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EPA-600/4-81-067
August 1981
FLOW AND DISPERSION OF POLLUTANTS OVER TWO-DIMENSIONAL HILLS
Summary Report on Joint Soviet-American Study
by
Leon H. Khurshudyan
Main Geophysical Observatory
Leningrad, U.S.S.R.
William H. Snyder
Meteorology and Assessment Division
Environmental Sciences Research Laboratory
U.S. Environmental Protection Agency
Research Triangle Park, NC 27711
Igor V. Nekrasov
Institute of Mechanics
State University of Moscow
Moscow, U.S.S.R.
ENVIRONMENTAL SCIENCES RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
RESEARCH TRIANGLE PARK, NC 27711
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DISCLAIMER
This report has been reviewed by the Environmental Sciences Research
Laboratory, U.S. Environmental Protection Aqency and the Main Geophysical
Observatory, Leningrad, U.S.S.R., and approved for publication. Mention of
trade names or commercial products does not constitute endorsement or
recommendation for use.
William H. Snyder is a physical scientist in the Meteorology and Assess-
ment Division, Environmental Sciences Research Laboratory, U.S. Environmental
Protection Agency, Research Triangle Park, NC. He is on assignment from
the National Oceanic and Atmospheric Administration, U.S. Department of
Commerce.
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PREFACE
This report presents a portion of the results of a US-USSR cooperative
program in the study of environmental protection. It culminates the joint
activities of three scientists working together over a period of five months.
A wind-tunnel study of flow and dispersion of pollutants over two-dimensional
hills was conducted. Simultaneously, computer programs were run to make com-
parisons with various theories and prediction techniques.
In this cooperative venture, a very large amount of data was collected
in a short time period. It was possible, in the time at hand, to assimilate
only a small fraction of the observations and to make only limited compari-
sons between the data collected and the multitude of theories. This report
is intended, then, as an overview of the methods and techniques of data
collection and a presentation of the most important conclusions. It is also
intended to give the reader some flavor of the quantity and quality of the
data collected and to exemplify the kinds of information contained in the
data volumes as well as the kinds of comparisons that can be made with theory;
in short, this report is intended to whet the appetite of the reader and to
encourage him to exercise the data for useful purposes.
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ABSTRACT
Wind tunnel experiments and theoretical 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. Measurements were made of mean and tur-
bulent velocity fields upwind, over and downwind each of the hills. Con-
centration 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 deve-
loped 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 slope, because of flow separation from the lee side of the
steepest hill and high turbulence and much-reduced mean velocity downwind
of the hill of medium slope.
IV
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CONTENTS
PREFACE i"
ABSTRACT iv
FIGURES vi
TABLES x
ACKNOWLEDGEMENTS xi
1. INTRODUCTION 1
2. SUMMARY AND CONCLUSIONS 6
3. THEORETICAL MODELS 9
3.1. Diffusion Calculations over Flat Terrain
in Wind Tunnel 9
3.2. General Description of Models for Calculating
Pollutant Dispersion over Hilly Terrain 10
3.2.1. Generation of a mass consistent
wind field 14
3.2.2. Calculating the turbulent diffusivity. ... 17
3.2.3. Numerical solution of the diffusion
equation 18
4. APPARATUS, INSTRUMENTATION AND MEASUREMENT
TECHNIQUES 19
4.1. Wind Tunnel and Simulated Atmospheric
Boundary Layer 19
4.2. Velocity Measurements 19
4.3. The Models 31
4.4. Pollutant Source 34
4.5. Calibration of Source 37
4.6. Concentration Measurements 45
4.7. FID Response Characteristics 48
4.8. Adjustment of Height of Wind Tunnel Ceiling .... 51
5. PRESENTATION AND DISCUSSION OF RESULTS AND
COMPARISON WITH THEORY 52
5.1. Flat Terrain 52
5.1.1. The boundary layer structure 52
5.1.2. Dispersion characteristics of the
boundary layer 58
5.1.3. Comparison with theory 71
5.2. Hills 77
5.2.1. Velocity measurements 77
5.2.2. Concentration measurements 88
5.2.3. Comparison with theory 101
5.3. Special Experiments 117
5.3.1. Reynolds number and hill-height effects ... 117
5.3.2. Effects of ceiling adjustment 120
5.3.3. Streamline patterns over hills 120
REFERENCES 126
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FIGURES
Number Page
1 Reynolds stresses indicated by yawed end-flow probes ... 22
2 Flow angles indicated by yawed end-flow probes 23
3 Mean velocities indicated by yawed end-flow probes 24
4 Longitudinal fluctuating velocities indicated by
yawed end-flow probes 25
5 Vertical fluctuating velocities indicated by
yawed end-flow probes 26
6 Comparison of mean velocities measured with
different probe types 27
7 Comparison of longitudinal fluctuating velocities
measured with different probe types 28
8 Comparison of vertical fluctuating velocities
measured with different probe types 29
9 Comparison of Reynolds stresses measured with
different probe types 30
10 Typical calibration curve for hot-wire anemometer 32
11 Shapes of model hills (to scale) 33
12 Diagram of source and flow measurement apparatus 35
13 Comparison of concentration profiles measured under
different source flow rates 36
14 Comparison of vertical concentration profiles measured
downwind of isokinetic release tube and porous sphere . . 38
15 Typical calibration curve for laminar flow element 39
16 History of calibration of stack "P4". 41
17 Results of experiments to determine influence of back
pressure on laminar flow element: flow rate versus
pressure differential 42
VI
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Number Pa9e
18 Results of experiments to determine influence of
back pressure on laminar flow element: back pressure
versus pressure differential 43
19. Comparison of concentration profiles measured under
same apparent conditions indicating difficulties
with source-calibration 44
20 Typical calibration of flame ionization detector
with ethylene 46
21 Typical concentration profile measured with four FIDs . . . 47
22 Response of FID's to step change in concentration 49
23 Response of FID's to square wave input 50
24 Typical mean velocity profiles in flat terrain 53
25 Typical Reynolds stress profiles in flat terrain 54
26 Typical longitudinal turbulence intensity profiles
in flat terrain 56
27 Typical vertical and lateral turbulence intensity
profiles in flat terrain 57
28 Surface concentrations from sources of various heights
in flat terrain 59
29 Similarity of surface concentration profiles in flat
terrain 60
30 Similarity of lateral concentration profiles in flat
terrain; Hg = 29mm 62
31 Similarity of lateral concentration profiles in flat
terrain; Hg = 117mm 63
32 Horizontal profiles through plume at X = 7488mm from
source of height HS = 117mm in flat terrain 64
33 Lateral plume widths as functions of height above
ground in flat terrain 65
34 Isoconcentration contours of plume 7488mm downwind
from source in flat terrain; H = 29mm 66
35 Isoconcentration contours of plume 585mm downwind
from source in flat terrain; H = 117mm 67
vii
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Number Page
36 Growth of lateral plume width in flat terrain 68
37 Development of vertical concentration profiles from
source of height H = 117mm in flat terrain 69
38 Reflected Gaussian fits to vertical concentration
profiles; Hg = 117mm 70
39 Growth of true standard deviation of vertical
concentration distributions in flat terrain 72
40 Comparison of numerical calculations of maximum
surface concentrations with wind tunnel data
in flat terrain 75
41 Comparison of numerical calculations of location of
maximum surface concentration with wind tunnel
data in flat terrain 76
42 Comparison of surface concentrations predicted by
Equation 44 with wind tunnel data in flat terrain. ... 78
43 Vertical profiles of mean velocity over hill 8 79
44 Flow-angle profiles over hill 8 81
45 Streamwise turbulence intensity profiles over hill 8 ... 82
46 Normal turbulence intensity profiles over hill 8 . . . . , 83
47 Reynolds stress profiles over hill 8 ,. 85
48 Mean velocity profiles inside cavity region of hill 3. . . 86
49 Mean velocity profiles measured at downwind base of
hill 5 87
50 Probability density of velocity fluctuations at 20mm
above downwind base of hill 5 89
51 Mean velocity profiles measured in the recirculating
wake of an abstacle 90
52 Surface concentration profiles over hills; upwind
base stack location; H = 59mm 91
53 Surface concentration profiles over hills; hill top
stack location; H = 59mm 92
o
vm
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Number Pa9e
54
55
56
57
58
59
6Q
61
62
63
64
65
66
67
68
69
70
Surface concentration profiles over hills; downwind
base stack location; H = 59mm
Surface concentration profiles over hills; downwind
base stack location; H = 59mm; semilogarithmic plot. .
Vertical concentration profiles over hill h; HS = hQ. . .
Vertical concentration profiles over hill 8; HS = h /4. .
Vertical concentration profiles over hill 3 showing
influence of recirculation zone; H = h ........
Growth of lateral plume width in presence of hills. . . .
Relation between maximum surface concentration and
distance to its location in presence of hills
Comparison of surface concentrations predicted by QPM
and experimental data; hill 8; H = h /2; x = (1). . .
Comparison of surface concentrations predicted by QPM
and experimental data; hill 8; HS = hQ/2; x = (2). . .
Comparison of surface concentrations predicted by QPM
and experimental data; hill 8; HS = hQ/2; xg = (3). . .
Comparison of maximum surface concentrations predicted
by WMDM and experimental data; hill 8; x = (1) . . . .
Comparison of distances to location of maximum surface
concentration predicted by WMDM and experimental
data; hill 8; x = (1)
Comparison of maximum surface concentrations predicted
by WMDM and experimental data; hill 8; xg = (2} . . . .
Comparison of distances to location of maximum surface
concentration predicted by WMDM and experimental
data; hill 8; x = (2)
Comparison of maximum surface concentrations predicted
by WMDM and experimental data; hill 8; x = [3) ....
Comparisons of distances to location of maximum surface
concentration predicted by WMDM and experimental
data; hill 8; x = C3]
Locus of zero-mean velocity in cavity as function
of Reynolds number and hill size. ....
9?
95
97
98
99
100
102
106
107
108
110
111
112
113
114
115
1.19
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Number Page
71 Dependence of surface concentrations on wind tunnel
ceiling adjustment; hill 8; Hg = hQ/2; x = (3) 121
72 Streamline pattern over hill 8 from experimental data. . . 122
73 Streamline pattern over hill 3 from experimental data. . . 124
74 Streamline pattern over hill 5 from experimental data. . . 125
TABLES
Number Page
1 Terrain Correction Factors for Maximum
Surface Concentration 103
2 Terrain Correction Factors for Location
of Maximum Surface Concentration 104
3 Comparison of Measured Maximum Concentrations
and Those Calculated with WMDM for Hill 8 116
4 Comparison of Measured Distances to Maximum
Concentration and Those Calculated with WMDM
for Hill 8 116
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ACKNOWLEDGEMENTS
The cooperation of the staff at the Fluid Modeling Facility is grate-
fully acknowledged. The authors are particularly indebted to Messrs.
L. A. Knight, R. E. Lawson, Jr., and W. R. Pendergrass, III for their help
with the myriad details involved in the collection of data, Mr. M. S. Shipman
for his difficult and innovative programming of the minicomputer, and
Mr. M. Manning for the construction of the models.
Dr. I. P. Castro, University of Surrey (England) provided assistance
with the pulsed-wire anemometer measurements during the spring and summer
of 1980. Mr. M. Capuano, North Carolina State University, helped with the
remeasurement of suspect data and supplementary measurements as well as data
processing. Drs. I. M. Zrazhevsky, E. L. Genikhovich, V. B. Kisselev and
Mrs. I G. Gracheva participated in useful discussions of the results of this
study during the US-USSR experts' meeting in Leningrad, U.S.S.R., in April,
1980.
Finally, thanks are extended to Messrs. A. D. Busse and C. Gale for
their assistance with the Univac computer and Mrs. B. Hinton for her toil
in typing the manuscript.
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1. INTRODUCTION
This report presents preliminary results of the Joint Soviet-American
Work Program for studying air flows and dispersion of pollutants in hilly
terrain. The work was conducted in the Fluid Modeling Facility of the
U.S. Environmental Protection Agency, Research Triangle Park, NC.
Investigations of pollutant transport and dispersion in the atmosphere
over complex relief are critical for the protection of air quality, since
industrial enterprises and other sources of air pollution frequently locate
within complex terrain. Although much effort has already be expended in
elucidating this problem and establishing guidelines for industry and con-
trol organizations to use in predicting of air pollution, the problem is
far from solved. At present, three main approaches are used to study the
problem:
THEORETICAL MODELING
To calculate pollutant dispersion, it is necessary to know how irregula-
rities 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 (Hunt and Mulhearn,
1973; Puttock and Hunt, 1979). Practically speaking, however, those results
can be used only if the distorted mean flow field (mean streamline pattern)
is known. Since mathematical modeling of flow structure is quite difficult,
these diffusion theories have been applied only with highly simplified
assumptions about the mean flow, e.g., potential flow. The most realistic
models of flows (some including diffusion calculations) over irregular
terrain constructed thus far have been obtained through solution of simpli-
fied equations of viscous flow with additional simplifying assumptions about
the turbulence structure (Berlyand and Genikhovich, 1971; Taylor and Gent,
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1974; Jackson and Hunt, 1975). In spite of differences between these models,
their underlying assumptions limit their applicability to gentle relief (hills
of small slope). As a further restriction, most of these theories are too
complicated to be used in the daily practice of air pollution prediction.
Hence, simpler models have become wide-spread. These simpler models usually
assume potential (or "quasi-potential") flow over irregular terrain (Berlyand
et al, 1968; Egan, 1975; Isaacs et al, 1979; the latter incorporates the
Hunt-Mulhearn theory). In the U.S., models are used that neglect, even for
neutral flow, the convergence of streamlines over obstacles as in the EPA
Valley Model (Burt and Slater, 1977). More recently, attempts have been
made to describe the flow structure over steeper obstacles where flow se-
paration may occur (Mason and Sykes, 1979). But these attempts deal only
with laminar flows (numerical solutions of Navier-Stokes equations at small
to moderate Reynolds number).
FIELD EXPERIMENTS
Full-scale experiments are very important, but expensive and time-con-
suming, especially in complex terrain (Barr et al, 1977; Hovind et al, 1979).
Extensive measurements and analyses are required of wind, temperature and
concentration distributions in order to gain sufficient insight and under-
standing of the fundamental physics so that mathematical models may be
constructed that are at least correct in principle. The generalization from
field data is difficult because of the peculiarities of specific sites and
meteorological conditions. Controlled variation of independent variables
is generally not possible. Complicating factors are generally abundant.
However, to obtain credibility, all models must ultimately be tested by
comparison with real-world data. Significant field experiments in complex
terrain are now being conducted by the Department of Energy (Dickerson and
Gudiksen, 1980), the Electric Power Research Institute (Hilst, 1978), and
the Environmental Protection Agency (Holzworth, 1980).
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WIND TUNNEL MODELING
The difficulties of mathematical and field investigations of atmospheric
flows and pollutant dispersion in complex cases such as hilly terrain have
stimulated the development of wind tunnel modeling, where the atmospheric
boundary layer and diffusion processes are simulated. This method has such
advantages as the simplicity of fixing and controlling the governing para-
meters as well as the reproducibility of conditions, which is impossible
in the real atmosphere. There remains, however, the technical impossibility
of simultaneously satisfying all similarity criteria. Most investigators
now have a consensus opinion of how to approximate atmospheric processes of
different scales in wind tunnels (Cermak et al, 1965; Snyder, 1972, 1981;
Zrazhevsky and Klingo, 1971). Since the simulation of flows and pollutant
dispersion under conditions of complex relief is one of the most attractive
areas for using wind tunnels, many investigations have been made on this
subject. 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 fundamental 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 in the U.S.S.R. (Gorlin
and Zrazhevsky, 1968; Berlyand, 1975). The generic approach is the more
scientific, although more demanding of time and effort. Generic studies
are most useful when combined with theoretical modeling in that theory and
experiments serve to direct each other. To simplify the investigation, one
frequently considers two-dimensional relief and neutral stratification of
the flow. This is, of course, an important step in elucidating the problem,
but numerous questions remain. Three-dimensional relief and non-neutral
stratification are equally, perhaps more, important, and inroads have also
been made in these areas (Hunt et al, 1978; Hunt and Snyder, 1980; Snyder
et al. 1979; additional references are contained in these works).
