United States EPA-600/7-82-037C
Environmental Protection
Agency May 1982
&EPA Research and
Development
VERIFICATDN AND TRANSFER OF
THERMAL POLLUTJDN MODEL
Volume III Verification of
Three-dimensional Rigid-lid Model
Prepared for
Office of Water and Waste Management
EPA Regions 1-10
Prepared by
Industrial Environmental Research
Laboratory
Research Triangle Park NC 27711
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RESEARCH REPORTING SERIES
Research reports of the Office of Research and Development, U.S. Environmental
Protection Agency, have been grouped into nine series. These nine broad cate-
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The nine series are:
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5. Socioeconomic Environmental Studies
6. Scientific and Technical Assessment Reports (STAR)
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RESEARCH AND DEVELOPMENT series. Reports in this series result from the
effort funded under the 17-agency Federal Energy/Environment Research and
Development Program. These studies relate to EPA's mission to protect the public
health and welfare from adverse effects of pollutants associated with energy sys-
tems. The goal of the Program is to assure the rapid development of domestic
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essary environmental data and control technology. Investigations include analy-
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This document is available to the public through the National Technical Informa-
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EPA-600/7-82-037c
May 1982
VERIFICATION AND TRANSFER
OF THERMAL POLLUTION MODEL
Volume III: VERIFICATION OF THREE-DIMENSIONAL
RIGID-LID MODEL
By
Samuel S. Lee, Subrata Sengupta,
Emmanuel V. Nwadike and Sumon K. Sinha
Department of Mechanical Engineering
University of Miami
Coral Gables, Florida 33124
NASA Contract No. NAS 10-9410
NASA Project Manager: Roy A. Bland
National Aeronautics and Space Administration
Kennedy Space Center
Kennedy Space Center, Florida 32899
EPA Interagency Agreement No. 78-DX-0166
EPA Project Officer: Theodore G. Brna
Industrial Environmental Research Laboratory
Office of Environmental Engineering and Technology
Research Triangle Park, North Carolina 27711
Prepared for:
U. S. Environmental Protection Agency
Office of Research and Development
Washington, D. C. 20460
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PREFACE
The Thermal Pollution Croup at the University of Miami has been
developing three-dimensional mathematical models for predicting the
hydrothermal behaviors of bodies of water subjected to a heated effluent.
Generally speaking, these models can be classified in two categories,
namely, the free surface models which take into account the variation
in water surface elevations and rigid-lid models which treat the water
surface as flat.
To enable the prospective user to use these models as accurate
predictive tools, particularly to assess the environmental impact in the
case of cooling lakes, they have to be calibrated and verified at a num-
ber of sites. The present volume describes the application of the rigid-
lid model developed by this group to a rather complicated site, namely,
Lake Keowee in South Carolina. Lake Keowee is rather unique since
it is used by a Nuclear Power Plant as a cooling lake as weil as two
other hydroelectric stations which use it as lower and upper ponds.
This is the final verification of these models concluding a series of
such verifications made possible by funding and technical assistance
provided by the National Aeronautics and Space Administration (NASA)
and the Environmental Protection Agency (EPA).
This model will eventually be made available to all prospective
users by NASA and EPA. The present volume together with the
"Three Dimensional Rigid-Lid Model User's Manual" is intended for
assistina such future users.
u
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ABSTRACT
The Rigid Lid was developed by the University of Miami, Thermal
Pollution Group, to predict three-dimensional temperature and velocity
distributions in lakes. This model was verified at various sites (Lake
Belews, Biscayne Bay, etc.) and the verification at Lake Keowee was
the last of these series of verification runs.
The verification at Lake Keowee included the following phases of
work.
1. Selecting the domain of interest, grid systems and comparing
the preliminary results with archival data.
2. Obtaining actual ground truth and infrared scanner data both for
summer and winter.
3. Using the model to predict the measured data for the above periods
and comparing the predicted results with the actual data.
The model results have compared well with measured data. Thus,
thejnodel can be used as an effective predictive tool for future sites.
in
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CONTENTS
Preface jj
Abstract jji
Figures v
Tables vili
Symbols ix
Acknowledgments x
1. I ntroduction 1
Background 1
Objectives of present work 1
Description of Lake Keowee site 2
2. Conclusions 3
3. Recommendations n
H. Mathematical formulation and Mode! Description 5
Choice of model 5
Description of model 5
Governing equations 6
Initial and boundary conditions 9
Spatial difference schemes 11
Stability 12
Marker matrices 12
5. Application to Lake Keowee 14
I ntroduction 14
Choice of domain and grid system 14
Summary of data 15
Calculation of input 18
6. Results and Discussions 23
References 29
IV
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FIGURES
Number Page
1 Lake Keowee 30
2 Grid system for the rigid-lid model 31
3 MAR markers matrix (main grid points) 32
4 MRH marker matrix (half grid points) 33
5 Map of area of interest 34
6 Measured isotherms (archival 9/10/75) 35
7 August ground truth data (measuring stations) 36
8 Flight plans for 1R data (August and February missions) . 37
9 Keowee hydro discharge data (August 24, 1978) 38
10 Keowee hydro discharge data (August 25, 1978) 39
11 Jocassee-pumped storage station discharge data
(August 24, 1978) 40
12 Jocassee-pumped storage station discharge data
(August 25, 1978) 41
13 Keowee February 1979 showing stations 42
14 Jocassee-pumped storage station discharge data
(February 27, 1979) 43
15 Jocassee-pumped storage station discharge data
(February 28, 1979) 44
16 Keowee hydro discharge (February 27, 1979) 45
17 Keowee hydro discharge (February 28, 1979) 46
18 Velocities at K = 1 after 8.64 hrs. (L001) 47
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FIGURES
Number Page
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
Velocities at I - 11 after 21.6 hrs. (L001)
Isotherms measured, and. predicted after 8. 64 hrs. (L001) .
Velocities at K - 1 after 8.64 hrs. (L002)
Velocities at 1 =11 after 8. 64 hrs. (L002)
Isotherms measured and predicted after 8.64 hrs. (L002) .
Velocities at K = 1 after 8.00 hrs. (LOOS)
Velocities at J - 7 after 4.32 hrs. (L003)
Isotherms measured and predicted after 8.64 hrs. (L003) .
Velocities at K - 1 after 4.32 hrs. (LOOS)
Velocities at J = 7 after 32. 4 hrs. (LOOS)
Isotherms measured and predicted after 32. 40 hrs. (LOOS)
Vertical temperature profiles (LOOS)
Comparison of surface velocities (I = 11 , J = 7, K=1) ..
Comparison of surface velocities (I = 11 , J = 2, K = 1) ..
IR Data corresponding to 1002 hrs., August 24, 1978 ...
Surface isotherms 1002 hrs., Auqust 24, 1978
( 30. 5, 30. 0, 29. 5°C)
Surface isotherms 1002 hrs., August 24, 1978
(29.5, 29.3, 29. 1°C)
IR data corresponding to 0903-0953 hrs., Auaust 25, 1978. •
Surface isotherms 33.23 hrs., Auqust 25, 1978
(30.0, 29. 5°C) 7
Surface isotherms 33.2 hrs., August 257 1978
(29.90, 29.70, 29. 60°C)
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
VI
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FIGURES
Number
40
41
42
43
44
Velocities at K = 1, 10.07 hrs., August 25, I
Velocities at K = 1, 34.24 hrs., August 25
IR data corresponding to 1648-1651 hrs.,
February 27 1 979
Surface isotherms 17.12 hrs., February 27,
(13.0, 12.75,12.5,12.0, 11.5, 11.0°C)
Surface isotherms 17.12 hrs., February 27,
(13.75. 13.0, 12.5. 12. 0°C)
978".
1978 ....
1979
1979
69
. . . 70
. . 71
72
73
45 1R data corresponding to 0948-0957 hrs.,
74
46
47
48
Surface isotherms 3J
(13.0 12. 5°C) ....
Velocities at K = 1,
Velocities at K = 1,
'4. 2 hrs., February 28, 1979
17.12 hrs., February 27, 1979
34. 24 hrs.. February 28. 1979
75
76
77
vii
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TABLES
Number
1 Monthly Gross Thermal Capacity Factors of
Oconee Nuclear Station 78
2 Operating Conditions of Oconee Nuclear
Power Plant (September 10, 1975) 79
3 Input Data for 3-D Model (Lake Keowee) 80
4 Volume and Area Data for Lake Keowee 81
5 Inflows and Outflows to Lake Keowee, August 24, 1978 .. 82
6 Inflows and Outflows to Lake Koewee, August 25, 1978 .. 83
7 Meteorological Data for Lake Keowee, August 24, 1978 ... 84
8 Meteorological Data for Lake Keowee, August 25, 1978 ... 85
9 Inflows and Outflows to Lake Keowee, February 27, 1979 . 86
10 Inflows and Outflows to Lake Keowee, February 28, 1979 . 87
11 Meteorological Data for Lake Keowee, February 27, 1979 .. 88
12 Meteorological Data for Lake Keowee, February 28, 1979 .. 89
13 Summary of Runs for Lake Keowee 90
14 Root Mean Square Difference Between IR and Predicted
Temperatures 91
viii
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SYMBOLS
AV
A
ref
A*
BV
BH
B
ref
"4
Eu
f
g
h
H
1
J
K
f*
P
Pe
Q
Re
Ri
T
T
ref
Horizontal kinematic eddy
viscosity
Vertical kinematic eddy
viscosity
Reference kinematic eddy
viscosity
AV/A
Horizontal eddy thermal
diffusivity
Vertical eddy thermal diffu-
sivity
Reference eddy thermal
diffusivity
BV/B f
Specific heat at constant
pressure
Euier number
Coriolis parameter
Acceleration due to gravity
Depth relative to the mean
water level
Reference depth
Grid index in x-direction or
a direction
Grid index in y-direction or
8 direction
Grid index in z-direction or
Y direction
Surface heat transfer coefficient
Horizontal length scale
Pressure
Surface pressure
Turbulent Prandtl number,
Pelffet number
Heat sources or sinks
Reynolds number (turbulent)
Richardson number
Temperature
Reference temperature
Equilibrium temperature
Surface temperature
t Time
t , Reference time
u Velocity in x-direction
v Velocity in y-direction
w Velocity in z-direction
x Horizontal coordinate
y Horizontal coordinate
z Vertical coordinate
Greek Letters
Horizontal coordinate in
stretched system, = x
Horizontal coordinate in
stretched system, = y
Vertical coordinate in
stretched system
Constant in vertical diffu-
sivity equation, or vertical
coordinate in stretched
system, = Z/H
Transformed vertical velocity
Density
Surface shear stress in
x-direction
Surface shear stress in
y-direction
a
8
Y
a
Q
P
Txz
V
IX
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ACKNOWLEDGMENTS
This work was supported by a contract from the National Aeronautics
and Space Administration (NASA-KSC) and the Environmental Protection
Agency (EPA-RTP).
The authors express their sincere gratitude for the technical and
managerial support of Mr. Roy A. Bland, the NASA-KSC project manager
of this contract, and the NASA-KSC remote sensing group. Special thanks
are also due to Dr. Theodore G. Brna, the EPA-RTP project manager, for
his guidance and support of the experiments, and to Mr. S. B. Hager,
Chief Engineer, Civil-Environmental Division, and Mr. William J. McCabe,
Assistant Design Engineer, both from the Duke Power Company, Charlotte,
North Carolina, and their data collection group for data acquisition. The
support of Mr. Charles H. Kaplan of EPA was extremely helpful in the
planning and reviewing of this project.
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SECTION 1
INTRODUCTION
BACKGROUND
Understanding the environmental impact of hot water discharge from
the condenser of a steam power plant is of considerable importance in
helping to preserve aquatic life and also the overall efficiency of the
power plant. In recent years, with the improvement of computing facili-
ties, a number of different types of mathematical models have been de-
veloped to predict such effects. These models, if properly calibrated,
are extremely useful in determining the complete environmental impact
arising due to normal as well as abnormal operating conditions, which
may be difficult to realise experimentally. This is particularly important
with respect to estimating these adverse effects during the planning
stages, thus, helping to minimize them in the final construction.
The mathematical models solve the basic fluid flow and energy
transfer equations subject to certain simplifications and assumptions.
These may be used to determine the long term heat budget for the cool-
ing lake as well as determine the detailed velocity and temperature dis-
tributions within it. The accuracy of predictions using these models is
extremely important and the only way to verify this is to apply these models
to certain known sites and compare the predicted values with actual
measured quantities. Measurements may be obtained by measuring the
water velocities and temperatures with anemometers and thermometers
as well as by infrared remote sensing photoyraphy. Each of these
techniques has its own advantages and disadvantages. To get a proper
representative data base, all of these have to be used simultaneously.
