Page 1

HOME HELP


LEGAL NOTICE I

T h i s nport wos prepored as an account of Government sponsored work.

Neither the United States,

nor the Commission, nor any person octinp on beholf of the Commission:

A. Maker any warranty or npnsantotion, expressed or implied, with respect to the accuracy, completeness, or usofulnoss of the information contained in this report. or thot the use of ~

any

method, or process disclosed i n t h i s raport may not lnhinge

information, opporotus,

privately owned rights; or

8. Assumes any l i a b i l i t i e s w i t h nsp~stto the ony informotion, opporotus. method, As used in the above, ' * p . r s a

controctor of the Commission,

0 '

of, or for d0mOg.l

acting on beholf of the Commission"

or

f*sultinQ from the Us*

Of

or process disclosad in this report. includes any employee or

omployee of such controctor, t o the extent thot such employoe

or contractor of the Commission, or omployee of such controctor pnpores, disseminohs, or provides access to, ony informotion p u r s w n t to h i s employment or controct w i t h the Commission, or his employment w i t h such controctor.

i I

I

i

1 i


OWL, TM-2029

Contract No. W-7405-eng-26

General Engineering Division

INVESTIGATION OF ONE CONCEPT OF A THERMAL SHIELD FOR THE ROOM M U S I N G A MOLTEN-SALT BREEDER REACTOR

W. K. Crowley J. R. Rose

NOVEMBER 1967

OAK RIDGE NATIONAL LABORATORY

UNION CARBIDE CORPORATION for the U. S. ATOMIC ENERGY COMMISSION


.

3

c


iii

CONTENTS Page

.......................... .. SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . DEVELOPMENT OF METHODS . . . . . . . . . . . . . Steady-State Condition . . . . . . . . . . . . . . . . . . . D e r i v a t i o n of Equations . . . . . . . . . . . . . . . . . C a l c u l a t i o n a l Procedure . . . . . . . . . . . . . . . . . T r a n s i e n t Case . . . . . . . . . . . . . . . . . . . . . . . . . PARAMETRIC STUDIES . . . . . . . . . . . . . . . . . . . . Cases Studied for Steady-State Condition . . . . . . . . . Case Studied f o r T r a n s i e n t Condition . .. . ... CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . .

Abstract..

1. 2.

3.

4.

INTRODUCTION.

0

0

ANALYTICAL

0

5.

Appendix A. Appendix B. Appendix C. Appendix D. Appendix E.

EQUATIONS NECESSARY TO CONSIDER A MULTIENERGETIC G A M M A C U R R E N T e . * o . o o . . o . . . . . . . . EVALUATION OF THE CONVECTIVE HEAT TRANSFER COEFFICIENT

.

.................... VALUES OF PHYSICAL CONSTANTS USED I N THIS STUDY . . TSS COMPUTER PROGRAM . . . . . . . . . . . . . . . NOMENCLATURE . . . . . . . . . . . . . . . . . . .

1

1 4 6

7 8

15 17 20 20 29

35

41

44 46 47 60


3

?

'c c:

I


V

LIST OF TABLES. Table Number

Title

Page Number

1

Results of Investigation of First Steady-State Case

22

2

Results of Investigation of Second Steady-State Case

23

3

Results of Investigation of Third Steady-State Case

24

4

Results of Investigation of Fourth Steady-State Case

25

5

Results of Investigation of Fifth Steady-State Case

26

6

Results of Investigation of Sixth Steady-State Case

27

7

Results of Investigation of Seventh Steady-State Case

28

Computer Program Used to Analyze the Proposed Reactor Room Wall for the Condition of Internal Heat Generation

31

Range of Parameters of Interest in Studies Made of Proposed Wall With An Incident Gamma Current of 1 x lola photons/cn? *sec

36

D. 1

Typical Data for 32 Cases With One Energy Group for the TSS Computer Program

54

D.2

TSS Output Data at the Bottom of the Air Channel for One Case

58

D. 3

TSS Output Data at Case

59

Top of the Air Channel for One


vii

$ 2

W

e

LIST OF FIGURES Figure Number

Title

Page Number

1

Proposed Configuration of Reactor Room Wall

2

2

Proposed Configuration of Reactor Room Wall With Corresponding Terminology

6

3

Designations Given Segments of Reactor Room Wall for Study of Transient Conditions

18

4

Temperature Distribution ' in Proposed Reactor Room Wall With Internal Heat Generation Rate Maintained During Loss-of-Wall-Coolant Transient Period

33

5

Temperature Distribution in Proposed Reactor Room Wall With No Internal Heat Generation During the Loss-of-Wall-Coolant Transient Period

