(NASA-CR-165623-Vo1-5) THERHAL POLLUTION N81-23558 HATHEHATICAL H O D E L . VOLUHE 5 : USER'S H A N U A L FOB THREE-DIHENSIONAL R I G I D - L I D HODEL F i n a l Report (Hiami Univ. ) 154 p Unc las HC A08/tlF A01 CSCL 138 G3/43 23983

THERMAL POLLUTION MATHEMATICAL MODEL

(Volume Five of Seven Volumes)

USER'S MANUAL FOR THREE-DIMENSIONAL RIGID-LID MODEL

Volume V

Samuel S. Lee, Subrata Sengupta, Emmanuel V. Nwadike and Sumon K. Sinha

Department of Mechanical Engineering University of Miami

Coral Gables, Florida 33124

Prepared for

National Aeronautics and Space Administration and

Environmental Protection Agency (NASA Contract NAS 10-9410)

August 1980

https://ntrs.nasa.gov/search.jsp?R=19810015024 2020-04-21T02:58:46+00:00Z

9

STANDARD TITLE PAGE

1. R o p ~ t r NO. 1 2. Govornmrnt Accession No. 3. R o c ~ ~ i r n t @ s Cotolog No.

The three-dimensional r i g i d - l i d model was developed by the thermal p o l l u t i o n group a t the Un ivers i ty o f Miami and v e r i f i e d f o r accuracy a t various s i t es . The model r e s u l t s have been found t o be f a i r l y accurate i n a l l the v e r i f i c a t i o n runs. The model i s intended t o be used as a p r e d i c t i v e t o o l i n f u t u r e s i t e s and t h i s manual has been w r i t t e n t o enable any user t o be able t o apply i t wi thout d i f f i c u l t y .

CR- 165623 I 1. T i t l o ond Subtit'.

Thermal P o l l u t i o n Math Model Volume V, User's Manual f o r Three-Dimensional R ig id -L id Model

7. *uthor(a) Drs. Samuel Lee and Subrata Sengupta; uel V . Nwadi ke and Sumon K. Sinha

9. Poriorming Orgonirotion Nomm and Address

John F. Kennedy Space Center Kennedy Space Center, F lo r i da 32899 Project Manager: Roy A. Bland Code PT-FAP

12. Jponsoring Agoncy Nomo and Addross

National Aeronautics and Space Adminis t rat ion and Environmental Pro tec t ion Agency Research Tr iangle Park, N .C.

16. K . r Words Thermal P o l l u t i o n

5. Report 0010

6. P o ~ i o r m ~ n g O r p n i r o t i o n cod*

TR 43-4 8. Potforming Orgonirotion Roport NO.

10. Work Un i t No.

1 I . Conrroct or Gronr No.

NAS10-9410 13. Typo of Roport and Period Covorod

F ina l 14. Sponsoring Agoncy Code

Waste Heat

15. Abswact 1

I Announce i n Star

~ l ~ l o s s ~ l . ( o i this rooor@) ( 20. Socur~tv Closc~f.(c

. .... -

Category 43

22. Price a i ?his pope) I

None I None

21. No. of Pogos

PREFACE

The three-dimensional rigid-lid model i s intended to be used fo r hydrothermal predictions o f closed basins subjected to a heated discharge together w i th various other Inflows and outflows. Th is volume has been wr i t ten In order to assist any prospect ive user in apply ing the model to specific sites. Derivat ion o f the governing equations and various other details have been omitted. T h e programs are fa i r l y general and only one subrout ine and a data fl le has to be rewr i t ten for specif ic cases.

Th is work was sponsored b y the National Aeronautics and Space Administration (NASA-KSC) and the Environmental Protection A ~ e n c y (EPA-RTP).

ABSTRACT

T h e three-dimensional rigid-lld model was developed b y the thermal pol lut ion g r o u p at the Un ivers i ty o f Miami and ver i f ied f o r accuracy a t var ious sites. T h e model resul ts have been found to be fa i r l y accurate in al l the ver l f lcat lon runs. T h e model i s Intended to b e used as a pred ic t i ve tool in fu ture sites and t h i s manual has been w r l t t e n to enable any user to b e able to apply It w i thout d l f f lcu l ty .

FIGURES

Number Paqe

................................ 1 Flow char t [main program) 30

............................ 2 Coordinates and a r i d system 32

3 Map of Lake Keowee ..................................... 37

4 Lake Keowee (region o f interest) ......................... 38

5 MAR matrix ............................................. 39

6 MRH matrix .............................................. 40

7 Keowee hydro discharge. February 27. 1979 .............. 43

8 Jocassee-pumped storage station discharge. February 27. 1979 ..................................................... 44

TABLES

N urn ber Page

..................................... 1 Governing Equations 5

.............................. 2 Subroutines for Calculations 26

......... .................. 3 Input Data to hlain Program .,. 33

.................................... 4 Subroutines for Plots 36

5 Meteorological Data for Lake Keowee, February 27, 1979 . , 4 1

6 Summary of Inflows and Outflows to Lake Keowee, February 27, 1979 ....................................... 42

Horizontal kinematic eddy viscosity Vert ical kinematic eddy viscosity Reference kinematic eddy viscosity A /A ~ x r i z 6 ~ f a l eddy thermal d i f fus iv i ty Vertical eddy thermal d i f fus iv i ty Reference eddy thermal d i f fus iv i tv 8 18 ~ & c i h ~ ~ heat at constant pressure Euler number Coriolis parameter Acceleration due to grav i ty Oepth relative to the mean water level Reference depth Gr id index In x-direction o r ardirection C r i d index in y-direction o r d-direction Cr id index in z-direction o r y-d l rection Surface heat transfer coefficient Hori zontal length scale Pressure Surface pressure Turbulent Prandtl number,

Heat sources o r sinks Reynolds number (turbulent) Richardson number

Temperature '

Reference temperature Equilibrium temperature Surface temperature T fme Reference time Velocity in x-direction Velocity in y-direction Velocity in z-direction Horizontal coordinate Horizontal coordinate Vertical coordinate

Creek Letters

Horizontal coordinate in stretched system, = x Horizontal coordinate in stretched system, = y Vertical coordinate in stretched system Constant in vertical dif fusi- v i t y equation, or vertical coordinate in stretctred sys- tem, = ZlH T ransformed vertical velocity Density Surface shear stress In x-direction Surface shear stress in y-dl rection

( Dhensional quantity [-) Dimensional mean quanti ty ( ) Dimensional quantity ( ) Dimensional quantity

( ) r e f Reference quantlty

ACKNOW LEDGft ENTS

Th is work was supported by a contract from the National Aeronau- tics and Space Administration (NASA-KSC) and the Environmental. Pro- tection Ager~cy (EPA-RTP) .

T h e authors express thei r sincere grz t i tude for the technical and managerial support o f Mr. Roy A. Bland, the NASA-KSC project manager o f th is contract, and the NASA-KSC remote sensing group. Special thanks are also due to Dr . Theodore G. Brna, The EPA-RTP project manager, for h is guidance and support of the experiments, and to Mr. S. B. Hager, Chief Engineer, Civil-Environmental Division, and Mr . William J. AlcCabe, Assistant Design Engineer, both from the Duke Power Company, Charlotte, Nor th Carolina, and their data collection group for data acquisition. T h e support o f Mr . Charles H, Kaplan o f EPA was extremely helpful in the planning and reviewinq o f th is project.

