United States
Environmental Protection
Agency
Environmental Sciences Researc
Laboratory
Research Triangle Park NC 277
Research and Development.
EPA-600/S4-81-067 Jan. 1982
Project Summary
Flow and Dispersion of
Pollutants Over Two-
Dimensional Hills: Summary
Report on Joint Soviet-
American Study
Leon H'^hurshudyan, William H. Snyder, and Igor V. Nekrasov
v Wind tunnel experiments and theo-
retical models concerning the flow
structure and pollutant diffusion over
two-dimensional hills of varying aspect
ratio are described and compared.
Three hills were used, having small,
medium, and steep slopes. Measure-
ments were made of mean and turbu-
lent velocity fields upwind, over, and
downwind each of the hills. Concen-
tration distributions were measured
downwind of tracer sources placed at
the upwind base, at the crest, and at
the downwind base of each hill. These
data were compared with the results
of two mathematical models devel-
oped in the U.S.S.R. for treating flow
and dispersion over two-dimensional
hills. Measured concentration fields
were reasonably well predicted by the
models for a hill of small slope. The
models were less successful for hills
of steeper slopes, because of flow
separation from the lee side of the
steepest hill and high turbulence and
much-reduced mean velocity down-
wind of the hill of medium slope.
This Project Summary was develop-
ed by EPA's Environmental Sciences
Research Laboratory, Research Triangle
Park. NC, to announce key findings of
the research project that is fully doc-
umented in a separate report of the
same title (see Project Report order-
ing information at back).
Introduction
This report presents preliminary re-
sults of the Joint Soviet-American Work
Program for studying air flows and dis-
persion of pollutants in hilly terrain. The
work was conducted in the Fluid Model-
ing Facility of the U.S. Environmental
Protection Agency (EPA), Research Tri-
angle Park. NC.
Investigations of pollutant transport
and dispersion in the atmosphere over
complex relief are critical for the protec-
tion of air quality, since industrial
enterprises and other sources of air pol-
lution frequently locate within such ter-
rain. Although much effort has been
expended in elucidating this problem
and in establishing guidelines for indus-
try and control organizations to use in
predicting air pollution, the problem is
far from solved. Presently, three main
approaches are used to study the prob-
lem:
Theoretical Modeling
To calculate pollutant dispersion, it is
necessary to know how irregularities of
the ground surface distort the mean and
turbulent structure of the incident flow.
Some investigations of peculiarities
of turbulent dispersion in distorted flows,
even separated flows, have been made.
Practically speaking, however, those
results can be used only if the distorted
mean flow field, i.e., mean streamline
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pattern, is known. Since mathematical
modeling of flow structure is quite diffi-
cult, these diffusion theories have been
applied only with highly simplified
assumptions about the mean flow, e.g.,
potential flow. The most realistic mod-
els of flows, some which include diffu-
sion calculations over irregular terrain,
have been obtained through solution of
simplified equations of viscous flow
with additional simplifying assumptions
on turbulence structure. In spite of dif-
ferences between these models, under-
lying assumptions limit their applicabil-
ity to gentle relief. Most of these theories
are also too complicated for use in the
daily practice of air pollution prediction.
Hence, simpler models that assume
potential (or "quasi-potential") flow over
irregular terrain have become wide-
spread. In the U.S., models are used that
neglect, even for neutral flow, the con-
vergence of streamlines over obstacles
as in the EPA Valley Model. More
recently, attempts have been made to
describe the flow structure over steeper
obstacles where flow separation may
occur. But these attempts deal only with
laminar flows which involve numerical
solutions of Navier-Stokes equations at
small to moderate Reynolds numbers.
Field Experiments
Full-scale experiments, while impor-
tant, are expensive and time-consuming,
especially in complex terrain. Extensive
measurements and analyses are re-
quired of wind, temperature, and con-
centration distributions to gain suffi-
cient understanding of the fundamental
physics. Generalization from field data
is difficult because of peculiarities of
specific sites and meteorological condi-
tions. Controlled variation of independ-
ent variables is generally not possible,
and complicating factors are abundant.
However, all models must ultimately be
tested by comparison with real-world2
data. Significant field experiments in
complex terrain are now being con-
ducted by the Department of Energy,
the Electric Power Research Institute,
and the EPA.
Wind Tunnel Modeling
The difficulties of mathematical and
field investigations of atmospheric flows
and pollutant dispersion in complex
cases such as hilly terrain have stimu-
lated the development of wind tunnel
modeling, where the atmospheric
boundary layer and diffusion processes
are stimulated. This method's advan-
tages are the simplicity of fixing and
controlling the governing parameters
and the reproducibility of conditions,
among others. While it is still techni-
cally impossible to satisfy simultane-
ously all similarity criteria, most inves-
tigators now have a consensus opinion
of how to approximate atmospheric
processes of different scales in wind
tunnels. Two basic approaches exist.