34

Assembly of Data Cards for TSS Computer Program

53

D.1


7 f


z

INVESTIGATION OF ‘ONE CONCEPT OF A THERMAL SHIELD FOR THE ROOM HOUSING A MOLTEN-SALT BREEDER REACTOR

‘ :

Abstract’:’ !C. 3

The concrete providing the biological shield for a 250~Mw(e) molten-salt breeder reactor must be protected from the gamma current within the reactor room. A configuration of a laminated shielding wall proposed for the reactor room was studied to determine (1) its ability to maintain the bulk temperature of the concrete and the maximum temperature differential at levels below the allowable maximums, (2) whether or not the conduction loss from the reactor room will be kept below a given maximum value, (3) whether air is an acceptable medium for cooling the wall, and (4) the length of time that a loss of this coolant air flow can be sustained before the bulk temperature of the concrete exceeds the maximum allowable temperature. Equations were developed to study the heat transfer and shielding properties of the proposed reactor room wall for various combinations of lamination thicknesses. The proposed configuration is acceptable for (1) an incident monoenergetic (1 Mev) gamma current of 1~ x 1012 photons/c& see and (2) an insulation thickness of 5 in. or more. The best results are obtained when most of the gamma-shield steel is placed on the reactor side of the cooling channel. l

1.

INTRODUCTION t

Thermal-energy to assess design /

.

their

intense is

housed.

reactor

economic

problems.

a conceptual

molten-salt

gamma current The concrete room must

and nuclear

One design

10001Mw(e) in

breeder-reactors performance

problem,identified

MSBR power

plant1

the-room

in-which

wall.providing

be protected

(MSBR) are

fromthis

and

to

during was that the

the

there

intense

identify the

made of

be a rather

breeder shield

gamma current

: ‘P. R. Kasten, E. Si Bettis, and R. C. Robertson, lOOO-Mw(e) Molten-Salt Breeder Reactors, ” USAEC Report Ridge National Laboratory, August 1966.

studied important

study

will

molten-salt

biological

being

reactor

around to

the

limit

“Design Studies ORNL-3996, Oak

of


2

gamma h e a t i n g i n t h e concrete.

Further, the c o n c r e t e must be p r o t e c t e d

from t h e high ambient temperature i n t h e reactor room.

One p o s s i b l e

method o f p r o t e c t i n g t h e c o n c r e t e is t h e a p p l i c a t i o n of l a y e r s o f gamma and thermal s h i e l d i n g and i n s u l a t i n g materials on t h e r e a c t o r s i d e of t h e concrete.

A proposed c o n f i g u r a t i o n o f t h e layered-type w a l l f o r t h e

r e a c t o r room i s i l l u s t r a t e d i n Fig. 1. ORNL

SKIN7

7

INSULATlON

r STEEL 7

OW#

61-12000

rCONCRElE

AIR

3

Fig. 1. Proposed Configuration of Reactor Room Wall. The study r e p o r t e d h e r e was made t o i n v e s t i g a t e t h i s proposed conf i g u r a t i o n of a r e a c t o r room w a l l for t h e modular concept? of a 1000-Mw(e)

MSBR power p l a n t .

This modular p l a n t would have f o u r s e p a r a t e and i d e n t i -

cal 250-Mw(e) r e a c t o r s w i t h t h e i r s e p a r a t e s a l t c i r c u i t s and heat-exchange loops.

T h i s p r e l i m i n a r y i n v e s t i g a t ’ i o a was made t o determine whether o r

n o t t h e proposed c o n f i g u r a t i o n f o r t h e reactor room w a l l w i l l

1. maintain t h e bulk temperature o f t h e c o n c r e t e p o r t i o n o f t h e w a l l a t l e v e l s below 212’F, 2.

maintain t h e temperature d i f f e r e n t i a l i n t h e c o n c r e t e lamination a t l e s s than 40°F (a f a i r l y c o n s e r v a t i v e value), and

3,

maintain t h e conduction loss from a r e a c t o r room a t 1 Mw o r less.

This study w a s a l s o performed t o determine whether o r n o t a i r i s a s u i t a b l e medium f o r c o o l i n g t h e reactor room w a l l and t o determine t h e l e n g t h o f t i m e over which t h e l o s s o f t h i s a i r flow can be t o l e r a t e d b e f o r e t h e


3

i 2

u b

bulk temperature of the concrete lamination.exceeds the maximum allowable

w

temperature of 212'F. Analysis of the proposed configuration for the wall of the reactor room was based on an investigation of the heat transfer and shielding n Fig. 1.

properties of t

osite wall sho

Equations were devel-

oped that would

these properties to be examined parametrically for

various combinations of lamination materials and thicknesses

L r

c


4

2

I?

w 2.

s

SUMMARY

\

Methods were devised to parametrically analyze a comp with internal heat generation produced by the attenuation current from the reactor room. Both steady state and tran were considered.