SECTION 1

INTRODUCTION

T h e need fo r mathematical modeling in pred ic t ing and monitor ing thermal pollution was discussed In previous reports by Veziroglu e t al. (1973, 1974). Predictive studies o f ecosystems can only b e made by mathematical models. A p r i o r knowledge o f the effects o f disturbances is essential fo r environmental impact studies. Thus, the mathematical model i s a crucial tool In decisions invo lv ing power p lant si t ing, land development, etc.

T h e Univers i ty o f Miami team undertook development of a methodology using remote sensing and numerical modelinq to s tudy thermal pollution. The use o f remotely-sensed data in modeling has been discussed by Sen- gupta e t al. (1979). T h e remote sensing e f fo r t has been discussed in . detai l in previous publications. Th is volume has been wr i t ten so as t o enable a user to apply the mathematical model to new sites fo r p red ic t ive purposes.

T h e hydrodynamics and thermodynamics o f a n ecosystem are con- t ro l led by geometry, meteorological conditions and physical character ist ics . o f the water such as density, sal ini ty and turbidity. In th is model the effects o f salinity and turbidity have been neglected. Hence, the govern- ing equations are composed o f the three-dimensional Navier-Stokes equa- t ions and the energy equation. Various assumptions can be made for d i f fe rent situations leading to simplification o r elimination o f equations. T h e main simplifying assumption in th is case i s the rigid-lid assumption. Th is means that surface height i luctuations are not simulated b y th is model, and this i s a reasonable assumption fo r most applications (e.g., Lakes) .

T h e rigid-lid model has the following capabilities :

1. It predicts the wind-driven circulation.

2. It predicts the circulation caused b y inf lows and outflows to the domain.

3. It predicts the thermal effects in the domain.

4. I t combines the aforementioned processes.

T h e calibration procedure consists o f comparing ground- t ru th cor- rected airborne radiometer data w i th surface isotherms predicted by the model.

SECT ION 2

RECOMMENDATIONS

Various numerical models have been developed to s tudy the effects o f heated discharge and meteorological conditions on bodies o f water. Most o f these models are one o r two dimensional. These modals have a high computational speed bu t on l y g ive horizontally o r ver t ica l ly averaged values o f temperatures.

Three-dimensional models, however, have a much f i ne r resolut ion but they consume larger computer time. The three-dimensional rlgid- lid model can be used to obtain detailed temperature and velocity d is t r l - but ions in a domain where surface g rav i t y waves are small compared to the depth o f the domain. Th is model, as compared to freersurface mo- dels, r u n s faster since surface g rav i t y waves are eliminated b y the rigid-lid assumption.

' A proper method o f using th is model would be to run a onedimen- sional model in i t ia l ly to obtain a rough p ic ture o f the temperatures and then us ing th is model to obtain a bet ter resolution, the 1-D results being used as ambient conditions.

The following improvements have been suggested for the model.

1. Since al l natural flows are turbulent, proper tu rbu lent closures are needed to make the model meaningful. A t present, t he simplest possible closures, namely constant eddy viscosities and eddy diffu- sivit ies, have been used. However, better results may be obtained b y using a h igher order closure.

2. A t present, the model uses uniform horizontal g r i ds and stretched ver t ica l gr ids, Nonuniform horizontal gr ids could be introduced fo r bet ter resolution near the boundaries.

3. The program has been wr i t t en to b e run as a batch-job on the c m - puter . It could be made interact ive so as to enable the user to run it on a terminal. However, th is would require some modifications in order to reduce the storage space.

SECTION 3

PROGRAM DESCRIPTION AND FLOW CHART

DESCRIPTION OF PROGRAM ALGORITHM

The govern ing equations for a body o f water which are der ived from the basic laws o f conservation o f mass, momentum and energy are shown in Table 1. These equations incorporate a vert ical ly-stretched coordinate system so as to make the model general enough to handle any kind o f bottom topography. The problem i s set u p as an in i t ia l va lue problem, T h e in i t ia l values o f the water velocities and temperatures a r e specified and the model i s r u n so as to give the values o f the above quant i t ies in subsequent time periods using an exp l ic i t scheme. The sequence o f the calculations are as follows:

1 , T h e in i t ia l values o f the velocities and temperatures are read in to the program, l he region o f interest w i th in the basin be ing classified in to in ter ior , corner o r boundary points. (Subroutines used are READ 3K, I N I T I A , INIT IT , HEIGHT.)

2. T h e data, which includes the boundary conditions: such as the various meteorological parameters l i k e surface wind speed, a i r temperattere, humidi ty and solar radiat ion are read Into t h e program using subrout ine READ 2.

3, Depending on the site chosen, the var ious discharges (volume flow rate, velocities and temperatures) in and out o f the basin are read in to the model. These are incorporated in the subrout ine INLET1.

4. T h e momentum, cont inui ty and energy equations are now solved to determine the velocities and temperatures in the subsequent time steps. The pred ic t ive equation for pressure (viz., the Poisson equation) i s solved i terat ively to determine the pressures at various points of the domain. (Note: Because o f the rigid-lid assumption, the surface o r lid pressure is no longer atmospheric.)

THE PROGRAM FLOW CHART I S SHOWN IN FIGURE 1

The various subroutines used are as well as a b r ie f descr ipt ion o f thei r functions a r e shown in Tables 2 a n d 3.

Symbols Used in Coverninq Equations

(Quantities w i th b a r are dimensional)

= density

i = temperature

ah a ii - - = y ( ~ - ? - + V-) + ha ax ax

i = a y a f

= i l h ( n ) y

0 = ?/L

a = GIL

u = GIUref

v = G/Uref

w = iv/Uref

t = i / t ref

i: = H I L

T = T-T ref

-Tret '" ref p = -

ref

A;( = AHIAref nondimensional horizontal eddy viscosity

A: = Av/Aret nondimensior.al vertical eddy viscosity

B k = BH/Bref nondimensional horizontal eddy viscosity

6; = BV/Bref nondimensional vertical eddy viscosity

- Re = (UrefL) /Aref. RR - Uref/fL. Pr Aref/Braf

Pe = Re. Pr, E,, = gHIUref2

Table 1. Governing Equations

Continuity Equation:

a(hu1 3(hv1 a n z o + + h - a 3 a a a Y

Momentum Equation :

a(hu) alhuu) a(huv) 3(f2u) h + + - + h - - - V J t a a a 3 a y Rs

a P - 3 1 3 av - -g - h& + -1_ 4 h - + - -(h-) a a * X a , ad R. a d a s Re

3(hv) a(huv1 a(hvv1 + h 3 ( 3 v ) + hu - + + - 3 t a a 3 3 J Y RB

Ps 1 L ( h i q = - h - - hB + - 1 3 h f ~ ) 3 9 y R. 3 0 3 3 +cd , a

3 v

and

Hydrostatic Equation :

