ML20148S036

Forwards Analysis in Support of Functional Form,Used in the Centerline Temp Rise Relationships for the Thermal Plumes. Also Attached Are Centerline Temp Rise Plots Showing Actual Field Data Points from Past Monitoring Years

ML20148S036
Person / Time
Site:	Cooper
Issue date:	11/15/1978
From:	Paily P HAZLETON LABORATORIES AMERICA, INC.
To:	Codell D Office of Nuclear Reactor Regulation
References
NUDOCS 7812010122
Download: ML20148S036 (10)

Text

~ _ _ _ - _ _ .

s 1 v N)' HAZLETOT so-29g M ENVIAONMENTAL SCIENCES CO APCAATION iSCO mONT AGE AC AD. NO AmB ACQK. WWS 60062. U S A j 1

15 November 1978 I

o U.S. Nuclear Regulatory Commission Operating Reactor Branch No. 3 Division of Operating Reactor Washington, D.C. 20555 Attention: Dr. Dick Codell

Dear Dr. Codell:

This has reference to our telephone conversation on 8 November I and the submission from Nebraska Public Power District regarding i thermal plume monitoring at the Cooper Nuclear Station, Brownville, Nebraska. As requested during the telecon, enclosed please find an analysis in support of the functional form used in the center-line temperature rise relationships for the thermal plumes. Also j attached are copies of centerline temperature rise plots showing '

actual field data points from past monitoring years.

I hope the attached material is sufficient to meet your require-ments. If any additional information is needed relative to the matter, please contact the Distr 4.ct at your earliest convenience.

Sincerely yours, P. P. Paily, Ph.D.

Enclosure cc (with enclosure):

Vernon L. Rooney, USNRC John Cooper, NPPD l \

l AHCNE (312) 564-0700 o TELE X 20-9483 (H AT.E S NBC vJ

\\\

7%laol olp . .. .. .- - . .

HAZLETON ENVIRONMENTAL SCIENCES COOPER NUCLEAR STATION THERMAL PLUMES Relationship for Centerline Temperature Rise 4

By  ;

P.P. Paily, Ph.D.

Ha71eton Environmental Sciences Corporation j l

l In a broad sense, the dimensionless centerline temperature rise 1 I

within a river thermal plume can be expressed as a function of l l

. several independent variables in the following manner:

ATc ATo

=f1 (X, D, W, bo ,ho,Vj,VR, V, Pa, Ap , g) (1) in which ATc = centerline temperature rise within the plume at any distance X downstream from the source. l AT g = effluent temperature rise at the source. )

X = = downstream distance from the source along the plume centerline  ;

trajectory.

D = river depth.

W = river width, bo = width of heated discharge channel.

ho = depth of heated discharge channel.

Vj = velocity of heated discharge jet at the source.

VR = ambient river velocity.

v = kinematic viscosity of water at the source.

pa = ambient water density.

Ap = density deficiency of heated water at the source.

9 = acceleration of gravity.

. HAZLETON ENVIRONMENTAL SCIENCES The functional relationship shown in Eq. (1) can be modified by forming dimensionless groups:

'o=f 2 ( , ,

O , .

h R

ji i F)

D (2) in which:

R$ = Vjho/v =' jet Reynolds number at the source.

FD = Vg/ (6E gho) = jet densimetric Froude number at the-source.

P  !

QR"VR D W = river discharge i

Og =V 3 ho-bo = heated discharge. '

Equation (2) can be further simplified by omitting D/hg and h o/bo, since both are practically constants; Rj, since the flow is highly turbulent; and Vj/V R , since the velocity ratio is related to the densimetric Froude number by a constant. The resulting functional e

relationship is:

$=f3 ('{ , E, F9) (3)

For the normal operating ranges of the Cooper Nuclear Station the variability in demsimetric Froude' number is small (between 2.5 and 4.5), so that F9 can be omitted from Eq. (3) to obtain:

ATg , , f4.(X ,

@) (4)

ATo- 50 0 0 The functional relationship represented by Eq (4) is valid for all values'of X/bo and Qa/Qo, since no restrictions have been placed oon the independent variables.

