United States
Environmental Protection
Agency
Industrial Environmental Research
Laboratory
Research Triangle Park NC 27711
Research and Development
EPA-600/S7-82-037 Dec. 1982
Project Summary
Verification and Transfer of
Thermal Pollution Model
Samuel S. Lee and Subrata Sengupta
Two three-dimensional time-depen-
dent models, one free-surface, the
other rigid-lid, have been verified at
Anclote Anchorage and Lake Keowee,
respectively. The first site is a coastal
site in northern Florida; the other is a
man-made lake in South Carolina.
These models describe the dispersion
of heated discharges from power
plants under the action of ambient
conditions.
A one-dimensional horizontally aver
aged model was also developed and
verified at Lake Keowee. The data base
consisted of archival in-situ measure-
ments and data collected during field
missions. The field missions were
conducted during winter and summer
conditions at each site. Each mission
consisted of four infrared (IR) scanner
flights with supporting ground truth
and in-situ measurements. At Anclote
special care was taken to characterize
the complete tidal cycle.
The three-dimensional model results
compared with IR data for thermal
plumes on an average within 1 °C root-
mean-square difference. The one-
dimensional model performed satis-
factorily in simulating the 1971-1979
period.
The results are reported in three
separate reports, one for each model.
Corresponding user's manuals have
also been prepared. This report sum-
marizes all six documents.
This Project Summary was developed
by EPA's Industrial Environmental
Research Laboratory, Research Tri-
angle Park, NC, to announce key
findings of the research project that is
fully documented in a separate report
of the same title (see Project Report
ordering information at back).
Introduction
Background
Two-thirds of the energy input to
power plants is rejected by the cooling
system to the surrounding environment.
This can disturb the receiving ecology. A
summary of these ecological effects is
available in papers in the proceedings of
conferences on waste heat management
and utilization1'2.
Discharges can be through open
systems into lakes, rivers, and coastal
areas, or through closed systems such
as cooling towers. However, both
systems ultimately transfer the heat to
the atmosphere. Open systems have
aquatic plumes. Closed systems have
atmospheric plumes. References 1 and
2 contain many papers on these topics.
To anticipate the effects of thermal
pollution, predictive modeling is neces-
sary. These models can be physical or
mathematical. Physical models have
problems of geometric and turbulent
scaling and costs of customized site-
specific construction associated with
them. Mathematical models can be
more general. A summary of mathemat-
ical models for surface discharges to the
aquatic environment is presented by
Dunn et al.3.
The University of Miami
Model Package
The thermal pollution group at the
University of Miami initiated an effort to
develop a three-dimensional numerical
model package that could be applied to a
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wide variety of aquatic discharges. The
underlying guideline was to obtain a
tool that was reasonably general with a
minimum level of site-specific assump-
tions. This effort resulted in two models:
one, free-surface; the other, rigid-lid.
Free-surface Model
This model is three-dimensional and
time-dependent, allowing the air/water
interface to be free. It is suited for
domains where surface wave heights
are significant compared to mean water
depth; e.g., estuaries and other coastal
regions. This model computes the
velocity, temperature, and surface
height variations with time, given a set
of initial conditions and time-dependent
boundary conditions. These conditions
are available from local meteorological
tidal and discharge conditions. The
model is easily adaptable to a new site
since domain boundary is input through
a marker matrix. The model includes a
vertical normalization that facilitiates
application to domains of varying depth.
This model solves the time-dependent
equations of motion and energy by
explicit numerical schemes. The hydro-
static assumption is used. Turbulence is
included through eddy transport coef-
ficient approximations for momentum
and heat transfer. The system of
equations is coupled by an equation of
state.
Versions of this formulation have
been calibrated and applied to Biscayne
Bay, Cutler Ridge discharge, Hutchinson
Island discharge, and Lake Okeechobee.
It has been verified as part of the present
project at Anclote River discharge.
Rigid-lid Model
This is a time-dependent three-
dimensional model where a rigid
surface that allows slip is imposed. The
surface elevation is no longer a pa-
rameter; an artificial lid pressure is
introduced. This model is suitable for
domains where surface wave height is
small compared to depth; e.g., inland
natural or man-made cooling lakes. This
model computes the time-dependent
velocity and temperature fields, given a
set of initial and time-dependent
boundary conditions. This model has
the same computational features as the
free-surface model that allows relatively
simple adaptation to different sites.