Thirty-one equations

gram was written to examine the heat transfer and shielding properties of the proposed wall for various combinations of lamination materials and Incident monoenergetic (1 MeV) gamma currents of 1 x

thicknesses. photons/ca?

sec through 3 x 10”

photons/ca? *sec were examined.

le2

A finite

difference approach, with the differencing with respect to time, was used in the transient-condition analysis to obtain a first approximation of the amount of time that the proposed wall could sustain a loss of coolant air flow. The results of these studies indicate that the proposed configuration of the laminated wall in the reactor room is acceptable for the cases considered with an incident monoenergetic (1 MeV) gamma current of 1 x 1Ol2 photons/ca?*sec and a firebrick insulation lamination of 5 in. or more. Under these conditions, a total of approximately 4 in. of steel is sufficient for gamma shielding. The best results are obtained when the thicknesses of the mild-steel gamma shields are arranged so that the major portion of the steel is on the reactor side of the air channel.

However,

the proposed configuration of the laminated wall for the reactor room does not protect the concrete from excessive temperature when the incident monoenergetic gamma current is 2 x lola photons/ca? osec. With an incident monoenergetic (1 MeV) gamma current of 1 x 10’” photons/c$

sec, the proposed laminated wall will maintain the temperature

differential in the steel to within 10°F or less for all the cases studied. The differential between the temperature of the steel-concrete interface and the maximum temperature of the concrete is less than 1S0F for all the cases studied.

The values of both of these temperature differentials are

well below a critical value. Based on the assumption that the floor and ceiling of the reactor room have the same laminated configuration as the walls, the proposed

w L


5

wall

will

allow

at a level of

below

1 x 10la

is

1 Mw for

With

5 in.

if

or more

a coolant

50 ft/sec,

air

room wall. approximately

9set,

the

air

flow.

nperu&ssibleii than

and if

of

least

of

room

the

4 in.

3 in.

for

to be maintained

(1 Mev)

gamma current

firebrick

insulation

of mild-steel

the

gamma

the

concrete

approximately a zero

incident

is

maintained will

reactor

at

remain

after

gamma’current

is

is

of

room remains

one hour

time

velocity

the.proposed

reactor

the. gamma’current of

and an air

cooling

of

loss-of-coolant-airiflow

greater

at

1 x lOla

below

a loss

of

the the

assumed,.the than

one hour

but

two hours.

maintenance

of

without

the

energy

balance

and

whether-or

not

desired

ambient

the

addition

of

should This

available.

surface.

at

medium

temperature

If

To determine

reactor

if

temperature

level.(212oF)‘for

coolant

reactor

thickness

channel’width

ambient

1106OF

photons/&

and

the

monoenergetic

the

an acceptable

the

from

_ air

is

If

critical

loss

an incident

is ikiuded.

shielding

4

conduction

photons/ct#*sec

lamination

less

the

balance

extend-out

a conduction temperature

auxiliary

cooling

be performed

when

should through

loss

start the

wall

of

within

the

or heating sufficient

with of

1 Mw will

permit

reactor

systems,

an overall

information

the

fissioning

the

reactor

room

becomes process

room

in

the

to an outside


6

3.

DEVELOPMENT OF ANALYTLCAL METHODS

I n t h e modular concept o f a 1000-Mw(e) MSBR power plant,'

the four

i d e n t i c a l b u t s e p a r a t e 250-Mw(e) molten-salt breeder r e a c t o r s would be One primary f u e l - s a l t - t o - c o o l a n t -

housed i n four s e p a r a t e r e a c t o r rooms. s a l t h e a t exchanger and one blanke

alt-to-coolant-salt

h e a t exchanger

would a l s o be housed i n each r e a c t o r room along with t h e reactor.

These

items o f equipment are t o be l o c a t e d 11 f t from each o t h e r in t h e 52-f long r e a c t o r room t h a t i s 22 f t wide and 4 8 - f t high. primary f u e l - s a l t - t o - c o o l a n t - s a l t

The r e a c t o r and t h e

h e a t exchanger are respons

gamma c u r r e n t i n each o f t h e r e a c t o r rooms.