Energy Equation :

SECTION 4

LlST OF PROGRAM SYMBOLS USED I N MAIN PROGRAM

DESCRIPTION OF MAIN VARIABLES

A. A - constant in equation o f state, p = A + BT + CT2

AREF - reference eddy viscosity

AA - value o f 'V' at plume in let

ABR - 1 IRossby number

AH - 1 /Reynolds number

A1 - coefficient in f ront o f pressure term

AP - coefficient in f ron t o f pressure term

ARBP - a r b i t r a r y pressure

1 H AV - 7 where E = E

R~

A3 - normalized ver t ica l eddy coefficient of viscosity

ANGLE - wind d i rect ion angle

B, B - constant in equation o f state, o = A + BT + C T 1

B B - value o f 'V' at plume inlet (at 1=10)

BV - normalized ver t ica l eddy d l f f us i v i t y , normalized w i th respect to reference eddy d f f fus iv i ty

C. C constant in equation o f state, p = A + BT + CT2

CC - value o f r (constant)

CW - temperature gradient at vert ical boundaries

CB - temporature gradient at the bottom

D. D - U at previous time step

a P DPX - ,, a P DPY - - 3 v i ps

DPSX - - ax

DT - tlmc Increment

DY - increment in y-direction

D Z - increment i n 2-direction

a (hu) D lHUX - - 3 x

D lHVY - - 3 ( h v ) 3Y 3(huu) DlHUUX - - 3 x

DlHUVY

3 u D l U Y - - 3 Y

- - - I..

E. E - V at prevlous time step

EPS - convergence c r l ter lon

EUL - Enler number

EX - residual e r r o r In pressure l terat lon

F. FH - forc ing funct ion in pressure equation

FW - factor in wind stress calculation formula

C . C - dummy variable for V ( f o r f u tu re time step)

H. ' H - dummy variable for U ( fo r f u t u r e tlme step)

h HI - nondimenslonal depth = R

HREF - reference depth

I. I N - maximum number o f grid points in x-dlrect lon

IWN - maximum number o f ha l f -g r i d points In x-direct ion, IWN = IN - 1

I - lndex o f x-axls, maln grid

I T N - lndex for number o f I terat ions

I W - Index for x*axls, half grid

IRUN - lndex for number o f runs = 0, f i r s t run = 1, from second tlme onwards

ISGNX, ISCNY - determine s igns o f TAUX and T A U X respect ively

J. J - index fo r y-axis, main grid

JW - index for y-axis, ha l f grid

JWN - maximum number o f ha l f -g r id points in y-d i rect ion JWN - JN - 1

JN - maximum number o f main grid points in y-d i rect ion

K. K - index for Z-axis

KSTORE - specified usage o f tape for s tor inq resu l ts

KN - maximum number o f main grid points in 2-direct ion

KISS - surface heat t ransfer coefficient (nondimensional)

L - maximum length o f the domain

LN - number o f time steps to b e computed

LLN - total number o f time s teps lLN

hl. MAR - number to describe general location o f a po in t in the main ,

grid

L l R H - number o f describe general location o f a po in t in the ha l f grid

MAXIT - maximum number o f Iterations

0 . OMEGA - relaxation factor

P. P - nondimensional pressure

PN - New pressure, nondimensional

PINTH - dummy variable for pressure ( fu tu re time step)

R. R - dimensional densi ty at main grid points

RE - Reynolds number

RB - Rossby number

RINTX - density in tegrated w i t h respect to x

RINTY - density in tegrated w i t h respect to y

RO - nondimensional density a t main grid points

ROW - nondimensional density a t ha l f grid points

RREF - reference density (gmlcc)

RW - dimensional densi ty at hal f grid points (gmlcc)

RADN - solar radiat ion (w lm2)

T, T - nondimensional temperature a t main grid points

TO - in i t ia l temperature (dimensional) ("C)

TAM6 - ambient temperature (dimensional) (OC)

TAIR - a i r temperature (dirnensional) (OC)

TAI - coeff ic ient in f ron t o f convective terms in the energy equa- tion, = 1.

T A H - + where Pe = Re x Pr e

T A V - 1 H v where E =

T E - equi l ibr ium temperature (dimensional) ( O C )

TTOT - total time elapsed

T AUX - a u 1 a y (nondimensional)

TAUY - a v / a y (nondlmensional)

TEM - dimensional temperature at main grid points

TEMW - dimensional temperature at hal f -gr id points

TREF - reference temperature

TW - nondlmensionai temperature at hal f -gr id points

TLL - temperature a t the discharge po in t (nondimensional)

TSU - water sur face temperature (nondimensional)

TDEW - dewpoint temperature (dlmensional)

U. U - veloci ty in x-d i rect ion (nondimensional)

V. V - veloci ty In y-direct ion (nondlmensional)

VVlS - ver t ica l eddy viscosity (nondimensional)

W. W - velocity in 2-direct ion (nondimensional)

WH - W at ha l f -g r id points

a WHLDT - time der ivat ive o f WH at lid (1.e.. Tt(WH) I2 = 0)

X. XINT - integra l o f x terms on the r ight-hand side o f Poisson's equation

X - horizontal coordinate across discharge

Y. YINT - in tegra l o f y terms on the r igh t -hand side o f Poisson's equation

Y - horizontal c w r d l n a t e across discharge

Z. Z - vert ical coordinate

MARKER hl ATRI CES

The following number convention is used for the MAR = matr ix sys- tem, which classifies points (o r nodes) on the main grid system = (Refer to Figure).

hlAR = 0, points outside the region o f interest.

MAR = 1, point on the far y-boundary.

hlAR = 2, point on the near y-boundary.

MAR = 3, point on the near x-boundary.

MAR - 4, point on the fa r x-boundary.

MAR = 5, outside corner on near x-boundary and fa r 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.

M A R = 10, outside corner on fa r x-boundary and far y-boundary.

MAR = 11, points in the in te r io r o f the region o f in terest ,

The following number convention is used to describe the MRH (ma- t r ix for the half-grid system).

MRH = 1, corner at far x-bo!~ndary and far y-boundary.

MRH - 2, points on near y-boundary.

MRH = 3, points on near x-boundary.

MRH = 4, corner a t 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 g r id points.

SECTION 5

PREPARATION OF RUNS

Th is section presents the steps t o be followed in order to run the model f o r a part icular location.

1, The boundaries are chosen depending on the par t icu lar situation, t he general idea being to include all inflows and outflows. I f a heated discharge enters the body o f water the region of interest must be chosen so as to include th is since it i s a major factor in determining the s i re and spread o f the resul t ing plume.

2. T h e grid sixe i s chosen depending o n the resolution required. T h e user should remember that the choice o f t he grid size d i rect ly deter- mines the maximum a!lowable time step since th is i s d i rect ly re- lated b y the various stabi l i ty criteria. (See choice o f time step in Section 6.)

3. Speci fy number o f full-grid points IN, JN, KN and number o f half- grid points IWN, JWN. Since the actual domain may be smaller than the total rectangular region, INxJNxKN, the marker matrices MAR and MRH are used to specify the domain so that points outside the domain o f interest sk ip the subsequent calculatlons.