The formulation is the divergence of
Navier-Stokes approach proposed by
Sengupta and Lick4. It combines the
vertically integrated momentum equa-
tions to derive an elliptic equation for
surface pressure. This equation is
solved iteratively. The velocities and
2
temperatures are obtained by using
explicit finite difference schemes. The
hydrostatic approximation is used
together with the eddy transport coef-
ficient hypothesis. An equation of state
couples the temperature and the momen-
tum equations.
Versions of this formulation have
been calibrated and applied to Biscayne
Bay, Cutler Ridge discharge, and Lake
Belews.
The present study verified this model
at Lake Keowee in South Carolina.
Details of development and past
applications are presented by Lee and
Sengupta5'6'7. Details of verification
of these models are presented in
Volumes I and III, summarized by this
document.
One-dimensional Model
While three-dimensional models are
ideal for predicting detailed behavior of
plumes, they are prohibitively costly for
long-term simulation. Since long-term
heat budgets can be a measure of
overall impact of thermal pollution,
simpler models are necessary.
The one-dimensional model, devel-
oped as a part of the present study, was
calibrated with a data set for Lake
Cayuga, NY, and has been verified at
Lake Keowee, SC. The model assumed
horizontal homogeneity. However, it is
unique among other models in that it
includes effects of area change with
depth together with mechanisms such
as radiative penetration through the
surface, nonlinear interaction between
wind and buoyancy gradients, and heat
transfer by convection from the surface.
Details of the 1-year simulation for
Lake Cayuga and the 9-year simulation
for Lake Keowee are presented in
Volume V, summarized by thisdocument.
Summary of Tasks Performed
The efforts to verify the models and
transfer the codes to EPA, described in
the six volumes of this report, are
summarized below.
Anclote Applications
The map of the site is shown in Figure
1. The grid used for the model is shown
in Figure 2.
Jacksonville
Daytona Beach
Anclote R.
Tarpon Springs
Tampa
Ft. Myers
Ft. Lauderdale
Melbourne
Gulf of Mexico
West
Palm
beach
Miami
Figure 1. Anclote Anchorage in Florida.
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Figure 2. Grid work for Anclote Anchorage,
Data Missions
1. Summer
a. Mission was carried out on June 19
and 20, 1978.
b. IR flights (ground truth data) were
carried out for the 2 days.
c. First IR flight started at EST 1733
and ended at 1852 on June 19
(low-low tide).
d. Second IR flight started at EST
0630 and ended at 0753 on June
20 (low tide).
e. Third IR flight started at EST 1103
and ended at 1234 on June 20
(high-high tide).
f. Fourth IR flight started at EST
1450 and ended at 1558 on June
20 (max. ebb tide).
2. Winter
a. Mission was carried out from
January 30 to February 1, 1979.
b. IR flights (ground truth data) were
carried out for these days.
c. First IR flight started at EST 1030
and ended at 1204 on January 30
(flood tide).
d. Second IR flight started at EST
1635 and ended at 1817 on
January 30 (ebb tide).
e. Third IR flight started at EST 1503
and ended at 1649 on February 1
(high tide).
Model Execution
1. Preliminary Runs
a. Simulation started at 1730 June
18, 1978.
b. Total simulation time lasted for
51 hours or four tidal cycles.
c. Current calculation began with
zero velocity at 1730 June 18,
1978.
d. Temperature calculation began
with ambient temperature at
27°C.
e. Temperature at discharge point
specified to be sinusoidal of 24-
hour period.
2. Verification for Summer
a. Calculated current with meas-
ured current data.
b. Calculated temperature compared
with IR data at four tidal stages.
c. Comparison in terms of isotherm
plots and derivation of calculated
temperature from IR-scanned
temperature.
3. Verification for Winter
a. Current calculation executed for
north-south phase shift calibra-
tion.
b. Calculated current found to be in
agreement with measured current
at similar tidal stages.
4. Accuracy of predictions is shown in
Table 1.
Keowee Application
Figure 3 describes the site of Lake
Keowee station. The grid for the rigid-lid
model applied to this site is shown in
Figure 4.
Data Missions
1. Summer
a. Mission was carried out from
August 22 to 25, 1978.
b. August 22/23: ground truth,
plume, velocity, and drogue data.
c. August 24/25: ground truth,
plume, velocity, and drogue data.
d. First IR flight started at 0853 and
ended at 1002 on August 24.
e. Second IR flight started at 1644
and ended at 1745 on August 24.
f. Third IR flight started at 0845 and
ended at 0953 on August 25.
