack
(figs. 5a, 6a, 7a and 8a).
Further examination of the characteristics of the turbulent boundary
layer is possible from the measurement of the one-dimensional energy spectrum.
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-20-
Figure 13 shows the turbulent spectra S(f) calculated from the measurement
of the longitudinal turbulent velocity for Run Ilia. Here, f is the frequency
2 2
in Hz, and S(f) is in cm /sec /Hz. The first two sets of data, indicated
by circles and crosses, were measured within the turbulent boundary layer at
z = 1.2 and 7.8 cm, respectively. The third set of data, indicated by
triangles, was measured outside the turbulent boundary layer at z = 29.6 cm,
and therefore, it can be considered the noise spectrum when examining the
turbulent spectrum. In the frequency range where most of the turbulent energy
is contained, the turbulent spectrum is about two decades above the noise spectrum.
The_turbulent spectrum measured at z = 7.8 cm is replotted in fig. 14
2
as fS(f)/u vs. k, where k is the wave number in cycle/m. The energy peak
appears at about k x 3 cycle/m or at a length scale of about 33 cm, which
is comparable to the thickness of the boundary layer. For comparison, the
field data, compiled by Davenport (1961) and available from Lumley and Panofsky
(1964), are plotted in fig. 14. The size of turbulent eddies measured in
present experiments is scaled upward by a factor of 2500 because the model
scale was 1/2500. In the range of the energy-containing eddies, the scaled-
up laboratory result is in good agreement with the field result. This finding
indicates that the energy-containing eddies in the atmosphere can be scaled
down and simulated with proper energy contents. This result also indirectly
shows that the plume dispersion in the atmospheric boundary layer can be simu-
lated in the laboratory as long as the plume dispersion is dominated by the
turbulent motion of energy-containing eddies.
5.1.2 Stable, Low-Wind Conditions
In these experiments, identical terrain models and tripping mechanisms,
as described in section 3.2, were used. The vertical profiles of the mean
velocity for the internal Froude number F = 2.7 and 5.4 are plotted in
n
figs. 15 and 16, respectively. Comparison of fig. 11 with figs. 15 and 16
shows marked differences in the mean velocity profiles under neutral and stable
conditions, as the result of the interaction of the stratified flow and the
rugged terrain. The most obvious differences are the appearance of the over-
shooting and the large wind shear observed in figs. 15 and 16.
The turbulent velocity N/ u^ is relatively low, and its distribution
is scattered. Adjacent to the terrain surface in a thin layer, (<6 cm),
is about 4 to 8% while, at the plume level, \l u^/U is practically zero.
oo
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-21-
The mechanical turbulence generated by the rough terrain tends to be rapidly
damped by the stable stratification. The TBL is confined only in a thin
layer, above which any disturbance is damped.
5.2 Ground Concentration Measurements
The temperature in the heated plume was used to indicate the pollutant
concentration. For ground concentration measurements, 10 thermistor probes
were installed 2 mm above the terrain surface in each model where high con-
centrations were likely to occur. The locations of the probes (fig. 2) were
designed for both neutral and stable conditions. Those probes installed up-
stream of the mountains were primarily for the neutral conditions, but also
provided records of the ambient temperature for the stable conditions.
5.2.1 Neutral Conditions
For all four models tested, we did not observe any measurable concen-
tration at the ground because the signals detected by the thermistor probes
are indistinguishable from the thermal noise (~0.01 C in the towing tank).
For the effluent at a temperature of 90 C and the ambient fluid at 20 C, the
-4
resolution in measuring the pollutant concentration level is 1.4 x 10 in
a dimensionless unit. A simple argument is given in the following to demon-
strate the low level of concentration possible for a plume dispersed in a
turbulent boundary layer. The heat flux released from the stack is calculated
by
Q = y D2W (Q - 0 ), (5.2)
x 4 s s a
where 9 is the effluent temperature and 6 is the ambient temperature. For
the plume downstream of the stack, the pollutant is assumed to be distributed
uniformly in a circular cross section of diameter d. The convection speed
of the effluent is simply assumed to be the free-stream speed U . Based on
the conservation of heat (or pollutant) flux, the concentration level is
calculated to be
L-JL-(£12^ (53)
8 -0 "(d) °- ' ' '
s a
From the photographs shown in figs. 5a, 6a, 7a and 8a, the diameter d of
the plume in the boundary layer is estimated to be about 20 cm for the region
where the plume touches the ground. By inserting the values D = 0.14 cm
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-22-
and W /U^ = 1.4, the concentration level is estimated to be
s _4
— = 0.7 x 10 ,
e - e
s a
which is even lower than the thermal noise level encountered in the towing
tank.