4. !RUN i s specified (= 0 f o r t h e f i r s t run, = 1 fo r subsequent runs) , KSTORE i s specified to indicate whether any tape has been assigned to store results of the run.

KSTORE = 0 i f no tape has been assigned.

= 1 i f tape has been assigned.

LLN I s specified to denote the number o f hours o f simulation to be car r ied out.

5. The depths at various places wi th in the domain are specified using subrout ine HEIGHT. T h e varlous inflows and outflows to the domain are specified using INLETI. (For details please re fe r to Blscayne Bay run, Sengupta et al. (19751,)

6, The various data l ike solar radiation, wind speed, wind direct ion and dewpolnt temperature are specifled in a data f l le whych is made by tho main program.

For fu r the r details see the next section.

SECTION 6

INPUT DATA

The data that Is required for the execution o f the main program i s l isted in Table 3 in the order it appears. Note, the data input symbols have already been defined in Section 4. Mormver, the following remarks should be observed.

* Free format i s used for all data input.

* Dist lnct ion must be made fo r in teger and real number.

* The order o f the cards must be followed.

SECTION 7

PLOTTING PROCRAhlS

T h e p lo t t ing programs fo r the 3-0 rigid-lid model a re d is t inc t from the main program and subrout ines used to run it. The user has a n opt ion o f ei ther using a tape (Un i t 8) during running the main program TMAINN to store the results o r just run it without s tor ing the results. For making subsequent cont inuat ion runs of TMAINN al l that i s requ i red i s the resul t o f the last hou r in the previous run. For plott ing, however, one needs the results o f all t h e hours for which results a re to be plotted, These resul ts are used as input data to run the various p lo t t ing programs.

DESCRIPTION OF PLOT PROGRAMS

T h e following are the main p lo t t ing programs.

PLOT - plots surface isotherms.

PLUV - plots u, v components of the velocities (i.e., 'K' sections).

PLUW - plots u, w components o f the velocities ( i . e . , 'jl sections).

PLVW - plots v, w components of the velocities (I.@. , 'it sections).

T h e various p lot programs and subroutines are shown in Table 4.

Other subroutines seen in these programs (e.g., ARROHD, FLINE, etc.) a re standard FORTRAN subroutines used fo r plott ing, us ing a CALCOMP x , y plotter, and are hence ommitted in the above l ist ing.

REFERENCES

Lee, S . , Sengupta, S., Nwadike, E. V. and 5 . K. Sinha. Veri f icat ion o f ThreeDimensional Rigid-Lid Model at Lake Keowee. Technical Report 1980, NASA Contract NAS 10- 941 0.

Sengupta, S., Lee, S. S. and R , Bland. Numerical Modeling of Circu- lat ion in Biscayne Bay. Transact ion o f the American Geophysical Union, J unc 1 975.

Sengupta, S. and W. Lick. A Numerical Model for Wind-Driven Circula- t ion and Temperature Fields in Lakes and Ponds. FTASKR-74-98, 1974.

Wilson, 6. W. Note on Surface Wind Stresses Over Water at Low and High Wind Speeds. Journal o f Geophysical Research, Vol, 65, No. 10, 1960.

APPEND ICES

APPENDIX A

EXAMPLE CASE

T h e area o f interest i s Lake Keowee in South Carolina, which was formed from 1968 through 1971 by damming the L i t t l e and Keowee r ivers. The lake i s located about 40 km west o f Greenvi l le and constitutes Duke Power Company's Keowee-Toxaway complex,

Lake Keowee has two arms connected b y a canal (maximum depth 30.5 m). The re are three power p lants on the lake, namely, the Oconee Nuclear Station, Keowee h y d r o station and Jocassee-pumped storage station. The Oconee Nuclear Station is a three unit steam-electric sta- t ion w i t h an installed capacity o f generat ing 2580 MW. T h e Oconee Nuclear Station draws in condenser-cooling water from the lower arm of Lake Keowee and discharges the heated ef f luent t o the upper arm of the lake. T h e intake s t ruc ture fo r the condcnser-cooling water allows water from 20 to 27 m depth (full pond) to pass through. The discharge ,

s t ruc ture has an opening from 9 to 12 meters below the water surface ( fu l l pond) th rough which the CCW re turns d i rec t ly to the upper branch o f the lake.

Lake Jocassee is located n o r t h o f Lake Keowee and i s used as a reser- vo i r for Jocassee-pumped storage station, Lake Keowee also serves as the lower pond for this station. T h e Jocassee station has reversible turbines wi th a maximum generat ing flow ( in to Lake Keowee) o f about 820 m3/sec and a maximum pumping flow (out o f Lake Keowee into Lake Jocassee) of about '175 rnl Is=, the ne t flow in to Lake Keowee from Jocas- see being about IS. 5 m lsec.

Lake Keowee has a full pond elevation o f 243.8 g above MSL. A t fu l l pond i t has a volume o f approximately 1.18 x 10 m3, an area o f 74 kmz, a mean depth o f 15 .0 m and a shoreline o f about 489 km. T h e outflow from Lake Keowee i s t h rough Keowee h y d r o station and may vary from approximately 1.4 m3 /sec [leakage] to 560 mJ lsec. h.laximum allow- able draw-down o f the lake i s 7.6 m.

A map o f the area o f in terest i s shown in F igure 3.

PROBLEM STATEMENT

The objective of the present work i s to find the three-dimensional temperature and velocity d is t r ibut ions in the region where the effects of the thermal discharge are noticeable. The effects of Jocassee-pumped

storage station, Keowee hyd ro stat ion as well as the meteorological condi- t ions have been incorporated.

The region o f in teres t i s chosen to inc lude the effects o f the Oconez Nuclear Station discharge, the outflow th rough Keowee dam and the impact o f the Jocassee-pumped storage stat ion on t h e velocity and temperature d is t r ibut ions in Lake Keowee. T h e depth o f the domain i s c u t o f f a t 16 meters, since th i s i s t he level at which the thermocline occurs. Hence, for running the model, a constant depth region i s considered, T h e plan view o f the domain i s shown in F igure 4. (Note: For variable dep th re fe r to Biscayne Bay simulation studies b y the Univers i ty o f Mlami thermal poi lut ion group.) In th is f igure, A 6 i s an open boundary which takes care o f the flow from o r to the Jocassee-pumped storage station. 'Ct shows the posit ion o f the flow in the canal connecting the two arms o f the lake. IDt i s t h e discharge point for the Oconee Nuclear Stat ion and 'El i s the outf low from Keowee h y d r o station.

The inclusion o f t h e above resul ts in a domain 2895.6 m x 2438.4 m in t h ~ horizontal plane. T h e horizontal grid sixe ( i n x and y directions) i s 152.4 m x 152.4 m, g i v i n g a total o f 20 x 17 (= 340) nodes in t h e horizontal plane, o u t o f which 293 l i e in the region of interest. T h e 1 6 m constant dep th region o f in terest i s d iv ided in to 4 equal slices of 4 rn each, g i v i n g a t tota l o f 5 nodes in the ver t ica l (Z) ld i rect ion. Hence, there are 293 x 5 nodes ( g r i d points) in the region o f interest. T h i s region i s specif ied using the MAR and MRH marker matrices (F igure .