Up until this time, most generic studies of flow and dispersion in com-
plex terrain have been concerned with hills of either very small or quite
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large slopes. Studies by Courtney (1979) and Britter et al (1981) exemplify
small -slope studies where separation on the lee slope was not expected to
occur. The works of Huber et al (1976), Arya and Shipman (1979, 1981), and
Wilson et al (1979) exemplify large-slope studies, where separation from
the lee slope was definitely expected. A few hills with moderate slopes
have been investigated, but these have been conducted in short wind tunnels
where the boundary layer was relatively thin and external turbulence was
generated by a grid (Zrazhevsky et al, 1968).
Flow structure over such hills is both interesting and important from
the points of view of obtaining fuller scientific knowledge and for using
the results in tha practical prediction of air quality. The work reported
here is concerned with hills with slopes ranging from small to large.
This work attempts to further the contributions made in this field thus far,
both to generate new experimental information and to compare the results
of the wind tunnel measurements with calculations based on previous mathe-
matical models (Berlyand et al, 1968; 1975).
Computer programs that calculated pollutant concentrations using the
above mentioned mathematical models were constructed for specific ground
surface shapes. These shapes were single two-dimensional hills (or valleys)
with the following parametric equations:
if
|5| a
x = i sign(s) [|?| + m/5* - az
z = 0
where ,
m =
d a
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h = height of hill, a = half-width of hill, and £ = arbitrary parameter.
x is directed along the approach flow direction (origin at hill center),
and z is directed vertically upwards. Since the surface is two-dimensional,
the equation does not include the y variable. When h < 0, these equations,
of course, describe a valley. The hills (or valleys) described by Eq. 1
have smooth forms that are symmetric about the z-axis and smoothly merge
into a flat plane at the points x = ±a. These equations describe not a
single surface but a two-parameter family of surfaces, the parameters being
the height h and aspect ratio n = a/h .
The hills studied in the wind tunnel had shapes described by Eq. 1 and
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;
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 comparisons of these results
with the experimental data.
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2. SUMMARY AND CONCLUSIONS
Wind tunnel measurements were made of the concentrations fields down-
wind of elevated point sources located at different positions relative to
two-dimensional hills. Three hill shapes, with aspect ratios n of 3, 5 and
8, were used. For reference purposes, measurements were taken over the flat
wind tunnel floor. To aid in interpretating and understanding the concen-
tration fields thus produced, mean and turbulent velocity fields were also
measured. These experimental results were compared with predictions of
theoretical models developed in the U.S.S.R.
Wind and concentration measurements within the artificially-thickened,
rough-wall boundary layer showed it to be a reasonable simulation of the
neutral atmospheric boundary layer. The following points of agreement were
demonstrated:
1. Lateral plume growth rates with Taylor statistical theory when a
particular value of the Lagrangian integral scale was assumed;
2. Vertical growth rates for ground-level sources with Lagrangian
similarity theory (previously shown);
3. Rate of decay of ground-level concentration at large downwind
-3/2
distances with gradient diffusion theory (C <* x ' ).
Comparisons of numerical models with experimental data have shown satis-
factory agreement (generally, within 10 to 15%) in predicting the locations
and values of maximum surface concentrations as the stack height was varied;
further improvements may be expected when values of lateral and vertical
diffusivities more precisely corresponding to the wind tunnel boundary layer
are input to the model.
The flow over the steepest hill (n = 3) separated on the lee slope and
formed a recirculation zone or cavity. This cavity extended to 6.5 hill
heights downwind of the crest. Within the cavity, the reversed mean flow
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was found to have a mean speed of about 20% of the free-stream velocity.
The flows over hills 8 and 5 did not separate, but the mean streamline patterns
were noticeably asymmetric in contrast with potential theory. The hori-
zontal mean wind velocity near the downwind base of hill 5 was very small:
about 10% of the velocity in the absence of the hill at a height of 0.2hQ;
but the longitudinal turbulence intensity was extremely large: twice the
mean velocity at 0.2h . 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 observed to be larger
over the steeper hills.
The dispersion characteristics were also, of course, changed by the
presence of the hills. The existence of a cavity region drastically influ-
enced the shapes of the vertical concentration profiles and the values of
the surface concentrations within the cavity. Concentrations within the
cavity region were essentially uniform with height. Surface concentrations
were sometimes greatly increased, sometimes 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 downwind distance, some surface concentration profiles
contained characteristic dips that identified the beginning and end of the
cavity region.
For hill 8, the deviations of the diffusion patterns from those over
flat terrain were much less significant. Changes in the concentration fields
were apparently not as much influenced by changes in turbulence structure
as by changes in the mean flow field, i.e., the convergence and divergence
of streamlines.
The terrain correction factors for the values and locations of maximum
surface concentration obtained from the wind-tunnel measurements were com-
pared with factors calculated using a quasi-potential model. Rather
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satisfactory agreement between theory and experiment was obtained: 80% of the
calculated values were within 25% of the measured 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 underpredicted the experimentally
observed 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
calculated and experimental values when the stack was located at the down-
wind base of the hills caused by the presence of the recirculation zone
and the zone of extremely low wind velocity. In these zones, streamwise
diffusion may not be neglected. 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 concen-
tration. 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 within 30%
of measurements) when the stack was located at the upwind base or top of
the hill, and satisfactory agreement (all within 40%) when it was at the
downwind base. Further refinement of the technique used for producing the
wind field and the application of more appropriate models for eddy diffusi-
vities should improve the agreement with experimental data.
Additional tests showed the flow structure (including separation) to be
insensitive to 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.
8
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3. THEORETICAL MODELS
3.1. Diffusion Calculations Over Flat Terrain in Wind Tunnel
Calculations were made of pollutant concentrations from an elevated
point source located over flat terrain. These concentrations were calcu-
lated with numerical solutions of the diffusion equation using a finite
difference method.
The diffusion equation in the case of flat terrain may be written in
the following form:
3x 3y y 3y 3z z 3z '
where u = wind velocity (it is supposed the wind blows along the x-axis) and
k . k = horizontal and vertical components of turbulent diffusivity, respec-
tively.
If k = k u (here k may be constant or a function of x), a separation
of variables may be performed. As a result, Equation 2 can be solved by
solving the diffusion equation for concentration c1 from a line source. In
these studies, the equation for c1 has been solved with a numerical method.
It has the following form
z-
The boundary conditions were as follows (assuming that source coordinates
are x = 0, y = 0, z = zs):
at x = 0, c1 = [Q/u(zs)]5(z - zs);
at z = 0, kz 3c'/3z = 0; ^'
and when z -> °°, c1 -» 0.
Here Q = source flow rate and <5 = Dirac delta function. The transformation
from c1 to c is determined along y = 0 by the expression:
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c(x,0,z) = c'(x,;
x
where G = k
(5)
It was also assumed that
u =
p*- ln(l + ~) when z < h
zo
ln(l + TT-) when z > h
zo
(6)
and
kz =
ku*(z + z ) when z <_ h
+ z ) when z > h
where u* = friction velocity, z = roughness length, h = surface layer
* * o
height, and k = von Karman's constant (0.4). Values of u*, z , and h were
determined in accordance with wind tunnel measurements. Different models
for k were used, as will be discussed in Section 5.
3.2. General Description of Models for Calculating Pollutant Dispersion
Over Hilly Terrain.
To calculate concentrations of pollutant from an elevated point source
located near a hill, two different models developed in the U.S.S.R. were used,
Both of them are based on gradient diffusion theory (also called K-theory)
and calculate pollutant concentrations by solving the diffusion equation
3x
sz " 9x
_
ay y 3y 3z z 3z
(7)
where, as usual, c = pollutant concentration, u, w = horizontal and verti-
cal wind velocity compoi
diffusivity components.
cal wind velocity components, respectively, and k , k , k = turbulent
x y z
10
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Quasi-Potential Model
The first model was described by Berlyand et al (1968) and further deve-
loped by Berlyand and Kisselev (1973) as well as by Berlyand et al (1979).
It was intended for application to atmospheric flows with neutral stratifi-
cation. It assumes there is no flow separation in the lee of the hill.
In the presence of a hill, the domain in which pollutant diffusion
occurs is curvilinear. This domain can be transformed to an upper semi-
plane using conformal mapping. For a hill having a shape determined by
Eq. 1, this mapping is analytical, a fact that greatly simplifies the method
of solution.
Let the function
T(X,Z) = (x,z) + i>(x,z) (8)
represent this conformal mapping. and <<> can be interpreted as the velocity
potential and stream function, respectively, of a potential flow in the
domain under consideration. Coordinates £ and ? are introduced as
C = 4>(x,z)/U , ? = 4<(x,z)/U , (9)
where U = wind speed in the approach flow far upstream.
Let us now substitute these coordinates into Equation 7 and use (c, c)
instead of rectangular coordinates (x, z). With the additional assumptions
that (1) the streamlines of our flow coincide with the streamlines of
potential flow in the same domain, (2) k = k = k , and (3) spreading of
x z <,
pollutant along streamlines caused by turbulent diffusion is negligible,
then Equation 7 may be reduced to the following form
u 1£= 1 -Ik i£ + _lk ^- rim
US 9C V^9y ky 3y + a? kc a? (10)
Here u = VE/VD> where v = wind velocity parallel to the streamlines and
V = dimensionless velocity (normalized by U) module of the potential flow.
Assuming further that k = k V v (a generalization of the assumption
made in the case of flat terrain, analogous to the procedure used in Equation
2), we can separate variables in Equation 10. As a result, we shall solve the
diffusion equation for concentration c' from a line source, which is much
11
-------
easier than solving Equation 10.
The relation between concentrations from point and line sources is given
by the following expression
c(e,y,?) = exp(-) , (11)
where 6 =
and £<- = the source coordinate.
The equation for c1 is as follows
5 3? a c 9 '
We shall use for u and k the same formulas as Eq. 6, with ? in place
of z; thus Equation 12 is mathematically identical to Equation 3. The
boundary conditions are also analogous to those in the case of flat terrain.
Assuming that source coordinates are c = £_, y = 0, 5 = ?<-, the conditions
are
at ? = cs , c1 = [Q/u(cs)] 5(c - cs);
at c = 0 , k 3c'/3? = 0; (13)
and when 5 -» °°> c1 -*- 0.
These notations have the same sense as in Equation 4.
The problem (Eq. 12) with boundary conditions (Eq. 13) is mathematically
equivalent to Equations 3 and 4 and may be solved using the same numerical
methods. In practice, surface concentrations are the most frequently used
pollutant dispersion characteristics; therefore, for the case of flat terrain,
Berlyand (1975) has constructed approximation formulas for surface concen-
trations based on numerical solutions of the diffusion equation. Because
of the mathematical identity between Eqs. 12 and 13 and Eqs. 3 and 4, these
approximation formulas are also appropriate for the model under consideration.
Using such formulas to calculate surface concentrations saves a great deal
of computer time compared to the amount required for numerical solutions.
12
-------
This model will be referred to henceforth as the "quasi-potential model" (QPM)
Wind-Measurement Diffusion Model
The second model used for calculations of pollutant concentrations in
hilly terrain was described by Berlyand et al (1975). It incorporates data
from wind tunnel measurements of wind velocities and turbulence character-
istics of the flow near a hill as input to calculate the entire flow field
as well as the concentration field from a source. This second model will
be referred to as the Wind-Measurement-Using Diffusion Model (WMDM).
Such a "mixed" model offers advantages in investigations of pollutant
spreading over complex terrain and helps to clarify the understanding of
its regularities. When sufficiently developed, this approach simplifies
wind tunnel modeling, since it excludes (1) concentration measurements
which demand special instrumentation as well as additional time and (2)
difficulties connected with these measurements (satisfying additional simi-
larity criteria, constructing a source with or without some specified plume
rise, influence of background concentrations, etc.). To apply this model
and to facilitate interpretation of results obtained on concentration fields,
a relatively large quantity of wind measurements are required. However, it
may be noted that wind measurements are usually conducted relatively quickly.
In the future, it may be possible to determine the optimal quantity of wind
measurements needed to obtain reliable results of concentration calculations.
This approach also offers good possibilities for testing different diffusion
models for hilly terrain when the mean wind field is known.
Setting aside the questions of similarity between atmospheric flow and
the corresponding flow in a wind tunnel, this model may be divided into
three parts:
1) Generating a mass-consistent wind field on the basis of wind tunnel
data;
2) Calculating the turbulent diffusivity on the basis of measurements and
theoretical assumptions;
3) Numerical solution of the diffusion equation.
Details of these parts are discussed in the following sections.
13
-------
3.2.1. Generation of a mass-consistent wind field
The generation of a mass-consistent wind field is the most important
part of the problem. In recent years the question of producing a mass-
consistent wind field using wind measurements has been studied by a few
American scientists (Dickerson, 1978; Sherman, 1978; Pepper and Baker, 1979).
Their technique, developed on the basis of the works of Sasaki (1958, 1970aa
1970b), is quite similar to the present model, but the area of application
is rather different. Their wind-field models are used to predict regional
or meso-scale pollutant transport. For input, they use available meteoro-
logical data in the regions being investigated.
Complementary mathematical/wind-tunnel modeling has good possibilities
for further development of mass-consistent wind-field models because the
experiments are well -controlled and the data are more accurate, allowing
better comparisons with calculations. This approach makes it easier to
determine the influence of the wind-field-producing technique on the final
results and to test virtual improvements of the techniques, for example, the
use of more sophisticated methods of interpolation and differentiation of
the measured wind field.
Calculation of the entire mass-consistent wind field is necessary to
solve the diffusion equation. Before making such an attempt, it is useful
to examine the equation again.
If only smooth obstacles are considered, the diffusion equation can be
used in the following form:
Assuming again that k = k u, we can again separate variables and reduce
the problem to solving for concentration c1 from a line source. This equation
is as follows
w
w
ax az az z sz '
The relation between concentrations from point and line sources is expressed
analogously as in Equation 5.
14
-------
The problem of calculating diffusion in hilly terrain is that the area
of diffusion in coordinates (x, z) is not rectanglular. To apply numerical
methods, it is easier to make a substitution of variables in Equation 15 in
order to transform the domain of its solution to a half-plane. If it is
known that the perturbation of air flow due to the influence of irregularities
in the underlying surface does not exceed level z = H, this transformation
can be performed using the following substitution of variables
x- - x- z' - H(z - h(x)) (16)
A A 9 L. ~ - 9 ^ 1U /
H - h(x)
transforming the area (- °° < x < °°) x (h(x) £ z £ H) to the strip
(- * < x' < ») x (0 £ z1 £ H). Within strip 0 £ z1 £ H, Equation 15 can be
rewritten as
u !£' + w ' - k ' (17]
3X1 3Z1 ~ 3Z1 Z 3Z1 ' U '
where
u = "u ^*' u,
and
T. _ H
"z H - h(x) V
Note that the quantities u and w are defined such that they satisfy the
continuity equation
lii + iHL = o , (19)
H V S 7 \ /
when the initial components of velocity u and w satisfy the equation
3U/3X + 3W/3Z = 0.
The problem of producing a mass-consistent wind field for the specific
case at hand can be formulated as follows. In the rectangle R = {0 £ x' £ L;
0 £ z' £ H}, the functions a(x', z1) and b(x',z') are fixed, calculated from
the measured velocity components of a flow by means of the first two rela-
tionships of Eq. 18. The quantities a(x', z1) and b(x', z1) have the sense
of horizontal and vertical velocity components converted to the coordinate
system of Eq. 16. It is necessary to construct the functions u(x', z1)
15
-------
and w(x', z1) to satisfy the continuity equation 19 such that they approxi-
mate a(x', z1) and b(x', z1).