5.2.2 Stable Conditions
As observed in the visualization results, the plumes are far above
the ground in the upstream of the mountains. Low ground concentrations in
this region are expected. Also, the visualization results show that the plumes
are carried close to the ground on the top and lee sides of the mountains,
and therefore, high ground concentrations are expected for the area around the
mountains. Among the seven runs, only three of them (Runs Ib, Illb and IIIc)
show measurable ground concentrations. For the other cases, no detectable
signal was observed.
In table 3, the results of temperature measurements are listed for
Runs Ib, Illb, and IIIc. The thermistor probes were numbered, and their loca-
tions downwind of the stack for the respective models are listed in the table.
For Run Ib, the maximum ground concentrations were detected on the leeward
side of Vickery Mountain (probes 7 and 8), where the downslope wind occurs,
and on the mountain top (probes 4 and 5). The maximum root-mean-square (rms)
concentrations, however, were detected farther downstream, where the plume
tends to be mixed intensively (fig. 5b). In Run Illb, the maximum mean and
rms ground concentrations were detected simultaneously at locations (probes
9 and 10) downstream of the leeward mountain slope. For Run IIIc, the internal
Froude number was reduced from 5.4 to 2.7, and the results are similar to those
of Run Illb. In Run IIIc, the downslope wind carries the plume closer to the
leeward surface of the mountain (fig. 7c) than in Run Illb (fig. 6b), and it
also carries the plume around the top of Ketcherside Mountain (fig. 7f). As
a result, the plume partially avoids probes 2 and 3; otherwise, the mean con-
centrations measured at probes 2 and 3 for Run IIIc would have been much higher
than those shown.
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6. Discussion and Recommendations
In the previous sections, results of the flow visualization have been pre-
sented to provide an overall view of plume dispersion in a complex terrain. Also,
the measurements of velocity profiles and ground concentrations provided some
quantitative understanding of the dispersion of pollutants. In this section,
we shall further examine these results, and their implications for the field
situation will be discussed. In the following discussion, we first assume
that the effluent concentration of SCL at the stack exit is 2000 ppm in the
field, and then, the ground concentration in the field is calculated based
on the laboratory measurements.
6.1 Neutral» High-Wind Conditions
Under neutrally stable conditions, we did not detect any measurable con-
centration of pollutant. A simple argument, based on the conservation of
the pollutant flux, was given in section 5.1 to show that the pollutant is
so diluted that its concentration is lower than the thermal noise level, .01 C>
-4
or in a dimensionless form, 1.4 x 10 , in the towing tank. This noise level
corresponds to a full-scale background concentration of .28 ppm, which is
lower than the Federal Ambient Air Quality Secondary Standard for S02 of .5 ppm
for a 3-hour average. Note that the sampling time in the experiment for the
attainment of ground concentrations ranged from 40 to 60 seconds, which cor-
responds to about 30 minutes in the full-scale case since the scaling factor
of time is 1/40. We therefore conclude that the ground concentrations are
unlikely to be higher than the S0~ secondary standard of .5 ppm under the
simulated neutrally stable atmosphere.
6.2 Stable, Low-Wind Conditions
We have measured significant ground concentrations in the area around
the mountain for Runs Ib, Illb and IIIc. For example, a concentration level
_3
as high as 2 x 10 was measured in the leeward side of the Ketcherside Mountain.
The corresponding concentration of SO. in the field would be 4 ppm, which is
much higher than the secondary standard. Note that the sampling time used to
obtain the mean concentration level was about 40 seconds, which corresponds to
20 minutes in the field case since the scaling factor of time is 1/30.