Other factors which affect the water conditions are the meteorological
conditions, viz. wind speed, solar radiation, air temperature and humidity.
OBJECTIVES OF PRESENT WORK
For the past several years the thermal pollution group at the Univer-
sity of Miami has developed a number of mathematical models for both long
and short term simulation. The model considered here is a three-dimen-
sional rigid-lid model designed for short time prediction of detailed three-
dimensional velocity and temperature profiles in the region of the thermal
plume. This model has been applied in the past years to several sites,
namely, Lake Belews (Lee, Sengupta, Mathavan, 1977). The predictions of the
model at the above sites compared reasonably well with measured data.
The results of these runs have been published by/ the University of Miami in
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earlier volumes in cooperation with NASA.
The success of this model at the above sites led to the belief that
this model could be used in future predictions. It was mainly for this
reason that a site was chosen which was quite complex in nature and
which would bring out the prediction capabilities and limitations of the
model. This would also be of great help to future users of the model
in order to obtain a proper interpretation of the results when used as
a predictive tool.
Lake Keowee in South Carolina provides such a site; hence it was
chosen for the final verification of the model. A description of the site
is given in the following section.
DESCRIPTION OF LAKE KEOWEE SITE
Lake Keowee is located on the north of the state of South Carolina
about 40 km west of Greenville. It was made Irom 1968 through 1971 by
damming the Little River and Keowee River. At present, it constitutes
Duke Power Company's Keowee Toxaway Complex.
The lake has two arms connected by a canal (maximum depth 30.5 m).
There are three power plants on it, namely, the Oconee Nuclear Station,
Keowee Hydro Station and Jocassee-Pumped Storage Station. The Oconee
Nuclear Station is a three-unit steam-electric station with an installed
capacity of generating 2580 MW. The Oconee Nuclear Station draws in
condenser cooling water from the lower arm of Lake Keowee and discharges
the heated effluent to the upper arm of the lake. The intake structure
for the condenser cooling water allows water from 20 to 27 m depth (full
pond) to pass through. The discharge structure has openings from 9 to
12 meters deep through which the CCW returns directly to the lower arm
of Lake Keowee.
Lake Jocassee is located north of Lake Keowee and is used as a
reservoir for Jocassee-pumped storage station. The upper arm of Lake
Keowee also serves as the lower pond for Jocassee-pumped storage sta-
tion. The Jocassee Station has reversible turbines with a maximum gene-
rating flow (into Lake Keowee) of about 820 m3/sec and a maximum pump-
ing flow of about 775 m3/sec; the net flow into Lake Keowee from Lake
Jocassee is about 15.5 m3/sec.
Lake Keowee has a full pond elevation of 243. 8 m above mean sea
level. At full pond it has a volume of approximately 1.18 x 10 m3, an
area of 74 km2, a mean depth of 15. 8 m and a shoreline of about 480 km.
The outflow from Lake Keowee is through Keowee hydro station. The
flow through Keowee hydro station varies from 1.4 m3./sec (leakage) to
560 m3/sec (during peak load operation). The maximum draw down of
the lake is 7. 6 m.
A map of Lake Keowee is shown in Figure 1. The above data was
obtained from Duke Power Company 1976.
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SECTION 2
CONCLUSIONS
The main objective of this work was to prepare a mathematical
model package to assess environmental impact due to a heated effluent.
Hence, the final test for the mode! was at Lake Keowee. The reasonably
good agreement of the predictions with data was shown in the last sec-
tion. The shape of the plume, as predicted by the model resembles
closely but does not correspond exactly to the plumes obtained from the
IR scanner photographs. An important comparison in this case is the
area covered by each isotherm which gives an indication of the spread
of the heated effluent. This area is approximately the same in the mea-
sured and predicted cases for both summer and winter runs. Another way
the accuracy of the model was determined was by the root mean square
deviations of the temperature between predicted and measured values
over the entire domain. These deviations are shown in Table 14.
The accuracy of the IR scanner isotherms is about 0. 5°C (from the
sensitivity of the process). The accuracy of the position of the isotherms
is within ±0. 5 x (grid space) in this case resulting from the lateral dis-
tortion in the Digicolor map and the process of transfer!ng this on to
the computational grid for the purpose of comparison.
Based on the above results, it may be concluded that the predictions
made by the model are reasonable beyond doubt when applied to cooling
lakes or a similar site. Hence, the model may be used as a predictive
tool for obtaining three-dimensional temperature and velocity profiles in
the vicinity of a thermal effluent discharge, and the results may be used
in evaluating the performance of existing or future thermal power plants.
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SECTION 3
RECOMMENDATIONS
Various numerical models have been developed to study the effects
of heated discharge and meteorological conditions on bodies of water.
Most of these models are one or two dimensional. These models have a
high computational speed but only give horizontally or vertically averaged
values of temperatures.
Three-dimensional models, however, have a much finer resolution
but they consume larger computer time. The three-dimensional rigid-
lid model can be used to obtain detailed temperature and velocity distri-
butions in a domain where surface gravity waves are small compared to
the depth of the domain. This model, as compared to free-surface mo-
dels, runs faster since surface gravity waves are eliminated by this
rigid-lid assumption.
A proper method of using this mode! would be to run a one-dimen-
sional model initially to obtain a rough picture of the temperatures and
then using this model to obtain a better resolution, the 1-D results being
used as ambient conditions.
The following improvements have been suggested for the model.
1. Since ail natural flows are turbulent, proper turbulent closures are
needed to make the model meaningful. At present, the simplest
possible closures, namely constant eddy viscosities and eddy diffu-
sivities, have been used. However, better results may be obtained
by using a higher order closure.
2. At present, the model uses uniform horizontal grids and stretched
vertical grids. Nonuniform horizontal grids could be introduced for
better resolution near the boundaries.
3. The program has been written to be run as a batch-job on the com-
puter. It could be made interactive so as to enable the user to run
it on a terminal. However, this would require some modifications in
order to reduce the storage space.
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SECTION 4
MATHEMATICAL FORMULATION AND MODEL DESCRIPTION
CHOICE OF MODEL
Two three-dimensional models have been developed by the thermal
pollution group at the University of Miami. The first one is a free-sur-
face model, which takes into account the variation in surface heights of
a basin. The second one is the rigid-lid model which assumes the verti-
cal velocities on the water surface as zero. These models have been de-
scribed in previous publications of this group. The choice of a particular
model for simulating flows depends on the nature of the site.
Lake Keowee is a relatively small, closed basin with maximum depth
of 30 m. The small horizontal numerical grid dimensions demand extremely
small integration time steps to satisfy the Courant-Lewy-Fredrichs condi-
tions inherent in free-surface formulations. Since the surface waves are
small compared to the depth, i.e. h/H«1, a rigid-lid formulation is suit-
able. This rigid-lid model allows acceptable accuracy with acceptable
time step size since the C.L.F. criterion is eliminated. This makes the
rigid-lid model a rather obvious choice.
The rigid-lid model has been applied previously to Biscayne Bay and
Lake Belews sites with reasonable accuracy, as mentioned in the previous
section. This led to the belief that it would be ideally suited for the
Keowee site.
DESCRIPTION OF THE MODEL
(Portions of the following section have been published earlier by
this group.)
The rigid-lid model has the following capabilities:
1. Predict the wind-driven circulation.
2. Predict the circulation caused by inflows and outflows to the domain.
3. Predict the thermal effects in the domain.
4. Combine the aforementioned processes.
The model solves equations for fluid flow (momentum and continuity)
-------
and heat transfer together with the equation of state in a three-dimen-
sional domain. Since most geostrophic flows are turbulent, the resulting
Reynolds stress terms in the governing equations are replaced by eddy
transport coefficients. The fluid is considered to be an incompressible
Boussinesq fluid and the hydrostatic assumption has been made.
The rigid-lid assumption imposes a zero vertical velocity condition
on the surface without affecting the horizontal velocities. This causes
the surface pressure to be different from atmospheric which under special
conditions may be translated into surface gravity wave heights if no lid
is present. This assumption distorts transient time scales but does not
affect circulation patterns as has been demonstrated by Berdahl (1970),
Crowley (1969, 1970), Hag and Lick (1973) and Young, Liggett and
Gallagher (1976). Since surface gravity waves no longer have to be
reproduced, computer time is saved considerably and this assumption is
quite adequate for cooling lake studies where surface waves are not
large and do not change rapidly.
To convert regions having irregular bottom topography to constant
depth regions for computation stability a vertical stretching, suggested
by Freeman et al. (1972), has been used.
GOVERNING EQUATIONS
The vertical stretching used in the rigid-lid model, originally
adopted by Sengupta and Lick (1974), is of the form
h(x,y)
This enables the same number of grid points to be used all over
the domain without using variable grid sizes. The resulting nondimen-
sional governing equations in the new (a, B/Y) coordinate system instead
of (x,y,z) are
Continuity Equation:
3(hu) t 3(hv) t h3Q _ Q
Momentum Equation:
3{hu) + 3(huu) + 3(huv) + h3(^u) _ h_
3t 3a 30 3y RpV
-------
TK £ (Av IT' (por the 'a'direction>
Hydrostatic Equation:
3P
Energy Equation:
8Y-Eu(1*p)h
8(hT) 3(huT) 3(hvT) .3(nT)
3t 3ct 98 3y
_L i_ n
P 3a"3a P 3 6
e e
Equation of State:
0 = 1.029431 - 0.000020 f - 0.0000048 f2
where J3 is in gm/cc and T is in °C
and _ t 3 .n ~ 3 n ^ p-^
where ~ _ 3 y
and w(2=0) = 0 (rigid lid)
where u = u/Uref, v = v/Uref/ w = w/£Uref
t = t/tref, x = x/L, y = y/L, 2 = Z/H
T " fref
e = H/L, P = P/pref U*rQf. T = T ref
ref
~pref
p=—^, A* = A,/A ,, A* A /A
H P r H h ref v = A /A
ref v v r
ref
B* = B../B ,, B* = B /B r
H H ref v v ref
-------
= UUref
Quantities with subscript 'ref are reference quantities; H and L are
vertical and horizontal length scales. The variables with wavy lines on
top are dimensional quantities.
U ,L U , A ,
R - ref R - ref p _ ref
e " Aref B " fL r ' Bref
D-D O -
Pe - V Pr -
If Prandtl number is equal to 1, then A , = B c,
ret ret
AH and A are the eddy viscosities in horizontal and vertical directions.
B,, and B are the eddy diffusivities in horizontal and vertical directions.
To obtain a predictive equation for pressure, the horizontal momentum
equations are integrated from Z=0 to Z=h, where h is the nondimensional
depth h/H. The integrated equations are then differentiated with respect
to a and 3 summed.
The Poisson equation for surface pressure becomes:
32P
+ TP1 • K f^Ax, * Ax2 + cx - V
+ c !-s(-A -A +C -Y)
h 36 Y, Y2 Y P
. _ ,
Rl3a9a 3833 3t
The last term is the Hirt and Harlow (1964) correction term which accounts
for nonzero vertical velocities at the rigid lid. The variables (B , B ,
and A , A etc.) are given below: x v
A
X1
8
-------
_ h ,1
x ~ F
A = ^- /' vdy
R~ o '
r _
Cx - FT
6
XP •
Ay,
A = -
'2 B
r - ' ,1 ,3 ,^3u^ 5/1, '"i . 1 '
' 1 * hle' + F h
Yp '
Bx • E
The set of equations (24-30) together with appropriate boundary
conditions constitute the mathematical model. The mode! has been de-
scribed in earlier publications by this group (Lee and Sengupta, 1976).
INITIAL AND BOUNDARY CONDITIONS
The nature of the equations requires initial and boundary conditions
to be specified. As the initial condition, the velocities, temperatures
and densities are specified throughout the domain. Boundary conditions
are specified at the air-water interface, geographical boundaries of the
domain, the bottom of the basin and the efflux points. At the air-water
interface a wind stress and a heat transfer coefficient are specified.
The conditions on the lateral walls are no-slip and no- normal velocity
for the momentum equations. These walls are assumed to be adiabatic.
At the floor of the basin, the conditions of no-slip and no-normal velo-
cities are applicable. The energy equation has a heat flux boundary
condition.
At points of efflux open-boundary conditions are specified. If the
flows are known at the points of efflux, the flow velocities are specified.
Usually, the temperature is known only at the point where the heated
discharge (from the power plant) enters the domain. At points where
the temperatures are not explicitly known, open-boundary condition (i.e.
zero gradient condition) is specified. The same holds true if the velo-
cities are not explicitly known (e.g. the connecting canal between the
-------
two arms of Lake Koewee).