The solution of this problem utilizes the fact that in a two-dimensional
flow, a stream function ^(x1, z1) may be constructed. Velocity components
are determined from this function using the equation
The measured velocities a and b should be approximated (according to Eq. 20)
with derivatives of the stream function in the best manner (in the mean-square
sense). Next there arises the variational problem of the minimization of
the functional
dx'dz1 [A - a)2 + p2 A + b)2]. (21)
| oZ dX
The non-negative "weight" p2 introduced here allows for the fact that the
velocity components a and b may be determined with different accuracies.
Note that the area of integration R should be selected such that at its
boundary 3R the function $ agrees with the stream function of the approach
flow 4i°(z'), corresponding to the velocity u° = -r|-r .
Using standard variational analysis techniques, the variational problem
can be transformed to the Euler equation for the desired stream function
3a
sz"1 " H~ 37'
o + = _ _ 2
P ^ ^ 1 P
In the simplest case (p = 1), this equation has an obvious physical inter-
pretation. The mass-consistent wind field approximation may be fulfilled by
preservation of the measured vorticity.
Let us introduce the symbols
* = *°(z) + V(x', z'); a = |£ + a'. (23)
The quantities of a1 and if/1 represent deviations from the corresponding
characteristics in the approach flow. Then Eq. 22 becomes (p = 1)
3V . aV _ a a1 3b_
9X1Z 8ZIZ 3Z1 3XP '
16
-------
with the boundary condition
*' 3R ' 0- <25>
Equations 24 and 25 can be numerically solved by a computer using finite
difference methods. Mathematically, these equations are equivalent to the
Dirichlet problem for the Poisson equation. Since area R is rectangular,
it is convenient to utilize a direct method, the fast Fourier transform (FFT)
technique (Ogura, 1969), for its solution.
3.2.2. Calculating the turbulent diffusivity
Calculating the turbulent diffusivity on the basis of measurements depends
of course on what measurements are made in the wind tunnel experiments. When
developing the model, the authors had data on mean velocity components and
turbulence intensities only; thus, it was necessary to use a method of
turbulent diffusivity calculation based on these data. In the model, the
following equation for diffusivity was used:
z
1/4.2..2 u* (25)
k., = kc£2U2
h(x)
This equation is a result of the differential equation for k suggested by
Berlyand and Genikhovich (1971). Here e is turbulence intensity (root-mean-
square of horizontal velocity normalized by local horizontal mean velocity),
k = von Karman's constant (0.4) and c = 0.046.
To calculate turbulent diffusivity in the atmosphere, the authors assume
that similar changes in diffusivity due to the influence of irregularities
in the underlying surface are seen both in the wind tunnel and in the atmos-
phere. In other words, the following model applies to the atmospheric
diffusivity:
k ,(x,z)
where k t and k t are the diffusivities in the atmosphere and wind tunnel,
respectively, and the superscript "o" represents the value in the approach
flow.
17
-------
3.2.3. Numerical solution of the diffusion equation
Some difficulties exist in the numerical solution of diffusion equation
17 because of the presence of the term W3c'/3z'. w may be either positive
of negative, even at fixed x1 in its dependence on z'. In this case, it is
difficult to find a finite difference scheme that is absolutely stable
over the entire domain of the solution. The problem may be resolved by
transforming Equation 17 (Samarskii, 1977) into the following:
1!?- T if «z !r (28>
which is equivalent to Equation 17. Here
z
f = exp (-
o
"dz1) . (29)
k
For the above equation, there are various finite difference schemes that
are absolutely stable over the entire domain. For example, the authors
use an explicit-implicit scheme except for a few steps on x1 near the source.
It is more complicated than implicit schemes, but unlike them, it preserves
the integral horizontal pollutant flux, which is desirable from a physical
point of view.
All numerical calculations of pollutant dispersion over hills and flat
terrain were conducted with computer programs developed in the Main Geophysical
Observatory (GGO), Leningrad, U.S.S.R. by L. H. Khurshudyan and I. G. Gracheva
and adjusted for use on EPA's Univac computer by L. H. Khurshudyan.
Results of these calculations are presented in Section 5.
18
-------
4. APPARATUS, INSTRUMENTATION AND MEASUREMENT TECHNIQUES
The detailed features of the EPA Meteorological Wind Tunnel, the
instrumentation and general procedures for velocity and concentration
measurements, and the minicomputer used for the acquisition and analysis
of wind tunnel data are described by Snyder (1979). Hence, only the main
features of the equipment and special instrumentation or different procedures
will be described here.
4.1. Hind Tunnel and Simulated Atmospheric Boundary Layer
The wind tunnel test section is 3.7 m wide, 2.1 m high and 18.3 m long.
The air speed in the test section may be varied from 0.5 to 10 m/s.
A simulated atmospheric boundary layer, nominally 1 m thick, was ob-
tained using a fence (vertical barrier) of height 15.3 cm that was placed
22.3 cm downwind of the entrance to the test section and gravel roughness
covering the tunnel floor downwind of the fence. The roughness was conven-
iently obtained commercially as a building construction material (trade name:
Sanspray), where river-washed gravel of approximately 10 mm and smaller dia-
meter was epoxy-cemented onto 10 mm thick plywood. Previous tests showed
that an equilibrium boundary layer (i.e., very slowly developing) that is
a reasonable approximation of a neutral atmospheric boundary layer was
established at a distance of 7 to 8 m from the fence (Arya and Shipman, 1979;
Courtney, 1979). Additional measurements of the boundary layer structure
and dispersion characteristics were made during the current study and are
presented in section 5.
4.2. Velocity Measurements
Measurements of the boundary layer and flow structure over the hills
were made with TSI, Inc. model 1054A anemometers in conjunction with model
1241-T1.5 (end-flow style) and 1243-T1.5 (boundary layer style) cross-hot-
19
-------
wire probes. The output signals from the anemometers were digitized at
the rate of 500 hertz and linearized and processed on the POP 11/40 mini-
computer. Sampling (averaging) times of two minutes were found to yield
reasonably repeatable resultsgenerally within ±5% on the measurement of
turbulence intensity.
All measurements made previous to the current study had been done using
hot-film probes (thin metallic-oxide coating on quartz fiber of 0.5 mm dia-
meter). The sensitivity of the film probes to transverse velocity fluctua-
tions (hence, also Reynolds stresses), however, had been found by Lawson
and Britter (1981) to depend upon the mean wind speed, decreasing rather
strongly in the range below about 3 m/s. Lawson and Britter derived "yaw-
response" correction factors as functions of mean wind speed and probe type
on the basis of specially designed experiments to compensate for this de-
creased sensitivity. However, their experiments did not specifically examine
the response of the probe when it was not aligned with the mean wind direction.
Because the normal situation when measuring flow over hills is that the probe
is not aligned with the mean wind (it is normally aligned parallel to the flat
wind tunnel floor), additional tests were desirable. Such additional tests
were made and the results are covered in this discussion.
A special mechanism was constructed and attached to the wind-tunnel
carriage. This mechanism permitted rotation of the probe through a known
angle in the vertical plane (x-z), while maintaining the probe tip (the
sensor itself) at a fixed position.
A simple analysis shows that the mean velocities indicated by the probe
should be
U = U cos<|> + W sin + W cos*, (30)
1 WD
and cf> = tan" -^ = - + 2uw sin<£ cos,
wT = IF sin24> + w7" cos24> - 2uw sin4> coscj>, (31)
and uw_= uw (cos24> - sin24>) - (U2" - w2) sin
20
-------
where capital letters and overbars indicate mean values, lower case letters
indicate deviations from the mean, U (or u) is the velocity component in
the horizontal plane, W (or w) is the component in the vertical plane, and
the subscript "p" denotes the value indicated by the probe when it is ro-
tated from the horizontal through the angle .
The Reynolds stresses indicated by each of the probes are shown as
functions of the probe rotation angle in Figure 1. Also shown for comparison
on the figure is the last of Equations 31. Results from the hot-wire compare
quite favorably with the corrected results (Lawson and Britter, 1981) from
the hot-film at zero angle. The hot-wire results, however, are consistently
closer to Equation 31 at non-zero angles.
Figure 2 shows that the angles indicated by the two probes are essentially
identical, but that both underestimate the true angle by 13%. Separate tests
showed that the indicated angle was independent of wind speed in the range
from 2 to 8 m/s. Consequently, to a first approximation, the actual flow
angle may be estimated by multiplying the indicated angle by 1.15.
Measurements of other parameters, mean velocity and horizontal and vertical
fluctuating velocities, showed the hot-wire response to be slightly better
than the corrected hot-film response at non-zero angles (Figures 3 to 5), so
that the hot-wire probes were used exclusively for velocity measurements
over the hills. End-flow probes were used wherever possible, but they could
not be placed close to the hill surfaces upwind of the crests because of
their physical configuration. Hence, boundary-layer style hot-wire probes
were used in those regions.
Comparisons of measurements of mean velocity, longitudinal and vertical
fluctuating velocities, and Reynolds stresses are made in Figures 6 through
9, respectively. Vertical profiles measured with both types of hot-wire
probes at a distance of 3a (a is half-length of hill) upwind of the center
of the hill with slope n = 8 are compared with profiles measured with hot-
wire and hot-film probes at a corresponding position but in the absence of
any hill. The hot-film measurements were taken from Courtney (1979), where
the freestream wind speed was 8 m/s. Courtney's measurements were scaled
to match the freestream speed of 4 m/s in the current study. In general,
21
-------
0.075-
0.050-'-
0.025-i-
E
01
cc
CO
REYNOLDS
!
o4
!
t
f
t
-0.025^
!
0.050
POSITION OF PROBE
x = 8m (FROM FENCE)
y * Om
z = 190mm
MEAN VELOCITY = 3.3 m/s
A HOT-FILM
D HOT-WIRE
Q. 31 APPLIED TO HOT-WIRE DATA
EQ.31 APPLIED TO
CORRECTED HOT-FILM DATA
T
-0.075-
-0.10CH
-30
-20
20
-10 0 10
PROBE ANGLE, degrees
Figure 1. Reynolds stresses indicated by yawed end-flow probes.
30
22
-------
25-
L
204
r
j-
15-
\
X
\
\
\
\
\
A HOT- FILM
D HOT-WIRE
O)
a
o
Uj"
<
a
LU
a
z
5"
o-.
.5-f
0.87
1.00
-10-
16t
r
-204
-25-
\
5
\
\
\
\
\ -
V
-30
-20
20
10 . 0 10
PROBE ANGLE, degrees
Figure 2. Flow angles indicated by yawed end-flow probes.
30
23
-------
3.5-
trt
~i
H-
O
0
LU
z
LU
5
a
LU
O
a
Z
3.0J ^
i-X^
IT
j-
t
L
1
i
2.5J
I
!
c
2.0-i-
1
1"
j-
r
i_
i
1.5-r
\
\
|-
i
u
1
i
i4
L
S
f
0.54
i_
r
i
i_
-30
^^^ ^* COSINE RESPONSE ^x.
^4^
^
t
}
i
i
j
!
T
;
1
i
~:
i
-
_.
"*
_
;
-.
-'_
A HOT- FILM
D HOT-WIRE
20 -10 0 10 20 30
PROBE ANGLE, degrees
Figure 3. Mean velocities indicated by yawed end-flow probes.
24
-------
0.2-
0.1 T
30
A HOT- FILM
H HOT-WIRE
-20
20
30
-10 0 10
PROBE ANGLE, degrees
Figure 4. Longitudinal fluctuating velocities indicated by yawed end-flow probes.
25
-------
0.24
0.11
i
30
A HOT- FILM
D HOT-WIRE
-20
20
-10 0 10
PROBE ANGLE, degrees
Figure 5. Vertical fluctuating velocities indicated by yawed end-flow probes.
30
26
-------
1000
-
A
n
o
0
PROBE
BL
EF
EF
EF
SENSOR
WIRE
WIRE
WIRE
FILM
U^, HILL
4 PRESENT
4 PRESENT
4 ABSENT
8 ABSENT
6$
' ' - J
&''"' J
1
i
£i- "!
_ i
100-^
E
S
N'
10-
1
1 "
c
,_,-,.
^ "
Iffi
: :
OB
0.5 1.0 1.5 2.0 2.5 3.0 35 4.1
U,m/s
Figure 6. Comparison of mean velocities measured with different probe types.
27
-------
1000
L
900 --
800-
700
600 --
HSEr
PROBE
A BL
D EF
O EF
0 EF
SENSOR JJ,
WIRE 4
WIRE 4
WIRE 4
FILM 8
HILL _j
PRESENT 1
i
PRESENT 1
~*t
ABSENT i
ABSENT I
E
E
500 --
r
r
».
400 1
|-
300 -f
h
L
(
200 -f
-i-
100
-
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55
u , m/s
Figure 7. Comparison of longitudinal fluctuating velocities measured
with different probe types.
28
-------
1000-
900--
800-
r
700-j-
r
600 --
500--
i
400
300 i
0 0.05 0.10 0.15 0.20 0.25
V w2 , m/s
0.30
Figure 8. Comparison of vertical fluctuating velocities measured with
different probe types.
J
1
-j
L PROBE SENSOR
\- A BL WIRE
200-j- 3 Ep WIRE
; O EF WIRE
^ EF FILM
100+
0-
.
LU
4
4
4
8
HILL
PRESENT -:- ~
PRESENT r _ -
ABSENT
ABSENT >r ^ ,_
'-' . *- _
:'~l . _1 v
J-ifc_ ___'
_.
:'.
j
j
-
-
__
-
0.35
29
-------
[
900-!-.;;
800 4 -C
f r*
f
7004
r
600-
f
i
i.
i
N- 5°°t
L
i
. . .
PROBE SENSOR U^ HILL
A BL WIRE 4 PRESENT
D EF WIRE 4 PRESENT
O EF WIRE 4 ABSENT I
O EF FILM 8 ABSENT
'
i~'
400 --
300 -
200-
100--
0-*
D ..^
0 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 0.045
- uw ,
Figure 9. Comparison of Reynolds stresses measured with different
probe types.
30
-------
the comparisons in Figures 6 through 9 show good agreement between measure-
ments made with various styles and sensor types. Second, they show that the
boundary layer structure was Reynolds-number independent, i.e., the flow
structure was independent of the free-stream velocity, at least in the range
of 4 to 8 m/s. Third, the influence of the hill was seen in the Reynolds
stresses and vertical fluctuating velocities, less in the longitudinal fluc-
tuating velocities, but not-at-all in the mean velocities. Fourth, the hot-
wire and corrected hot-film measurements compared quite well for end-flow
probes, but some discrepancy was seen between the boundary-layer and end-
flow hot-wire measurements of vertical fluctuating velocities and Reynolds
stresses. This discrepancy may have been caused by improper alignmentdue
to poor construction of the boundary-layer style probe during calibration
and subsequently during measurements, but the comparison was adequate for
the purposes of the present study.
The hot-wire probes were calibrated each day of measurements and fre-
quently more often, against a pitot-static tube mounted in the freestream
of the wind tunnel above the boundary layer. The calibrations were made
over the velocity range of interest, typically 5 to 7 points over the range
1 to 5 m/s, and "best-fit" to King's law
E2 = A + Btla , (32)
where E = output voltage of anemometer and U = wind speed indicated by Pi tot
tube. A, B, and a are constants that were determined through an iterative
least-squares procedure. A typical calibration curve is shown in Figure 10.
Corrections for varying ambient temperatures were made according to the
method of Bruun (1975).