6.3 Recommendations
Based on the results of this laboratory simulation, we recommend the
following locations for the installation of pollutant samplers:
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-24-
(1) Install samplers in the vicinity of Vickery Mountain. The sampling
area should cover the range from x = 4 to 7 km directly downstream of the
stack (figs. 5b and 5d).
(2) Install samplers in the vicinity of Ketcherside Mountain. The
sampling area should cover the area from x = 4 to 7 km downstream of the
stack along the centerline (with reference to the stack) of the model (figs.
7b and 7e) and about .5 km east of the centerline (figs. 7c and 7f).
(3) In the areas of Hogan Mountain and the unnamed mountain in model
IV, we suggest to install some samplers although we did not detect any measur-
able ground concentration for the atmospheric conditions tested. When an
elevated inversion layer occurs at a level about the same height of the mountain,
high ground concentrations are expected. In the vicinity of Hogan Mountain,
the sampling area should cover the range from 3 to 7 km directly downstream
of the stack. In the vicinity of the unnamed mountain in model IV, the sampling
area should cover from 4 to 7 km downstream of the stack. The samplers should
be installed along the valley in the lee of the mountain, as indicated by the
plume (figs. 8e and 8f).
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-25-
7. Conclusions
From the results of flow visualization and of quantitative measurements
with probes, we make the following conclusions.
7.1 Neutral, High-Wind Conditions
(i) Velocity profiles of the tripped turbulent boundary layer (TBL)
at the stack location compare well with other flows over rough surfaces.
A major portion of the vertical profiles of mean velocity, measured
at the vicinity of the stack, can be approximated by the power law,
U = l*\ 1/3
U.~U) '
For the four models, the tripped boundary layer thicknesses are about
600 m, which is approximately three times the stack height. The
profile of the longitudinal turbulent velocity over a complex terrain
model contains a thick region, about 1/3 to 1/2 of the boundary layer
/ 9
thickness, in which the turbulent intensity v u has a value of about
10 to 12X of the free-stream velocity.
(ii) The energy spectrum of the longitudinal turbulent velocity fluc-
tuation measured in the TBL is in good agreement with field data compiled
by Davenport (1961). This agreement is important evidence that the
atmospheric boundary layer and the associated pollutant transport can
be realistically simulated in a towing tank.
(iii) The dyed plume released into the TBL shows that the turbulent
motion of the TBL affects the plume dispersion even in the region very
near the stack. The plume trajectory fluctuates, in contrast to the
plume trajectory observed in a laminar background flow. Farther down-
stream, the plume is broken up and shows no coherent trajectory. The
patchy formation of the plume indicates the existence of large eddies
in the TBL.
(iv) The stack is relatively tall, compared with the surrounding
topography. Apparently, the plume axes remain aloft throughout the
entire lengths of the models (up to 7 km from the stack)? In the area
modeled, the maximum concentration at a given downstream distance does
not occur on the ground.
(v) The temperature data shows that the ground concentrations are
o -4
comparable to the thermal noise level, .01 C (or 1.4 x 10 in a
-------
-26-
dimensionless unit) in the towing tank. This corresponds to a full-
scale background concentration of .28 ppm (if a source concentration
of 2000 ppm is assumed), which is lower than the S0« secondary standard
of .5 ppm for a 3-hour average.
7.2 Stable, Low-Wind Conditions
(i) Velocity data show the presence of distinctive overshooting and
regions of high vertical shear at various elevations above the ground;
their presence indicated the complicated nature of the interaction of
the stratified flow and the rugged terrain. Laminar flows were observed
in most of the region, except in the thin layer adjacent to the ground
where turbulent flows exist.
(ii) The plumes rapidly rise to their terminal heights and level off.
The plumes are basically turbulent, but tend to relaminarize far
downstream of the stack.
(iii) Under the conditions simulated, the plumes are aloft upstream
of the mountains. No direct impingement is observed on the upstream
sides of the mountains.
(iv) Downslope winds traced by the plumes are observed in the lees
of the mountains for all four models. The pollutants in the plumes
are carried closer to the leeward mountain slopes by the downslope
wind.