The proposed c o n f i g u r a t i o n

t i o n s devised t o p r o t e c t t h e c o n c r e t e from t h e gamma c u r r e n t

r room i s shown i n Fig. 2 w i t h t h e corresponding terminology used i n t h e parametric s t u d i e s made o f t h e omposite w a l l .

'P. R. Kasten, E. S. Bettis, and R. C. Robertson, "Design S t u d i e s o f lOOO-Mw(e) Molten-Salt Breeder Reactors," USAEC Rep0 ORNL- 3996, Oak Ridge National.Laboratory, August 1966. ORNL Dug. 67-10001

I

AIR

-4

Fig. 2. Proposed Configuration o f Reactor Room Wall With Corresponding Terminology.

U *


7

2 lj ‘i

In

the

direction

outer

surface

of

rial

comprising

the-variable

wall,are

8. ft

for air

is

an exterior

-considered

fixed

of

over

the

concrete

ci

of

the

the

thickness

ing

room within

the

facility

the

coolant

is

assumed

air

channel,

air and

the

velocity

heat

current.

from

the

steady-state condition later

was considered problem

of

properties

of

metrically

for

i

nesses.

LJ

tures

E

uniform.

were

of

the

interior

(the

mate-

insulation,

the

and

insulato be

stainless

concrete

is

and the

either

width

of

interior

the

room wall

is

is

first

and the

a loss

of

combinations analysis and exterior

of

or of

at

70°F

an adjoin-

(entrance) to’be

of

the

SO ft/sec.

attenuation

were

of

a composite of

plane the

considered:

condition.

gamma

the

The steady-state

transient

condition

was considered

was examined.

Condition

.to mallow wall,

to be uni-

thickness

involving

coolant

The

The temperature

assumed

by the

wall

1100’F.

wall)

bottom

one

transient

8-ft

wall).

air

and the

at

temperature

be lOOoF at the the

reactor

is -considered

ambient

Two conditions

\

the

an exterior

room.

A one-dimensional

of

shield,

of

the

wall

for

is>basically

the--compositevarious

the

earth

of

develoPed

the

considered

wal.1,

SOoF for

Steady-State : Equat,ionk-

to

firebrick

and constant

caused

. of

the

are

of

generation

reactor

condition

when the ,’ 1

surface

at

the

to

with

internal

‘the

for’an

examined

firebrick

of

of

surface

concrete

The situation

layers

a mild-steel-gamma

an interior

interior

of of

the

skin,

thickness

for

and constant

the

2),

The thickness

the

surface

for

wall

3-ft

study.

room out

in.

over

temperature

Fig.

gamma shields

3 ft

exterior

surface

(the

channel,

in.,

at.3

to be uniform

temperature form

l/16

wa.ll:or

is

in

reactor

The thicknesses

this

at

The temperature

cc

an air

the

steel

two,mild-steel

fixed

channel

to right

shfeld:

of, the

of

a-stainless

parametersin

skin

interior

(left

gamma shield,

and each

steel

the

wall

concrete;biological

tion

the

the the

a mild-steel the

from

shown of

the

heat

transfer

in

Fig.

2,

lamination

was used, surfaces

materials

the

shielding

to be examined

assuming of

and

wall

para-

and thick-

that were

the

tempera-

constant

and


8 Derivation o f Equations

A s t e a d y - s t a t e energy balance on a d i f f e r e n t i a l element o f t h e r e a c t o r room w a l l can be expressed s e m a n t i c a l l y as follows.

The h e a t conducted

i n t o t h e element through t h e l e f t f a c e during t h e time A0 p l u s t h e h e a t generated by sources i n t h e element d u r i n g t h e t i m e A0 e q u a l s t h e - h e a t conducted o u t of t h e element through t h e r i g h t f a c e d u r i n g t h e time 08. This i s expressed a l g e b r a i c a l l y i n Eq. 1.

where

k = thermal conductivity, Btu/hr*ft*'F, A,.

= u n i t a r e a on wall, f t a ,

T = temperature,

0

F,

x = distance perpendicular t o surface o f the w a l l , f t , 0 = time, hours, and Q = volumetric gamma h e a t i n g rate, Btu/hr*ft?.

Application of t h e mean-value theorem t o dT/dx g i v e s t h e e x p r e s s i o n o f

Eq. 2.

where

M i s a p o i n t between x and x + Ax.

Equation 2 i s s u b s t i t u t e d i n t o

Eq. 1 and A0 i s canceled.

The common term '

= @T/d$.

-&

:Ix

i s canceled, and i t i s noted t h a t

The r e s u l t i n g expression i s given i n Eq. 4. Q 4 & = - krtaT p,gl&.