5 and Figure 6).

Boundary Conditions

On the Jocassee effect boundary, the f l o ~ ~ ~ e l o c i t y (vary ing w i t h time) i s specified. Open-boundary condit ion (- = 0) i s specified fo r the temperature. aY

The same i s done fo r the Keowee h y d r o boundary. T h e only d i f fe r - ence i s that t he values specified a re at th ree points in the vert ical plane (i. e. , at K = 1, 2 a n d 3) since th is region covers the discharge area.

For the Oconee Nuclear Station, the discharge velocity as well as the discharge temperature i s specif ied at t he discharge point.

Open-boundary conditions are specif ied fo r the temperature and velocity a t the canal. This, however, leads to a possible violation o f mass balance in the region o f interest. T h i s mass unbalance wi l l actually show up as a variat ion in the water level in t h e lake which is beyond the capabi l i ty o f the rigid-lid model.

A t a l l solid boundaries as well as the ar t i f i c ia l bottom (since t h e bottom i s cu t o f f a t 1 6 m) ' perfect insulat ion (temperature gradient = 0) and xero velocity condit ions are assumed.

A t the surface, the vert ical component o f the velocity i s specified

as zero ( r ig id- l id constraint) . Suroface wind shear stress and heat t ransfer coefficient are specified.

I ni t ial Conditions

The in i t ia l values o f the water velocities are assumed to be zero. T h e in i t ia l temperature o f the lake i s assumed to be equal to the am- b ient water temperature (determined by running a one-dimensional model) and i s taken to be uniform throughout the domain.

CALCULATION OF PARAMETERS AND INPUT DATA

Reference Quantit ies

Reference length = L = maximum length o f the domain = 2895.6 m.

Reference horizontal eddy viscosity Aref = 0.002 L 413

For bet ter agreement w i t h data the value chosen i s 60,000 un2 Isec.

Reference depth = H = 16 m.

Reference vert ical A,, = 0.002 x (H) 413.

Eddy viscosity = 37.43 cm2 /see.

Reference velocity = Vref = 30 cmlsec.

Reference temperature = Tref = 10.O°C.

Reference time = LIVref = 9652 sec.

Calculation o f Inf lows and Out f lows in to the Domain (Used in INLET11

Oconee Nuclear Station Discharge Velocity-- The discharge i s considered to take place th rough a point at a

depth o f 12 m (k = 3). T h e discharge velocity i s calculated as follows:

The total discharge in to the basin is equal to:

. (100 x V x 152.9 x 12) = (1

where Q = average discharge in m3 /sec

= 7.42207 cm lsec

The average values of Q over 24 h r s i s taken since the variat ion is negligible.

v - " = 0. 24744 Nondimenslonal discharge velocity = v - 3 r e f

Keowee Hydro Discharge Velocity-- The outflow through the Keowee hyd ro station i s th rough a channel

152.4 m x 12 m.

The volume flowrate Q = (1 52.4 x 12 x V ) m3 lsec

where V = discharge velocity (m lsec)

) cmlsec . ' . V = [ Q I ( 1 5 2 . 4 x 1211 mlsec = (152,4x1a100

Q i s specified as a function o f time in INLET1.

The procedure for nondimensionaii zation i s similar.

Jocassee Flow Velocity-- The ent i re flow to o r from the Jocassee-pumped storage stat ion i s

assumed to take place through the ent i re upper boundary ( A 6 in Figure 4) . The flow through th is area (shown below) Is assumed to b e uniform and i s assumed to take place s i m u l t a n ~ u s l y w i th the outflow through the Jocassee station.

Q = flow through Jocassee (rn3 Isec).

Q i s posit ive when Jocassee i s generat ing (1.e.. the flow i s i n to the region o f interest) and negative when pumping (l.e., flow out o f region o f in terest) .

SAMPLE INPUT

The following are the inputs to TMAINN contained i n the data file IPUT (which includes values calculated earl ier).

Input No. of Data Symbol # I n Card

Value

1 3 IRUN = 0

KSTORE = 1

LLN = 3

V V 1 S = 37.43160,OOO = 0.00062384

ABR = 0.78

AP = 1.0

EPS = 0.001

OMEGA = 1. 8

ARBP = 1.0

DZ = 4 / 1 6 = 0.25

T A1 = 1.0

T A H = AH = 0.01 228172

T AV = AV = 402.08304

Input No. of Data # I n Card

Symbol Value

EUL

TLL

TAU = 0.01 52 cm2 lsec

Criterion (convective)

A x 1 5 2 . 4 ~ 1 0 0 = A t < - = U 3 0

= 504 secs > 504 secs

Hence, convective criterion dominates; choose AT = 300 secs

Note: choose best time step by trial and error

CTTOT

ISOTOP

WS

TSU

TDEW

RADN

ISGNX

ISGNY

ANGLE

See Table S

See Table 5

LAKE KEOWEE APPLICATION-EXECUTION DECK

T h e following execut ion deck i s for use in the UNIVAC 1100 computer a t the Univers i ty o f Miami. These may have to be modified i f a d i f fe ren t computer is used.

(ALL PROGRAMS AND SUBPROGRAMS COMPILED AND STORED I N FILE)

F i r s t Run

1. 8 ASG, AX FILE.

(THE F I E I S ASSIGNED FOR THE RUN]

2. 8 ASG,T 8, 16N, TAPENAME.

(A TAPE FlLE NAMES '8' IS BEING ASSIGNED. THE TAPE IS 9-TRACK, AND THE REEL NUMBER IS 'TAPENAME')

3. 0 PRT,S FILE. ThlAINN

(THE MAIN PROGRAM IS PRINTED)

4. 8 PACK FILE.

(THE FlLE I S PACKED)

5. 8 PREP FILE.

[ENTRY POINT TABLE IS PREPARED)

7. I N FILE. TMAINN

8. L I B FILE.

9. END

10. 8 XQT

11. 0

(VALUE FOR IRUN,FIRST RUN: IRUN=O)

(NUhlBER OF HOURS REQUIRED, MINlMUM=I HOUR, MAX=24)

(0 I F MACNETIC TAPE I S REQUIRED TO STORE RESULT, I F NOT, ANY NUMBER)

14. 8 ADD FILE. INPUT

(INPUT DATA FILE FOR THE PARTICULAR RUN)

15. 8 FIN

EXECUTION DECK FOR PLOT PROGRAMS

1. @ ASC,AX FILE.

3. 8 ASG,T 11., 16N, PLOTTAPE.

(A MAGNETIC TAPE FILE NAMED '11' IS BEING ASSIGNED. THE TAPE IS 7-TRACK AND THE REEL NUMBER IS 'PLOTTAPE'. THE PLOTS ARE STORED ON THIS TAPE)

4. @ PRT,S FILE. PLOTTER

(THE PLOT PROGRAM IS PRINTED)

5. 8 PACK FILE.

6. 8 PREP FILE.