(v) Generation of lee waves is demonstrated by several traces of the
plumes (figs. 6b, 6c, 8b and 8c). For the same model, the wavelength
decreases with a decreasing Froude number. Downstream of the first
wave trough, the vertical spreads begin to increase (figs. 6b and 8b).
The waves tend to break off for low internal-Froude-number cases, and
abrupt enlargement of the plume size occurs farther downstream (figs.
5b, 7c, 8c, 5d and 8f).
(vi) Close to the surface of the leeward mountain slopes, the terrain
effect on plume dispersion is strong. The plume is carried around the
mountain peak (fig. 7f). In other cases, the plume is diverted from
the wind direction and is forced to meander along a valley (figs. 8e
and 8f) on the leeward side of the mountain.
(vii) Ground concentrations as high as 4 ppm are measured at, and
downstream of, the locations where downslope winds occur, and the plumes
are brought into direct contact with the ground (figs. 5b, 7b and 7c),
-------
-27-
(viii) Based on the results of this laboratory simulation, we recom-
mend that full-scale samplers be installed in areas where high ground
concentrations are likely to occur.
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-28-
References
Briggs, G. A. (1969) Plume Rises, U.S. Atomic Energy Commission Critical
Review Series, TID-25072.
Counihan, J. (1969) "An Improved Method of Simulating an Atmospheric Boundary
Layer in a Wind Tunnel," Atmospheric Environment 3, 197-214.
Davenport, A. G. (1961) "The Spectrum of Horizontal Gustiness Near the Ground
in High Winds," Quart. J. Roy Meteorol. Soc. 87, 194.
Hinze, J. 0. (1959) Turbulence, McGraw-Hill Book Company, Inc., New York.
Hoult, D. P. and Weil, J. W. (1972) "Turbulent Plume in a Laminar Cross Flow,"
Atmospheric Environment jj, 513-531.
Lin, J. T., Liu, H. T., Pao, Y. H., Lilly, D. K., Israeli, M. and Orszag, S. A.
(1974) "Laboratory and Numerical Simulation of Plume Dispersion in Stably
Stratified Flow Over Complex Terrain," Report No. 654/4-74-044, USEPA,
Research Triangle Park, North Carolina.
Liu, H. T. and Karaki, S. (1973) "Studies of Particulate Plume Diffusion Over
Laboratory Wind-Generated Water Waves," Atmospheric Environment 7, 869-
890.
Liu, H. T., Lin, J. T., Pao, Y. H., Veenhuizen, S. D., Peecher, D. W. and
Hiatt, G. L. (1974) The Plume Dispersion in Stably Stratified Flow
Over a Flat Plate and a Three-Dimensional Terrain, Flow Research Film
No. 6.
Liu, H. T., and Lin, J. T. (1975) "Laboratory Simulation of Plume Dispersion
in Stably Stratified Flows Over Complex Terrain, Phase 2," Flow Research
Report No. 57.
Liu, H. T., Lin, J. T., Peecher, D. W. and Shearer, W. C. (1975) "Laboratory
Simulation of Plume Dispersion from a Lead Smelter: Glover, Missouri,"
Flow Research Film No. 8.
Orgill, M. M. , Cermak, J. E. and Grant, L. 0. (1971) "Laboratory Simulation
and Field Estimates of Atmospheric Transport-Dispersion Over Mountainous
Terrain," Technical Report CER70-71MMO-HEC-LOG40, Colorado State
University.
Lumley, J. L. and Panofsky, H. A. (1964) The Structure of Atmospheric Turbulent,
Datascience Publishers, New York.
Pao, Y. H., Lin, J. T., Carlson, R. L. and Smithmeyer, L. P. C. (1971) "The
Design and Construction of a Stratified Towing Tank with an Oil-
Lubricated Carriage," Flow Research Report No. 4 (APL/JHU POR-3530).
Plate, E. J. (1971) Aerodynamic Characteristic of Atmospheric Boundary Layers,
AEC Critical Review Series.