M Dividing Eq. 4 by &Ax and a l l o w i n g & t o approach zero a s a l i m i t so t h a t a value a t M becomes a v a l u e a t x, t h e volumetric gamma h e a t i n g r a t e ,

CPT Q = - k q ,


-

9

L

u c Âś

A

Equation 5 is integrated twice, and if Q T(x) =

3

# Q(x),

+ G x + C,

x?

.

(6)

The applicable boundary conditions for any particular lamination in the at x = 0 and T = T at x = L, where T, = the temperature wall are T = ‘I& L of the lamination interface at zero location designated in Fig. 2 and

L = the thickness of the material in a lamination in feet. ditions are applied to Eq. 6.

Tkese con-

The internal heat generation encountered in this study is caused by a deposition of energy in the form of heat when the gamma rays are attenuated by the materials in the wall of the room.

Because of this atten-

uation of the gamma rays, the volumetric gamma heating rate, Q, is a function of the distance perpendicular to the surface of the wall, x. The equations derived in this study are based on the assumption that the incident gamma current is monoenergetic, but appropriate equations for a multi-energetic gamma current are given in Appendix A.

For a mono-

energetic g a m a current where buildup and exponential attenuation are considered, the equation for Q(x) becomes Q(x) = Q[Aewx

+ (1

- A)e -PPX],-Px ,

where

A,

(31,

and p = dimensionless constants used in the Taylor buildup enuation coefficient, ft-1.

When

= the volumetric

te at the surface on the reactor n, Btu/hr*ft?, current, MeV,

go = incident gamma current, photons/cn? i

%

sec, and

= gamma energy attenuation coefficient, ft-1.


10 Substituting Eq. 9 into Eq. 5,

-

Equation 10' is integrated twice to yield

+c;x+cq=o. (11) The previously stated boundary conditions are still applicable, and the result of applying these conditions to Eq. 11 is that

The temperature distribution in any particular lamination o f the wall is given by Eq. 12 when the appropriate constants for that lamination are used.

Equation 12 is used primarily to determine the maximum temperature

in the concrete and to determine the location of this maximum temperature.

To locate the position of the maximum temperature in the concrete, Eq. 12 is differentiated with respect to x, the resulting derivative (dT/dx) is set equal to zero, and the equation is solved for X. The value of x obtained gives the distance from the concrete-steel interface to the position of the maximum temperature in the concrete.

Equation 13 is a transcendental equation in x, and as such, it must be solved by using a trial-and-error technique.

There are only two terms

in Eq. 13 that contain x, and these terns are rearranged to put Eq. 13 in a form more easily solved by trial and error.


All

of

the

terms

in

the

the

= $6 - TL>+ +(YC k

A (a - l)=

+ (B1+-lfa

11 - e

coefficients on the

on the

right

side

are

x,

the

this

into

K’s

value

Eq.

and a’s

are

of

called

x is

12 to obtain

To determine reactor each

room, separate

duction

of

the

face

Eq.

9 over

the

14 are

Therefore,

Eq.

.

(14)

known,

and all

of

14 may be written

written

lamination

in

the~wall.

thickness

the

gamma heat, the the

wall

is

There gamma heating referred.

to

gamma current, of

ip o(j)

is

assumed

which

L,

the

the

- ‘)

)

incident two possible

rate as the

at “j-th”

ways

in

to

E@o(j)%

generated

in

a length

equal

a

The total

a direction

-PUB 1e _-

- ++

normal

to

by integrating

.

+ 0

incident

which

way is ~to calculate

To obtain

l

(17)

volumetric

interface,

equation

-113

(16)

rate.

the

The first.

=

con-

+ ‘)] dx

material

@ at each’interface. o(J)’ is substituted into the

across

lamination.

evaluate

interface.~

.

lamination

gamma heating

some.particular

‘(3

area

+-. (1 - A)e”~x(p ._~~~ .-. -

volumetric

simple

heat

through

the

drops

are

the

any particular

A eCrL(a - 1) _ .---:ll - 1)(

from

lamination.

unit

particular

q*,

equations of

for

substituted

temperature

particular

per

for

of

the

all

solved

concrete.

loss,

to be conducted

of

found

L & [Aepta

are

in

the

conduction

These

14 is

= xT max is

of

to give

q TI deposited

length,

the

the

(15)

When Eq.

The va1ue.x

of

equations

,;

temperature

were

=Sro2 Q

maximum

magnitude

= k

numbers.

equations

J

value

-cl.L(cr - 1)

of Eq.

=%kx

xT.max;

of

of

ke

calculable

is

qT =

where

known.