7. 8 MAP,S

8. I N FILE.PLOTTER

9. L I B FILE.

10. END

11. 0 X Q T

12. @ ADD FILE. INPUT

13. d FIN

Table 2. Subrout ines Required in Main Program TMAINN

DVISU

-.

No.

1

DVVY

DUVY

Name

DVlSV

D l NERU

TPRINK

PRUV

PRITEX

Description

Computes 0 IVY, D2VYn O l V X and D N X .

T P R l N l

STORE2

Remarks

Called b y subrout ine INTE. Schemes used similar to DVISU.

RWR

Computes DIUX, DZUX, and D1UY.

1 Computes DIHVVY.

Computes D 1 HUVY.

Computes DlHUUX and DlHUVX.

Pr in ts temperatures at a grid point.

Pr in ts the values o f U and V at all main grid points.

Pr in ts the No. o f i terat ions (ITN) and f inal residual e r r o r in solving the Poisson equat io~

Pr in ts the input parameters,

Stores values o f input para- meters and physical quanti t ies on tape 98

Computes real vert ical veloci- tles from modified vert ical velocities used in equations a t Integral grid points.

au Q Called by INTE. - a r e computed at inid;io%? boundary o r corner p t s by scheme similar t o the one used in DINERU.

a Called by INTE. - (hvv) i s computed fo r in?efior. boundary o r corner by a scheme similar to t h e one used in DINERU.

a Called by INTE. - (huv) i s computed fo r in?e!ior, boundary and corner p t s by a scheme similar to the one used in DINERU.

Called b y INTE. T h e re- sul ts are used in Poisson equation for pressure.

Called by TMAINN.

I Called by TMAINN.

1 Called by TMAINN.

I Called b y TMAINN.

Called b y TMAINN.

Table 2. Subroutines Required in Main Program TMAINN (Continued) -

No.

1 2

1 3

1 4

1 5

16

17

18

19

20

2 1

- -

Name

RWRH

DENSTY

TEQ 6

0 LDT

TEMB2

. TEMI 4

RWH

OLDUV

UVTOP

UVT

--

Descript ion Remarks

Computes real vert ical veloci- ties at hal f -gr id points.

Called by TMAI NN.

Uses the equation o f state and computes density f ield from the temperature field.

Sets the values of temperature field at time step 'nu equal to the temperature f ield at (n+l) after al l computations fo r time step In' are completed.

Called by TMAINN.

Allows for vert ical mix ing at a particular grid point. Program is called by TMAINN.

I f the temp at the g r i d pt just above It i s less and the difference i s more than a specified maximum, the two temperatures are averaged.

Computes temperatures at the boundary points in the domain o f interest.

Computes vert ical velocities at Called by TMAINN. half-gr id points. I

Called by ThIAINN.

Computes temperatures at the inter ior points o f the domain o f interest.

Called by TMAINN.

Sets the values of D and E equal to U and V respectively in order to re ta in value, o f U and V at one time step lag.

Called by T X1Ai NN.

Computes U and V a t the top using wind stress boundary conditions.

Called by TMAINN. Com- pirtations are made for MAR = 11 only ( internal grid points).

Computes U and V fo r variable density at successive time steps.

Called by TMAINN,

Table 2. Subroutines Required in Main Program TMAINN (Continued) -

FORCE Computes R. H.S. o f Poisson's Called b y TMAINN.

2 3 ~ I Equation at hal f -gr id points.

22

Computes OPSX and DPSY, 1 Called b y TMAINN.

Remarks No.

ROINTY Computes Y in the Poisson's Called by TXlAINN. 2 5 1 I Equation. P

PRE lL

Name Description

Computes pressure for far f ield from Poisson's Equation a t hal f -gr id points.

26

Called by TMAI NN.

27

ROINTX

2 8

CORINT

29

Computes X in the Poisson's Equation. P

INTE

30

Called b y TMAINN.

Adds integral of Cotiolis' component XINT and YINT.

WHATIJ

Called b y TMAI NN.

Computes XINT, YINT, DPSX, and DPSY.

WHTOP

31

32

Called b y INTE.

Computes the values o f W at I, J from the values o f WH at IW, JW.

Calculates " H i r t and correct ion term at half-gr id points and at the surface (WHLOT).

ERROR

33

Called b y TMAINN.

Sets the value o f WH equal to zero at the surface.

Called b y TMAI NN.

I READ2

34

Called by TMAINN.

INLET1 I

Reads in inpu t parameters and physical quantit ies stored on tape 47.

Puts in velocities u and v I Called by TMAINN. pheme discharge, etc. i n to the model.

HEIGHT

Corresponds to store 2. Called in by TMAINN.

Inputs depths o f the basin in to the model.

Th is subrout ine i s fo r a constant depths model. Cal led by TMAINN.

Table 2. Subroutines Required in Main Program TMAINN (Continued)

IN lT lA Initializes values o f U, V, WH, Called by TMAINN. 3 6 1 I W, '3, E and PINTH.

35

No. Description Name

IN IT IT

37

Remarks

i IPUT

Sets ini t ial temperature field.

READ 3K

Data files containing values of input data for the respective days.

Sets the temperature f ield equal to r e f temp at al l grid points. Called by TMAI NN.

Classifies region o f Interest Into interior, corner and boundary points using matrix MAR.

Called by TMAINN.

Jn I READ3K - Classifies the re- I 1

F i r s t run? (IRUN gion into in ter ior , corner o r boundary points. I

READ2 - Reads tape for WH, D , E and P.

data of revious run P I INITIT - lni t ial fzes T and p . HEIGHT - Inpu ts depth. I

1 INLETI - lnputs V, U, ( I INLET1 - inputs V, 'u, T D TO to s ta r t run. I

ERROR - Computes WHLDT WHT OP - Sets WH equal to zero WHATIJ - Computes W l NTE - Computes XINT, YINT, DPSX and DPSY ROINTX - Computes Xp ROINTY - Computes Y F DPSXY - Computes D SX, DPSY FORCE - Computes FH PRElL - Computes PN UVTOP - Computes U and V a t the top OLDUV - S e t s 0 = U a n d E = V RWH - Computes vert ical velocit ies at half-gr id points WHATIJ - Computes W at grid points +EM1 4 - Computes temperatures at in ter ior points TEMB 2 - Computes temperatures at boundary points 0 LDT - Updates temperatures TEQ B - Allows for vert ical mix ing DENSTY - Computes density f ie ld INLET1 - lnpu ts V, U and T D every time step

No I

RWRH - Computes real ver t ica l velocities RWR - Computes real ver t ica l velocities STORE2 - Stores computed resul ts o n magnetic tape (un i t 8) T P R l N l - Pr ints input parameters PRITEX - Pr in ts number o f i terat ions and e r ro r

F igure 1. Flow chart (main program)

. . . .