4.3. The Models
Four model hills were constructed; all had shapes given by Equation 1,
and extended across the width of the test section of the wind tunnel. Three
had heights of 117 mm and aspect ratios (n = a/hQ) of 3, 5 and 8 (maximum
slopes of 26°, 16° and 10°, respectively). The fourth had a height of 234 mm
and an aspect ratio of 3. They will be referred to henceforth as hill 3,
hill 5, hill 8, and big hill 3. Figure 11 shows the hill shapes to scale
31
-------
I I I I I I I I I I I ! I I I t I j I I I
PROBE H359-2
SLOPE - 1.468
INT. « 2.784
ALPHA = 0.450
CALIB. TEMP. = 23.9°C
WIRE TEMP. = 200°C
o CALIBRATION POINTS
ZERO FLOW VOLTAGE
i i I i i i i i I I I I i i i i
iiii
2.0
Figure 10. Typical calibration curve for hot-wire anemometer.
32
-------
2 »
i l\
«- Z -f \ *
o
p
^
3
O
LU
LU
I
CO
-1
0
0.
D
Q
LU
ec ,
.E MEASU
DTUNNEI
= Z -
HI
O
CO
o
U5
0)
a
o
£
<4_
O
-------
and compares the ideal shape of hill 3 with that measured after it was installed
in the wind tunnel. The actual shape differed from the ideal shape by less than
±3 mm. All the models were covered with gravel to match the roughness of the
wind tunnel floor (described in section 4.1). The difference between the
ideal and actual shapes shown in Figure 11 is primarily due to the uncertainty
of measuring to the tops of the gravel stones.
The centerlines of all hills were placed 8.7 m downwind of the fence
at the entrance of the test section.
4-4- Pollutant Source
In accordance with the purposes of the present investigation, the tracer
was to be neutrally buoyant and released from a point source. The tracer
chosen, ethylene (C2H»), was emitted from a "stack" that was adjustable in
height. It contained a 90° bend and a porous stone sphere as shown in
Figure 12. Since ethylene is only slightly less dense than air (mol. wt. =
28; s.g. = 0.974 at 15°C) and since it was emitted at relatively small flow
rates into a 2 m/s (or greater) air stream, it may be safely considered as
neutrally buoyant.
In previous studies, a 6 mm dia., bent-over tube released ethylene iso-
kinetically into the air stream. In the current study, because the wind was
not always horizontal (as on the windward sides of the hills) and possibly in
the reverse direction (as in the separated regions on the lee sides of the
hills), a different source configuration was used. The ethylene was emitted
through a porous sphere placed at the end of the bent-over tube (Figure 12).
The sphere had a diameter of 15 mm; it was machined to shape from a commer-
cially available porous stone (home aquarium aerator). Because the source
flow rates were proportioned to the local wind speeds in the absence of the
hills (they were equal to the isokinetic release rates as in the previous
studies in order to maintain downwind concentrations within the range of
the measurement devices), the surface emission velocities were reduced by a
factor of 25 and hence were approximately 4% of the crosswind speed. To de-
termine whether the source emission velocity had an influence on the down-
wind concentration field, a special test was run by increasing the source
flow rate Q by 50%. The results, shown in Figure 13, show that the source
34
-------
MANOMETER I"
A
T ~l /MANOMETER
PRESSURE
REGULATOR
jErO
C2H4
IP
=e
^pb
f-
H42.4-*]
M^Lx POROUS
)-STONE
SPHERE
76.7mm \ ' DIA. = 15mm
LAMINAR
FLOW
ELEMENT
Figure 12. Diagram of source and flow measurement apparatus.
35
-------
E
£
350-
300-
250-
200-1-
r
150-1-
1004
50 T
0.0001
D
Q, cm^/min x, mm
3642
5390
5390
585
702
vX
a
-
L !
0.001
0.01
0.1
10
X " CHU2/Q
Figure 13. Comparison of concentration profiles measured
under different source flow rates.
36
-------
emission velocity had no influence when the concentration was normalized
as x = CUH2/Q.
Vertical concentration profiles measured downwind of the two types of
sources over the flat wind tunnel floor are compared in Figure 14. It may
be observed that the profiles close to the sources differ in a predictable
manner because of the different source diameters, but farther downwind, such
differences disappear.
Stacks were located at one of three positions such that the center of
the porous sphere was above the upwind base (leading edge, x = (1)), the
top (center, x = (2)) or the downwind base (trailing edge, xg = (3)) of
the hills.
4.5. Calibration of Source
The tracer was high-purity ethylene (CP grade; minimum purity of 99.5
mole percent). The ethylene flow rate 0 was measured and continuously moni-
tored using a Meriam laminar flow element (model 50MJ10-1/2) and a Meriam
micromanometer (model 23FB2TM-20, null type) as shown in Figure 12.
The laminar flow element (LFE) consists of a bundle of very small dia-
meter tubes housed within a stainless steel block containing pressure ports
at the entrance and exit of the tube bundle. Under normal operating condi-
tions, because of the small tube diameters, the flow through each tube is
laminar and the pressure drop through the tubes is proportional to velocity.
If the density is maintained sensibly constant, then, the volumetric flow
rate through the LFE is proportional to the pressure differential, which is
easily measured quite accurately with a micromanometer (AP'S are typically
in the range of 1 to 20 cm of water). However, because the temperature and
absolute pressure of the gas may vary from one situation to the next, and
because viscosities vary from one gas to the next, the LFE should be calibrated
for each set of operating conditions. This system was calibrated using a
bubble meter and stop watch or a volumetric flow calibrator (Brooks model
1050A 1J1) which has a rated accuracy of 1/2%. A typical calibration curve
for this system is shown in Figure 15.
37
-------
350-
300-
A SOURCE
A ^ BALL
A
A c BALL
* o TUBE
0 A o BALL
Q*
Q A A TUBE
n A
x, mm
330
330
330
847
847
!
1
i
!
i
]
-j
i
j
250-^
E
£ 200--
I-
100-
50-
-
C:
*
Gfc
>
3-
,3.
0.001
0.01
0.1
10
X CUH2/Q
T
100
Figure 14. Comparison of vertical concentration profiles measured downwind
of isokinetic release tube and porous sphere.
38
-------
7000 -f
c
£
"§
6000--
5000
234
Ap, INCHES OF WATER
Figure 15. Typical calibration curve for laminarflow element.
39
-------
Some difficulties were experienced with a shifting of the calibration
of the flow rate through the porous stack, primarily during measurements
for hill 3. Figure 16 shows, for example, the history of stack "P4".
According to these data, the flow rate varied by 30% from one set of experi-
ments to the next at the same pressure differential Ap across the LFE.
Special experiments were conducted to determine the cause of this discre-
pancy. The resistance at the outlet, hence, the back pressure p, (relative
to atmospheric) within the LFE was varied to determine its influence. These
data (Figures 17 and 18) show that, whereas p. was varied over a very wide
range, the flow rate was predictable to within a few percent by Ap alone and
correctable to within .05%, even at moderately large p,. These experiments
suggested that the discrepancy (Figure 16) was caused by a leak somewhere
in the tubing from the LFE to the stack, even though previous searches for
leakage were unsuccessful. Thereafter, both Ap and p, were simultaneously
monitored and no further difficulties were experienced.
Unfortunately, this discrepancy was discovered toward the end of the
experimental period, and thus cast some doubt on the absolute accuracy of
the concentration data (as they are only meaningful when normalized by the
source strength Q). For example, Figure 19 shows two concentration profiles
measured at the same position under the "same" conditions, but it is apparent
that the source strength differed between the two runs. Suspect data were
identified through a comparison of points from different profiles and by
checking the mass continuity relationship:
Q =
CUdydz. (33)
Note that the profile shapes (including the standard deviations, locations
of maximums, etc.) were not suspect (as verified in Figure 19)--only the
magnitudes of the concentrationsand only in a relatively few files. All
suspect data have been identified, additional measurements were made, and
faulty data have been replaced.
40
-------
4.0'
3.5-
3.0 4
2.5 T
flC
LU
I
1
0.5
1000
2000
4000
3000
Q, cc/min
Figure 16. History of calibration of stack "P4".
5000
41
-------
7000
6000-
5000-r
4000
i
e
'i
"E
3000--
2000-
1000--
Q = CAp (1_+_pb/p0)
WHERE C = 1269 cm3/min/in. water
2 3
Ap, INCHES OF WATER
Figure 17. Results of experiments to determine influence of back pressure
on laminarflow element: flow rate versus pressure differential.
42
-------
LL
O
V)
UJ
CJ
Z
1234
Ap, INCHES OF WATER
Figure 18. Results of experiments to determine influence of back pressure
on laminar flow element: back pressure versus pressure differential.
43
-------
0
o
II
X
10
0.1
D
0.01
0.001
A SURFACE PROFILE
D POINTS FROM VERTICAL PROFILES
Hs = 117mm
Xs = (1)
100
1000
x, mm
10000
Figure 19. Comparison of concentration profiles measured under same apparent
conditions indicating difficulties with source-calibration.
44
-------
4.6. Concentration Measurements
Concentration profiles were obtained by collecting samples through 1.6 mm
OD tubes that were fastened to the instrument carriage. These samples were
drawn through Beckman model 400 hydrocarbon analyzers (flame ionization de-
tectors, FIDs) operating in the continuous sampling mode for analysis. As
many as 4 FIDs were used simultaneously in conjunction with sampling rakes
which contained sampling tubes of fixed spacing.
The FIDs were initially calibrated and checked for linear response using
certified gases of (nominally) 1, 0.5, 0.05, and 0.005% ethylene in hydro-
carbon-free air from Scott Environmental Technology, Inc. A typical cali-
bration curve is shown in Figure 20.
The "span" (full scale) and "zero" settings were adjusted before beginning
measurements and checked after finishing measurements each day. Background
(room) hydrocarbon level measurements were made at the beginning and end of
each profile and frequently more often. The computer program HCA subtracted
a background level from each sample measurement by assuming a linear change
in background with time between sequential background measurements. Typical
background levels were 5 ppm at the beginning and 30 ppm at the end of the
day.
The output signals from the FIDs were digitized at the rate of 1 hz (each
unit) and processed on the POP 11/40 minicomputer. The HCA computer program
controlled the sampling, processed the data (scaling, averaging, etc.), and
stored the data from each of the four instruments in separate files.
A typical concentration profile is shown in Figure 21. It was evident from
examination of figures such as this whether or not a particular FID was mal-
functioning; for example, it is probable that FID number 4 (Figure 21) was
indicating low concentration near the ground, as those points are not in line
with the others. Lateral and vertical profiles were obtained from four FIDs
operating simultaneously, but, because of possible probe interference, only
one analyzer was used for measuring surface (streamwise along the ground)
profiles.
The "corrected" concentrations (i.e., with background subtracted) were
normalized by
45
-------
1)
a
O
z
111
O
O
u
O
a
ai
0.001 -
0.001 0.01 0.1
CERTIFIED GAS CONCENTRATION,percent
Figure 20. Typical calibration of flame ionization detector with ethylene.
46
-------
400
3504
300-
250-
L
s r
£ 200 T
150-
n
\
u
-i
i
T
-i
j
100
50 4
FID NUMBER
1
2
3
4
0.0001
0.001
1
0.01 0.1
X =" CUH2/Q
Figure 21. Typical concentration profile measured with four FIDs.
10
47
-------
x = CUJ^/Q , (34)
where x is the normalized concentration (used in all graphs), C is the corrected
concentration (in parts per million by volume), Uoo is the free stream velocity
(normally 4 m/s), H is a convenient length scale (H = 234 mm was used through-
out this study, since it is the height of the large hill), and Q is the ethy-
lene flow rate.
Two minute sampling (averaging) times were found to yield reasonably
repeatable values of concentrationgenerally within ±5% on mean concentrations.
For each stack height, each stack position, and each hill (also in the
absence of the hills), vertical, lateral (cross-wind) and surface (streamwise
approximately 5 mm above the top of the gravel) profiles of concentration
were measured. Four primary stack heights were used: 29, 59, 117, and 176 mm;
more limited measurements were made at other stack heights. As mentioned
previously, stacks were placed at the upstream base, top and downwind base
of the hills.
4.7. FID Response Characteristics
A few experiments were conducted to determine the response characteris-
tics of the FIDs. The responses of the FIDs to step changes in concentration
and to square waves are shown in Figures 22 and 23, respectively. To a first
approximation, the response of the analyzer may be described as a delay-line
in series with a first order filter (see Mage and Noghrey, 1972) with a time
constant T ^ 1.2s. The delay time depends upon external parameters such as
the length of the connecting tubes (about 10 m in these experiments), their
diameter, the sample flow rate, and the internal volume of the sampling pump,
as well as internal parameters, i.e., individual properties of each FID.
From Figure 22, for example, even though the external parameters were ostensibly
the same, the delay time was 9s for one FID and 13s for the other.
The root-mean-square error a in the measurement of a mean concentration
m may be estimated as
c / ~r \
(35)
48
-------
-1.000
10
15 20
TIME, seconds
Figure 22. Response of FID'sto step change in concentration.
49
-------
INPUT
(SQUARE WAVE)
-0.875 -
-1.000
70
75
90
80 85
TIME, seconds
Figure 23. Response of FID's to square wave input.
95
50
-------
where a is the standard deviation of concentration fluctuations at the out-
put of the FID, T is the integral time scale (correlation time) of the con-
L*
centration fluctuations (also at the output of the FID), and T is the sampling
period (120s). Neither T nor a were evaluated directly, but it is evident
that T > 2t . Subjective judgements made from observing the signals on the
C 0
oscilloscope indicated that T ^ 4 sec and 0.2 < a/m < 1. (The ratio a/m
L«
depends strongly upon the measurement point relative to the plume axis; typical
values are given here). Hence, the errors a/m indicated by Equation 35 range
from 4 to 20% for an individual point. This range agrees quite well with
the experimental observations.
4.8. Adjustment of Height of Wind Tunnel Ceiling
As discussed by Snyder (1981), it was necessary to locally raise the
ceiling of the wind tunnel above the hills in order to minimize "blockage"
effects which would, of course, be absent in the atmosphere. The ceiling
height was adjusted by a trial and error procedure until the freestream
velocity (1.6 m above the wind tunnel floor) was constant, i.e., independent
of longitudinal position. This procedure ensures that the longitudinal
pressure gradient will be zero, which appears to be the most natural criterion
to apply in simulating full-scale conditions. Typical maximum adjustments
were half the hill heights.
51
-------
5. PRESENTATION AND DISCUSSION OF RESULTS AND COMPARISON WITH THEORY
5.1. Flat Terrain
5.1.1 The boundary layer structure
Additional measurements of the boundary layer structure made in the
current study confirmed the results of previous studies. As seen in Figure 24,
the mean velocity profile is essentially independent of downwind distance in
the range of 7 to 15 m downwind of the fence (-2 to 6.5 m from the hill centers),
It may be approximated very closely by
U/u* = (l/k)ln((z - d)/zQ)
V V
to a height of 600 mm, where k is the von Karman constant (0.4), u* is the
friction velocity, d is the displacement height and z is the roughness length.
The mean velocity profile may thus be characterized by u* = 0.185 m/s,
d = -0.5 mm and z = 0.157 mm. The displacement height is negative (but is
indeed very small) because z was measured from the tops of the gravel stones.
The roughness length is quite close to the 0.13 mm measurement by Courtney
(1979) under the same physical arrangement, but at a freestream wind speed
of 8 m/s. The overall boundary layer depth 5 is approximately 1 m.
The Reynolds stress profiles, plotted in Figure 25, show considerable
scatter near the surface, but there is a slight tendency for the surface
shear stress to decrease with downwind distance. The turbulence structure
thus reached equilibrium more slowly than did the mean flow.
Strictly speaking, a "constant stress" layer did not exist, as the verti-
cal distribution may be conveniently approximated as a linear decrease with
height from its surface value to zero at z = 5:
uw(z) = 4(1 - z/5).
52
-------
1000-
100-
E
E
10-t-
1 +
D5
x, mm FROM FENCE
A 6828
O 8700
D 15252
1
0.1-
0 0.1 0.2 0.3 0,4 0.5 0.6 0.7 0.8 0.9 -1.0 1.1
Figure 24. Typical mean velocity profiles in flat terrain.