Equation (4) is the basis for deriving the centerline tempera -

ture rise relationships for the Cooper Nuclear Station thermal plumes. These relationships are:

l

+

.we- ,y 7 w+v,ge, -pie-..ws,- . , - , - . , .e-.,g- +,-yi-r.---.-w. ,m+ ,.iw, ow,w,,,,c-w- ,-e ,-e.-e ,v-ww-og-es , we - w re-s-e*w--g

0

,- ,. 1 HAZLETON ENVIRONMENTAL SCIENCES l for summer plumes. .

I 0 00025 X (5)

= 0.13 - 0.0033 ( j+ 0.38 3 for winter plumes: )

1 0.000068 X (6) f"=0.248-0.0097 Og)+ 0.396 e Oo Note that in Eqs. (5) and (6), the coefficient before X also includes the diviser ho which has a constant value of 120 ft. l The plume relationships derived for Cooper Nuclear Station are i comparable in functional relationship to that proposed by Shirazi l and Davis (Workbook of Thermal Plume Prediction, Vol. 2, Surface Discharge, US E;'A, 1974):

0.149 -0.149 -0.364 -0.5 ATn = 1.2 02 D W 7 -0. 54 9 (a ) 2. 2 4 5 X (7) l ATo (Qo) QQ I @o) Q)

In the foregoing relation, a is the angle of discharge. The Shirazi and Davis formula is based on an aspect ratic, ho/b o, of 0.2-5.0, while that for Cooper Nuclear Station is usually less than 0.06.

. . . _ . - . . . . _ _ _ . . -.m._. . _ . _ . . . . . _ . . _ _ . . _ _ . . _ _ _ _ _ _ . _ _ . . _ . . . . . _ _ . _ _ . . . . _ . _ . . . _ _ _ _ . . . _ _ . . . _ . . . . . . _ . _ . . . . . . _ . . . _ _ . __

~

4

.02 p O.e - 2 4' ~ )

r i 3 0 4 G-60.6- m r

4 2.

m .<

us 3

z 0 O w S 0.4 - 2 4

% z O 5 g' wlNTER 3 o n 2

~ O -4

@ O D

' O. 2 - c O O SUMMER j -r k c- g i O . O i O 5 O O 2

O.O .- . . .

U

- 0 2000 4000 6000 8000 m

g DOWNSTR EA M DISTANCE, FT.

6 h_

e

] Figure 12.1. Variations of maximum excess temperature ratios, ATc/ATo, at four loca-i tions in the Missouri River downstream from the Cooper Nuclear Station, 1977. (Solid line represents a best fit curve. AT c =_ maximum' centerline

excess temperature; AT g = initial excess temperature measured at the dis-i - -

charge canal).

8 1

I I

j l

l NALCD ENVir4cNMENTAL SCIENCES l l l 1

b.

0.20- I O l o.15 -  ;

O .

b O'yC o.1 o - 4 -

l M O  :

y o.05 - O  !

ga Q

<l <3  !

" O Ml#

i SUMMER O ,

O.oo - O @ A -

1. O ^ '

<! <3 A v O @ j i

.o.o5 - @ O  !

i

- 0.10 - j b l 6

g i

' i i a 20 25 30 35 40 FLOW ratio, o n/ 0 0 1

Figure 12.2. Difference between measured (M) and calculated (C) i maximum excess temperature ratios, AT c/AT o, as a function of flow ratio, On/Qo for Cooper Nuclear Station thermal plumes, 1977. (ATc = maximum center-line excess temperature; ATo = initial excess temperature measured at the discharge canal outlet; OR = river flow rate; Qo = Station effluent discharge rate).

255 [

1.0 I

o= O g /O o n@

\ <

- -b = Og / 0o M . r-

\. D p O.8 - k D

<1 s

i

' e \ <

' 4 D

\

g- O.6 0

r z g-e \ ~

m cr o,4

\g. -

2 3

m 9 C-U \ G 5 9 a a\ x E

w O2

- a E.

N- O- A e -- - -. -

U

___g--- m m

o

! ' ' , , t ' ' '

O.O 2000 4000 6000 8000 DOWNSTR E A M DISTANCE , FT.