-a,x;

Lamaination

two-thirds

amount

1L

the

and convection

particular to

side

I

form %e

where

left

pL(c%- 1) il - e

Q

W’

this

shall

be the

calculated


12 The second method o f e v a l u a t i n g t h e i n c i d e n t volumetric gamma h e a t i n g

rate involves s u b t r a c t i n g t h e t o t a l amount o f gamma h e a t d e p o s i t e d p e r u n i t area i n t h e j - t h lamination, q

.I

from t h e gamma energy c u r r e n t p e r

u n i t area i n c i d e n t upon t h e j - t h lamination

qo(j),

t o approximate t h e

gamma energy c u r r e n t p e r u n i t area i n c i d e n t upon t h e f a c e of t h e followi n g lamination qo(j

+

1) * “(j-

+ 1) =

qo(j)

- qj

The volumetric gamma h e a t i n g rate i n c i d e n t upon a p a r t i c u l a r lamination, Qoij)

, and

lamination

t h e gamma energy c u r r e n t p e r u n i t area i n c i d e n t upon t h e j - t h qo(l)y

are r e l a t e d by t h e following equation. qo(3)

= Qo(j,/h(J)

There f o r e (18b)

Qo(j + 1)

These two methods are i n f a i r 1

i n c e t h e v a l u e s for

t h e v a r i o u s material c o n s t a n t s were n o t w e l l f i x e d a t t h i s p o i n t i n t h e design f o r t h e reactor room w a l l ,

t h e second method o f e v a l u a t i n g t h e

i n c i d e n t volumetric gamma h e a t i n g rate was u s e d i n t h i s study.

The

second method i s simpler t o u s e and easier t o c a l c u l a t e . The equations f o r t h e s t e a d y - s t a t e temperature drops a c r o s s each o f t h e material laminations on t h e reactor s i d e o f t h e a i r channel are given below and t h e temperature p o i n t s are as i l l u s t r a t e d i n Fig. 2.

where

q* QS

E

h e a t conduction rate o u t o f t h e r e a c t o r room, Btu/hr*ft?,

E

gamma h e a t d e p o s i t i o n rate i n t h e s t a i n l e s s steel o u t e r s k i n , Btu/hr*f?,

Ls = t h i c k n e s s o f t h e s t a i n l e s s steel skin, f t , and kS

= thermal c o n d u c t i v i t y o f t h e s t a i n l e s s s t e e l s k i n , Btu/hr*ft*’F.


13

(cp + 4,

TL - Ta = where

the

subscript

I refers

(20)

?

to

kI insulation

the

lamination

shown

in

Fig.

2.

(q* + q, + 41 + &LFS Y

-T3.=

%

: where the

the

subscript

reactor

FS refers-to

side

of

the

(21)

kFS

air

the

first

mild-steel

gamma shield

(on

channel).

%

- T, =

of

the

q* + q, + qI + qFS Y h

(22)

where Ta = temperature h=

convective

heat

The ‘average

convective

air

channel

is

for

a mean temperature

gamma heating and 22 were conduction-

heat

added rate’

air

and out

channel,

transfer

of

across

B, and the

130 to

channel

is

150’F.

It

room

the

walls

air

of

the

off 5 was determined

was assumed

was solved

to

the

Equations

equation

reactor

value

negligible.

resulting

the

Btu/hr=ft?*OF.

coefficient

from

the

OF, and

coefficient,

in Appendix of

the

in-the

transfer

evaluated

in

air

that 19,

for

the

20,

21, The heat

q*.

channel,

:. (&

- Ta)

2 Ls LI J~+F+-+[o 8 .I

-‘qs

Lps

1

kFS

h

1 ..

q* E

(23)

On the is

the

side .of- the air channel, the TV- ~ temperature of the concrete, Tmax.

maximum

-determined concrete

by using

Eqs.

interface,

The simple the

concrete

concrete

Tn,

conduction side

.of

12 and must

14,

but

be known

the before

air-channel

.are

these

of

equations

for given

.of primary

interest

This-temperature

temperature

and convection’equations the

value

the

the

may be steel-!

can be used.

laminated

wall

on

below.

Qss + 4; + QR Q

- Ta 4

h

Y

(24)


~

14

..r

‘I

where qss = gamma h e a t d e p o s i t i o n r a t e i n t h e second m i l d - s t e e l gamma s h i e l d , Btu/hr*ft? qr

,

= rate a t which t h e gamma h e a t generated i n t h e c o n c r e t e is conducted back toward t h e a i r channel, B t u / h r - f e , and

QR

= r a d i a n t h e a t t r a n s f e r rate between t h e walls of t h e a i r chan Btu/hr f t?