52
-------
1000
900-
800- Q 4
700 +
600
£ 500--
400--
300-
r
200-I-
100
0.2
0.4
0£
0.8
1.0
1.2
Figure 25. Typical Reynolds stress profiles in flat terrain.
54
-------
This is similar to high-Reynolds-number wind-tunnel boundary layers, e.g.,
Zoric and Sandborn (1972). (A plot of their data is also shown as Figure 15
in Snyder, 1981). For practical purposes, however, the lowest 200 mm of the
boundary layer may also be considered as a "constant stress" layer.
Longitudinal, lateral and vertical turbulence intensity profiles are
shown in Figures 26 and 27. They also indicate a decay of energy with down-
wind distance, especially the vertical component, but the rate of decay ob-
viously decreased. Note that the u* used for normalization of these inten-
sities was obtained from the slope of the mean velocity profile (Figure 24)
and that near the surface, a /u* ^ 2.5, a /u* ^ 1.2, and a /u* ^ 1.8, in
good agreement with other investigations of simulated and atmospheric boundary
layers (Hunt and Fernholz, 1975; Counihan, 1975). Similarly, u^/U^ = 0.047
is quite reasonable.
A brief discussion is in order concerning the scaling relationship
between this wind tunnel boundary layer and the atmospheric boundary layer.
In accordance with Counihan (1975), the average depth of the neutral atmos-
pheric boundary layer is 6 = 600 m. Proceeding from this figure, on the
basis of geometric similarity ((Z0/s)m ~ (z /
-------
1000-
900^-
I
800 i
700 T
600
J.
£ 500-
400-f
300-
n £j
i
2007
100
D C' ^
0.5
1.0
1S
2.0
25
3.0
Figure 26. Typical longitudinal turbulence intensity profiles in flat terrain.
56
-------
1000-
900-
800 J-
700 T
600 i
r
500 +
400--
300--
r
200-
100-
x, mm
6828
c aw 8700
a aw 15252
0 av 15252
H
D
J
0.5
1.0
1.5
2.0
Figure 27. Typical vertical and lateral turbulence intensity profiles in flat terrain.
57
-------
direct application of geometric similarity appears to be the best method under
the circumstances.
It is concluded that even though this boundary layer is slowly developing,
it provides a reasonable simulation of the neutral atmospheric boundary layer.
5.1.2. Dispersion characteristics of the boundary layer
Surface concentration profiles measured for source heights of 29, 59, 117,
176, 234, and 351 mm are shown in Figure 28. These source heights correspond
to h /4, h /2, hQ, 3h0/2, 2hQ and 3hQ, where hQ is the small hill height.
As expected, the maximum surface concentration xm decreased and the distance
II I A
to the point of maximum concentration x increased as the stack height h
lll/\ i>
increased. All profiles converged asymptotically far downwind where the sur-
-15
face concentration decreased with the -3/2 power of x, i.e., x^x . Such
behavior is also predicted by the theory of Berlyand (1975) if it is assumed
that the lateral diffusivity k is independent of x or, equivalently, that
j 05
the lateral plume width grows as the 1/2 power of x, i.e., a <*x ' .
Similarity in the shapes of these profiles is shown in Figure 29, where
normalized concentrations C/C are plotted as functions of distance from the
MIA
source normalized by distance to the point of maximum concentration x/x .
I [|/\
Also plotted for comparison is the analytical solution of the diffusion
equation 2. This solution was obtained by Beryland (1975) using the assump-
tions that U = U, (z/z,)53, k = k, (z/z,) and k = k u (k = constant, p = 0.15
to 0.2 and t = 1 for neutral flows, z, = a reference height and U, and k, are
mean velocity and diffusivity at the height z,). The solution provides a uni-
versal (independent of source height) expression for C/C as a function of
inX
x/x along the plume center! ine y = 0:
I! lA
The experimental data collapse quite well onto the analytical expression,
especially beyond the point of maximum concentration.
Lateral concentration profiles measured at various downwind distances
(through the point of maximum concentration in the corresponding vertical
58
-------
100
10--
o
ii
X
1-t
0.14
0.01
Hs = 29mm
10
100
1000
10000
x, mm
Figure 28. Surface concentrations from sources of various heights in flat terrain.
59
-------
X
£
0.001
ANALYTICAL EXPRESSION
0.01-f &
10
100
x/x.
mx
Figure 29. Similarity of surface concentration profiles in flat terrain.
60
-------
profile) are shown in Figures 30 and 31 for source heights of 29 and 117 mm,
respectively. All shapes are very close to Gaussian. Figure 32 shows
numerous lateral profiles measured at different elevations through the plume
from the source of height 117 mm. It is evident that the maximum concen-
tration was at ground level and that close to the ground the plume width a
grew with height. Figure 33 shows that the plume width reached a maximum
at a height of about 300 mm (^ 0.35) excepting the anomalous point at the
ground from the elevated plume. Because of surface reflection, this profile
shape was exceptionally flat. This behavior appears to be practically inde-
pendent of stack height or downwind position, but firm conclusions would
require more extensive measurements. This finding is contrary to Gaussian
diffusion theory, wherein a is independent of the elevation at which it is
measured. For practical purposes, however, these differences are probably
not significant.
Figures 34 and 35 show cross-sectional, isoconcentration plots from a
low-level source and an elevated source, respectively. The irregularities
such as in the lower left and upper right of the plume in Figure 34 are the
result of scatter in the data, as no smoothing was applied.
Lateral plume widths for all plumes (and all elevations) are plotted
as functions of downwind distance in Figure 36. There is no apparent varia-
tion of a with stack height. For small x, cr <*x, whereas for large x,
1/2 y "
a «x , as predicted by Taylor statistical theory. The solid curve represents
an interpolation formula assuming a Lagrangian integral scale of 400 mm.
The formula agrees well with the data except for small x. The agreement could
be made considerably better at small distances by assuming a virtual origin
located approximately 35 mm upwind of the source, because the source was not,
in fact, a point source, but rather a sphere of 15 mm diameter.
The evolution of the vertical concentration profiles is shown in Figure 37.
The profile shapes are neither Gaussian nor reflected Gaussian in form, as is
made more apparent in Figure 38. These latter curves are "best-fit" Gaussian,
having the same standard deviations as the data set and assuming perfect re-
flection from the ground surface. Even relatively close to the source, before
reflection from the ground becomes important, the profiles are asymmetric and
61
-------
0.1--
0.0014-
0.0001
-5 4-3-2-1 01
2345
Figure 30. Similarity of lateral concentration profiles in flat terrain; Hs = 29mm.
62
-------
0.1-1-
jE 0.01 --
0.001--
351 117
936 100
1872 60
7488 10
Onnm
^ "1
i
LJ LJ _
;
}
5-4-3-2-1 01 23 45
Figure 31. Similarity of lateral concentration profiles in flat terrain; Hs - 117mm.
63
-------
o
-------
s
400-
350-
,1
300-
250-
200-
r
150-t-
100-»-
A '~'-C'~~ ^
\ '_r~i-r~:-[Z-iZ " ~u~
' U ~ A
O
a
Hj, mm
, __ r
117
29
117
x, mm J
«^__^ 3
7488 1
7488
585
100
200
300
400
z, mm
500
600 . 700
800
Figure 33. Lateral plume widths as functions of height above ground in flat terrain.
65
-------
£
£
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CN
Si
CJ
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u
c
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S
in
n
0)
U1LU
67
-------
1000
100--
10
100
1000
10000
x, mm
Figure 36. Growth of lateral plume width in flat terrain.
68
-------
E
1000-
900-
U
800 -JA
700 --
600-
500-
f '
400--
300--
200-
100--
s
a
A
A
IS
x, mm
330
585
936
2000
3744
7488
a-
0.001
0.01
0.1
X = CltxH2/Q
10
Figure 37. Development of vertical concentration profiles from source of height
Hs = 117mm in flat terrain.
69
-------
900 f
£
£
f.
800
700«
600
500-
400-
x, mm
330
936
3744
300 -
200 T
100-f
0.001
0.01
1
j
s
10
0.1
X = CU00H2/Q
Figure 38. Reflected Gaussian fits to vertical concentration profiles; Hs = 117mm.
70
-------
flatter than Gaussianthey decrease much more slowly in the tails than
Gaussian curves of the same standard deviation.
It is interesting to note that at the downwind distance where the maxi-
mum surface concentration occurred (about 1900 mm for stack height 117 mm),
the maximum concentration in the vertical prifile was elevated at a height
of about 0.6h , and its magnitude was about 25% larger than the surface value.
Numerical calculations using the model described in Section 3.1 as well as
Pasquill-Gifford curves (Turner, 1970) have predicted comparable results.
Slightly farther downwind, the maximum in the vertical was at the surface.
Figure 39 shows the growth of the standard deviation a of the vertical
concentration distributions. These a 's are the true standard deviations
about the centroids as opposed to those derived from "best-fit" reflected-
Gaussian curves, because of the poor agreement between the latter and the
data. However, in order to make meaningful comparisons between c^'s, it is
necessary to have some similarity in the shapes of the distributions. Since
the shapes of the distributions varied with downwind distance as well as with
stack height, this graph is presented with trepidation. Further work is
required to find similarity functions that would allow more meaningful
descriptions of the vertical growth of plumes.
5.1.3. Comparison with theory
Calculations of pollutant dispersion in the wind tunnel have been made
using the model described in Section 3.1. For calculating pollutant concen-
trations using the solution of the diffusion equation, it was necessary to
determine the lateral and vertical diffusivities k and k . It was not
possible, of course, to directly measure these values in the wind tunnel.
As mentioned in Section 3.1, the vertical diffusivity k was calculated with
Equation 6, a commonly used expression for the surface layer. Although the
vertical turbulent diffusivity began to decrease at large heights in the wind
tunnel, it may be noted that when the source height is small compared with
the boundary layer height, the behavior of k at the upper part of the boundary
layer should have little influence on surface concentrations. This obser-
vation has been verified through additional calculations wherein k was pre-
scribed as increasing linearly with height to 250 mm then linearly decreasing
71
-------
1000-
H j, mm
29
117
117
117
29
E
£
N
O
100-
n
10-
100
1000
10000
x, mm
Figure 39. Growth of true standard deviation of vertical concentration
distributions in flat terrain.
72
-------
with height to zero at the top of the boundary layer. Discrepancies in maximum
surface concentrations from sources of height up to 176 mm because of this
change in the k profile were small.
For determining the lateral diffusivity k , the following hypothesis of
Berlyand (1975) was used:
ky ' kou
as has also been discussed in Section 3.1.
(36)
It is possible to relate k and the root-mean-square lateral turbulent
particle displacement a through
ky = (l/2)day2/dt .
(37)
In accordance with the hypothesis of "frozen" turbulence, the above
equation may be rewritten as:
(38)
ky =
day2/dx ,
where U = mean wind velocity and x = distance downwind of the source, i.e.,
t = x/U.
From Eqs. 38 and 39 follows
kQ = (l/2)day2/dx .
(39)
The wind tunnel concentration data showed that a had the following
J
asymptotes
when x -> 0
when x -> °°
(40)
where a2 = V^/U2 (v = lateral turbulent velocity) and L = integral length
scale of turbulence.
Consequently for k the equation may be written as
k =
0
a2x when x -> 0
a2L when x -> »
(41a)
(41b)
73
-------
The wind tunnel data showed that an = 0.1 and L = 400 mm (Figure 36).
1
by
For the entire range of x, it is possible to approximate the behavior of a
1/2
ay - [1 . (42)
The corresponding expression for k is, therefore:
k = 2L 2x(x + 2L) - x* _ (43)
09 (x + 2L)2
This formula is very close to the more usual exponential formula derived using
an exponential correlation function (Pasquill, 1974),
a2 = 2a2L2(x/L - 1 + exp(-x/L)).
Numerical calculations of the values as well as locations of maximum
surface concentrations from elevated point sources of different heights were
made using Equations 41a, 41b, and 43. The results are shown in Figures 40
and 41. It is immediately evident that the form chosen for k has a strong
influence on the results. As might be expected, the smallest discrepancy
between the calculations and the measured data occurred when the interpolation
formula 43 was used. Equation 41a gave satisfactory results for small stack
heights when the location of the maximum surface concentration was relatively
close to the source. Equation 41b was satisfactory for large stack heights.
Excluding the smallest stack heights, the calculations underpredicted maximum
surface concentrations and overpredicted distances to the maximums. When
using Eq. 43, there was an average discrepancy of 9% for the concentration,
and 13% for the position. For the stack height 29 mm, the calculations gave
a value for the location of the maximum surface concentration close to that
measured, but overpredicted the concentration itself by about 19%.
It should be noted that in the calculation, slightly different values
of u* and zn were used than those aiven in section 5.1.1. The latter values
o
were obtained only after additional measurements had been made near the end
of the experimental program.
Surface concentration distributions as functions of downwind distance
from the source are known to depend upon the type of model chosen for lateral
74
-------
100 T
(N
8
o
10 -
0.1
0.01
10
41 b
43
DIFFUSIVITY FROM
EQUATION 41a
100
j, mm
1000
Figure 40. Comparison of numerical calculations of maximum surface
concentrations with wind tunnel data in flat terrain.
75
-------
10000-
s
£
i 10004
£ '
100
DIFFUSIVITY FROM
EQUATION 41a
10
100
1000
Hs, mm
Figure 41. Comparison of numerical calculations of location of maximum
surface concentration with wind tunnel data in flat terrain.
75
-------
diffusion, e.g., (Berlyand, 1975). Since lateral diffusion taking place in
the wind tunnel is best approximated using interpolation formula 42, it has
been used to derive an expression for the surface concentration profile.
The expression has the following form
(44)
NX x j-1 + f(p)/2p jl/2
xmx 1 + 7^-f(p)/2p
xmx
where x = downwind distance from the source, c = maximum surface concentration,
n -I mX 1/0
xmx = location of Cmx, p = L/2xm°, f(p) = £ [1 - 8p/3 + ((1 - 8p/3)2 + Sp)1^],
and x ° = location of maximum surface concentration predicted using Equation 41b
II l/\
for k . In Figure 42, these profiles are compared with profiles measured for
different stack heights. The agreement between them is good.
Some attempts were made to calculate pollutant dispersion assuming the
mass diffusivity was not equal to that for momentum, e.g., assuming the tur-
bulent Schmidt number was 0.70 - 0.74. Comparisons with measured data on
values and locations of maximum surface concentrations were not good.
This question demands further, more detailed investigation of the eddy diffu-
sivity in the wind tunnel boundary layer and the incorporation, within the
numerical calculations, of models that more precisely correspond to wind
tunnel conditions. Perhaps an experiment is in order to evaluate the magni-
tude of the turbulent Schmidt number under conditions similar to those of
the present study.
5.2. Hills
5.2.1. Velocity measurements
Vertical profiles of mean and fluctuating velocities as well as Reynolds
stresses were measured at numerous positions upwind, over and downwind of all
model hills. Mean velocity profiles over hill 8 are shown in Figure 43.
Note that longitudinal as opposed to streamwise velocities are presented;
they may differ slightly near the surface, of course, because the mean velo-
cities there are essentially parallel to the surface. Decreases in mean
77
-------
x
s
o
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0.01--
0.001-
-
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I A 29
i! n 59
| O 117
0.1 1 10
\
-
1
10(
x/x,
mx
F\qure 42. Comparison of surface concentrations predicted by Equation 44
with wind tunnel data in flat terrain.
78
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velocity (compared with those at the same distance above the surface far up-
stream) were observed at the upwind and downwind bases, whereas increases
were observed elsewhere. A maximum speed-up occurred at the hill top. The
decrease over the downwind base was significantly greater than that over the
upwind base, contrary to predictions of potential flow theory. The ratio
of the velocity at a height h /3 over the downwind base to the velocity at
the same elevation far upwind was 0.58. The ratio of that above the upwind
base to that far upstream was 0.82. The decrease in velocity at the downwind
base was relatively sharp and occurred mainly below the elevation of the
hill top. The speed-up over the top covered a much greater depth of the
boundary layer. The maximum speed-up took place at an elevation of hQ/6
and had a value of U(h /6)/Uoo(h /6) = 1.5. The mean velocity profile had
almost completely recovered (within 10%) 100 hill heights downwind.