I PRUV - Prints U and V YPRlNK - Prints temperatures I

' No Time Up? '

1 Yes

I Put another EDF on tape (unit 8) I

Figure 1 (Continued). Flow chart (main program)

Table 3. lnput Data t o TMAiNN

Defini t ion N a l u e

= 0 f o r f i r s t run

= No o f hours o f simulation

= 0 i f no tape i s assigned = 1 i f tape i s assigned

= Nondimensional vert ical eddy v iscosi ty

fL = 1 IRossby No. = r e f

= Coeff ic ient in f ron t o f iner t ia term = 1.0

= 1 /Reynolds No. = Ref eddy hoz viscosity

" re f

= (1 /c2Re) (s = H / L l

= Coeff ic ient in f ron o f pressure term = 1.0

= Convergence factor = 0.001

= Maximum number o f i terat ions fo r Poisson Equation

= Relaxation factor = 1.8

= A r b i t r a r y pressure = 1.0

= Horizontal grid spacing (x d i r . )

= Horizontal grid spacing (y d i r . ) = A y / L

= Vert ica l grid spacing ( z dlr.) = Az/H

= Coefficient o f convective terms in energy equation = 1.0

= Horizontal eddy d l f f us i v i t y = AH (usual ly)

Symbol

IRUN

LLN

KSTORE

VVlS

ABR

A l

AH

AV

AP

EPS

MAXIT

OMEGA

ARBP

DX

DY

DZ

TAI

TAH

lnput t

1

2

3

4

5

6

No. o f Data In Card

3

2

4

4

4

3

3

1 nput #

Table 3. Input Data to TMAINN (Continued) I I

I TAV I = Vert ica l eddy d i f fus iv i ty = AV (usually)

N o . o f D a t a In Card

TO

EUL

CW

= 1.000428 These are coefficients = -0.000019 in the equation of = -0.0000046 state f o r water where

p = A + B T + CT2 (gm I c c l

Symbol

= Reference temperature (bC)

Defini t ionlValue

= Euler No. = *

= Temperature gradient at ver t ica l boundary

= Temperature gradient at the . / CB I bottom

I = Nondimensional discharge veloci ty = (discharge velocity) lUref I CC I = No dimensional depth = h lHref

1 I TLL I = Nondimensional discharge tem- pera ture = (T,, - To) /To

T A U

DT

CTTOT

= Surface shear stress (from Wilson Curve) (Refer to F igure 7)

= Nondimensional time step = bT(L/Urel)

= Converts nondimensional time to hours

1 I ISTOP I = Number of hours o f previous run

6 I WS I = Wind speed (mlsec)

I TSU ( = A i r temperature ('C)

I TDEW 1 = Dewpoint temperature (OC)

RADN = Inc ident solar radiation (w lm2)

Table 3. lnput Data to TMAINN (Continued)

= +I i f x component of W S is negative

= - 1 if x component of W s is positive

= +1 if y component o f W S is negative

= - 1 if y component o f W s is positive

lnput #

No. of Data I n Card

17

Definition /Value

= Direction o f W g (degrees) with respect to the x axis

1 ANGLE

Table 4. P lot t ing Programs

No.

1

2

3

4

5

6

7

Name

PLOT

PLUV

PLUIV

PLVW

ECHKON

CONLIN

ENDER

Program Descript ion

Plots surface isotherms

Plots velocities, K section

Plots velocities,, j sectlon

Plots velocities, i section

Calculates equal temperature points

Draws the isotherms

Writes the values o f the tempera- tu re on the isotherms

Remarks

Called by PLOT

Called by ECHKON

Called by ECHKON

Jocassee Dam

OCONEE COUNTY

Nuclear Stn.

Figure 3. Lake Keowee

- -- - pp

Figure 5. MAR marker matr ix

F i g u r e 6, h!RH m a r k e r matr ix

Table 5. Meteorological Data for Lake Keowee (February 27, 1979)

Wind Direction (Degrees)

1 So

75O

60 O

1 So

50 O

85 O

85 0

60 O

So

75O

15O

40 O

80

70 O

80 O

7S0

55O

15'

30"

25O

5S0

55O

50 O

60° -

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. 31

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

Dewpoint Temp ( O 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

- 5.00 -5.56

A i r 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

Time (hrs from midnight)

1

2

3

4 '

5

6

7

8

9

10

1 1

12

13

14

15

Wind Speed [m 1s)

1,833

1.073

2. 325

1.565

2.056

1,788

2.01 2

2.280

0.626

1.386

1.609

1.788

3.129

2.593

1. 520

16

17

18

19

20

21

22

2 3

24

1.207

1.565

1.609

2.056

1.162

1.772

2.861

2.995

1.386

13.89 1 -5.56

13.83

13.72

11.72

9. 72

8. 33

7. 78

7.00

5. 28

-5.61

- 3.33 -4.44

- 2.78 5. 28

5, 56

5. 28

3. 89

Table 6. Inflows and Outflows to Lake Keowee

Keowee Hydro Flow

(c. F.s.)

4 8

4 8

4 8

4 8

4 8

48

48

3668

17540

8488

8096

2680

4 8

48

48

4 8

48

48

4 8

4 8

4 8

4 8

4 8

48

4 8

Net Jocassee Flow

(c. F.s.)

- 14395

- 18754

- 18805

- 1 871 3

- 18698

- 18688

- 15939

3484

16823

13503

5470

100

100

100

100

100

100

100

100

100

100

100

100

100

- 4382

Oconee Discharge ~ e m p (OC)

18. 6

18. 5

18. 4

18. 5

18. 3

18. 3

18. 3

18. 2

18. 3

18. 2

18. 3

l a . 3

18. 4

18.5

18. 5

18. 4

18. 4

18. 4

18. 4

18. 4

18. 3

18. 2

18. 2

18. 2

18 .2

Time Feb* 27#

12.00 a.m.

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

10.00

11.00

12.00 p.m.

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

10.00

11.00

12.00 a.m.

Oconee Discharge (m2/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

7101.9

7507.5

7511.0

751 6.2

751 8. 9

7520.4

751 6.6

7509.4

7507. 2

Figure 7. Keowee hydro dlscharae (February 27, 1979)

Figure 8. Jocassee-pumped storage station discharae data (February 27, 1979)

APPENDIX B

FORTRAN SOURCE PROGRAM LISTING

LIST OF MAIN PROGRAM AND SUBROUTINES

* f l E . i 1 4 : l l . * N : ? o . * cS15 ' . u t 15 ~ h , n f * I l

. ~ U I ~ . ! W I . - . I d m T l I - h , J m ' ~ l , X I 4 1 1 f ' l e >.-'dt O W 1 1 r ' a ~ d ' l l # f i r ( l ! h . J h I , i P S l l f % r J % l t .S IC' l l J l # f . l t .513'1 l l l ! . , r ? 1 ~ * 4 1 ~ I l l l N , J ' d , L \ l , d 1 ' 6 1 1 1 1 CSIS\ 1. I I .Y I . . td . r t * Y s 1 3 f d ~ A 1 1 5 t , C , * h l I . I S S

PRECEDING PAGE BLANK NOT ntWOb

t 4 f r i 1 s: l:! I r ? I : ! :.. I:! t i ' I s ' 1:i I . a

J 8 ..*...*... b t i d 9 :

ma... I*...