-------
-29-
Schiermeier, F. A. and Niemeyer, L. E. (1968) "Large Power Plant Efflucent
Study" (LAPPES), Vol. 1 - Instrumentation, Procedures, and Data Tabula-
tions, National Air Pollution Control Administration Publication No.
APTD70-2.
Schlichting, H. (1968) Boundary Layer Theory, 6th Edition, Mc-Graw Hill Book
Company, New York.
Sedov, L. I. (1959) Similarity and Dimensional Methods in Mechanics, Academic
Press, New York and London.
Shea, E. P. (1973) "Emissions from Lead Smelter at American Smelting and
Refining Company, Glover, Missouri," Report No. EMB 73-PLD-l, USEPA,
Research Triangle Park, North Carolina.
Slade, D. H. (1969) "Low Turbulence Flow in the Planetary Boundary Layer and
Its Relations to Certain Air Pollution Problems," J. of Applied
Meteorology 8, 514-522.
Turner, J. S. (1973) Buoyancy Effects in Fluids, Cambridge University Press,
Cambridge.
Veenhuizen, S. D., Lin, J. T., Pao, Y. H., Peecher, D. W. and Hiatt, G. L.
(1973) "Laboratory Simulation of Plumes from Kennecott Copper Smelters
in Garfield, Utah: Neutral Atmosphere," Flow Research Report No. 9.
Yu, H. Y. and Lin, J. T. (1975) "A Technique for Generating a Turbulent Boundary
Layer in a Wind-Wave Tank, Flow Research Note No. 71, presented at 2nd
U.S. National Conference on Wind Engineering Research, 23-25 June, 1975,
Colorado State University, Fort Collins, Colorado (APL/JHU POR-3663).
-------
-30-
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-------
TABLE 3
-32-
DATA OF GROUND CONCENTRATIONS
RUN Ib
5-5
Thermister
Probe
Number
1
2
3
4
5
6
7
8
9
10
Thermister
Probe
Number
7
6
5
4
3
2
8
1
9
10
Thermister
Probe
Number
7
6
5
4
3
2
8
1
9
10
x (km)
4.3
5.3
5.5
5.5
5.5
5.9
6.1
6.7
6.8
x fkml
I J
4.4
4.5
4.7
4.9
5.3
5.5
5.6
5.8
6.2
6.5
x fkml
4.4-
4.5
4.7
4.9
5.3
5.5
5.6
5.8
6.2
6.5
y [m]
0
91
101
61
162
0
61
61
91
91
RUN
y [m]
I 1
61
76
91
91
76
76
122
76
0
0
RUN
y [m]
61
76
91
91
76
76
122
76
0
0
. H
360
375
457
485
486
483
448
375
314
351
Illb
2 H
469
488
512
512
494
457
415
418
329
338
IIIc
. [m]
469
488
512
512
494
457
415
418
329
338
6|°C|
20.47*
20.48
20.50
20.53
20.53
20.51
20.52
20.53
20.50
20.50
9" °C|
*• '
-
19.61
19.60*
19.60
19.61
19.66
19.66
19.67
19.74
19.74
11
°°1
-
19.58*
-
-
19.61
19.67
19.. 67
19.66
19.67
19.67
a
e -e
s a
0
1.4 x 10~4
4.3 x 10~4
8.6 x 10~4
8.6 x 10~4
5.8 x 10~4
7.2 x 10~4
8.6 x 10~4
4.3 x 10~4
4.3 x 10~4
e-e
a
e -e
s a
1.4 x 10~4
0
0
1.4 x 10~4
-4
8.5 x 10
8.5 x 10~4
9.9 x 10~4
2.0 x 10~3
2.0 x 10"3
6-6
a
e -e
s a
.