2. Winter
a. Mission was carried out on
February 27 and 28, 1979.
b. IR flights, ground truth, plume,
velocity, and drogue data were
carried out for the 2 days.
c. First IR flight started at 1549 and
ended at 1741 on February 27.
d. Second IR flight started at 0850
and ended at 1002 on February
28.
e. Third IRflight startedat 1514and
ended at 1616 on February 28.
Model Execution
1. Execution for September 10, 1975,
was conducted and results compared
with in-situ measurements obtained
from Duke Power Co. records.
Table 1. Root-Mean-Square Difference Between IR and Predicted
Temperatures (Anclote Anchorage)
Time RMS Difference
EST 1030 June 20. 1978
EST 1430 June 20, 1978
EST 1730 June 20, 1978
EST 2030 June 20, 1978
EST 1100 January 30, 1979
EST 1600 January 30. 1979
0.36°C
0.36°C
0.54°C
0.36°C
0.74°C
0.65°C
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N
Lake
Jocassee
' «r- - Oconee
Oconee I f Nuclear Sta.
Nuclear ^Keowee Discharge
Station D^m
Little
River Dam
Figure 3. Lake Keowee.
Discharge £
Outflow
Figure 4. Lake Keowee (region of interest) showing inputs and outputs for
three- dimensional model.
Table 2. Root-Mean-Square Difference Between IR and Predicted Temperatures
(Lake Keowee)
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
2. Summer Verification
a. Run number: L006, August 24
and 25 verification runs.
b. Run started at 2400 on August 23
and ended at 2400 on August 25,
1978.
3. Winter Verification
a. Run number: L007, February 27
and 28 verification runs.
b. Run started at 2400 on February
26 and stopped at 2400 on
February 28.
4. Accuracy of predictions is shown
in Table 2.
Conclusions
Conclusions from the application of
the three models are summarized
below. Detailed conclusions are pre-
sented in Volumes I through VI of the full
report.
Free-Surface Model
1. The model has simulated the be-
havior of a heated discharge into an
ambient basin where drastic depth
changes are occurring within accep-
table computational cost.
2. The model has accommodated signi-
ficant changes in ocean currents as a
function of tidal forcing and produced
stable accurate solutions over sev-
eral tidal cycles.
3. The model performs equally well
over summer and winter conditions
and significantly different atmos-
pheric conditions.
4. Comparisons of model-predicted
surface isotherms with measured
infrared surface temperatures indi-
cate agreement to approximately 1 °C
root-mean-square deviation.
5. The effects of inaccuracies in specifi-
cation of initial conditions are negli-
gible after half a tidal cycle for a
shallow basin such as Anclote
Anchorage.
6. Adequate data for execution of the
model can be obtained from routine
measurements ongoing at most
power plants.
Rigid-Lid Model
1. The model has simulated the hydro-
thermal behavior of the thermal dis-
charge to Lake Keowee within
acceptable computational cost in
spite of relatively small grid spacings.
2. Significant changes in the plume
caused by other inputs and outputs
to Lake Keowee, such as Jocassee-
pumped storage discharge and
Oconee hydroelectric plant, have
been simulated accurately.
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3. It has been demonstrated that short
term behavior of a plume over a few
days can be modeled satisfactorily by
considering the mixing only in the
epilimnion.
4. The effects of inaccuracies in specifi-
cations of initial conditions become
insignificant after about 8-12 hours.
5. The agreement both during the
summer and winter simulations
between infrared measurements of
surface temperature and model
simulations was around 1°C root-
mean-square deviation.
6. The data base needed to execute the
model is readily available from
routine measurements at most
power plants.
One-Dimensional Model
1. This model provides better results at
mid depths compared to other
existing one-dimensional stratifi-
cation models for lakes. This is
attributed to the inclusion of effects
owing to area change with depth,
which is unique to this model.
2. The model predicted the thermal
stratification in Lake Keowee over a
period of 9 years with no year-to-
year degeneration in results. The
model can be used to predict the
approximate stratification in a lake
with thermal discharges and other
inputs and outputs such as pumped
storage and hydroelectric plants over
a long term period.
User's Manuals and Codes
1. The program codes have been satis-
factorily transferred to EPA's compu-
ter system at Research Triangle Park.
Accurate transfer has been checked.
2. The user's manuals were prepared
as separate volumes to facilitate their
use.
3. The ease with which the staff at Re-
search Triangle Park executed the
programs using very brief instruc-
tions suggests that other users will
find the programs easy to use by
following the user's manuals.
Recommendations
Recommendations include:
1. The turbulent closures used for both
the free-surface and the rigid-lid
models could be changed to include
effects of buoyancy through a Richard-
son number formulation. Higher
order closures could also be in-
cluded. Though there is no guarantee
that this would improve predictions.
it would include more of the mecha-
nisms of turbulent transport.