Hence, the boundary conditions are:
At the surface
y = 0
Q = 0 (Rigid Lid)
3u , hH
hHK
\ t-r - T \
JUE V
3j/ _ , hH . ,
~
where T and T are wind stresses in the x and y-directions respectively.
ZX Z y
Tp is the equilibrium temperature.
T is the water surface temperature.
K is the surface heat transfer coefficient.
T and T are calculated from the wind velocity usinq Wilson
zx zy curve (B. W. Wilson, 1960).
K and T are calculated as follows:
s e
K = 4. 5 + 0.05 T + BF(w) + 0. 47(w)
where T is in °C.
F(w) = 9.2 + 0.46W2 (wm~2mmHg~1).
B = 0.35 + 0.015 T + 0. 0012 T 2(mmHg/°C).
m m
T . = Dewpoint temperature (°C).
TE=Td+Hs'Ks-
H = Surface solar radiation (w/m2)
10
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At the bottom of the basin
Y = 1
fi = 0
u = 0
v = 0
3T = 0
ay
On lateral wails
u = 0
v = 0
a = o
3T _ 3T Y 3h 3T _
3x ~3a~h3a3Y
3T _ 3T Y 3h 3T _ Q
3y "33 ~h 3g 3y
SPATIAL DIFFERENCE SCHEMES
The numerical solution of the momentum and energy equations are
explicit. The values of velocities and temperatures at a future time are
determined completely using the values at the present and previous
time steps. Finite difference forward time and central space difference
schemes are used. Diffusion terms are written using a Dufort-Frankel
finite difference scheme to relax the diffusive stability criterion. The
convective stability criterion, however, is not affected.
A horizontal staggering is used in the computational grids. Hori-
zontal velocities and temperatures are calculated at the main-grid points
while vertical velocities and pressures are calculated at half-grid points
The predictive Poisson equations for calculating rigid-lid pressures
is finite differenced using a five-point scheme. This is solved by
successive over relaxation (Liebmann Method). Terms on the right hand
side of the pressure equation are obtained by integrating terms in the
horizontal momentum equations over the depth using the trapezoidal rule.
At the boundaries, single-sided schemes are used since the boundary
points do not have two adjacent points. A curve is fitted through the
11
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two most adjacent points towards the Interior of the domain. The values
of the variables, where they are not defined, are obtained by averaging
the values at four points around the point where the values are defined".
STABILITY
It is not possible to make a strict stability analysis of the system
of equations under consideration. It is customary, however, to take
advantage of the stability analysis for the one-dimensional Burger's
equation since this contains an unsteady term, a convective term and a
diffusion term.
In the present case these criteria can be written as follows for the
choice of the time step At
Convective r Ax
At < -g-
where U is the maximum horizontal velocity in the domain.
Diffussive ,r . (Ax)2
2AH
MARKER MATRICES
Since natural bodies of water have irregular boundaries, the physical
boundaries have to be approximated in a rectangular coordinate system
using marker matrices (Fortran variable MAR for the full grids and MRH
for the half grids). The convention used is as follows:
MAR = 0, point outside the region of interest (i.e., on dry land)
In approximating such a boundary using a rectangular grid system
only a portion of the resulting grid falls within the water. To prevent
computations to be carried out on dry land markers have to be used to
distinguish between points lying within and outside the region of in-
terests. Such markers have to be used both for the main and half-grid
points. Fortran symbols used are MAR for the main grid and MRH for
the half-grid system. The convention used is as follows:
MAR = 0, point outside the region of interest (i.e., on dry land).
MAR = 1, point on far y-boundary.
MAR = 2, point on near y-boundary.
MAR = 3, point on near x-boundary.
MAR = H, point on far x-boundary.
12
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MAR = 5, outside corner, on near x-boundary and far y-boundary.
MAR = 6, inside corner on far x-boundary and far y-boundary.
MAR = 7, outside corner on near x-boundary and near y-boundary.
MAR = 8, inside corner on near x-boundary and near y-boundary.
MAR = 9, outside corner on far x-boundary and near y-boundary.
MAR = 10, outside corner on far x-boundary and far y-boundary.
MAR = 11, interior points (within region of interest).
Similarly for the half-grid points.
MRH = 1, corner on far x-boundary and far y-boundary.
MRH = 2, points on near y-boundary.
MRH = 3, points on near x-boundary.
MRH = 4, corner at near x- and near y-boundaries.
MRH = 6, far corner on x-axis.
MRH - 7, corner at far x- and y-boundaries.
MRH = 9, interior grid points.
13
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SECTION 5
APPLICATION TO LAKE KEOWEE
INTRODUCTION
The three-dimensional rigid-lid model described in Chapter II has
been applied to Lake Keowee, South Carolina, to predict the wind-driven
circulation, circulation caused by inflows and outflows, and the thermal
dynamics of a region of this lake. This region includes the buoyant
plume, the Keowee hydro dam, the connecting canal and an open-boun-
dary where the effects of inflow and outflow to Jocassee-pumped storage
station are felt.
Lake Keowee is a warm monomictic lake having one circulation period
during the year, beginning in fall, and is thermally stratified during the
summer. During the circulation period, the water mass is vertically
mixed. This type of lake can also be termed holomictic (Hutchinson,
1957). Lake Keowee could also be classified as a subtropical lake as
it exhibits thermal stratification, a period of total circulation preceded
by the fall overturn, and surface temperatures above 4°C. The highest
surface temperatures typically occurred in July and August and ranged
from approximately 27 to 29°C. During the periods from November through
February the lake was isothermal or nearly so. It can be concluded from
the above that a series of meteorological events primarily govern Lake
Keowee's thermal characteristic. However, as will be shown below, the
near field region which makes up the region of interest in this present
study, is very strongly affected by the buoyant plume, inflow and out-
flow and the Jocassee-pumped storage station.
CHOICE OF DOMAIN AND GRID SYSTEM
The region of interest has already been mentioned in the last sec-
tion. Here, an attempt will be made to justify this choice and then a
description of the grid system will be given.
The study and prediction of the thermal impact on the hydro-dyna-
mics of Lake Keowee has been done in two main sections:
1. Using a 1-D continuous temperature profile prediction model over
the period 1971-1979, the area of interest includes the two main
arms of Lake Keowee and the connecting canal. The application of
this model has been published by the thermal pollution group of the
University of Miami (Sengupta et al 1980).
-------
2. Using the 3-D rigid-lid model, which is described in this report.
The division has been necessary since the 1-D model predicts
temperature profiles continuously over a period of time (several years
if required); it can be used to predict the initial conditions required to
run the 3-D model. The 3-D model, on the other hand, has better
resolution and is therefore used for predicting the near-field thermal
impact on the lake. This near-field area of interest is shown in Figure
5. In selecting this area some preliminary runs were made. These are
described later.
The region of interest is divided into a square grid as shown in
Figure 5. The I and J axes (corresponding to u and v-velocity axes)
are numbered as shown in the above figure. For the top 'open boundary1,
'J1 increases from 7 to 20. The left side boundary shown M1 increasing
from 1 to 17; the right side boundary shows 'I1 increasing from 1 to 16,
and finally, the bottom boundary shows 'J1 increasing from 1 to 18. The
orientation of these boundaries with the north-south direction is also
shown in this figure. The squares are (152.4 x 152.4) square meters.
Arrows indicate directions of flow into or out of domain.
SUMMARY OF DATA
For the purposes of calibrating and verifying the model, an archival
data base was established and two remote sensing and field data collection
missions (summer and winter) were undertaken.
Archival Data Base
The archival data base are summarized in Figure 6 and Tables 1
through 4. These figures were taken from Duke Power Company (1976).
Figure 6 shows the measured surface isotherms for September 10, 1975.
This figure constitutes the data base on which the comparisons for the
preliminary and archival runs are based. The runs are described below.
Table 1 shows the monthly gross thermal capacity factors for Oconee
Nuclear Station (1973-1977). Table 2 is a summary of Oconee Nuclear
Power Plant for September 10, 1975. Table 3 shows the input data
used for the preliminary and archival runs. The data include the flow-
rate, inlet temperature, discharge temperature and velocity, ambient
temperature, depth at discharge, discharge width, air temperature,
wind speeds and the vertical and horizontal eddy diffusivities. Table 4
is a summary of the volume and area data for Lake Keowee.
August 1978 Data
To obtain an understanding of seasonal behavior of Lake Keowee,
data was gathered both in summer and winter. This data was used to
verify temperatures predicted by the model. Two extreme weather
conditions were selected with the idea that if the mode! predictions were
accurate for these conditions it would be so for other intermediate con-
15
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ditions (viz., spring or fall).
In spite of the fact that the model was used for predictions in the
vicinity of the thermal plume, temperature and velocity readings were
taken for the entire lake. This was done in order to ensure complete-
ness of the data and also to check the choice of the domain of interest
within the lake.
Summer data missions were carried out during the period of August
24 and 25, 1 978. The data collection team consisted of representatives
from NASA, EPA, University of Miami and Duke Power Company. Three
boats provided by Duke Power Company were used in the collection of
ground truth data. The data collection stations are shown in Figure 7.
This included measurements of water temperatures at various depths
(from the surface to about 30 m) using YSI type thermistors and velocity
measurements using an Endeco Type 110 current meter. The thermistors
were calibrated before each set of readings using a mercury thermometer.
At each measuring station the boat was anchored and the thermistors
and velocity meters were lowered by cables. The cables were marked
thus indicating the depth beiow the water surface where readings were
taken. The current meter indicated both the magnitude and direction
of the horizontal component of the water velocity. The main problem
encountered here was that most of the velocities were very small and
close to the threshold of the instrument. Hence, drogues were used to
determine average surface velocities.
While the ground truth data was being collected, overflights were
made by NASA aircraft to obtain synoptic IR scanner data. The aircraft,
a twin engined (Beechcraft) (NASA-6), was specially equipped for this
purpose. Flights were made at altitudes of 1000, 2000 and 3000 ft. A
diagram of the flight plan is shown in Figure 8. The scanner photo-
graphs were taken with window settings between 78 and 84°F. To cor-
rect the IR scanner photographs with the ground truth data for each
set of flights, the water surface temperature was measured with the
aircraft overhead for at least one station. This was to correct the scan-
ner readings due to errors caused by water vapor attenuation.
The scanner used was a daedalus series DS-1250 and remote sensing
of 8-14 ym radiation is achieved by a Hg: Cd: detector. The detector
had a 0.015 inch square sensitive area, which was optimum for the reso-
lution and temperature sensitivity required. This detector was mounted
in an end-looking, metal cored dewar which had sufficient liquid nitrogen
coolant capacity for approximately six hours of operation before refilling.
This system projected through the floor of the airplane, NASA 6, and
had a scan angle of 120° centered above the vertical. A horizontally-
mounted telescope with its axis along the direction of flight of the air-
plane was contained within the scanner. A mirror rotating at 3600 RPM
and mounted at 45° to the telescope directed heat radiation from the
ground into the system. A one-third revolution of the mirror covered a
complete step perpendicular to the scanner axis. Optical resolution
16
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obtained by this method was about 1.7 milliradians, so the ground areas
detected become a function of flight altitude; the data accuracy is 0. 5°C.
The video signal from the infrared detector was amplified and re-
corded on magnetic tape in the aircraft. A method developed by Daedalus
called Digicolor was used to convert this stored information directly into
color coded strip imagery. This process limits the number of output
colors to light (from white 'hottest1 to black 'coldest') for any input con-
dition. The six colors between white and black indicate the six calibrated
levels of the set of interest. The scanner's thermal reference sources
were present in flight to 66°F and 84°F respectively, and the settings
were recorded on the same track with the detector video to insure accu-
rate voltage relationships irrespective of all amplifier gain adjustments.
The color bands in the final Digicolor map indicate zones of con-
stant temperature within the accuracy of resolution of the scanner; hence,
the line formed by the junction of two adjacent color bands indicate an
isotherm. The actual temperature of the isotherm is obtained by adding
a ground truth correction term to the temperature indicated in the map.
Altogether, three IR flights were made during the summer data
collection mission. Out of these, two runs were made on August 24.
The first run was from 0853 hrs EST. On August 25, a single run was
made from 0908 hrs to 0953 hrs EST.
The Digicolor maps were transfered on to enlarged maps of the region
of interest so as to obtain a map of surface isotherms which could be com-
pared directly with the values predicted by the model. Out of the three
runs made, only two, namely August 24 morning and August 25 morning,
were used for comparisons since the resolution of the colors in the re-
maining Digicolor map was very poor.