Separate flow visualization studies using smoke showed no separation,
at least in the usual sense, of the flow on the lee side of hill 8; however,
intermittent separation was observed, as occasional (but rare) puffs of smoke
were observed traveling short distances, and for very short time durations,
in the reverse direction, i.e., up the lee slope.
Mean flow angles are shown in Figure 44. The trends here are as expected,
with maximum angles of about 9° compared with a maximum hill slope of 10.5°.
Angles very close to the surface, however, appeared to decrease toward zero.
This is obviously an incorrect indication and probably resulted from the
decreased angular sensitivity of the hot-wire anemometry at the very low flow
speeds and very large, local turbulence intensities.
Streamwise as contrasted with longitudinal turbulence intensity profiles
are presented in Figure 45. Except near the downwind base, changes of turbu-
lence were generally less than 10%, decreasing in the upslope region and
increasing near the top and on the downslope. An excess of about 30%, however,
was seen at an elevation of h /2 above the downwind base. Similar trends
occurred with the normal, as contrasted with vertical, turbulence intensities,
presented in Figure 46. Note, in reviewing this figure, that there was a
measurable decrease in the vertical turbulence intensity in the boundary layer
in the absence of the hill, which is not shown on the figures.
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The Reynolds stresses are described in a "natural" coordinate system that
is parallel and perpendicular to the streamlines (Figure 47). In the lower
layers, the Reynolds stresses were considerably increased, reaching nearly
a factor of 2 at the downwind base.
On the lee sides of hill 3, flow separation clearly occurred, as con-
firmed using flow visualization. Downwind of the separation point, there
was a deep cavity region whose height was about equal to the hill height.
The hot-wire anemometer was able, of course, to measure only the velocity
magnitude, but not its direction. For velocity measurements on the lee side
of hill 3, therefore, not only hot-wire anemometers, but also double-ended
Pi tot tubes were used. Comparisons of the two techniques are made in
Figure 48, where mean velocity profiles over the downwind base of hill 3 are
plotted. The data obtained with the Pitot tube show the existence of the
reversed mean flow in the recirculation zone, whereas the hot-wire anemometer
measurements indicate proper magnitudes of velocity, but obviously, the
wrong direction. Note that the elevation of the zero-longitudinal mean velo-
city was about half the hill height. This figure contains additional infor-
mation on special experiments with large hill 3 and variations with Reynolds
number (see later discussion in Section 5.3).
Mean velocity profiles over the upwind base and top of hills 3 and 5
resembled those over hill 8, except that the deviations from the velocity
profile in the incident flow were larger. Downwind of the hill centers, of
course, the flow structure changed drastically because of the separation.
Velocity measurements within the suspected cavity region of hill 5 were
also made with a pulsed-wire anemometer, which is sensitive to flow direction
(Bradbury and Castro, 1971). Velocity profiles measured by both pulsed-wire
and hot-wire anemometers at the downwind base of hill 5 are presented in
Figure 49. It is evident that, at least above 10 mm height, there was no
flow separation in terms of the mean velocity pattern. This was surprising
because the smoke visualization showed transport up the lee slope, opposite
in direction to the free-stream flow. The visualization seemed to indicate
that a cavity region existed with height equal to at least half the hill
height! This discrepancy, however, may be understood through careful study
84
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1000
s
100
10 -i-
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D
DO
INSTRUMENT U^, njs HILL
HOT-WIRE 4 3
PITOTTU8E 4 3
PITOT TUBE 8 3
PITOTTUBE 4 BIGS
0.3
0.15
0.30
0.45
0.60
0.75
0.90
Figure 48. Mean velocity profiles inside cavity region of hill 3.
1.05
86
-------
300
250-
200-
S
£ 150
100-r
50--
A PULSED-WIRE
D HOT-WIRE
4
i
12 3
U,m/s
Figure 49. Mean velocity profiles measured at downwind base of hill 5.
87
-------
of the probability density distribution of velocity fluctuations, shown in
Figure 50. The average velocity U» was small but positive. The turbulence
intensity was extremely large compared with the mean velocity, and the
instantaneous velocity was negative perhaps 40% of the time. Thus, the
longitudinal turbulent transport exceeded the mean transport, giving the
illusion of a separated recirculating cavity region. In this figure, at a
height of 20 mm, the longitudinal turbulence intensity was twice as large
as the mean velocity. (The large probability at zero velocity as well as
the small probabilities near zero are due to the limited yaw response of
the pulsed-wire as explained by Bradbury (1976); they should be ignored).
From Figure 49, it is evident that the hot-wire anemometer indicated
larger velocities in the region below 50 mm; this is so because the hot-wire
rectified the velocity signal, which was frequently negative. It is evident
that the values measured by the hot-wire need to be corrected when the indi-
cated longitudinal turbulence intensity exceeds ^ 45%.
The double-ended Pi tot tube can also rectify signals and over-estimate
the value of mean velocity because of its nonlinear response. A comparison
of this device with the pulsed-wire anemometer measurements inside the re-
circulation zone downwind of an obstacle is shown in Figure 51. It is impor-
tant to note for later discussion that the point of zero-mean velocity was
located with reasonable accuracy. Below the point of zero-mean velocity, the
intensity of turbulence exceeded 60%, and the double-ended Pitot tube indi-
cated larger absolute values of velocity (up to 40% larger).
5.5.2. Concentration measurements
Surface concentrations resulting from the stack of height 59 mm (h /2)
placed at different positions relative to the three small hills are shown in
Figures 52 through 54 (x = (1): upwind base; x$ = (2): top center; x$ = (3):
downwind base of hills). When the stack was placed upwind of the hills, the
maximum surface concentrations occurred at or upwind of the hill crests, and
the values of these were significantly increased. For hill 3, x was in-
nix
creased by a factor of 2.5 over that which would have occurred over flat
terrain, albeit further downstream. The influence of the highly turbulent
-------
1.05'
0.90-
0.75-
0.60-J-
0.45 T
0.304-
0.154
\
\
-2
-1
U/(7U
Figure 50. Probability density of velocity fluctuations at 20 mm above down
wind base of hill 5.
89
-------
600-
5004
400-r
£ 3001
200-
100--
PULSED-WIRE 1
DUAL PITOT TUBE
0.5
0.5
1.0
U/Ua
Figure 51. Mean velocity profiles measured in the recirculating wake of
an obstacle.
90
-------
100
10--
_ HILL 3
D HILL 5 <"> "
G HILLS j
1
"1
5 00 -j
J d -I
NO HILL 555 -j
u. u
u.
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a. a. a. -1
0 C
1- H
° 1
i
1-
0.1-
r
0.01
CT'X
10
100
1000
10,000
x,mm
Figure 52. Surface concentration profiles over hills; upwind base
stack location; Hs = 59 mm.
91
-------
100
-
c- HILL
G HILL
C< HILL
3
5
-
1
(
1 -|
s « in 03 j
B _! -I -1 1
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-
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LL LL LL 1
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C/3 W) V) '
< < <
CD CD CO j
J
j
4
o.i4
0.01
10
100
1000
10,000
x,mm
Figure 53. Surface concentration profiles over hills; hill top
stack location; Hs = 59 mm.
-------
100
HILL3
HILLS
HILLS
NO HILL
104
0.1
0.01
10
U
100
1000
10,000
x,mm
Figure 54. Surface concentration profiles over hills; downwind base
stack location; Hs = 59 mm.
93
-------
zone is noticeable for hill 5; the influence of the separate flow region is
unmistakable for hill 3.
For this particular configuration, surface concentrations within the
cavity region were sharply reduced from the upstream value. The bulk of the
plume evidently remained outside the cavity. This cavity region appeared
to have a permanent influence on concentrations farther downwind in that
they followed the same dilution rate but the magnitude of the concentrations
was reduced by about 20%. This phenomenon was probably the result of greatly
increased lateral diffusion (see later discussion) because of the flow se-
paration in the lee of the hill.
Figure 53 shows results of placing the stack on the top of each of the
hills. The significant reductions in surface concentrations and increases
in the distances to the points of maximum concentration were probably caused
by the divergence of streamlines from the top to the downwind bases of the
hills. For hill 3, however, an abrupt change in the curvature of the sur-
face profile occurred slightly beyond the downwind base. The location of
the maximum concentration evidently marks the reattachment point of the
separation streamline, which is the end of the cavity region.
When the stack was placed at the downwind base (Figure 54), maximum
concentrations were increased and distances to the points of maximum concen-
tration were decreased. For hills 3 and 5, maximum surface concentrations
were increased by an order of magnitude. Maximum concentrations for hills 3
and 5 were located very close to the base of the stackfor hill 5, virtually
beneath the stack, and for hill 3, slightly upwind (!) of the stack, as may
be seen on Figure 55. The maxima were located at the same positions when
the stack height was 29 mm. In both cases, significant concentrations were
measured upwind of the stack. These phenomena reflect the presence of the
highly turbulent zone, where the turbulent transport exceeded the mean trans-
port. An additional cause for hill 3 was the reversed wind flow.
The largest terrain correction factor (TCF) from all the measurements
made was with a stack of height h /4 located at the downwind base of hill 5,
that is, the maximum surface concentration was found to be 15 times the maxi-
mum observed in the absence of the hill. For hill 3, the largest TCF (^ 11)
94
-------
100-
10-
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r1- i' r:
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Figure 55. Surface concentration profiles over hills; downwind base stack
location; Hs = 59 mm; semilogaritnmic plot.
95
-------
was observed when the stack height was equal to the hill height, so that the
source location was very close to the reattachment streamline. In this case,
the region of very low mean wind speed (hill 5) was evidently more dangerous
than the reversed flow in the cavity region (hill 3).
Figure 56 shows the development of vertical concentration profiles down-
wind of a source 117 mm high (h ) placed upwind of hill 8. Profiles obtained
from the same source in flat terrain are shown for reference. At the crest
of the hill, the profile shapes are similar, but the plume over the hill is
obviously narrower and closer to the surface than is the reference plume.
This resulted, of course, from the convergence of streamlines over the hill.
Just the opposite occurred at the downwind base; the plume was wider and
farther from the surface than the reference plume, due to the rather strong
divergence of streamlines there. Sixteen hill heights downwind of the crest,
the profiles were practically indistinguishable.
Similar but less noticeable changes were observed for the plume from
the 29 mm source shown in Figure 57. These were rather surprising, since
more marked changes would be expected with the smaller stack. However, the
maximum concentration was located very close to the source, hence, very
close to the upwind base of the hill, a fact that may help to explain the
less noticeable changes.
Figure 58 shows that the effect of hill 3 on an upwind stack 117 mm
high was to downwash the plume on the lee side. Resulting surface concen-
trations downwind of the hill were significantly higher than in the absence
of the hill. Notice that in the cavity region, concentrations were essentially
uniform with height, indicating very rapid mixing.
Lateral plume widths were generally enhanced by the presence of the hills.
As shown in Figure 59, the amount of enhancement depended upon the source
height, the position of the stack relative to the hill, and to the hill shape;
enhancement was greater for shorter stacks, downwind base locations and
steeper hills. When the stack was placed on the top of hill 8, however, the
lateral plume widths were very slightly decreased.
Interestingly, the data for all hills, all stack heights and all stack
positions can be collapsed reasonably well onto a single curve when plotted
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100
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x, mm
Figure 59. Growth of lateral plume width in presence of hiils.
100
-------
as x versus x . This is shown in Figure 60, where a virtual origin of
II1A, lll/\
50 mm has been assumed in order to straighten the curve at small distances.
In a sense,.this graph indicates that the maximum surface concentration de-
pended only upon the travel distance of the plume in getting from the source
to the point of maximum concentration, independent of the means of travel
(whether through diffusion or through distortion of the mean streamline
pattern).
5.2.3. Comparison with theory
The QPM model was used to calculate terrain correction factors for pre-
dicting the values and positions of maximum surface concentrations and also
surface concentrations as functions of downwind distance from the source.
The results of these calculations were compared with the experimental data.
Calculations were made with typical field input parameters, since QPM
was developed for predicting terrain correction factors (TCP's) in the real
atmosphere. The assumed height of the full-scale hill was chosen as 50 m.
In this case, the model scale ratio was about 400 and the corresponding field
roughness length was approximately 5 cm. The value of the field roughness
length was obtained using the roughness length in the wind tunnel as 0.127 mm.
(The differences between that value and the corrected value of z = 0.157 is
not significant here). Given z , it was possible to determine the ratio of
the wind speed in the incident flow u, (at 1 m height) to the corresponding
eddy diffusivity k,. Since the TCP does not depend on u, or k, separately,
but only upon their ratio, the friction velocity u* for the atmospheric flow
was chosen as 0.27 m/s (not 0.2 m/s as in the wind tunnel) in order to have
more realistic field values of wind speed and eddy diffusivity (e.g.,
Uj = 2 m/s and k^ = 0.114 m2/s).
TCP's are listed in Tables 1 and 2 for the values and locations, respec-
tively, of maximum surface concentrations calculated with QPM and obtained
from measurements. The TCP's for the value of the maximum surface concentra-
tions are the same for stack positions 1 and 3 (upwind and downwind base)
because of the symmetry of the QPM. Comparison of the TCP's with the measured
data was rather difficult, because of the unavoidable scatter in the measured
data.
101
-------
100
I--,
o
10-r
o
-------
TABLE 1. TERRAIN CORRECTION FACTORS FOR MAXIMUM SURFACE CONCENTRATION
H
s
h
0
0.25
0.50
1.00
1.50
0.25
0.50
1.00
1.50
0.25
0.50
1.00
1.50
xs =
From
Measur.
1.45
1.12
1.47
1.16
1.96
2.04
1.74
1.20
2.81
2.47
1.78
1.87
HILL,
(1)
Calcul.
1.42
1.37
1.24(1.31)*
1.20
HILL,
1.70
1.59
1.35(1.46)
1.28
HILL,
2.29
2.02
1.52(1.70)
1.39
N=8
xs =
From
Measur.
0.91
0.56
0.78
0.82
N=5
0.54
0.63
0.86
1.04
N=3
0.34
0.69
0.91
0.94
(2)
Calcul .
0.66
0.67
0.74(0.68)
0.75
0.53
0.54
0.65(0.58)
0.67
0.38
0.41
0.55(0.47)
0.59
xs =
From
Measur.
3.43
2.99
2.39
1.68
15.00
8.12
5.63
2.90
7.50
6.42
10.80
7.77
(3)
Calcul .
1.42
1.37
1.24(1.
1.20
1.70
1.59
1.35(1.
1.28
2.29
2.02
1.52(1.
1.39
34)
46)
70)
Values obtained using Equation 41a.
103
-------
TABLE 2. TERRAIN CORRECTION FACTORS FOR LOCATION
OF MAXIMUM SURFACE CONCENTRATION
u
S
0
0.25
0.50
1.00
1.50
0.25
0.50
1.00
1.50
0.25
0.50
1.00
1.50
xs =
From
Measur.
0.6
0.81
0.81
0.82
0.66
0.61
0.64
0.76
0.26
0.45
0.62
0.58
HILL;
(1)
Calcul.
0.90
0.84
0.82(0.80)*
0.87
HILL;
0.82
0.72
0.79(0.77)
0.84"
HILL,
0.66
0.56
0.74(0.72)
0.80
, N=8
xs
From
Measur.
1.14
1.63
1.31
1.11
, N=5
1.00
1.26
1.05
1.25
, N=3
1.87
1.33
1.00
0.97
= (2)
Calcul .
1.05
1.14
1.20(1.20)
1.19
1.12
1.32
1.31(1.31)
1.28
1.51
1.54
1.46(1.46)
1.39
xs =
From
Measur.
0.30
0.44
0.55
0.75
__
0.11
0.26
0.49
__
_ _
0.084
0.24
(3)
Calcul.
