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-
gories were established to facilitate further development and application of en-
vironmental technology. Elimination  of  traditional grouping was consciously
planned to foster technology transfer and a maximum interface in related fields.
The nine series are:

    1. Environmental Health Effects Research

    2. Environmental Protection Technology

    3. Ecological Research

    4. Environmental Monitoring

    5. Socioeconomic Environmental Studies

    6. Scientific and Technical Assessment Reports (STAR)

    7. Interagency Energy-Environment Research and Development

    8. "Special" Reports

    9. Miscellaneous Reports

This report has been assigned to the INTERAGENCY ENERGY-ENVIRONMENT
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
energy supplies in an environmentally-compatible manner by providing the nec-
essary environmental data and control technology. Investigations include analy-
ses of the transport of energy-related pollutants and their health and ecological
effects;  assessments of, and  development of, control technologies for energy
systems; and integrated assessments of a wide range of energy-related environ-
mental issues.
                       EPA REVIEW NOTICE
This report has been reviewed by the participating Federal Agencies, and approved
for publication. Approval does not signify that the contents necessarily reflect
the views and policies of the Government, nor does mention of trade names or
commercial products constitute endorsement or recommendation for use.

This document is available to the public through the National Technical Informa-
tion Service, Springfield, Virginia 22161.

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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)

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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

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                  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

-------
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

-------
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

-------
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

-------
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

-------
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

-------
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

-------
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

-------
                  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

-------
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

-------
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

-------
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

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                                          Figure 1.  Lake Keowee

-------
Thermal.
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                             31

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                      32

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-------
                 *-'  <-'
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                                  35

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-------
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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

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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

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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

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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

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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

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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

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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

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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/
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30 SECURITY CLASS (This page/
Unclassified
c. COSATi Field/Group
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08H,08J
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21. NO. OF PAGES
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22. PRICE
EPA Form 1220-1 (t-7J)
92

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