~ , H ~ , O V , P I * * l l : 4 i J V I

m...... . r T l 4 .*.*... h U V I , M A R 1 , * 1 i 3 1 l % . J ' 4 l

a . ! r ! t l l , : . , l c:.i c a : A f : g :v c -i* !C 4 1 1 1 : 1 5 : 1 ; ,.. I * m * * * * * s * ~ * * m * * s s * * * o * * * * * * * * * * * * * . * m m * * * * m ~ * * * * . - 1 ' 1 % ~ d ~ ~ : u l ! ' s ~ c : " ; ~ f c s 2 1 * # # ? 1 ; ...***-..a-• . . . - . - * * # * * . . * . . . o... * , . * * . . * * * ~ s m m * * * O m

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SAMPLE PLOTS

RUN NOS LBO 7. O f SCHRROE VELOCITY r 6 *04CH13EC UISCHRRDE TEflPERATURE a 1 0 . 4 ' ~ HIND SPEED CflAXl a 4.SlH13EC CURRENTt3OCRSEE FLOHIr 4.0 CH13EC TOTAL SIHULRTED TIHE 8 1 - 0 1 HRS

. lo1 LENOTH SCALECtiETERSf 0 000 61 =OO +

I

I ,

I

I I

I

-

' . .., ISOTHERMS RT K= 1. LRKE KEBWEE-LRIGIO-LIO flBOELf SIHULRTIQNS FOR FEB. 27 1979

RUN N0a LOQ 7. o ISCHRRDE VELBC ITY 1 B . ~ ~ C ~ / S E C 0 ISCHRROE TEHPERRTURE a 1 0 . 4 ' ~ WINO SPEED [ ~ R X I 8 ~ . S ~ H / S E C CURRENTtJBCRSEE FLOWlr 4.8 CH/9EC

. TOTRL SIHULRTEO TIHE 1 2.01 HRS 810'

LENGTH SCRLE[nETERSl 0 a 0 0 61 a 0 0

+

-- . -- .-.- -. ISOTHERflS RT K= 1. LRKE KEBWEE-(RIGID-L ID flBDELf S I f l U L R T l B N S FOR FEB* 27 1979

----

- - VELOCITIES AT K = 1 . LRHL HEOWEE-[RIGID-LIO flOO€LI SIf lULATIONS FOR FEB. 27 1979

RUN HBa LO0 8. OISCHRROE VELOCITY I ~ . ~ Z C ~ / S E C OISChRROE TEHPERRTURE I 3 1 . 7 ' ~ .

WINO SPEED t f l R X l 8 3 * 0 9 f l / S E C CURRENTtJOCRIBE F L O W I r 1 . 1 CH/SEC TOTAL SIHULRTEO TIfiE r 1.01 HRS

# l o 1 LENOTH SCALE[ HETERS 1 0 a00 61 a00 + VELOCITY SCALE[Cn/3ECl 0.00 12 a00

- * *

t ( @

r * \ . . , I ,

I 4 4 @ O @ @

d d I J I I # # i @

- # I I I I I # o # t

- I I I I # I B ~ r @

- I # # d I . @ v

- I d r r . r b @ r (

O O ~ ~ r b ) ( (

- / 0 . . , - - * . * -

r o ~ r - b o * *

t - a * \ t - . * * \ #A\ \

-

I I

. -

- . . . . . V E L O C I T I E S AT K= 2 . LAKE KEOWEE- IRIOIO-LID MODEL) S I f lULATIQNS FOR FEE* 27 1979

RUN NO8 LOO 6. OISCHRROE VELOCITY r 7*42CH/SEC OISCHRROE TEHPERRTURE 8 3 1 . 7 ' ~ WINO SPEEO tHRX1 8 3*09H/SEC CURRENTtJOCRSSE FLOW18 1.1 CHlSEC TOTAL SIHULATED T I M 8 1.01 HRS

~ 1 0 ' LENOTH SCRLECHETERSI 0 .00 61 a00 + VELBCITY SCRLEtCt!/SECI 0 a00 12 a00

L

r

L

b \ \ ! t :,\ \

- - - .--

' :-->\ I I

t

4

t

C

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9 b

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- - - . . . a .

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- - * * * * b

- - - - . . . . b 1 ' * m * * * - - - \ \ \ b b & , . ,

* . - - * * - \ \ \ t t 4

b . . S \ \ t t b

RUN N01 LO0 6. OISCHAROE VELBCITY a 7 *42CH/SEC OI8CHRROE TEHPERRTURE a S 1 . 7 ' ~ HXNO SPEED [HAXI a 3 *09H/8EC CURRENT t JOCRSSE FLBH 1 1. 1 C ~ / S E C TBTRL SIHULATED T I H E a 1 a 0 1 HRS

. loL LENGTH SCRLEt llETER3 I

61 a 0 0 0;oo , +

VELBCIrV SCRLEtCH/aECl 0 .oo 12.00 - - 9

t - @ b

* t v

- \ \ * - - a & & b b

- * \ ' 5 * r r b b b b b

* . * S S * * * . * * * * b

* \ * * * * b b

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a * - * * \ \ % \ t 4

- r ~ \ \ \ \ \ \ # t b r r r

a... \ \ \ \ \ \ t t 4 . . t 4 ,

b \ \ \ \ -

VELOCITIES RT K= 3 . - - - - - -- - _ . __ .___

LAKE HEIWEE-(RIOIO-LID MODEL1

- - . - - - - - .-. VELOCITIES R T K= 4 a LRKE KEOWEE-(RIOIO-LIO flQOELl SIMULRTIONS FOR FEBa 27 1979

RUN NO1 180 6. OISCHAROE VELOCITY I 7 *42Cn/SEC OISCHRROE .TEHPERRTURE 1 31 * 7 ' ~ WINO SPEED ( ~ R X I 8 ~ . O ~ H / S E C CURREHT(JBCR39E F L B H I r 1.1 CHISEC TBTRL SIHULRTED T I R E I 1.01 HRS

.1 o1 CENOTH SCRLEt nETER3 1 61 -00 0;OO ,

+ VELOCITY SCRLE[CH/SECI 12.00 0;oo ,

- t - - 4 r b b

* I t

r * r 4 b b b

c * r . b b b b h

. , . . , b ' . * * @

- r * b b b

r r r r * % b b

* ' * \ % % % $ $

c * b r

r r \ \ \ \ b r b r .

r * \ \ \ \ $ t 4 4 .

* \ \ f \ $ b

\ f ! t - . \ \ \ f . ..\ \ , L

.

i

RUN NO8 LOG 6 . OISCHRROE VELBCIXY a 7 *42Cti/9EC OISCHAROE TEHPERATURE r 3 1 . 7 ' ~ WINO 8PEEO ( t I A X 1 a 3.09H/SEC CURRENT[ JBCR83E FLBW 18 1 *l Cti/SEC TBI'AL SIHULATED TIHE a 1.01 HRS

. l o1 LENGTH SCALE[ HETER9 I

0 *OO 6 1 a00

+ VELBCITY SCRLEtCH/SECI

O..OO 12.00

I I

I

I

-

I 1 A

_ _-_ - - - --- VELOCITIES AT K= 5 . _ _ . - - - - LRKE KEOWEE-(RIGID-LID neoELl SIMULATIONS FOR FEE* 27 1979