0.90
0.89
0.89(0.90)
0.90
0.84
0.84
0.85(0.85)
0.87
0.75
0.76
0.79(0.79)
0.82
* Values obtained using Equation 41a.
104
-------
Their calculation involved quotients of measured values, and the scatter
in the quotients was naturally greater than the scatter of the individual
values. Hence, the true situation may appear significantly distorted,
especially when the TCP's are close to unity. It is noteworthy that, in
some cases, the changes in the TCP's for maximum surface concentration were
nonmonotonic with stack height (fixed stack position). This feature is
especially puzzling in the cases of hills 8 and 5, where the flow did not
separate from the lee side of the hill. For hill 3, such nonmonotonic be-
havior may be explained as due to the influence of the recirculation zone,
especially when the stack was positioned at x = (3). To elucidate this
question, further theoretical and experimental efforts are needed.
Although QPM usually assumes a linear growth of lateral diffusivity with
downwind distance (characteristic of field conditions for distances up to
a few tens of kilometers), in this study different dependences of the lateral
diffusivity were used to make the calculation model closer to the wind tunnel
conditions. For stack heights lower than the hill height, a formula analogous
to Eq. 41a was used; for higher stacks, Eq. 41b was used. Table 1 shows that,
for hill 8, the TCP for the maximum surface concentration was significantly
greater for stack position x = (3) than for x = (1). This was the most
important difference (for hill 8) between the data and QPM predictions.
When the stack position was x = (1) or x = (2), the measured data and QPM
both showed similar magnitudes for the changes in TCP's.
The comparison of the TCP's calculated using QPM with those obtained from
the wind tunnel data is rather poor for hills 3 and 5 because of the existence
in these cases of the recirculation zone or zone of very high turbulence inten-
sity. Nevertheless, there is reasonable agreement between both sets of values
when the stack is located at position x = (1) or x = (2).
Surface concentration profiles were obtained using a formula similar to
Eq. 44. In all cases, the variable ? was substituted for x in Equations 41a,
41b and 44.
Figures 61 to 63 show normalized surface concentrations plotted as func-
tions of normalized distance from the source x/x for hill 8. The triangles
on these figures mark the curve calculated using Eq. 44. It may be seen
105
-------
1-r
\
0.001 -
-\
'-A
0.01 -'-
:\
CJ
\
QPM
- EQUATION 44
I. MEASURED
0.0001 L-
0.1
10
100
x/x,
mx
Figure 61. Comparison of surface concentrations predicted by QPM and
experimental data; hiil 8; Hs = h0/2; x = (1).
106
-------
/^
0.14
-\
u
£ 0.01-,-
0.001-
0.0001-
QPM
_ EQUATION 44
'I. MEASURED
0.1
10
100
x/x,
mx
Figure 62. Comparison of surface concentrations predicted by QPM and
experimental data; hill 8; HS = hQ/2; xs =(2).
107
-------
3.4
O!O
S 0.01 -
0.001
QPM
_ EQUATION 44
I MEASURED
0.0001
0.1
10
100
x/x
mx
Figure 63. Comparison of surface concentrations predicted by QPM and
experimental data; hiil 8; Hs = ho/2; xs = (3).
108
-------
that the hill had very little influence on the shape of the profile. The
difference between the calculated curve and that obtained from measurements
is also small. For the steeper hills, 3 and 5, a comparison between cal-
culated and measured profiles is not appropriate, since 0PM admits neither
flow separation nor great increase of turbulence, which change the profile
shape (see Figure 52).
For hill 8, numerical calculations of maximum surface concentrations
were made using WMDM. The parameters used in the calculations were adjusted
to match the wind tunnel flow, not the corresponding atmospheric flow. The
incident flow structure was modeled in accordance with Eq. 5, the parameter
values being taken from the measured data. The results are shown in Figures
64 to 69. Figure 68 shows that, when the stack is located at the downwind
base of the hill, WMDM predicts maximum surface concentrations significantly
better than QPM, which gives the same maximum surface concentrations inde-
pendent of whether the stack is located at the upwind or downwind base of
the hill. Nevertheless, the discrepancy between the measured data and those
calculated is notable. The agreement between the measurements and the cal-
culations improves when the stack is located at the upwind base or at the top
of the hill. (See Figures 64 and 66). The model was a poor predictor of
maximum surface concentrations (see Figures 65, 67, and 69), especially for
low stacks located at the downwind base of the hill. TCF's for all these
data are listed in Tables 3 and 4.
In summary, the calculations, for both hilly and flat terrain, usually
underpredicted values of maximum surface concentrations and overpredicted
distances to their position, but the discrepancy was larger over the hills.
Comparisons of the results of WMDM with the experimental data bear further
study, particularly regarding (1) the mean flow patterns produced by WMDM;
(2) the measurements for short stackswhy they give such small distances
to maximum surface concentration; and (3) further calculations for different
source locations. WMDM could not be used to make calculations for hills 3
or 5, since the wind velocity measurements were not completely reliable at
the time the calculations were conducted. When regions of reversed mean
flow and/or very small mean velocity exist in conjunction with very high
turbulence intensities, longitudinal diffusion must be included in the model,
109
-------
100 -,-
10
X
£
X
I
1-1
r
r
\
0.1-
10
100
1000
H» , mm
Figure 64. Comparison of maximum surface concentrations predicted by WMDM
and experimental data; hill 8; xs = (1).
110
-------
1oooo r
I i
x 1000^
£
X I
i-
100--
10 100 1000
He , mm
Figure 65. Comparison of distances to location of maximum surface
concentration predicted by WMDM and experimental data; hill 8; xs = (1).
Ill
-------
100
10-
x
E
x
0.1-
10
100
1000
, mm
Figure 66. Comparison of maximum surface concentrations predicted by WMDM
and experimental data; hiil 8; xs = (2).
112
-------
10,000-r-
s
c
X
E
X
1000-^-
i
100-1-
10
100
H-, rnm
1000
Figure 67. Comparison of distances to location of maximum surface concentration
predicted by WMDM and experimental data; hill 8; xs = (2).
113
-------
100
x
£
x
10 -
0.1
10
100
H», mm
1000
Figure 68. Comparison of maximum surface concentrations predicted by WMDM
and experimental data; hill 8; xs = (3).
114
-------
10000
x
g
x"
1000-r
100 J-
10 100 1000
H. , mm
Figure 69. Comparisons of distances to location of maximum surface
concentration predicted by WMDM and experimental data; hill 8; xs = (3).
115
-------
TABLE 3. COMPARISON OF MEASURED MAXIMUM CONCENTRATIONS
AND THOSE CALCULATED WITH WMDM FOR HILL 8
Hc
s
0.25
0.5
1.0
1.5
xs =
Measur.
13.44
2.96
0.97
0.36
(1)
Calcul.
15.25
3.11
0.71
0.32
xs =
Measur.
9.28
1.49
0.49
0.26
(2)
Calcul.
6.74
1.58
0.42
0.23
xs =
Measur.
30.79
8.93
1.55
0.53
(3)
Calcul.
36.52
5.76
0.97
0.37
TABLE 4. COMPARISON OF MEASURED DISTANCES TO MAXIMUM
CONCENTRATION AND THOSE CALCULATED WITH WMDM FOR HILL 8
H,.
xs = (1)
Measur. Calcul.
xs = (2)
Measur. Calcul.
xs = (3)
Measur. Calcul.
all dimensions in mm
0.25
0.5
1.0
1.5
180
578
1488
2520
293
772
2012
3118
342
1196
2500
3364
491
1147
2527
3879
91
310
1040
2300
176
468
1357
2738
116
-------
a task that WMDM cannot perform without further development.
Attempts were made to evaluate the accuracy of WMDM. For this purpose,
the wind field over hill 8 assumed in 0PM was used. The values of the wind
velocity components at the points where the measurements were conducted in
the wind tunnel were input to WMDM. The eddy diffusivity in this case was
also assumed to be the same as in QPM. The values of the TCP's for maximum
surface concentration were calculated. The source location was changed in
the same way as in the wind tunnel experiments. The discrepancy between the
predictions of QPM and WMDM was on average about 7%. Of course, these cal-
culations can be considered only as a rather approximate example of the vali-
dation of WMDM. Further work should be done along these lines. As was
mentioned in Section 3.2, WMDM could be improved by the use of a more accurate
interpolation of wind field measurements (rather than bilinear interpolation
as was used in this study). Further improvements may be expected with the
emergence of models for predicting structural changes in turbulence over
irregular terrain.
5.3. Special Experiments
A few additional experiments were conducted to examine, at least in
limited fashion, the effects of otherwise unvaried parameters. These special
tests included (1) variation of mean flow speed to determine whether the flow
structure was Reynolds-number independent, (2) maintenance of a flat wind-
tunnel ceiling (non-zero longitudinal pressure gradient) to determine whether
the ceiling height adjustment was critical, and (3) use of a larger but
similar-shaped hill 3 (big hill 3) to determine whether the ratio of hill
height to boundary-layer height had a significant influence on the flow struc-
ture over the hill. These experiments as well as some streamline patterns
derived from the measured velocity profiles are presented in this section.
5.3.1. Reynolds number and hi 11-height effects
As mentioned in Section 5.2.1, a double-ended Pi tot tube was used to
probe the velocity profiles in the separated flow region or cavity on the lee
side of hill 3 (see Figure 48). Additional measurements were made to deter-
mine the locus of zero-mean longitudinal velocity within the cavity region,
117
-------
since this was felt to be a sensitive measure of the mean flow structure.
This locus of zero-mean velocity is shown in Figure 70 to be slightly greater
than half the zero-streamline height. The cavity, defined as the region en-
closed by the lee side of the hill and the separation-reattachment stream-
line (or zero-streamline), is seen to extend to approximately 6.5 hill heights
downwind, but to be limited in vertical extent to less than the hill height.
The freestream wind speed, hence, the Reynolds number, was then doubled, and
the locus of zero-mean velocity was measured again. The difference in the
loci is indistinguishable, indicating Reynolds number independence, at least
within this limited range. (Note that the boundary layer structure was pre-
viously shown to be Reynolds number independent in the range of 4 to 8 m/s).
Big hill 3 was next installed in the tunnel and similar measurements
were conducted at free-stream wind speeds of 2, 4 and 8 m/s. These results
are also shown in Figure 70 (see also Figure 48). Whereas the big hill 3
results at 4 and 8 m/s are indistinguishable from the small hill 3 results,
those at 2 m/s are noticeably different. Because the big hill 3 results at
4 and 8 m/s matched the small hill 3 results at 4 and 8 m/s, one may conclude
that the ratios of hill height to boundary layer height and roughness length
to hill height are relatively unimportant parameters. The deviations at 2 m/s
could result from any of 3 effects: (1) direct variations with Reynolds number,
(2) indirect variations with Reynolds number (possibly the approach flow struc-
ture varied with Reynolds number), or (3) insensitivity of the measuring device.
Effect (1), direct variations with Reynolds number, is ruled out because
the Reynolds number for big hill 3 at 2 m/s is the same as that for small hill
3 at 4 m/s, which was previously shown to be Reynolds number independent.
Effect (2), indirect variations with Reynolds number, is a possible cause, as
independent measurements of the approach boundary layer structure at 2 m/s
were not made. Effect (3), insensitivity of the measurement device, however,
is the most likely cause for the discrepancy in the results. Study of Figure
48, for example, shows that, in order to determine the location of the zero-
mean velocity point to within 10 mm, the double-ended Pitot tube/manometer
combination must be able to sense mean wind speeds (and within a highly tur-
bulent flow) of less than 10 cm/s, a dubious possibility at best. We thus
conclude that, within the limitations of the instrumentation and over the
118
-------
o
p
o
00 u.
LU
cc
j CO PO 00 O
J M O O O g
X CO GQ CO N
O
O
c
O
c
_o
4-^
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to
as
U
c
03
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OS
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119
-------
limited ranges measured, the flow structure is relatively insensitive to Reynolds
number, h /6, or zQ/6.
It may be hypothesized that the flow structure is independent of Reynolds
number up to very large values such as found in the field. In fact, measure-
ments by Wilson et al (1979) suggest that separation may disappear at a large
enough Reynolds number, but his results have not yet been substantiated.
Proof will be available only after adequate field measurements have been con-
ducted.
5.3.2. Effects of ceiling adjustment
Measurements made to examine the effects of the ceiling adjustment were
surface concentration profiles for hill 8 with a stack height of half the
hill height and the stack located at the downwind base of the hill. Measure-
ments were made with adjusted (zero-longitudinal pressure gradient) and
non-adjusted (flat) ceilings. This configuration was expected to be one of
the most sensitive ones with respect to ceiling adjustment. Surface concen-
tration profiles thus measured are compared in Figure 71. It is apparent
that the ceiling adjustment had some effect on the concentrations field near
the stack, presumably because, with the flat ceiling, the streamlines con-
verged more strongly on the lee side. Time limitations prevented a detailed
examination of this effect. It is widely believed that the proper ceiling-
height adjustment is that which produces a zero-pressure gradient flow, i.e.,
a non-accelerating free-stream.
5.3.3. Streamline patterns over hills
Figure 72 shows streamline patterns over hill 8, derived from the velo-
city profiles measured over the hill. As suggested in Section 5.2.1, the
streamlines diverged upstream of the upwind base, converged over the upwind
slope, diverged over the downwind slope, and converged beyond the downwind
base. The separation between the streamlines above the downwind base is
significantly larger than between those above the upwind base. The "kinks"
in the streamline above the upwind base, especially noticeable at the higher
elevations, probably resulting from an error of only 2% in the measurement
of the reference velocity. With this in mind, it may be surmised that the mean
120
-------
1-
x 0
,i
0.01-
_ FLAT CEILING
Z ADJUSTED CEILING
NO HILL
0.001-
10 100 1000 10000
x, mm
Figure 71. Dependence of surface concentrations on wind tunnel ceiling
adjustment; hill 8; Hs = h0/2; xs = (3).
121
-------
o
§
to
§
o
Ifl
O
o
o
s
E
CO
o
o
to
o
o
o
o
o ^
(C
-a
c
Ol
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§
c
V
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en
ID
CN
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122
-------
velocity profiles are extremely accurate, or at least, extremely consistent
with one another.
Streamlines patterns over hill 3 are shown in Figure 73. The cavity
region is clearly evident. In some respects, it would be useful to treat
the hill/cavity combination as a solid body for the purpose of calculating
streamline trajectories. After the streamline trajectories were obtained,
concentrations outside the cavity could possibly be calculated with QPM or
WMDM, whereas concentrations within the cavity could be calculated using
the kind of model constructed by Puttock and Hunt (1979).
The streamline patterns over hill 5 are shown in Figure 74. The small
kinks in the streamlines over the downwind slope probably result from the
usage of data obtained with the pulsed-wire anemometer. In contrast to the
hot-wire, the pulsed-wire does not rectify the signal, but the data probably
have slightly different normalization factors. (Likewise, the kinks over
the cavity region on Figure 73 are probably due to the usage of the double-
ended Pi tot tube).
As discussed earlier, a recirculatinq cavity region does not exist on
the lee slope of hill 5 (at least not in the mean), but the divergence of
streamlines over the lee slope is very significant. The ratio of a stream-
line height over the downwind base to that of the same streamline in the
approach flow may be taken as a quantitative measure of this phenomenon.
For example, this ratio for the streamline at a height of 29 mm (h /4) far
upwind is 4 for hill 5 and 2 for hill 8. These ratios allow a rough explana-
tion of the TCF's for maximum surface concentration. The measured TCF's were
_2
15 and 3.43, respectively. If it is assumed that xm ^h -,, where h -, is the
TTIX SI 51
height at the stack position of the streamline qoing through the source, then
the TCF's are 16, and 4, respectively, quite close to the measured values.