The values of Oconee Nuclear Stations flows and temperatures every
hour are obtained from continuous water quality monitoring stations of
Duke Power Company. Flow through Jocassee-pumped storage station
and Keowee Hydro Station as well as meteorological conditions (viz., air
temperature, wind speed and direction, humidity and incident solar radi-
ation) were also obtained from continuous monitoring stations. The flows
through Jocasse, Keowee and Oconee as well as the discharge temperatures
are shown in Tables 5 and 6. The meteorological data (obtained hourly)
are shown in Tables 7 and 8. Figures 9 and 10 show the hourly variation
of Keowee Hydro Station flowrate on these two days. Figures 11 and 12
show the same for Jocassee-pumped storage station.
February 1979 Data
The winter data mission was carried out during February 27, 28,
1979. The same equipment were used in this mission. Three boats
were used to measure water temperatures and velocities up to a depth of
30 m. Two of the boats were equipped with thermistors only and were
17
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used to measure temperatures in both branches of Lake Keowee. The
third boat carried the current meter as well as a thermistor. The stations
where readings were taken are indicated in Figure 13. Station #13 was
used for ground truth correction of the 1R scanner data. This point was
chosen since it is virtually unaffected by the discharge, and the tempera-
tures here remained fairly constant.
Ground truth measurements were taken from 0950 hrs to 1353 hrs
EST and 1600 hrs to 1833 hrs EST on February 27. Due to technical
problems with the aircraft (NASA-6) the 1R flights were delayed and
were only from 1549 hrs to 1711 hrs EST on this date. The flight plan
was identical to that used in the August data, mission. Black body set-
tings of 38°F and 74°F were used and the flight altitudes were 2000,
3000 and 1000 feet.
On Feburary 28, 1979 ground truth measurements using three boats
were taken from 0851 hrs to 1201 hrs EST and 1420 hrs to 1830 hrs EST.
IR flights were run from 0850 hrs to 1002 hrs at altitudes of 2000 and
3000 ft. The black body settings used were established by NASA. IR
isotherms were constructed for the domain of interest at the University
of Miami. These maps were used for verifying the results predicted by
the computer.
For obtaining meteorological data and flows through Oconee Nuclear
Station, Jocassee-pumped storage station and Keowee Hydro Station,
continuous monitoring stations of Duke Power Company, were used.
Since the velocities in the lake were found to be extremely small, drogues
were also used. The flows through the three power stations are shown
in Tables 9 and 10. The data obtained was hourly and the variation of
the flows through J ocas see and Keowee are shown in Figures 14 and 15
and Figures 16 and 17 respectively. The meteorological data collected on
February 27 and 28 are shown in Tables 11 and 12 respectively.
The ground truth data collected during the summer and winter
missions are presented by Duke Power Company (1978 and 1979).
CALCULATION OF INPUT
The 3-D rigid-lid model as described in Section 4 solves the three-
dimensional momentum, continuity and energy equations. As shown be-
fore, these equations are a set of nonlinear, coupled partial differential
equations and require the following for complete solution.
1. Initial values of the velocities and temperatures must be specified
at ail points within the domain.
2. Boundary conditions for the above variables must be specified at
all boundaries.
The choice of the domain of interest as well as the grid system has
18
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been described in earlier sections. At ail solid boundaries the velocities
and temperature gradients are specified as zero. At the surface the
rigid-lid constraint of zero vertical velocities is assumed. The initial
conditions assumed for starting the runs are zero velocities and con-
stant temperatures everywhere within the domain. For subsequent runs
the results of the previous run is used as the initial condition. Hence,
the quantities yet to be specified are:
1. Temperatures and flow velocities at the Oconee Nuclear Station dis-
charge.
2. Temperatures and velocities at the Keowee Hydro Station.
3. The same at the Jocassee boundary and at the canal. (Items 1 and 2).
4. Surface horizontal velocities and temperatures.
The above quantities are termed as inputs to the model and the
procedure used for obtaining them are discussed briefly below for the
sake of completeness. For further details regarding the actual running
of the programs, the reader is. advised to refer to the 3-D riqid-lid
User's Manual (Sengupta et al, 1980) prepared for this purpose.
The calculations shown below were for February 27, 1979 simulations.
Reference Quantities Used
Reference length = L = maximum length of the domain = 2895.6 m.
Reference horizontal eddy viscosity A , = 0.002 L = 38311.48 cm2 /sec.
(Note: The constant '0.0021 changes with different sites. This particu-
lar value was used in running the model at Lake Belews and at Biscayne
Bay. In this case the best value of the constant was found to be '.003'
which yielded a value of A - = 60,000 cm2 /sec.
Reference depth = H = max depth considered = 16 m
4/3
Reference vertical eddy viscosity Ay = 0.002 x H =37.43 cm2 /sec.
Reference velocity U = 30 cm /sec.
Reference time Trgf = L/V f = 9652 sec.
Oconee Nuclear Station Discharge Velocity
The discharge is considered to take place through a point at a depth
of 12-m (k=3). The discharge velocity is calculated as follows.
19
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12 m
152. 4 m
The total discharge = (100 — x V(—) x 152.4 x 12) = Q
= m sec
(where Q = average discharge in m3/sec.)
.'.V = 7.4207 cm/sec
The average value of 'Q1 over 24 hrs is taken since the variation
is negligible.
Nondimensiona! discharge velocity = ^ - = "30
ref
Keowee Hydro Discharge Velocity
= ®m 24740.
The outflow through the Keowee hydro station is throuah a channel
(152.4 m) x (12 m).
The volume flowrate Q = (152. 4 x 12 x V) m3/sec.
(where V = discharge velocity (m/sec.)
Q
V = [Q/(152. 4 x 12)] m/sec =
152.4x12x100
cm /sec
Q is specified as a function of time with the help of polynomials and
other functions. The curve is approximated and specified in subrou-
tine 1NLET1; (refer to the user's manual (Sengupta et al, 1980).
Keowee hydro flow approximation: refer to the user's manual (Senqupta et al,1
(February 27 Data)
SX = Conversion factor for converting discharge (incfs) to nondimenstonal
velocity.
SV1 = Nondimensiona! velocity.
The velocities are approximated as follows:
SV1 = 0.048 0 < TSDT < 6
20
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SV1 = SX * (((17.54 - 0.048)72.) * (TSDT - 6.0) + 0.48)
6 < TSDT < 8
SV1 = SC * (((.048 - 17.54)74.) * (TSDT - 8.0) + 17.54)
8 < TSDT < 12
SV1 = SX * (0.048) 12 < TSDT < 24
J ocas see Flow Velocity
The entire flow to or from the J ocas see-pumped storage station is
assumed to take place through the entire upper boundary. The flow
through this area is shown in the following figure.
i^ v
16 m
Jt_
The flow is assumed to be uniform over this area (i.e., equal flow
velocities at all internal grid points within this area) and is assumed to
take place simultaneously with the flow through Jocassee-pumped storage
station.
V = Q/[(16 x 13 x 152.4) x 100] cm/sec
(Q = flow through Jocassee-pumped storage station (m3/sec).)
Q is positive when Jocassee is generating (i.e., the flow is into the
region of interest) and negative when pumping (i.e., flow out of the
region of interest).
Jocassee flow approximation:
(February 27 Data)
TSDT = Time from start of run (hrs).
SV = Velocity of flow through Jocassee boundary (nondimensional).
SF = Conversion factor to convert flowrate (cfs) to nondimensional
velocity
= 0.00322579
The velocity is approximated as follows.
21
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SV = SF * (-14.395 - (18.75 - 14.395) * (TSDT)
1 < TSDT < 0
SV = SF * (-18.754) 1 < TSDT < 5
SV = SF * (((16. 823 + T8.754)/3.). * (TSDT - 5.0) + 18.754)
5 < TSDT < 8
SV = SF * (((16.823- 0.1)/3.) * (TSDT - 8.0) - 16.823)
8 < TSDT _< 11
SV = SF * 0.1 11 < TSDT < 23
SV = -SF * ({4.5 + 0.1) * (TSDT - 0.1)
23 < TSDT < 24
A similar procedure was followed for simulations of the other days.
Condition at Open Boundaries
Open boundaries are those where the values of temperatures and/or
velocities cannot be specifically obtained but continuity of flow has to be
maintained. One such boundary is at the mouth of the canal connecting
the two arms of Lake Keowee. The condition — = 0 is sepcified here
both for velocities and temperatures. At the Jocassee and Keowee boun-
daries, the same kind of zero gradient conditions is specified for tempera-
tures only. The calculation of parameters (T^/ TAU, etc.) for the sur-
face boundary conditions are shown in Section 2.
22
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SECTION 6
RESULTS AND DISCUSSIONS
The results of simulation using the 3-D rigid model at Lake Belews
and Biscayne Bay are shown in previous publications by the University
of Miami (Lee, Sengupta and Mathavan, 1977, and Lee and Sengupta,
1976). In the above two cases the predictions made by the model agreed
closely with 1R scanner and ground truth data. The following section
discusses the runs made for Lake Keowee.
Preliminary Runs and Results
These runs were primarily made for the selection of the boundary
conditions, initial conditions and to test the behavior of the model when
incomplete and/or arbitrary data are used. These runs are summarized
in Table 13.
1. Run Number LOOT
(The Number LOOT is a sequence number and must only be interpreted
as such.)
This run was essentially made for debugging the computer program
modifications. The features include a discharge velocity of 5.65 cm I
sec, a discharge temperature of 32. 3°C and a 16 meter constant depth
region of interest. The total simulated time was 20.6 hours. The
results are summarized in Figures 18, 19 and 20. The surface
velocities after 8.64 hours are shown in Figure 18, while Figure 19
shows the velocities in a vertical plant (1=11) after 21.6 hours.
Since the effects of wind were not included in this run and there
were no effects of J ocas see, the velocities are by the discharge
velocity and the buoyant plume. The isotherm comparison of the
archival run and this simulation run is shown in Figure 20. The
ambient temperature is 29°C. The archival isotherms are higher
than the predicted isotherms. This is expected since this run
(without wind) was not undertaken primarily for comparison pur-
poses, and the simulation did not reach steady state.
2. Run Number L002
This run is similar to 'LOOT but with variable depth of the region
of interest. The simulation time was only 8. 64 hrs. This time is
long enough to determine how well the model handles a variable
23
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depth domain. The surface velocities and vertical velocities (at
1=11) are shown respectively in Figures 21 and 22. For complete-
ness, the simulated surface isotherms are compared with the archival
isotherms. This comparison is shown in Figures 23. For the same
reason described in the previous subsection, the comparison cannot
be expected to be more precise.
3. Run Number LOO3
Run L002 is now repeated with the effects of wind included. The
total time simulated was only 8.00 hrs. The reason for the short
simulation time is as explained above . The surface and
vertical velocities (J=7) are shown in Figures 24 and 25 respectively.
A comparison of Figures 21 and 24 shows the small effects of wind on
the surface velocities after such a small simulation time. The wind
speed is 4 ml sec. A comparison of the predicted and archival iso-
therms is shown in Figure 26. Compared with the other isotherm
comparisons, this figure appears to have improved the difference be-
tween measured and predicted.
Archival Runs and Results
Two runs were made (L004 and LOOS) using the archival data base
described in the last section.
1. Boundary Conditions
The following specifications were used at the main input boundaries.
a. At 1=1, J=8 to 19 for all depths (K)
The water velocity at the Jocassee end is specified as 6.9 cm/
sec. Open boundary is specified for temperatures as this end.
b. At 1=11, J=1, K=3
This discharge velocity is specified as 5.65 cm/sec, and the
dishcarge temperature also specified as 32. 4°C.
c. Finally, at 1=13, J=7, K=1 to 3
Keowee dam discharge velocity is specified as 10.4 cm/sec.
2. Run Number L004
This is the first archival run and was made with variable depth
topography for the near-field region of interest.
3. Run Number LOOS
24
-------
Run L004 is repeated but for constant depth region of interest.
The domain was cut off at 16 meters from the water surface. This
is the depth of the thermodine for Lake Keowee.
4. Archival Results
Figure 27 shows the comparison between the measured (archival
> 9/10/75) and calculated (L004) isotherms. The ambient temperature
was 29°C. This comparison can be seen to have improved when
compared to those of the preliminary runs already described. The
surface velocities are similar to 'L0051 which are shown in Figure 28.