The first is the investigation of specific
topographic sites. Such "specific"
studies are usually requested by an
industrial company or by a controlling
air-protection organization. The second
category, "generic" studies, focuses on
idealized situations to obtain funda-
mental understanding of the principal
governing parameters and the physical
processes involved. Such investigations
have been developing in recent years in
EPA's Fluid Modeling Facility and the
U.S.S.R. To simplify the investigation,
one frequently considers two-dimen-
sional relief and neutral stratification of
the flow. Inroads have also been made
on three-dimensional relief and non-
neutral stratification.
Until recently, most generic studies of
flow and dispersion in complex terrain
have been concerned with hills of either
small or large slopes. Separation on the
lee slope was not expected to occur for
hills of small slopes but was definitely
expected for hills of large slopes. A few
hills with moderate slopes have been
investigated, but these have been con-
ducted in short wind tunnels where the
boundary layer was relatively thin and
external turbulence was generated by a
grid. The work reported here concerns
hills with slopes ranging from small to
large. This work attempts to generate
new experimental information and to
compare the results of the wind tunnel
measurements with calculations based
on previous mathematical models.
Computer programs that calculate
pollutant concentrations using the above
mentioned mathematical models were
constructed for specific ground surface
shapes. These shapes were single two-
dimensional hills or valleys generated
from a set of parametric equations.
The shapes of hills studied in the wind
tunnel are_ shown in Figure 1 with
aspect ratios of n =3,5 and 8 (maximum
slope angles of 26°, 16°, and 10°,
respectively). The working program
consisted of:
a. Wind tunnel measurements of
mean and fluctuating velocities of
the neutrally stable flow in the
presence of rough hills as well as
pollutant concentrations from
elevated point sources located in
different positions relative to the
hills;
b. wind tunnel measurements of
concentrations from an elevated
point source located over the
rough flat floor; and
c. numerical calculations of surface
concentrations in the presence of
the hills as well as for the flat
ground surface on the basis of the
theoretical models, and compar-
isons of these results with the
experimental data.
Results and Discussion
Wind and concentration measure-
ments within the artificially-thickened,
rough-wall boundary layer showed that
the latter is a reasonable simulation of
the neutral atmospheric boundary layer.
The following points of agreement were
demonstrated:
1. When a particular value of the
Lagrangian integral scale was
assumed, lateral plume growth
rates agreed with Taylor statistical
theory.
2. Vertical growth rates for ground-
level sources agreed with
Lagrangian similarity theory.
3. Rate of decay of ground-level
concentration at large downwind
distances agreed with gradient
diffusion theory (C <* x~3/2).
Comparisons of numerical models
with experimental data generally
agreed within 10 to 15% in predicting
the locations and values of maximum
surface concentrations as the stack
height was varied; further improve-
ments may be expected when values of
lateral and vertical diffusivities more
precisely corresponding to the wind
tunnel boundary layer are put into the
model.
The flow over the steepest hill (n = 3)
separated on the lee slope and formed a
recirculation zone or cavity (see Figure
2). This cavity extended to 6.5 hill
heights downwind of the crest. Within
the cavity, the mean speed of the
reversed mean flow was 20% of the
free-stream velocity. The flows over
hills 8 and 5 did not separate, but the
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Figure 1. Shapes of model hills (to scale).
-20
Figure 2. Streamlines over hill 3 computed from experimental data.
-4
-2
2 4
x/h
b) hill n = 3
10 12 14 16
Figure 3. Strean..'ines over hill 8 computed from experimental data.
mean streamline patterns were notice-
ably asymmetric in contrast with poten-
tial theory (see Figure 3). The horizontal
mean wind velocity near the downwind
base of hill 5 was very small: 10% of the
velocity in the absence of the hill at a
height of 0.2ho. The longitudinal turbu-
lence intensity, however, was
extremely large — twice the mean
velocity at 0.2ho. Even though the flow
was not observed to separate in the
mean, instantaneous flow reversals
were frequently observed through
smoke visualization. Probability density
distributions measured with a pulsed-
wire anemometer showed that the flow
was negative up to 40% of the time, and
that the mean was small but positive.
Changes in the turbulence structure
due to the presence of hill 8 were not
highly significant, whereas changes
over hills 3 and 5 were quite strong. The
speed-up of the flow over the tops and
the slow-down on the lee sides were
larger over the steeper hills.
The dispersion characteristics were
obviously also changed by the presence
of the hills. The existence of a cavity
region drastically influenced the shapes
of the vertical concentration profiles
and the values of the surface concen-
trations within the cavity. Concentra-
tions within the cavity region were
essentially uniform with height.
Surface concentrations were
sometimes greatly increased, some-
times somewhat decreased when
compared with values over flat terrain.