123
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6. REFERENCES
Arya, S.P.S. and Shipman, M.S., 1979: A Model Study of Boundary Layer Flow
and Diffusion Over a Ridge, Proc. AMS Fourth Symp. on Turbulence, Diffusion
and Air Pollution, Jan. 15-18, Reno, NV, Am. Meteorol. Soc., Boston, MA, p.
584-91.
Arya, S.P.S. and Shipman, M.S., 1981: An Experimental Investigation of Flow
and Diffusion in the Disturbed Boundary Layer over a Ridge; Part I: Mean
Flow and Turbulence Structure, Atmos. Envir. (In Press).
Barr, S., Luna, R.E., Clements, W.E. and Church, H.W., 1977: Workshop on
Research Needs for Atmospheric Transport and Diffusion in Complex Terrain,
Available from Nat. Tech. Info. Serv., Springfield, VA, 17p.
Berlyand, M.E., 1975: Contemporary Problems of Atmospheric Diffusion and
Air Pollution, Hydromet. Press, Leningrad, USSR, 448p.
Berlyand, M.E. and Genikhovich, E.L., 1971: Atmospheric Diffusion and the
Structure of the Air Flow above an Inhomogeneous Surface, Proc. Int. Syrcp.
on Meteorol. Aspects of Air Poll., 1968, Leningrad, p. 49-69, Hydromet. Press,
Leningrad, USSR.
Berlyand, M.E., Genikhovich, E.L., Gracheva, I.G. and Onikul, R.I., 1979:
Peculiarities of Pollutant Diffusion over Crossed Terrain, Atmos. Diff. and
Air Poll., Trudy GGO, no. 417, p. 19-35, Hydromet Press, Leningrad, USSR.
Berlyand, M.E., Genikhovich, E.L. and Khurshudyan, L.H., 1975: Use of the
Results of Modeling of an Air Stream in Wind Tunnels for the Calculation of
Air Pollution, Atmos. Diff. and Air Poll., Trudy GGO, no. 352, p. 3-15,
Hydromet. Press, Leningrad, USSR (EPA Trans!. TR-79-0431).
Berlyand, M.E., Genikhovich, E.L. and Kurenbin, O.I., 1968: The Influence
of Relief on the Diffusion of Pollutants from a Source, Atmos. Diff. and Air
Poll., Trudy GGO, no. 234, p. 28-44, Hydromet. Press, Leningrad, USSR.
Berlyand, M.E. and Kisselev, V.B., 1973: On Influence of Relief en Dispersion
of Pollutants Taking Plume Rise into Account, Meteorology and Hydrology,
no.3, p. 3-10, Hydromet. Press, Leningrad, USSR.
Bradbury, L.J.S., 1976: Measurements with a Pulsed-Wire and a Hot-Wire
Anemometer in the Highly Turbulent Wake of a Normal Flat Plate, J. Fluid
Mech., v. 77, pt. 3, p. 473-97.
Bradbury, L.J.S. and Castro, I.P., 1971: A Pulsed-wire Technique for Velocity
Measurements in Highly Turbulent Flows, J. Fluid Mech., v. 49, pt. 4, p. 657-
91.
126
-------
Britter, R.E., Hunt, J.C.R. and Richards, K.J., 1981: Air Flow over a Two-
dimensional Hill: Studies of Velocity Speed-up, Roughness Effects and
Turbulence, Quart. J. Roy. Meteorol. Soc., v. 107, p. 91-110.
Bruun, H.H., 1975: On the Temperature Dependence of Constant Temperature
Hot-wire Probes with Small Wire Aspect Ratio, J. Physics E: Rev. Sci.
Insts., v. 8, p. 942-51.
Burt, E.W. and Slater, H.H., 1977: Evaluation of the Valley Model, Paper pres
at the AMS-APCA Joint Conf. on Appl. of Air Pol. Meteorol., Salt Lake City,
Utah.
Cermak, J.E., Sandborn, V.A., Plate, E.J., Binder, G.H., Chuang, H., Meroney,
R.N. and Ito, S., 1966: Simulation of Atmospheric Motion by Wind Tunnel Flows,
Fluid Dyn. and Diff. Lab. Rpt. No. CER66JEC-VAS-EJP-GJB-HC-RNM-SI17, Colo.
State Univ., Ft. Collins, CO, 102p.
Clarke, R.H. and Hess, G.D., 1974: Geostrophic Departure and the Functions
A and B of Rossby-Number Similarity Theory, Bound.-Layer Meteorol., v. 7, no.
3, p. 267-87.
Counihan, J., 1975: Adiabatic Atmospheric Boundary Layers: A Review and
Analysis of Data from the Period 1880-1972, Atmos. Envir., v. 9, p. 871-905.
Courtney, L.Y., 1979: A Wind Tunnel Study of Flow and Diffusion over a Two-
Dimensional Low Hill, M.S. Thesis, Dept. of Meteorol., NC State Univ.,
Raleigh, NC, 134p.
Dickerson, M.H., 1978: MASCON - A Mass Consistent Atmospheric Flux Model for
Regions with Complex Terrain, J. Appl. Meteorol., v. 17, p. 241-53.
Dickerson, M.H., and Gudiksen, P.H., 1980: The Department of Energy's Complex
Terrain (ASCOT) Program, Proc. AMS/APCA 2nd Jt. Cof. on Appl. of Air Poll.
Met., Mar. 24-27, New Orleans, LA, Amer. Meteorol. Soc., Boston, MA.
Egan, B.A., 1975: Turbulent Diffusion in Complex Terrain, Workshop on Air
Poll. Meteorol. and Envir. Assess., Amer. Meteorol. Soc., Sept. 30-Oct. 3,
Boston, MA.
Gorlin, S.M. and Zrazhevsky, I.M., 1968: Study of Flow around Model Relief and
Urban Construction in a Wind Tunnel, Atmos. Diff. and Air Poll., Trudy GGO,
no. 234, p. 45-59, Hydromet. Press, Leningrad, USSR.
Nilst, G.R., 1978: Plume Model Validation, EPRI EA-917-SY, Electric Power
Research Institute, Palo Alto, CA.
Holzworth, G.C., 1980: The EPA Program for Dispersion Model Development for
Sources in Complex Terrain, Pres. at 2nd Jt. Conf. on Appl. of Air Poll.
Meteorol., March 24-27, New Orleans, LA, 4p.
127
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Hovind, E.L., Edelstein, M.W. and Sutherland, V.C., 1979: Workshop on Atmos-
pheric Dispersion Models in Complex Terrain, Envir. Prot. Agcy. Rpt. No. EPA-
600/9-79-041, Res. Tri. Pk., NC, 213p.
Huber, A.M., Snyder, W.H., Thompson, R.S., and Lawson, R.E. Jr., 1976: Stack
Placement in the Lee of a Mountain Ridge: A Wind Tunnel Study, Envir. Prot.
Agcy. Rept. No. EPA-600/4-76-047, Res. Tri. Pk., NC., 45p.
Hunt, J.C.R. and Fernholz, H., 1975: Wind-Tunnel Simulation of the Atmos-
spheric Boundary Layer: A Report on Euromech 50, J. Fluid Mech., v. 70,
pt. 3, p. 543-59.
Hunt, J.C.R. and Mulhearn, P.J., 1973: Turbulent Dispersion from Sources
Near Two-Dimensional Obstacles, J. Fluid Mech., v. 61, pt. 2, p. 245-74.
Hunt, J.C.R., Puttock, J.S. and Snyder, W.H., 1979: Turbulent Diffusion
from a Point Source in Stratified and Neutral Flows around a Three-Dimen-
sional Hill: Part I: Diffusion Equation Analysis, Atmos. Envir., v.13,
p.1227-39.
Hunt, J.C.R. and Snyder, W.H., 1980: Experiments on Stably and Neutrally
Stratified Flow over a Model Three-Dimensional Hill, J. Fluid Mech., v. 96,
pt. 4, p. 671-704.
Hunt, J.C.R., Snyder, W.H., and Lawson, R.E. Jr., 1978: Flow Structure and
Turbulent Diffusion around a Three-Dimensional Hill: Fluid Modeling Study on
Effects of Stratification; Part I: Flow Structure, Envir. Prot. Agcy. Rpt. No.
EPA 600/4-78-041, Res. Tri. Pk., NC.
Isaacs, R.G., Bass, A. and Egan, B.A., 1979: Application of Potential Flow
Theory to a Gaussian Point Source Diffusion Model in Complex Terrain, Fourth
Symp. on Turb., Diff. and Air Poll., Jan. 15-18, Reno, NV, Am. Meteorol.
Soc., Boston, MA, p. 189-96.
Jackson, P.S. and Hunt, J.C.R., 1975: Turbulent Wind Flow Over a Low Hill,
Quart. J. Roy. Meteorol. Soc., v. 101, p. 929-55.
Lawson, R.E. Jr. and Britter.R.E., 1981: A Note on the Yaw Sensitivity of
Heated Cylindrical Sensors, J. Phys. E., Rev. Sci. Insts. (In Press).
Mage, D.T. and Noghrey, J., 1972: True Atmospheric Pollutant Levels by Use of
Transfer Function for an Analyzer System, J. Air Poll. Contr. Assoc., v. 22,
no. 2, p. 115-8.
Mason, P.J. and Sykes, R.I., 1979: Flow over an Isolated Hill of Moderate
Slope, Quart. J. Roy. Meteor. Soc., v. 105, p. 383-95.
Ogura, M., 1969: A Direct Solution of Poisson Equation by Dimension Reduction
Method, J. Meteorol. Sec. Japan, v. 47, no. 4.
Pasquill, F., 1974: Atmospheric Diffusion, 2nd Ed., Chichester, Ellis
Horwood Ltd., John Wiley and Sons, NY, NY, 429p.
128
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Pepper, D.W. and Baker, A.J., 1979: Modeling Pollutant Dispersion over Irreg-
ular Terrain with Second Moments and Cubic Splines, Proc. Fourth Symp. on
Turb., Diff. and Air Poll., Reno. NV, Am. Meteorol. Soc., Boston, MA.
Puttock, J.S. and Hunt, J.C.R., 1979: Turbulent Diffusion from Sources Near
Obstacles with Separated Wakes; Part I: An Eddy Diffusivity Model, Atmos.
Envir., v. 13, p. 1-13.
Samarskii, A.A., 1977: Theory of Finite Difference Schemes, Nauka Press,
Moscow, USSR, 656p.
Sasaki, Y., 1958: An Objective Analysis Based on the Variational Method, J.
Meteorol. Soc. Japan, v. 36, p. 77-88.
Sasaki, Y., 1970: Numerical Variational Analysis Formulated under the Cons-
traints Determined by Long Wave Equations and Low-Pass Filter, Mon. Wea. Rev.
v. 98, p. 884-98.
Sasaki, Y., 1970: Some Basic Formalisms in Numerical Variational Analysis,
Mon. Wea. Rev., v. 98, p. 875-83.
Sherman, C.A., 1978: A Mass-Consistent Model for Wind Fields over Complex
Terrain, J. Appl. Meteorol., v. 17, p. 312-9.
Snyder, W.H., 1972: Similarity Criteria for the Application of Fluid Models
to the Study of Air Pollution Meteorology, Bound. Layer Meteorol., v. 3,
no. 2, p. 113-34.
Snyder, W.H., 1979: The EPA Meteorological Wind Tunnel: Its Design, Construc-
tion, and Operating Characteristics, Envir. Prot. Agcy. Rpt. No. EPA-600/4-79-
051, Res. Tri. Pk., NC, 78p.
Snyder, W.H., 1981: Guideline for Fluid Modeling of Atmospheric Diffusion,
Envir. Prot. Agcy. Rpt. No. EPA-600/8-81-009, Res. Tri. Pk., NC, 200p.
Snyder, W.H., Britter, R.E. and Hunt, J.C.R., 1979: A Fluid Modeling Study
of the Flow Structure and Plume Impingement on a Three-Dimensional Hill in
Stably Stratified Flow, Proc. Fifth Int. Conf. on Wind Engr. (J.E. Cermak,
ed.), v. 1, p. 319-29, Pergamon Press, NY, NY.
Taylor, P.O. and Gent, P.R., 1974: A Model of Atmospheric Boundary Layer Flow
above an Isolated Two-dimensional Hill: An Example of Flow above Gentle Topo-
graphy, Bound.-Layer Meteorol., v. 7, p. 349-62.
Turner, D.B., 1970: Workbook of Atmospheric Dispersion Estimates, Office
of Air Programs, Pub. No. AP-26, U.S. Envir. Prot. Agcy., Res. Tri. Pk., NC.
Wilson, D.J., Winkel, G. and Neiman, 0., 1979: Reynolds Number Effects on
Flow Recirculation behind Two-dimensional Obstacles in a Turbulent Boundary
Layer, Proc. Fifth Int. Conf. on Wind Engr. (J.E. Cermak, ed.), v. 2, p. 965-
74, Pergamon Press, NY, NY.
129
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Zoric, D.L. and Sandborn, V.A., 1972: Similarity of Large Reynolds Number
Boundary Layers, Boundary-Layer Meteorol., v. 2, p. 326-33.
Zrazhevsky, I.M., Doroshenko, V.N. and Chepik, N.G., 1968: Investigation of
the Effect of Various Types of Relief on the Characteristics of an Air Stream
in a Wind Tunnel, Atmos. Diff. and Air Poll., Trudy 6GO, no. 207, Hydromet.
Press, Leningrad, USSR.
Zrazhevsky, I.M. and Klingo, V.V., 1971: Modeling of Atmospheric Turbulent
Movements over an Inhomogeneous Surface, Atmos. Diff. and Air Poll., Trudy
GGO, no. 254, p. 39-56, Hydromet. Press, Leningrad, USSR.
130
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TECHNICAL REPORT DATA
(Please read Instructions on the reverte btfort completing!
1 REPORT NO
EPA-600/4-81-067
3. RECIPIENT'S ACCESSION-NO.
4. TITLE ANDSUBTITLL
FLOW AND DISPERSION OF POLLUTANTS OVER TWO-DIMENSIONAL
HILLS
Summary Report on Joint Soviet-American Study
6. REPORT DATE
August 1981
6. PERFORMING ORGANIZATION CODE
AUTHORISI
Leon H. Khurshudyan1, William H. Snyder2, and
Igor V. Nekrasov3
|B. PERFORMING ORGANIZATION REPORT NO
Fluid Modeling Report No. 11
PERFORMING ORGANIZATION NAME AND ADDRESS
Environmental Sciences Research Laboratory
Office of Research and Development
U.S. Environmental Protection Acency
Research Trianole Park. NC 27711
10. PROGRAM ELEMENT NO
ADTA1D/03-1313 (FY-81)
11. CONTRACT/GRANT NO
12. SPONSORING AGENCY NAME AND ADDRESS
Environmental Sciences Research Laboratory
Office of Research and Development
U.S. Environmental Protection Agency
Triancle Park. NC 27711
- RTP, NC
13. TYPE OF REPORT AND PERIOD COVERED
In-house
14. SPONSORING AGENCY CODE
EPA/6CO/09
IS. SUPPLEMENTARY NOTES
, *Main Geophysical Observatory, Leningrad, U.S.?.P..
Oceanic and Atmospheric Admin., U.S.Dept. of Commerce.
20n assignment from National
3Moscow State Univ..Moscow,U.S.S.
16. ABSTRACT
Wind tunnel experiments and theoretical 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. Measurements were made of mean and
turbulent velocity fields upwind, over and downwind each of the hills.
Concentration 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 developed 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 slope, because of flow separation
from the lee side of the steepest hill and high turbulence and much-reduced
mean velocity downwind of the hill of medium slope.
7.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.lDENTIFIERS/OPEN ENDED TERMS C. COS AT I Field/Group
8. DISTRIBUTION STATEMENT
RELEASE TO PUBLIC
19. SECURITY CLASS (This Report)
UNCLASSIFIED
21. NO. Of PAGES
143
2O. SECURITY CLASS (This paft)
UNCLASSIFIED
22. PRICE
tPA Form 2220-1 (»-73)
131
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