Flow through the Keowee dam can be seen very clearly on the right
boundary of the figure. Figure 29 shows the velocity field at J=7,
which also shows the flow through the Keowee dam. The isotherm
comparisons of measured (9/10/75) and predicted (LOOS) is shown
in Figure 30. This is the best comparison of the runs described so
far. The agreement is particularly good for the 29. 5 and 30°C iso-
therms. The shapes of the measured and predicted 30. 5°C isotherms
are similar. However, the measured area under the isotherm appears
bigger. This discrepancy can be explained in terms of the nearness
of this isotherm to the discharge. The total time simulated was 32.4
hrs, which is also the time when steady state was reached. The
temperature profiles for locations 1=11, J=7, K=1 to 4 through the
simulated period are shown in Figure 31. The temperature profiles
are vertical as expected since computations were carried out above
the thermocline. A comparison of the surface velocities at this loca-
tion is given in Figures 32. It can be seen from this figure that the
u-component velocities predominate. It can also be seen from this
figure that all the velocities stabilize after about 30 hours, showing
steady state conditions. A similar plot. Figure 33, for the same
variables but for location 1=11, J=2 and K=1 is shown. Similar con-
clusions hold for this figure.
L001 through LOOS were archival runs. The following section dis-
cusses the results of simulations for the August data base (L006)
and February data base (L007). Both these runs were made in
stabs of 24 hrs of simulation at a time for a total period of 48 hours
of simulation in each case. Results were stored and printed at the
end of every hour of real time. The results at the end of the first
24 hrs simulation were used as initial conditions for the next 24 hrs.
Summer Runs
Simulation was started from 0000 hrs August 24. The model was
started 'cold1 i.e., initial conditions used were zero velocities and con-
stant temperature (29°C) throughout the domain. This conditions re-
quired that the model had to be run for sometime before the effects of
the cold start could be ignored.
The inputs used in running the model have been discussed in the
25
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previous section. The wind speed driving the upper layer varied from
0.76 to 3.09 m/sec. The current or the flow through the Jocassee
boundary varied from 0.61 to 1.12 cm/sec. The Oconee nuclear station
discharge velocities and temperature were 7.42 cm/sec and 31.7°C re-
spectively. (Average values were taken since the fluctuation was negli-
gible.) AH the above data were fed in every hour in running the model.
The surface isotherms and velocities at each horizontal section
(K=1, 2, 3, 4 and 5) were plotted using a Calcomp plotter. Results at
the end of each hour were stored and plotted. The results used for
comparison were the surface isotherms plots. Measured surface isotherms
were obtained from IR scanner digicolor maps. By drawing both the
data and the predicted values on the same grid system direct comparison
could be made.
The first IR runs were made on August 24 from 0853 hrs EST to
1002 hrs EST. The isotherms drawn for this data are shown in Figure
34. The isotherms shown are for 30. 5°C, 30.0°C and 29. 5°C. Only the
above three isotherms fell within the domain of interest and represent
the water surface temperatures at 1002 hrs EST, August 24, 1978. The
results produced by the model are shown in Figure 35 and 36. Figure 35
shows the same isotherm i.e., 30.5°C, 30.0°C and 29. 5°C corresponding
to 1007 hrs real time. It is seen that the temperatures predicted by the
mode! are lower than the actual temperatures, showing that the plume
spread was underpredicted. Figure 36 shows different predicted iso-
therms corresponding to the same time. The temperatures of the iso-
therms are 29.5°C, 29.3°C and 29.1°C. Comparing Figure 36 with 34
it is seen that 29.5°C in the IR data agrees very well with the 29.1°C
isotherm predicted by the model. The measured 30. 5°C and 30.0°C iso-
therms compared with the predicted 29. 5°C and 29. 3°C isotherms respec-
tively. Hence, the errors in prediction in the three isotherms (30. 5°C,
30.0°C and 29.5°C measured) are approximately 1°C, 0.7°C and 0. U°C
respectively.
The IR digicolor map for the August 24 afternoon data could not be
used to construct isotherms because of bad resolution between different
colors. Hence, the next useful comparison was made for the August 25
morning data (0903-9553 hrs EST). The IR isotherms are shown in
Figure 37. The same three temperatures, namely 30.5°C, 30.0°C and
29. 5°C, are represented here since the other isotherms lie beyond the
domain of interest. Figure 38 shows the same isotherms as predicted by
the model. The spread of the 29. 5°C isotherm is overpredicted while
the 30.0°C isotherm is underpredicted. However, Figure 39 shows iso-
therms for 29. 90°C, 29.70°C and 29.6°C as predicted by the model.
These isotherms compare very well with the IR isotherms in Figure 37.
The errors in this case are .6°C for the 30. 5°C isotherm, 0. 3°C for
the 30.0°C isotherm and -.1°C for the 29. 5°C isotherm. This shows a
considerable improvement in the predictions as compared to August 24,
showing the effects of cold start gradually vanishing.
26
-------
Figure 40 shows the plot of the horizontal velocities of the surface
as predicted by the model for 1007 hrs, August 24. During this time
(1007 hrs EST), as can be seen from the Jocassee-pumped storage sta-
tion flow and Keowee hydro station flow data, the flows through these
stations were negligible. This leads to zero velocities at Jocassee boun-
dary and zero velocity through the Keowee hydro discharge point in
Figure 40.
Figure 41 shows the surface horizontal velocities predicted by the
model for August 25 (33.2 hrs run time). During this time (approxi-
mately 1000 hrs, August 25) Jocassee-pumped storage station just started
generating and Keowee hydro was generating. This accounts for the flows
through the two boundaries.
The main driving forces responsible for determining the shape of
the isotherms are the ambient temperature, discharge temperature and
flows through the Jocassee boundary. The wind is seen to affect the
velocities in the upper layer only. This characteristic is displayed
both in the data and the simulation results. Figure 34 (August 24 IR
data) and Figure 37 (August 24 IR data). Looking at the Jocassee and
Keowee flows it is seen that the flow through Jocassee is negligible dur-
ing both these periods. The flow through Keowee is negligible at 10.00
a.m. on August 24 but is 9352 cfs on 10 a.m., August 25. The average
discharge temperature is also lower on August 25 as compared to August
24. This causes the area under the isotherms in Figure 37 to be lower
than those in Figure 34. The same difference is seen between the cor-
responding predicted isotherms, namely Figure 36 (August 24, 1978) and
Figure 39 (August 25).
Winter Runs
Simulation was started from (0000 hrs) February 24, 1979. The
model was started using zero velocities and constant temperature (= 10°C)
as initial conditions.
The inputs used for this run (L007) have been discussed in detail
in previous sections. The Oconee discharge velocity (average value) was
6.84 cm/sec and the discharge temperature (average value) was 18. 4°C.
The wind speed varied from 1.61 to 4.52 m/sec and the Jocassee-pumped
storage station boundary flow velocity ranged from 0. 61 to 4.14 cm /sec.
Values of velocities and temperatures were printed at the end of
every hour. Surface isotherm plots and velocity plots were generated
from these results. Figure 42 shows the IR scanner isotherms for 1648-
1651 hrs, February 27. The temperatures are 13.0°C, 12.5°C, 12.0°C,
11.5°C and 11.0°C. The same isotherms as predicted by the model are
shown in Figure 43. These correspond to 17.12 hrs after the cold
start. Comparing these two figures it is seen that the isotherms pre-
dicted by the model have a greater spread. Figure 44 shows predicted
isotherms corresponding to 13.75°C, 13.0°C, 12.75°C, 12. 5°C and 12.0°C.
27
-------
This figure agrees better with Figure 42 showing an error of prediction
of 0.75°C, 0. 5°C, 0.75°C and 1°C respectively for each of the isotherms.
Figure 45 shows IR scanner isotherms for February 28, 1979 corre-
sponding to 0948-0957 hrs EST. The two isotherms within the domain
are for 13.0°C and 12. 5°C. Figure 46 shows the same two isotherms as
predicted by the model. These correspond to 34.2 hrs of run time after
the cold start at approximately 10 a.m., February 28. Figure 46 is in
excellent agreement with Figure 45. Isotherms for IR data corresponding
to February 28 afternoon could not be drawn because of bad resolution
among different colors in the digicolor map.
Figure 47 shows velocities at the surface as predicted by the model
for February 27, 17.12 hrs after the cold start. The flows through the
Jocassee and Keowee hydro boundaries agree with the data obtained.
Figure 48 shows the same for February 28, 34.2 hrs after cold start.
Excellent agreement is obtained in this case between the velocities shown
on the map and measured flows at Keowee hydro station and Jocassee-
pumped storage station. As in one of the summer runs, the isotherms
are affected by the Oconee discharge, Keowee hydro and Jocassee-pumped
storage station. Figures 42 and 45 (isotherms for February 27 and 28
respectively) show that the isotherms have spread out further on the
second date. Keowee hydro and Jocassee-pumped storage station flows
are negligible on both the dates. The average Oconee discharge tempera-
ture during 1600 hrs, February 27, was lower than that during 1000 hrs,
February 28. This accounts for the greater spread of the isotherms.
The same is depicted in the results produced by the model.
28
-------
REFERENCES
Duke Power Company. Oconee Nuclear Station Thermal Plume Study.
1978.
Duke Power Company. Oconee Nuclear Station Thermal Plume Study.
1979.
Duke Power Company. Oconee Nuclear Station Environmental Summary
Report, 1971-1976. 1976.
Freeman, N. G., Hale, N. C. and M. B. Danard. A Modified Sigma
Equations Approach1 to the Numerical Modelling of Great Lakes
Hydrodynamics. J. Geo. Res., Vol. 77, No. 6. 1972.
Haq and W. Lick. The Time-Dependent Wind-Driven Flow in a Constant
Depth Lake. Presented at the 16th Conference on Great Lakes
Research, Huron, Ohio. 1973.
Sengupta, S. and W. Lick. A Numerical Model for Wind-Driven Circu-
lation and Temperature Fields in Lakes and Ponds. 1974.
FT AS/TR-74-98.
Sengupta, S., Lee, S. S. and R. Bland. Numerical Modelling of
Circulation in Biscayne Bay. Presented at the 56th Annual Meeting
of the American Geophysical Union, 1975. Appeared in Transactions
of the American Geophysical Union, June 1975.
Sengupta, S., Lee S. and S. K. Mathavan. Three-Dimensional Numerical
Model for Lake Belews. 1977. NASA Contract NAS10-9005.
Sengupta, S., Lee, S. and E. V. Nwadike. Verification of One-
Dimensional Numerical Model at Lake Keowee. 1980. NASA Contract
N AS 10-9410.
Sengupta, S., Lee, S., Nwadike, E. V. and S. K. Sinha. Verification
of Three-Dimensional Rigid Model at Lake Keowee. 1980. NASA
Contract NAS 10-9410.
Wilson, B. W. Note on Surface Wind Stresses Over Water at Low and
High Wind Speeds. Journal of Geophysical Research, Vol. 65, No.
10. 1960.
Young, D., Liggett, J. A. and R. H. Gallagher. Unsteady Stratified
Circulation in a Cavity. J. of Engrg. Mechanics Div. ASCE. Decem-
ber 1976.
29
-------
U)
o
Little
River
Dam
N
Lake
Jocassee
OCONEE COUNTY
Oconee
Nuclear Stn.
Discharge
Dam
Figure 1. Lake Keowee
-------
Thermal.
Discharge
1
2
1
2
I = IN
Ffgure 2. Coordinate and grid system
31
-------
100000073
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= 0000 9 o" 1 : 31
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900 2 i: 11 11 11 11
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1
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33333333
11 13 31 13 11 11 11 1!
11 U 11 31 11 11 13 31
3 i 11 13 11 11 13 13 11
33 11 11 11 11 11 11 11
31 31 11 11 11 11 I! 31
11 11 11 11 11 11 13 11
11 11 11 13 11 11 13 £
11 13 11 11 11 11 6 10
31 11 13 11 11 33 3 0
11 11 11 11 11 13 J__ __3
1! 11 6 4 8 11 3! i:
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13 1 0 0 0 2 3 : 3 :
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Flqure 3. MAR marker matrix (main grid points)
32
-------
(sjuiod pu6
XUIBUJ
0 C C 0
0 C i F
0 C C 6
o c o r
0 C 0
0 0 C £
or c o
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-------
Discharge
D
Outflow
Ficjure 5. Lake Keowee (region of interest) showinq inputs and outputs (for 3-D model)
-------
*-' <-'
<=o_ r-^'V? :o y^
XO H\ -j> X< ~~
Observed Predicted
1.5C° 0.2 km,(0.2«) 5.5 km^(7 .4%)
1.0C° 0.8 km;(l.l%) 9.9 km2
° ^
0.5C° 9.1 km (12.3%) 17.6 km^(23.6%)
^* KEOWEE DAM
//r'
SURFACE ' / -..
DISCHARGE /
^ TEMPERATURE ^
i'
\ i
V.