,

where t

Stefan-Boltzmann c o n s t a n t

= 0.1714 x E

loa

= s u r f a c e e m i s s i v i t y o f a i r channel w a l l s , assumed t o t h e same for both s u r f a c e s .

% - % =

+

2

yss)Lss

kSS

.

(26)

I n t h i s study, t h e r e is a p o i n t i n t h e c o n c r e t e a t which t h e temperat u r e of the concrete

i s a maximum.

A l l of t h e gamma h e a t generated on

t h e a i r channel s i d e o f t h a t p o i n t w i l l be conducted toward t h e a i r channel; t h a t is, i n t h e d i r e c t i o n o f d e c r e a s i n g temperature. q’, C

This amount o f h e a t ,

may be c a l c u l a t e d by e v a l u a t i n g dT/dx i n t h e c o n c r e t e a t x = 0, u s i n g

Eq. 13.

~-

recognizing t h a t .

9; = kc

dx

dTI x = o

where t h e s u b s c r i p t c denotes concrete.

?

The r i g h t s i d e o f Eq. 28 i s

p o s i t i v e r a t h e r than n e g a t i v e because Eq. 27 makes p o s i t i v e conduction i n t h e d i r e c t i o n from t h e a i r channel toward t h e concrete, b u t q; is

..

. I

j


15

:

&Iii 5

to be made positive

in

channel.

24,

Equations

equation lated

i

in which from

the

the

the

direction

25,

26,

only

equations

from

27,

unknown for

the

and 28 were is Q.

the

concrete

reactor

‘toward~the

combined

The-value side

of

to

for

air

yield

one

T3 can be calcu-

the-air

channel.

where B’ =

. 11

‘i.qB + 1) + (pl+-l+i1.- e The constants to be for fore,

in

Eq.

concrete.

29a that

have

Equation

29.is

also

.must

be used

a trial-andferror

method

qk are known,

% can be calculated

Calculational

Procedure

Since

the.calculation

that

the

order

value

in which

thickness inside are

specified. air

selected,

other

the

of.each (reactor

coolant are

of

of

of

the

room)

are

also

used

For the

is

(earth,or

internal)

current

and the

given

&.

quantities there

for

in Appendix

There-

Once ‘J& and

requires is

a particular

wall

The constants are

for

be known,

in

ganrna

specified..

and those

desired

the

understood

equation.

solve

of

be worked.

and -outside

The incident

to

Eq.- 25.

laminations

are

a transcendental

quantities

must

subscripts

by using

certain

desired

problem

no identifying

(294

a certain case)

-the

selectedi

and

wall

-temperatures

temperature

of

the

-equations

C:

various

the

the


16 With t h e proper c o n s t a n t s f o r each d i f f e r e n t lamination, Eq. 17 is f i r s t used t o c a l c u l a t e t h e gama h e a t d e p o s i t i o n s i n each o f t h e sepaEquation 23 i s then used rate laminations (qs, qI, qFs, qss, and 9,). to c a l c u l a t e t h e conduction l o s s from t h e r e a c t o r room q*. The temperat u r e drops and t h e i n t e r f a c e temperatures on t h e r e a c t o r s i d e o f t h e a i r channel a r e c a l c u l a t e d by u s i n g Eqs. 19, 20, 21, and 22.

Equation 29 is

used t o c a l c u l a t e t h e value o f %, and then t h e v a l u e o f qR is c a l c u l a t e d by u s i n g Eq. 25.

Then q:

i s c a l c u l a t e d by u s i n g Eq. 24, and t h e v a l u e

o f & i s c a l c u l a t e d by u s i n g Eq. 126. Once t h e v a l u e o f Ts is known,

i s obtained by u s i n g Eq. 14, and t h e maximum temperature of t h e T max c o n c r e t e is c a l c u l a t e d by e v a l u a t i n g Eq. 12 a t x = xT max.

X

A t t h i s p o i n t , i t is p o s s i b l e t o c a l c u l a t e t h e v e r t i c a l temperature

g r a d i e n t (OF/ft)

i n t h e coolant a i r .

T h i s temperature g r a d i e n t ,

where Ua = bulk v e l o c i t y o f c o o l a n t a i r , f t / s e c ,

Pa

= d e n s i t y o f a i r , lb/ft?,

Lch = width o f a i r channel ( d i s t a n c e between steel laminations), f t , C = s p e c i f i c h e a t o f a i r a t c o n s t a n t p r e s s u r e , Btu/lb*OF. Pa The temperature o f t h e a i r a t t h e top of t h e channel,

where H = t h e v e r t i c a l l e n g t h o f t h e a i r channel i n f e e t . The e n t i r e c a l c u l a t i o n a l procedure can now be repeated u s i n g t h e new a i r temperature a t t h e t o p of t h e a i r channel, Ti.