These variations depended upon the
stack height and location with respect to
the hill center. Instead of being
smoothly varying functions of down-
wind distance, some surface concentra-
tion profiles contained characteristic
dips that identified the beginning and
end of the cavity region.
For hill 8, the deviations of the diffus-
ion patterns from those over flat terrain
were much less significant. Changes in
the concentration fields were appar-
ently not influenced as much by
changes in turbulence structure as by
changes in the mean flow field.
A simple way to evaluate the effects
of terrain on concentration is to calcu-
late a terrain correction factor, which is
defined as the ratio of the maximum
surface concentration occurring in the
presence of the complex terrain to the
maximum that would occur from the
same source located in flat terrain.
The terrain correction factors for the
values and locations of maximum
surface concentration obtained from
the wind-tunnel measurements were
compared with factors calculated using
a quasi-potential model. The results are
tabulated in Table 1. Satisfactory agree-
ment between theory and experiment
was obtained: 80% of the calculated
values were within 25% of the meas-
ured values when the stack was located
at the upwind base or top of hill 8. When
the stack was located at the downwind
base, the theory significantly under-
predicted the experimentally observed
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concentration values. This disparity is
apparently related to the inability of the
quasi-potential model to account for the
asymmetry of the flow over the hill.
For hills 3 and 5, there was, as
expected, a large disparity between cal-
culated and experimental values when
the stack was located at the downwind
base of the hills caused by the presence
of the recirculation zone and the zone of
extremely low wind velocity. Stream-
wise diffusion may not be neglected in
these zones. Nevertheless, there was a
certain amount of agreement when the
stack was located at the top or upwind
base: 70% of the calculated values were
within 25% of the measured values.
A comparison was also made
between results of a numerical model
and experimental measurements for
values and locations of maximum
surface concentration. Input to the
numerical model were wind-tunnel
data on the mean and turbulent flow
fields over hill 8. The comparisons of
maximum surface concentrations
showed relatively good agreement; all
calculations were within 30% of
measurements when the stack was
located at the upwind base or top of the
hill; there was satisfactory agreement,
all within 40%, when the stack was at
the downwind base.
Table 1. Terrain Correction Factors for Maximum Surface Concentration.
Stack Height
Hill Height
0.25
0.50
1.00
1.50
0.25
0.50
1.00
1.50
Source at
• Upwind Base
From
Measur. Calcul.
1.45
1.12
1.47
1.16
1.96
2.04
1.74
1.20
1.42
1.37
1.24
1.20
1.70
1.59
1.35
1.28
Source at
Hill Top
From
Measur. Calcul.
HILL, n = 8
0.91
0.56
0.78
0.82
HILL, n=5
0.54
0.63
0.86
1.04
HILL. n=3
0.66
0.67
0.74
0.75
0.53
0.54
0.65
0.67
Source at
Downwind Base
From
Measur. Calcul.
3.43
2.99
2.39
1.68
15.00
8.12
5.63
2.90
1.42
1.37
1.24
1.20
1.70
1.59
1.35
1.28
0.25
0.50
1.00
1.50
2.81
2.47
1.78
1.87
2.29
2.02
1.52
1.39
0.34
0.69
0.91
0.94
0.38
0.41
0.55
0.59
7.50
6.42
10.80
7.77
2.29
2.02
1.52
1.39
Recommendations
Further refinement of the technique
used for producing the wind field and
the application of more appropriate
models for eddy diffusivities should
improve the agreement with
experimental data.
Additional tests showed that the flow
structure and separation is insensitive
to the Reynolds number over a limited
range, but it is not known for certain that
the relatively low-Reynolds-number
wind-tunnel flow simulates the very
large-Reynolds-number flow in the
atmosphere. Nevertheless, it is
important that theoretical models be
developed to predict separated flows
such as this wind tunnel flow, since
separation definitely occurs on the lee
sides of steep-enough full scale hills.
Leon H. Khurshudyan is with the Main Geophysical Observatory, Leningrad,
U. S.S.R.; the EPA author William H. Snyderfalso the EPA Project Officer, see
below) is with the Environmental Sciences Research Laboratory, Research
Triangle Park, NC 27711; Igor V. Nekrasov is with the Institute of Mechanics.
State University of Moscow, Moscow. U.S.S.R.
The complete report, entitled "Flow and Dispersion of Pollutants Over Two-
Dimensional Hills: Summary Report on Joint Soviet-American Study, "(Order
No. PB 82-121 179; Cost: $13.50, subject to change) will be available only
from:
National Technical Information Service
5285 Port Royal Road
Springfield. VA 22161
Telephone: 703-487-4650
The EPA Project Officer can be contacted at:
Environmental Sciences Research Laboratory
U.S. Environmental Protection Agency
Research Triangle Park. NC 27711
U.S. GOVERNMENT PRINTING OFFICE: 1982—55*092/3413
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