SCiLE IN
i
Figure 6. Measured isotherms (Archival 9/10/75)
35
-------
U)
Ol
Tl
•5'
'Q
C
tn
r*
IQ
O
C
3
a
rt-
3"
a
ST
3
a>
01
'-Q
(A
r+
Q)
r*
5'
3
(A
j^O
TV
-------
Ul
Figure 8. Flight plans for IR data (Auqust and February missions)
-------
IQ
C
CO
DISCHARGE VELOCITY (m/sec)
to
1
CD
fD
•f*
1—
CO
Q.
(/I
O
0)
•a
a
01
r*
0)
C
u>
g
w
to
CO
-------
co
(O
11
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C
(D
7s
1
CD
rr
a
o
o
Dl
iQ
0)
a
tt>
r+
0)
C
JQ
C
(A
Ul
DISCHARGE(C.F.S. x 1000)
8
c/i
INJ '
CO
-------
12
o
o
o
Fn
•
CJ
w
H
o
s
H
W
§
12 24
TIME (HOURS)
Figure 11. Jocassee-pumped storaqe station discharge data
(August 24, 1978)
-------
Tj
UQ'
T
fl>
N>
^> o
CIJ
ft)
•Q w
C oi
U) (D
r+ fl)
K)"O
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i*
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r*
O
0)
!.Q
fD
U)
c*
0)
r-t-
5"
a
0)
r+
01
FLOW (C.F.S. X 1000) GENERATING
-------
N <^
V iVr
^L 3
S ^ \l
•Sr-CW-
, r .
i^r
-M V
; i^"?v
^^- T ^ V A
r^ ~ TJ
£n
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XX j^x.' ^^ —
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^ ' ^J>
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^ r^CV-^Ji
V '; ^ ^ V
p " sw-
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,,A^3. . ..\
v - - J-T^^,O -»
>x i?
-------
20-
o
o
o
as
20 A
12
TIME (HOURS)
Figure 14. Jocassee-pumped storage station discharge data
(February 27, 1979)
-------
"ft
-5*
c
a*
in
•no
a
n>
a
Q)
r+
a>
FLOW RATE (C.F.S. x 1000)
-------
16"
o
o
CO
•
to
B 8
5
O
12
TIME (HOURS)
24
Figure 16. Keowee hydro discharae (February 27, 1979)
-------
o
o
o
X
OT 6
12
TIME (HOURS)
24
Fiqure 17. Keowee hydro discharge data (February 28, 1979)
-------
RUN NO : LQQ 1 -
OISCHRRGE VELQCITY :
OISCHRRGE TEMPERRTURE :
WIND :
CURRENT :
TQTRL SIMULRTEO TIflE s
LENGTH SCRLECMETERS)
VELQCITY SCRLE(CM/SEC)
5-SSCM/SEC
32 .39C
o.oon/SEC
0-0 CM/SEC
6.54 MRS
*10l
Q.QO
0-00
61 -00
30-00
i
V V X » I
X \ \ * \
X \ \ \ t
X \ \ \ \
X \ \ \ t
\ \ \ V
X
\ \
Figure 18. Velocities at K = 1, Lake Keowee (rigid-lid model)
-------
RUN N8» L831.
OISCHHR3E YEL3CITY J S.SSCfl/SEC
OI3CHRRGE TEflfERRTUREs 32.3*C
HIND : Q.QOM/SEC
CURREHT » Q.O Crt/SEC
T8TRL SIMULRTEO TlflE a 21.6GHRS
SCHLE3
LENGTH SCaLEtMETERS)
Q.OQ
51 .00
i
VEL3CITY SCflLECCtt/ScC5
12.GO
i
SCRLE3 tVERTICRL)
LENGTH SCHLE(METERS)
20.00
VEL3CITY SCflLECCM/SEC) °LQO
S.QC
.
S// 1 \
-^ \ x. ^
v *
• f t
Figure 19. Velocities at I -11, Lake Keowee (rigid-lid model)
-------
RUN NO: LOG 1.
DISCHRRGE VELOCITY : S-SSCfl/SEC
DISCHRRGE TEMPERRTURE: 32.38C
WIND : O.OOM/SEC
CURRENT : Q .Q Ctl/ScC
TQTRL SIHULflTED TIME : 8-64 HRS
LENGTH SCflLECHETERS)
VELOCITY SCHLECCM/SEC)
ARCHIVAL DATA ("9/10/7 5)
PREDICTED
0.00
L
*10!
-x
61 -00
0.00 30.00
i i
Fiqure 20. Isotherms: measured and predicted (temperatures above ambient)
-------
RUN NQi L3Q 2.
OISCHP.RGE VELOCITY J 5.65C.1/SEC
DISCHRRGE TEMPERRTURE i 32-3*C
HIND » Q.OQfl/SEC
CURRENT » Q.Q CM/SEC
TQTflL SIMULRTEQ TIME i 8.64 » fc k
% b
•»•»•»••
«, - •
• A *
L
X H % V » % 1
\ \ \ \ 4
\ \ \ t 4
\ \ \ f -
,\
Figure 21. Velocities at K =1, Lake Keowee (nqid-Iid model)
50
-------
RUN NO: L3Q2.
OISCHHRGE VELQCITY : 5.6SCH/SEC
OISCHRRGE TEflPERRTUREi 32.3*C
MIND i O.OOH/SEC
CURRENT » 0.0 CI1/SEC
TQTRL SIMULRTEO TIME : 8.S4 IIRS
SCRLES CHQRIZ3NTRL)
LENGTH SCRLECMETERSJ
C.QQ
c .00
VEL3CITY SCRLECCM/SECJ i
SI-DO
12.00
i
SDILES (VERTICRL3
LENGTH SCRLECMETERS3
0.00
20.00
VELQCITY SCRLECCH/SEC3
Figure 22. Velocities at I =11, Lake Keowee (rigid-lid model)
51
-------
RUN Mfli LOO 2.
OISCHflROE VELOCITY t 5 .65CH/SEC
DISCHflROE TEflPERfiTUREi 32.39C
HIND j O.OQ'i/SEC
CURRENT i Q.Q CM/SEC
TGTRL SIHULflTED TIME i 0.64 HRS
LENGTH SCflLEf METERS 3
°
VELOCITY SCRLECCM/SEC) D.'OQ
ARCHIVAL DATA (9/10/75)
PREDICTED
61 .00
12.00
Figure 23. Isotherms: measured and predicted (temperatures above ambient)
52
-------
RUN NO: LOG 3.
DISCHflRGE VELOCITY : 5 .65Cf1/SEC
QISCHRRGE TEMPERRTURE: 32.3*C
HIND J X.OOM/SEC
CURRENT s 0.0 CH/SEC
TOTflL SIMULflTED TIME » 8.00 hRS
aid'
Q.OQ 61.00
LENGTH SCflLEIMETERS)
VELOCITY SCRLEfCM/SEC)
C.QO
12.OQ
-4
4 #
L.
4 » * f « 4
• » t t t *
* \ \ \
x \ A
,\
l
Figure 24. Velocities at K = 1, Lake Keowee (rigid-lid mode!)
53
-------
RUM >JO s LOC3 -
OISCHRROE VELOCITY : S.65Cn/S£C
DISCHARGE TEnPERRTURE: 32>3°C
UI>JO -- 4.00M/SEC
CURftErfT : 0-0 CH/SEC
TOTftL SlnULRTEO TInE s 4.32 MRS
SCRLES tHOR!ZO)JTRL)
-101
0.00 61 .00
LENGTH 5CRLECHETERS)
VELOCITY SCRLECCn/SEC) »1 L2"°°
SCRLES (VERTICRL)
0-JO 20.00
LENGTH SCRLECnETERS)
VELOCITY SCRLECCH/SEO
Figure 25. Velocities at J = 7, Lake Keowee (rigid-lid model)
-------
RUN NO: LOO 3.
OISCHRRGE VELOCITY i 5-65CM/SEC
OISCHflRGE TErtPERflTURE» 32.3°:
WIND : 4.QCW/SEC
CURRENT » 0.0 CM/SEC
TOTRL SIMULflTEO TIME a 8.64. HRS
LENGTH SCflLEIMETERSJ
VELOCITY SCflLEICM/SEC)
ARCHIVAL DATA (9/10/75)
PREDICTED
0.00
0.00
61.00
12.00
Figure 26. Isotherms: measured and predicted (temperatures above ambient)
55
-------
RUN NO: L004
DISCHARGE VELOCITY : 5.65 CM/SEC
DISCHARGE TEMPERATURE: 32.3 °C
WIND : 0.00 M/SEC
CURRENT : 0.0 CM/SEC
TOTAL SIMULATED TIME : 8.64 HRS
10
LENGTH SCALE (METERS)
VELOCITY SCALE (CM/SEC)
ARCHIVAL DATA (9/10/75)
PREDICTED
0.00
I
61.00
0.00
t
12,00
-X-
Fiqure 27. Isotherms: measured and predicted (temperatures above ambient)
56
-------
RU:? .S'3: L38 3.
OISCHRP.GE VELOCITY : S .S5C."./3EC
OISCHP.RGE TEttPE3aTu?.E: se.i'c
MIND : 4.0Q:i/?EC
CURRENT : 0.7 Cfl/ScC
TOTfiL 31MULRTEQ TlflE i 4.3°. HK3
«105
C.OQ 61-00
5CflLE(r:ETE?.SJ
VEL8CITY SCHLECCn/SEC) °.'°Q
12.00
Figure 28. Velocities at K = 1, Lake Keowee (rigid-lid model)
57
-------
RUN N3 : i 005 -
CISCHHRGE VELOCITY : 5-65C.:1/oEL
CISCHP.RGE TEMPERRTURE- 32.-ia<-
U IND : 4 .001, 5cC
CURRENT : Q."7 .-M
10TRL SinULRTEO TI.1E • J2-l3riR5
oCRLES [HQRIZQNTPLJ
LENGTH SCRLECMETERS]
\ELQCiTf SCflLEt CM/SEC J i I,2'00
SCRLES CVERTLCRL)
LENGTH SCRLEEflETERS)
VELOClTr SCRLE(Cn/5EC)
Figure 29. Velocities at J = 1, Lake Keowee (rigid-lid model)
58
-------
RUN NO t I 005.
CISCHRRf-E VELOCITY
CiSCHRRGE TEMPERRTUREt
UINO :
LURRhNT
IQIfil biflULRlED 1 IME :
LENGTH SCRLECMETERS 3
b -Gb. '1/LiLC
U-"7 Li .itL
o.oo
I
VELOCITY SCRLECCH/SEC). °t'OQ
ARCHIVAL DATA (9/10/75)
PREDICTED
61.00
12.00
Figure 30. Isotherms: measured and predicted (temperatures above ambient)
59
-------
2.16 Hours 4.32 Hours
0
4
8
12
16
27
m
°r
4,
. 8.
12
i
16 .
28 29 30 27 28 29 30
Temperatures Temperatures
12.96 Hours 19.44 Hours
0
4
8
12
16
27
>
,
,
(
Or
4,
8.
12.
16 ...
28 29 30 27 28 29 30
Temperatures Temperatures
V* \f
3
0
4
8
12
16
2
2.4 Hours
k
•
(
Location: I
7 28 29
Temperatures
6.34 Hours
°r
4 .
8
12 ,
16 .
27 28 29 30
Temperatures
°C
25.93 Hours
0 r
4 ,
8 ,
12 .
16 ...
27 28 29 30
Temperatures
= 11, J = 7
Figure 31. LOOS, temperature profiles
60
-------
4..0
3.0
o
-------
12
11
10
8
o
0)
i
a 6
•H
0
O
H c
v - velocity
u - velocity
10 20
Time (Hours)
50
Figure 33. LOOS, velocity vs. time, I = 11, J =2, K = 1
62
-------
Temperature in C
Ground Truth Correction 1.7 C
Figure 34. !R data coreesponding to 1002 hrs, August 24, 1978, Lake Keowee
63
-------
RUN M9» 189 6.