2. The surface heat transfer conditions
in the three-dimensional models
could be improved where more data
is available to separate individual
components of heat transfer rather
than using the surface heat transfer
coefficient formulation.
3. The programs could be improved to
facilitate use of variable horizontal
grids. This would provide increasing
spatial resolution near the discharge.
4. For the rigid-lid model, when a use-
able direct Poisson solver for the ir-
regular domain Neumann problem
becomes available, it should be in-
cluded in the model to solve the sur-
face pressure equation. This would
make the rigid-lid model significantly
more efficient. It would reduce the
computation time for solving the sur-
face pressure field, which, at pre-
sent, is the most time consuming
part of the program.
5. Tests could be conducted with the
models to determine sensitivity to
open-boundary conditions when the
domain is not completely surrounded
by solid shorelines.
6. The one-dimensional model could be
modified to simulate multiple domains
connected by input/output terms.
This would decrease the inaccuracies
resulting from assuming horizontal
homogeneity in multiple basin do-
mains.
7. All the codes could be modified to be-
come quasi-interactive to allow for
easier execution by the user.
References
1. Lee, S. S., and S. Sengupta. Pro-
ceedings of the First Conferernce on
Waste Heat Management and Utili-
zation. Miami Beach, FL May 9-11,
1977.
2. Lee, S. S., and S. Sengupta (com-
pilers). Proceedings: Second Con-
ference on Waste Heat Management
and Utilization (December 1978,
Miami Beach, FL), Volumes 1 and 2,
EPA-600/9-79-031a and -031b
(NTIS PB 80-112311 and 80-112329).
August 1979.
3. Dunn, W. E., A.J. Policastro, and R.
A. Paddock. Surface Thermal Plumes:
Evaluation of Mathematical Models
for the Near and Complete Field,
Argonne National Laboratory, Ar-
gonne, IL (Parts One and Two). 1975.
4. Sengupta, S., and W. J. Lick. A
Numerical Model for Wind-Driven
Circulation and Temperature Fields
in Lakes and Ponds. Ph.D. Thesis,
Case Western Reserve University.
1974.
5. Lee, S. S., and S. Sengupta. Three-
Dimensional Thermal Pollution
Models, Volume I - Review of Mathe-
matical Formulations. NASA CR-
154624. 1978(a).
6. Lee, S. S., and S. Sengupta. Three-
Dimensional Thermal Pollution
Models, Volume II - Rigid-Lid Models.
NASA CR-1 54624. 1978(a).
7. Lee, S. S., and S. Sengupta. Three-
Dimensional Thermal Pollution
Models, Volume III - Free-Surface
Models. NASA CR-154624.1978(a).
U. S. GOVERNMENT PRINTING OFFICE: 1983/659-095/0564
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S. S. Lee and S. Sengupta are with the University of Miami, Coral Gables. FL
33124.
Theodore G. Brna is the EPA Project Officer (see below).
The complete report consists of six volumes, entitled "Verification and Transfer
of Thermal Pollution Model:"
"Volume I. Verification of Three-Dimensional Free-Surface Model," (Order
No. PB 82-238 569; Cost: $13.00, subject to change)
"Volume II. User's Manual for Three-Dimensional Free-Surface Model,"
(Order No. PB 82-238 577; Cost: $16.00, subject to change)
"Volume III. Verification of Three-Dimensional Rigid-Lid Model," (Order
No. PB 82-238 585 Cost: $13.00, subject to change)
"Volume IV. User's Manual for Three-Dimensional Rigid-Lid Model, "(Order
No. PB 83-116 103; Cost: $16.00, subject to change)
"Volume V. Verification of One-Dimensional Numerical Model," (Order
No. PB 82-238 601; Cost: $14.50, subject to change)
"Volume VI. User's Manual for One-Dimensional Numerical Model, "(Order
No. PB 82-238 619; Cost: $10.00, subject to change)
The above reports will be available only from:
National Technical Information Service
5285 Port Royal Road
Springfield, VA 22161
Telephone: 703-487-4650
The EPA Project Officer can be contacted at:
Industrial Environmental Research Laboratory
U.S. Environmental Protection Agency
Research Triangle Park, NC 27711
United States
Environmental Protection
Agency
Center for Environmental Research
Information
Cincinnati OH 45268
Postage and
Fees Paid
Environmental
Protection
Agency
EPA 335
Official Business
Penalty for Private Use $300
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