0
4.3 x 10~4
1.3 x 10"3
1.3 x 10~3
1.1 x 10"3
1.3 x 10~3
1.3 x 10~3
/ flz Pr
/ o M
\l L J
-3**
l.lx 10 J
2.6x 10~3
2.4 x 10~3
3.9x 10~3
—3
2.9 x 10
4.9 x 10~3
2.4 x 10~3
3.6 x 10~3
5.9 x 10~3
8.3 x 10~3
r==~ \ \
1 e2 rcj
V
1.4 x 10~3
-U**
9.7 x 10
1.1 x 10~3
4.9 x 10"4
O
1.4 x 10
5.7 x 10~4
1.1 x 10~3
2.1 x 10~3
2.0 x 10~3
y'—iiLir"
J*2 l°cl
—
2.2 x 10~3
5.2 x 10~3
2.9 x 10~3
2.1 x 10~3
2.4 x 10"3
2.4 x 10~3
3.9 x 10~3
Average Ambient Temperature
Ambient Noise Level
-------
-33-
•P
(0
-P
C
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cn
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-------
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10
20
u
W
Q
30
40
50
60
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Stack
Exit
70
I
I
I
1. 00
1.01
1. 02
1. 03
1. 04
1.05
1. 06
SPECIFIC GRAVITY
Fig. 3 A Stratification Profile Measured with a
Conductivity Probe in the Towing Tank
(Run IVb)
-------
6.
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CO
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20.6
20.7 20.8
TEMPERATURE °C
20.9
21.0
Fig. 4 A Calibration Curve of a Thermistor Probe
(Run IVb)
-------
-38-
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FREQUENCY f(Hz)
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10'
Fig. 13 One-Dimensional Spectra of Velocity Data
Measured in the Vicinity of the Stack in
Model III.
Wind Direction = 206
U = 12.6 cm/s
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO.
EPA-450/3-75-066
2.
3. RECIPIENT'S ACCESSION-NO.
4. TITLE AND SUBTITLE
Laboratory Simulation of Plume Dispersion From a Lead
Smelter in Glover Missouri: Neutral and Stable
Atmosphere
5. REPORT DATE
April 1975
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
Hsien-Ta Liu and Jung-Tai Lin
8. PERFORMING ORGANIZATION REPORT NO.
Flow Research Report No. 55
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Flow Research, Inc.
1819 S. Central Avenue
Kent, WA 98031
10. PROGRAM ELEMENT NO.
2 AC 129
11. CONTRACT/GRANT NO.
68-02-1294
12. SPONSORING AGENCY NAME AND ADDRESS
Office of Air Quality Planning and Standards
Environmental Protection Agency
Research Triangle Park, NC 27711
13. TYPE OF REPORT AND PERIOD COVERED
FINAL May 1974 - Feb 1975
14. SPONSORING AGENCY CODE
15. SUPPLEMENTARY NOTES
16. ABSTRACT
A series of laboratory experiments which simulated dispersion of pollutants from a
lead smelter in Glover, Missouri were conducted in a stratified towing tank at Flow
Research, Inc. Results of the experiments, including flow visualization records
in the form of still and moving pictures and quantitative measurements with probes,
were used here to determine the locations where high ground concentrations were most
likely to occur under the simulated conditions.
In the laboratory, neutral and stable conditions corresponding to from typical to
adverse cases observed in the atmosphere were produced. Four terrain models with a
1/2500 scale, simulating four wind directions, were constructed. Under neutral
conditions, the plumes were considerably diluted within the simulated atmospheric
boundary layer. Ground concentrations were low everywhere on the four models. Under
stable conditions, the plumes were aloft upstream of the mountains, and ground
concentrations were low. High ground concentrations were measured in some cases
downstream of the mountains and at the locations where downslope winds occur. When
the pollutants in the plumes were brought by the downslope wind into direct contact
with the leeward mountain slope, the mean ground concentrations were high. Based on
the results, one of the most unfavorable situations occurs when a strongly stable
atmosphere is present. Therefore, it is recommended that samplers be installed on
top of and downstream of the mountains.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.IDENTIFIERS/OPEN ENDED TERMS
c. COSATI Field/Group
Atmospheric diffusion
Plumes
Tests
Stratification
Terrain
04A
21B
14B
14G
08F
13. DISTRIBUTION STATEMENT
RELEASE TO PUBLIC
19. SECURITY CLASS (ThisReport)
UNCLASSIFIED
21. NO. OF PAGES
63
20. SECURITY CLASS (Thispage)
UNCLASSIFIED
22. PRICE
EPA Form 2220-1 (9-73)
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