DISCHARGE VEL9CITY i 7.42Cf1/S£C
DISCHARGE TEttPERflTUREi 31-79C
HINO SPEEd CflflXJ » 3.Q9f1/S£C
CURRENTCJ9CRSEE Ftawji 1.1 Crt/SEC
T8THL SinULflTED TIME i 1Q.Q7HRS
LENGTH SCfiLECflETERS)
O.QQ
101
61.00
29.5
30.0
30.5
Figure 35. Isotherms at K =1, Lake Keowee (rigid-lid model),
simulations for August 24, 1978
-------
RUN NO: L006
DISCHARGE VELOCITY
DISCHARGE TEMPERATURE
WIND SPEED (MAX)
CURRENT (JOCASSEE FLOW)
TOTAL SIMULATED TIME
7.42 CM/SEC
31.7 °C
3.09 M/SEC
1.1. CM/SEC
10.07 HRS
10
LENGTH SCALE (METERS)
0.00
61.00
i
Fiqure 36. Isotherms at K =1, Lake Keowee (rigid-lid model),
simulations for Auqust 24, 1978
65
-------
Temperature in C
Ground Truth Correction +2.6 C
Figure 37. IR data correspondinq to 0903-0953 hrs, Auaust 25, 1978 Lake Keowee
66
-------
RUN NO: L006
DISCHARGE VELOCITY
DISCHARGE TEMPERATURE
WIND SPEED (MAX)
CURRENT (JOCAS.SEE FLOW):
TOTAL SIMULATED TIME
7.42 CM/SEC
31.7 °C
2.50 M/SEC
2.2 CM/SEC
33. 23 HRS
10
.LENGTH SCALE (METERS)
0.00
61.00
29.5
30.0
Figure 38. Isotherms at K = 1, Lake Keowee (rigid-lid model),
simulations for Auaust 25, 1978
67
-------
RUN NO: L006
DISCHARGE VELOCITY
DISCHARGE TEMPERATURE
WIND SPEED (MAX)
CURRENT (JOCAS.SEE FLOW)
TOTAL SIMULATED TIME
7.42 CM/SEC
31.7 °C
2.50 M/SEC
1.1 CM/SEC
33. 2 HRS
10
LENGTH SCALE (METERS)
0.00
i
61.00
Figure 39. Isotherms at K = 1, Lake Keowee (rigid-lid mode!),
simulations for August 25, 1978
68
-------
RUN N8: L88 6.
DISCHRROE VEL8CITY » 7.42CJ1/SEC
OISCHRROE TEHPERftTUREi 31.7*0
HIND SPEED CnaXJ i 3.09H/SEC
CURRENTCJ8CR3SE FL8J4J: 1.1 Cfl/SEC
TBTflL SIflULRTEO TlrtE i 10.07HRS
*10l
0.00
LENGTH SCRLEtMETERS)
VEL3CITY SCRLECCn/SECJ
0.00
61.00
12.00
\
t
\
\ \
\ \
\ \
N \
\ \
H \
N » » * I .
\ \ \ \ i L
\ \ \ \ \ I t
\ \ \ \ \ \ f
\ \ \ \ v\ A
\\\\v\
Figure 40. Velocities at K = 1, Lake Keowee (rigid-lid model),
simulations for August 24, 1978
69
-------
RUN NG: LQQ S-
DISCHARGE VELOCITY : 7.42CM/SEC
DISCHRRGE TEMPERRTURE s 31.7*0
HIND SPEED CflRXJ : 3.Q9H/SEC
CURREHT(JQCRSSE FLOW): 1-1 CM/SEC
TQTRL SIflULRTED TIflE : 34.24HRS
LENGTH SCRLECflETERSJ
0-QO
61 .00
YELQCITY SCflLEC CM/SEC J °il£!L
12.00
\
\
\ \ \ \ \ \
4 4
\\\\ \ \ \
\\V\\A\
Figure 41. Velocities at K = 1, Lake Keowee (riqid-lid model),
simulations for August 25, 1978
70
-------
Temperature in C
Ground Truth correction +0.7 C
Figure 42. IR data corresponding to 1648-1651 hrs, February 27, 1979,
Lake Keowee
71
-------
RUN NO: L007
DISCHARGE VELOCITY
DISCHARGE TEMPERATURE
WIND SPEED (MAX)
CURRENT (JOGAS SEE FLOW)
TOTAL SIMULATED TIME
LENGTH SCALE fMETERS)
6.84 CM/SEC
18.4 °C
2.95 M/SEC
1.1 CM/SEC
17.12 HRS
104
0.00
I
61.00
Figure 43. Isotherms at K = 1, Lake Keowee (riqid-Iid model),
simulations for February 27, 1979
72
-------
RUN NO: L007
DISCHARGE VELOCITY :
DISCHARGE TEMPERATURE:
WIND SPEED (MAX) :
6,84 CM/SEC
18. 4°C
2. 95 M /SEC
CURRENT (JOCASSEE FLOW): 1.1 CM/SEC
TOTAL SIMULATED TIME : 17.12 HRS
10J
LENGTH SCALE (METERS)
0.00
61.00
Figure 44. Isotherms at K = 1, Lake Keowee (rigid-lid mode!)
simulations for February 27, 1979
73
-------
Temperature in C
Ground Truth Correction +1.3 C
Figure 45. IR data corresponding to 0948-0957 hrs, February 28, 1979
Lake Keowee
-------
RUN NO: L
DISCHARGE VELOCITY
DISCHARGE TEMPERATURE
WIND SPEED (MAX)
CURRENT (JOCASSEE FLOW)
TOTAL SIMULATED TIME
LENGTH SCALE (METERS)
6.84 CM/SEC
18.4 °C
2. 95 M /SEC
0.42 CM/SEC
34.2 HRS
10J
0.00
61.00
i
Figure 46. Isotherms at K = 1, Lake Keowee (rigid-lid model),
simulations for February 28, 1979
75
-------
RUM N8: L98 6.
OISCHRROE VEL6CITY i 7.42CH/SEC
OISCHRROE TEflPSRRTUREi 31 .7*C
HIND SPEED CMRXJ » 3.09«/SEC
CURRENTCJQCaSSE FL9HJ* 1.1 CM/SEC
T8TRL SIJ1ULRTED TIJlE » 17.12HRS
*10l
0.00
LENGTH SCRLECflETERSJ
VEL8CITY SCRL££C«/SEC3
0.00
61 .00
i
12.00
Figure 47. Velocities at K = 1, Lake Keowee (rigid-lid model),
simulations for February 27, 1979
76
-------
RUN N3» L83 S.
OISCHflRSE VELOCITY » 7.42CH/SEC
DISCHBROE TEflPERHTURE* 31.7*C
WIND SPEEO CMflX) » 3.Q9M/SEC
CURREMT(J8Ca3SE FL3HJ» 1-1 C«/SEC
TBTflL SinULflTED TInE i 34.24HR3
*10l
LENGTH SCflLECttETERS)
VEL8CITY SCHLEfCM/SEC)
0.00
0.00
61.00
12.00
);;:
Figure 48. Velocities at K = 1, Lake Keowee (rigid-lide model),
simulations for February 28, 1979
77
-------
Table 1. Monthly Gross Thermal Capacity Factors (Percent)
for Oconee Nuclear Station
MONTH
Jan.
Feb.
Mar.
Apr.
May
Jun.
Jul.
Aug.
Sep.
Oct.
Nov.
Dec.
Annual
Average
1973
0
0
0
0
4
9
15
15
16
23
23
27
11
1974
13
28
29
26
5
43
38
31
46
19
31
30
28
1975
37
22
57
61
76
78
80
82
76
75
92
92
69
1976
30
49
47
27
33
64
59
90
77
61
52
55
59
1977
90
77
72
92
76
46
44
36
Data based on three- unit capability for entire period.
Actual MWH(t) x 100
7704MW(t) X Hours in Period
78
-------
Table 2. Operating Conditions of Oconee Nuclear Power Plant
at Lake Keowee (September 10, 1975)
Flow Rate
Inlet Temperature
Outlet Temperature
7087 m/min
26.6 °C
32.4 °C
The hourly averages of wind, air temperature and
relative humidity:
Time
9:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
Wind
Speed(MPH)
7.7
6.8
8.3
7.2
9.7
11.3
-
10.2
Wind
Direction (°N)
15
65
80
95
115
205
-
75
Air
Temp.
69.0
74.0
77.0
77.0
78.0
79.0
77.0
73.0
Relative
Humidity
100
70
60
63
66
64
66
84
79
-------
Table 3. Input Data for the 3-D Model (Lake Keowee)
Flow Rate:
Inlet Temperature:
Discharge Temperature:
Discharge Velocity:
Ambient Temperature:
Depth at Discharge:
Discharge Width:
Air Temperature:
Wind Speed:
Vertical Eddy Diffusivity:
Horizontal Eddy Diffusivity:
118.12 m3/sec
25.6 °C
32.4 °C
5. 65 cm /sec
28.9 °C
30 meters
152. 4 meters
26.11 °C
12. 83 ft /sec
86.1 cm2 /sec
_3
9. 2 x 10 /sec
80
-------
Table 4. Volume and Area Data for Lake Keowee
WATER SURFACE
ELEVATION
(m) (ft.)
246.9
245.4
* 243.8
242.3
240.8
239.3
237.7
237.1
** 236.2
234.7
231.6
228.6
225.6
222.5
219.4
216.4
213.4
210.3
207,3
204.2
201.2
198.1
810
805
800
795
790
785
780
778
775
770
760
750
740
730
720
710
700
690
680
670
660
650
SURFACE AREA
(SQ. KM.)
83.3
78.8
74.4
70.1
65.8
61.2
56.6
55.1
52.8
48.9
41.5
35.3
27.8
22.5
17.8
13.2
9.6
5.7
3.1
1.3
0.6
0.3
STORAGE VOLUME
(lO^3)
1.42
1.30
1.18
1.07
0.97
0.87
0.78
0.75
0.70
0.62
0.48
0.36
0.27
0.19
0.13
0.08
0.05
0.02
0.01
0.004
0.001
* FuH Pond
** Maximum Allowable Drawdowi
-------
Table 5. Inflows and Out flows- to Lake Keowee, August 24, 1978
TIME
Aug. 24
1978
12.00 AM
01.00
02.00
03.00
04.00
05.00
06.00
07.00
08.00
09.00
10.00
11.00
12.00 PM
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
10.00
11.00
12.00 AM
OCONEE
DISCHARGE
(m3/min)
8172. 9
8177.5
8178.6
8180.1
8185.4
8179.4
8181.7
8313.0
8183.5
8176.4
8183.9
8177.1
8159.9
8155.9
8247.2
8169.5
8438.7
7935.2
7543.1
8091.9
8119.6
8132.8
8141.9
8143.8
8151.8
OCONEE
DISCHARGE
TEMP.
°C
31.8
31.8
31.9
32.1
32.3
32.4
32.5
32.3
32.4
32.5
32.5
32.5
32.6
32.6
32.7
32.7
32.4
30.7
31.0
30.3
30.2
30.2
30.2
30.2
30.3
NET JOCASSEE
FLOW
(CFS)
-2638
-6059
-7982
-12036
-12066
-11985
-10598
-5970
-995
100
100
100
100
100
100
100
100
8726
10905
9823
4557
6482
4183
100
100
KEOWEE
HYDRO FLOW
(CFS)
6636
6696
5416
5416
6756
2276
48
48
48
48
48
48
48
48
48
48
48
14224
8432
4544
48
48
48
48
48
82
-------
Table 6. Inflows and Outflows to Lake Keowee, J\ugugt 25, 1978
TIME
Aug. 25
1978
12.00 AM
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
10.00
11.00
12.00 PM
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
10.00
11.00
12.00 AM
OCONEE
DISCHARGE
(m3/min)
8151.8
7952.3
7097. 2
7098.4
7098.8
7103.7
7102.6
7104.4
7279.7
8012.8
7760.4
7759.2
8059.8
8130.6
8112.8
8141.9
8102.2
8108.6
8107.5
8110.1
8114.7
8126.8
8148.3
8141.9
8141.9
OCONEE
DISCHARGE
TEMP.
°C
30.3
28.9
28.5
29.1
29.6
30.0
30.5
30.7
30.9
30.5
30.7
30.9
30.7
30.8
30.9
31.1
* 31.3
31.3
31.4
31.5
31.5
31.5
31.5
30.4
30.3
NET JOCASSEE
FLOW
(CFS)
100
4938
838
100
100
100
100
100
100
100
100
100
1632
5442
11553
19048
17180
10615
10158
10076
2185
29.83
3151
2647
100
KEOWEE
HYDRO FLOW
(CFS)
48
3576
608
48
48
48
48
48
3484
8624
9352
1392
2564
8820
9500
7624
7856
8852
8172
2660
48
48
48
48
48
83
-------
Table 7. Meteorological Data for Lake Keowee, August 24, 1978
Time
(Hrs. from
midnight)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Wind Speed
(m/s)
1.788
2.76
1.96
2.53
7.45
2.27
1.38
2.85
1.56
1.29
1.69
1.96
2.90
2.86
2.90
1.82
1.78
1.42
1.47
1.16
0.71
1.82
1.16
1.61
Air Temp
C°C)
21.9
21.4
20.8
20.8
20.3
20.0
19.4
20.4
21.4
23.3
26.1
27.2
28.1
28.9
29.4
29.4
29.4
29.4
29.9
27.2
25.8
25.28
24.17
23.89
Dew Pt.
Temp.