Figure 12.2. Variations of maximum excess temperature ratios, AT c /AT o , at four locations.in the Missouri River downstream from the Cooper Nuclear Station, 1976. (Solid lines represent best fit curves. ATc = maximum centerline excess temperature; ATo - initial

- excess temperature measured at the discharge canal).

i

- - ~ '

_ ________________________________.m-_ _ _ _ _ _ _ _ - _ _ _ _ _ _ _ _ _ _ _ _ - _ _ - _ _ _ '

O N ALCO ENVI ACNM:5NTAt. SCIENCES l

y = (-0.0025) X 4 0.I,4 -

+ 0.10 .-

e l l,

o *O.05 l

$$ \ **  :

3 I s

O.00 -

g i

_s

• E-

)

e k 8 i

v -0.05 -

e

- 0.10 40 50 60

'O.lO - ' R 0 y = (-0.0064) X + 0.26 e e

+0.05 -

g m* ,

i

'X ff _ x _.

e v

i O.00 - ,

s e

^ e e

1. 0 S

< <3 e

~0.05 -

O.10 36 37 38 FLOW RATIO, OR !O o Figure 12.3. Dif ference between measured (-u) and calculated (-c) maximum' excess temperature ratios, ATc/aTo, as a function of flow ratio, QR/Qo for Cooper Nuclear Station thermal plumes, 1976. . (ATc'= maximum centerline excess temperature:

ATo = initial excess temperature measured at the discharge canal outlet; QR = river flow rate; Qo = Station ef fluent discharge rate).

1p' \

. . .- ;j it!l i

I ;

i i N ALCO ENVir-10NMENTAL GCtENCEG l .

i.

6  ! l i

1.0 -

1. l I'

LEGEND i 0 Og / Oo> 40 O.8 A Og/ Oo < 40 ,f ' l ii'  !

99 &

4s ,

V OR / Oo < 22 } }

On < 22000 cfs)

~

[ A p

o' h O.6 -

5 W _

l m ,

D l; 5 OA - l,,

,g f

e v

-y-  ;

F- _ g V A A A -7 )

,L A A  !!

O.2 - a a s-- 4 o

• b V

o __

g d ,;

O 8000 10000 I2000 '

0 2000 4000 6000 DOWNSTREAM DISTA NCE, FT [

il l

Figure 2. Variation of maximum excess temperature ration, '

ATc /AT o , at five locations in the Missouri River Solid downstream f romthe Cooper Nuclear Station.  ;

lines represent best fit curves, aT c = miximum centerline excess temperature; ATo= initial excess 9 temperature measured at the discharge canal outlet.  ;

r 32 1

i I

NALCD CNVinONMENTA1. GCIENCCD

+0.10 T 31 Jul'75 A 28 Jul'75(#2) ,

7 I Aug'75 0 30 May 75 '

l o 28 Jul'75(#1)

• 5 Dec'75 0 30 Jul'74 o 18 Sep'75

'. o, a 27 Jun'74 A 30 Jun'75 '

+005 - a o  ? 20 Mar'75 A 23 Moy,'74

• 30 Apr 75 u

n o D y 9;

<3 <3 no v o av a

• I O.0 o-o OO Oo y O Eb o  %

<l <3 A o AA v 6 O.F~~> 40 ]

00

-0.05 - -

r 9' !

-0.10 30 So 70 90 h(

ji,!, l FLOW RATIO, O R/O 0 l!

+0.10 . ,

o e 23 Jon'75 o 28 Jon 75- - 4 h{

i O O a 27 Sep'74 5j '

g

< A 17 Oct '74 b

+0.05 - o 22 Aug '74 m h I

3 m 7 Nov'74 '

{

^

o [i

1. 4# On/Co<22 } f .1

<3 '

On < 22OOOJ . . oa O.0 e

o

((l

l. ,

a A

' i{,i .

_ + o A .

og < 40 o +

- Q05 -

, o  :,

o t.d -

e jl'!

-0.10 12 20 28 36 I.

e FLOW R ATIO, On/Oo E .

Figure 3 .

Difference betwoon measured. ( m) and calculated  :

p'j l

(~c) maximum excess temperature ration, ATe/ATg, l l'  !

as a function of flow-ratio, Og /0 0 for Cooper '

Station thermal plumes. ATc = maximum centerline cxcess temperat.ure: ATo = initial excess temperature f'h measured at the discharge canal outict: Og = river o r, .

flow rate; 00 = plant offluent dischargo rate. 1 33 -

ff '

c-