(°C)
21.94
21.39
20.83
20.83
20.28
20.0
19.4
20.0
20.83
21.67
23.06
23.89
24.44
25.56
25.83
25.28
25.28
26.67
26.53
25.97
25.28
25.0
24.17
23.89
Solar
Radiation
(w/m2)
0.0
0.0
0.0
0.0
0.0
0.0
34.85
170.77
326.43
592.45
710. 94
815.49
864.28
836.4
752.76
599.42
397.29
214.9
81.32
5.81
0.0
0.0
0.0
0.0
Wind
Direction
30.0
10
30.0
20
35.0
20.0
30.0
15.0
10.0
40.0
20.0
30.0
40.0
15.0
85.0
60.0
70.0
85.0
75.0
90.0
30.0
20.0
5.0
25.0
-------
Table 8. Meteorological Data for Lake Keowee, August 25, 1978
Time
(Hrs . from
midnight1)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Wind Speed
(m/S)
1.028
2.951
2.414
2.995
1.833
1.833
2.235
1.922
1.833
0.760
1.162
1.565
1.654
1.967
2.503
2.012
2.056
1.743
1.967
1.654
2.414
1.341
1.073
3.085
Air Temp
(°C)
23.1
23.1
22.2
22.2
21.9
21.7
21.4
21.7
23.3
25.3
26.9
28.6
29.7
30.6
30.8
30.8
30.8
30.0
29.4
28.3
27.2
25.8
25.6
25.6
Dew Pt.
Temp.
(°C)
23.0
23.0
22.2
22.2
21.9
21.7
21.4
21.7
20.0
17.2
18.3
16.1
16.9
16.7
16.1
16.1
16.7
20.0
22.7
21.1
25.6
25.6
25.6
25.6
Solar
Radiation
(w/m2)
0.0
0.0
0.0
0.0
0.0
0.0
0.0
27.89
168.52
348.67
534.62
691.52
796.12
1041. 35
807. 74
708.96
575. 30
284. 74
185.96
58.11
0.0
0.0
0.0
0.0
Wind
Direction
(Degrees)
55.0
40.0
20.0
55.0
30.0
35.0
25.0
40.0
10.0
15.0
10.0
45.0
55.0
55.0
70.0
45.0
55.0
90.0
80.0
70.0
65.0
90.0
10.0
40.0
85
-------
Table 9. Inflows and Outflows to Lake Keowee, February 27, 1979
TIME
Feb. 27,
1978
12.00 AM
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
10.00
11.00
12.00 PM
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
10.00
11.00
12.00 AM
OCONEE
DISCHARGE
(m3 /min)
7505.3
7498.1"
7492.0
7492.0
7491.6
7494. 3
7488.2
7481.8
7485.6
7488.2
7497.7
7504.1
7503.4
7506.0
7506.4
7503.4
7501. 9
7507.5
7511.0
7516.2
7518.9
7520.4
7516.6
7509.4
7507.2
OCONEE
DISCHARGE
TEMP.
(°C)
18.6
18.5
18.4
18.5
18.3
18.3
18.3
18.2
18.3
18.2
18.3
18.3
18.4
18.5
18.5
18.5
18.4
18.4
18.4
18.4
18.3
18.3
18.2
18.2
18.2
NET JOCASSEE
FLOW
(C.F.S.)
-14395
-18754
-18805
-18713
-18698
-18688
-15939
3484
16823
13503
5470
100
100
100
100
100
100
100
100
100
100
100
100
100
-4382
KEOWEE HYDRO
FLOW
(C.F.S.)
48
48
48
48
48
48
48
3668
17540
8488
8096
2680
48
48
48
48
48
48
48
48
48
48
48
48
48
86
-------
Table 10. Inflows and Outflows to Lake Kecwee, February 28, 1979
TIME
Feb. 28,
1978
12.00 AM
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
10.00
11.00
12.00 PM
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
10.00
11.00
12.00 AM
OCONEE
DISCHARGE
(m3/min)
7507.2
7616.4
7655.5
7356.3
7233.4
7494.7
7605.3
7618.6
7300.2
7239.8
7241.9
7243.0
7246.2
7239.0
7241.0
7235.3
7207.8
7196. 3
7200.0
7211.5
7212.
6829.4
71 89. 1
7287. 8
7036.7
OCONEE
DISCHARGE
TEMP.
(°C)
18.2
19.8
19.5
19.8
20.1
19.5
19.1
19.1
19.5
19.5
19.4
19.3
19.1
19.0
18.9
18.9
18. 9
18.7
18.9
19.2
19.0
18.3
18.5
18.1
15.8
NET JOG AS SEE
FLOW
(C.F.S.)
-4382
-18050
-18621
-18602
-18692
-18559
-15139
3045
19245
8338
100
100
100
100
100
100
100
100
100
100
100
100
100
-1544
-15141
KEOWEE HYDRO
FLOW
(C.F.S.)
48
48
48
48
48
48
48
48
5788
48
48
48
48
48
48
48
48
48
48
48
48
48
48
48
48
87
-------
Table 11. Meteorological Data for Lake Keowee, February 27, 1979
Time
(Hrs from
midnight)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Wind Speed
(m/s)
1.833
1.073
2.325
. 1.565
2.056
1.788
2.012
2.280
0.626
1.386
1.609
1.788
3.129
2.593
1.520
1.207
1.565
1.609
2.056
1.162
2.772
2.861
2.995
1.386
Air Temp
(°C)
-0.33
-0.72
-1.61
-2.22
-1.83
-2.17
-2.72
-1.67
0.01
3.06
5.83
8.83
11.06
12.28
13.39
13.89
13.83
13.72
11.72
9.72
8.33
7.78
7.00
5.28
Dew Pt.
Temp.
C°C)
-2.78
-1.67
-1.61
-2.28
-1.89
-2.22
-2.78
-2.78
-3.33
-2.22
-2.22
-1.39
-2.78
-5.0
-5.56
-5.56
-5.61
-3.33
-4.44
-2.78
5.28
5.56
5.28
3.89
Solar
Radiation
(w/m2)
0.0
0.0
0.0
0.0
0.0
0.0
20.94
195.39
369. 85
544. 31
655. 96
725.75
746.68
704. 81
579.20
383. 81
146.55
20.94
0.0
0.0
0.0
0.0
0.0
0.0
Wind
Direction
(Degrees)
15°
75°
60°
15°
50°
85°
85°
60°
5°
75°
15°
40°
80°
70°
80°
75°
55°
15°
30°
25°
55°
55°
50°
60°
88
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Table 12. Meteorological Data for Lake Keowee, February 28, 1979
Time
(Hrs. from
mid night)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Wind Speed
(m/s)
2.280
2.101
1.967
2.414
2.593
4.068
3.398
3.934
4.515
4.381
3.710
2.235
1.878
1.609
3.442
2.950
2.325
2.012
2.235
2.950
2.772
2.638
2.191
2.369
Air Temp
(°C)
4.94
4.00
3.00
2.28
2.61
4.11
3.83
4.22
6.67
7.78
9.28
10.78
11.72
12.28
13.33
13.61
13.33
12.72
11.39
10.39
10.61
10.44
10.00
9.83
Dew Ft.
Temp.
(°C)
4.17
4.17
2.22
1,67
2.22
3.06
0.28
-2.78
-3.89
-5.00
-5.00
-3.89
-3.89
-3.89
-3.33
-2.78
-1.67
-0.56
1.39
2.28
2.22
2.22
2.22
2.22
Solar
Radiation
(w/m2)
0.0
0.0
0.0
0.0
0.0
0.0
20.94
153.52
279.13
439.64
676. 90
907.18
537. 33
565.24
690.85
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
Wind
Direction
(Degrees)
55
55
60
50
80
75
60
60
85
60
70
45
60
50
45
45
45
5
65
55
85
50
65
70
89
-------
Table 13. Catalogue of Runs for 3-D Lake Keowee
Run
Identification
L001
(Selection of
B.C. ' s and i.e. 's
L002
(Model Execution
for One Physical
parameter - Vari-
able Depth)
L003
(Model Execution
for Two Physical
parameters -
Depth and wind
L004
(First Execution
for Archival Data
LOOS
(Second Execution
for Archival Data)
Up Date: L006
(For Ground Truth
Data)
L006
August 24/25 Data
Base Comparison
L007
February 27/28
Data Base Com-
parison
Wind
(M/Sec)
No
NO
4.00
12.83
12.83
Variable
(0.76 to
3.09)
Variable
(1.61
to 4.52)
Current
(Cm/Sec )
No
No
No
0.69
0.69
Variable
(0.61
to 1.12)
Variable
(0.61
to 4.14)
Discharge
Velocity
(Cm/Sec)
5.65
5.65
5.65
5.65
5.65
7.42
6.84
Discharge
Temperature
( C)
32.3
32.3
32.3
32.4
32.4
18.4
18.4
Depth (Meters)
Variable
No
Yes
Yes
Yes
No
No
No
Constant
Yes (16
Meters
No
No
NO
Yes (16
Meters)
Yes (16
Meters)
Yes (16
Meters)
Remarks
Total Simulated
Time: 21.60 Hrs.
Total Simulated
Time- 8.64 Hrs.
Total Simulated
Time: 8.64 Hrs.
Total Simulated
Time; 8.64 Hrs.
Total Simulated
Time- 32.4 Hrs.
Total Simulated
Time- 48 Hours
Total Simulated
Time: 48 Hours
-------
Table 14. Root Mean Square Difference Between IR
and Predicted Temperatures
Time
RMS Difference
Morning, August 24, 1978
Morning, August 25, 1978
Afternoon, February 27, 1979
Morning, February 28, 1979
0.55 °C
0.34 °C
0.82 °C
0.01 °C
91
-------
TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
i REPORT NO. 2.
EPA-600/7-82-037c
4 T'^**° SUBTITLE verification and Transfer of
Thermal Pollution Model? Volume III. Verifica-
tion of Three-dimensional Rigid-lid Model
7.AUTMORIS) „_,. __ L _--.-,., ,
S.S.Lee, S.Sengupta, E.V.Nwadike, and
S.K.Sinha
9 PERFORMING ORGANIZATION NAME AND ADDRESS
The University of Miami
Department of Mechanical Engineering
P.O. Box 248294
Coral Gables, Florida 33124
12 SPONSORING AGENCY NAME AND ADDRESS
EPA, Office of Research and Development
Industrial Environmental Research Laboratory
Research Triangle Park, NC 27711
3. RECIPIENT'S ACCESSION NO.
5 REPORT DATE
May 1982
6. PERFORMING ORGANIZATION CODE
8 PERFORMING ORGANIZATION REPORT NO.
10. PROGRAM ELEMENT NO.
11. CONTRACT/GRANT NO.
EPA IAG-78-DX-0166*
13. TYPE OF REPORT AND PERIOD COVERED
Final: 3/78-9/80
14. SPONSORING AGENCY CODE
EPA/600/13
is. SUPPLEMENTARY NOTES IERL-RTP project officer is Theodore G.Brna, Mail Drop
61, 919/541-2683. (*) IAG with NASA, Kennedy Space Center, PL 32899,
subcontracted to U. of Miami under NASA Contract NAS 10-9410.
is.ABSTRACT The six-volume report: describes the theory or a three-dimen-
sional (3-D) mathematical thermal discharge model and a related one-
dimensional (1-D) model, includes model verification at two sites, and
provides a separate user's manual for each model. The 3-D model has two
forms: free surface and rigid lid. The former, verified at Anclote An-
chorage (FL), allows a free air/water interface and is suited for signi-
ficant surface wave heights compared to mean water depth; e.g., estu-
aries and coastal regions. The latter, verified at Lake Keowee (SC), is
suited for small surface wave heights compared to depth (e.g., natural
or man-made inland lakes) because surface elevation has been removed as
a parameter. These models allow computation of time-dependent velocity
and temperature fields for given initial conditions and time-varying
boundary conditions. The free-surface model also provides surface
height variations with time. The 1-D model is considerably more econo-
mical to run but does not provide the detailed prediction of thermal
plume behavior of the 3-D models. The 1-D model assumes horizontal
homogeneity, but includes area-change and several surface-mechanism
effects.
17. f - KEY WORDS AND DOCUMENT ANALYSIS
t DESCRIPTORS
Pollution
Thermal Diffusivity
Mathematical Models
Estuaries .
Lakes
Plumes
13 DISTRIBUTION STATEMENT
Release to Public
b.lOENTIFIERS/OPEN ENDED TERMS
Pollution Control
Stationary Sources
10 SECURITY CLASS (Thil Rtport/
Unclassified
30 SECURITY CLASS (This page/
Unclassified
c. COSATi Field/Group
13B
20M
12A
08H,08J
21B
21. NO. OF PAGES
102
22. PRICE
EPA Form 1220-1 (t-7J)
92
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