This c a l c u l a t i o n o f t h e temperature o f t h e a i r a t t h e t o p o f t h e channel is n e c e s s a r y because a h i g h e r T c a u s e s t h e maximum temperature o f t h e c o n c r e t e t o be a

higher, and t h e magnitude o f t h i s maximum temperature is one of t h e c o n s t r a i n t s i n t h i s study. A program was developed f o r t h e CDC 1604-A computer t o s o l v e Eqs. 8

through 31 f o r t h e s t e a d y - s t a t e condition.

The TSS (Thermal S h i e l d Study)


17

z LJ

computer

4

program

is

in

the

calculations material

described order

laminations

room wall

in

Appendix

described

(excluding

and up to eight

air

basically

of

a transient If

tion.

the

an appreciable

the

steel

with

the

that

such

ence

approach

the

superscript

of

groups

for

of n in

segment,

as shown

given

was assumed and

entire

thick,

and

plus

the

in

in

3.

Fig.

firebrick

stainless

steel

the

air

the

temperature

up to

proposed

five

reactor

gamma current.

room wall

internal

channel

excessive.

the

the

be sustained equations

with

the

amount

is

to

values

lost

and/or situation

of

a finite

respect

denotes

wall

this

safely,

is

genera-

concrete

To investigate of

is

heat

in in

approximation

balance

in

the

selected

for kCA

+TSn C

nodal Each

thick,

skin

reactor

points

each

time differ-

time

and

after

the

the

time

of

the

time

wall

the

segment into

+q+=

each

region

of

the

gamma thick,

segment

segment

l/16

3 in.

a segment

during

in.

thick.

can be expressed

seman-

the

time

A0

during

the

time

A6 equals

the

heat

A6 plus

the

heat

conducted

out

of

5s given

algebraic below

equation with

Segment

for

the

a

4

‘,

purposes. W=ccp ne

of

mild-steel

a single

into

center

to be 1 in.

as a single

The corresponding

composite

illustrative

- G.“)

the

concrete in

was treated’as

then segment

A0.

the

was broken the

was assumed

The heat~conducted

during

in

segment

a particular

in

room wall located.at

segment

was treated for

segment

segment

the

insulation

channel

generated

segment-during

b f

with

time,

of

with

the

heat

typical

reactor

the

could

lengths

as follows.

stored

the

through

following

to be 1 ft

The energy tically

for

The differencing

the

incident

air

configuration

of

the

flow

the

the

interval.

segments

shields

air

in

handle

the

problem

a first

was taken.-

The proposed

wall

coolant

may become

obtaining

a loss

time

of

will

performs

Case

conduction

length

of

of

coolant

laminations goal

loss

heat

flow

for

n-th

the

it

channel)

Transient

The problem

The program

and

above,

the

energy

D.

?T4

n+l-

T4n)

kCA

+ +T4”

- %“I*

C

(32)


18

<

6T-12002

ORNL O r g

/STAINLLSS STELL \ SKIN FIREBRICK INSULATION

<

FIRST MILD-STEEL BAMYA SHIELD r(AIR

CHANNEL SECOND MILD-STEEL GAMMA SHIELD CONCRETE

i

z

0

+ 1

f CURRENT

.....

NODAL WIN1

SEGMENT

ZC

I I7 16 I!

I

I1

I 6 4 5 9 1

Fig. 3. Designations Given Segments of Reactor Room Wall for Study of Transient Conditions.

Rearranging Eq. 32,

A characteristic equation at an interface between two different

materials is given in Eq. 34. l+"

+

1

-

qn

+

-

p ksm L Z C (Gn T7n) 6 s Ps

+

-k

s-cA0

p sLsLcCp S

G n-

%

T79

+

c

L s

8

,

Ps

(34) where the subscript s denotes the stainless steel skin, the subscript'c

-

denotes the concrete, and ks-C is an equivalent conductivity given by

where the subscripts a and b refer to any two adjacent materials,


19 Eighteen equations similar t o those j u s t given were derived t o carry the a n a l y s i s across the e n t i r e reactor room wall, and a simple computer program was written t o perform the c a l c u l a t i o n s required f o r one s p e c i f i c transient condition.

I

\


*

20

hd i.

4. PARAMETRIC STUDIES

The parametric s t u d i e s of t h e proposed c o n f i g u r a t i o n of a laminated w a l l f o r t h e r e a c t o r room, shown i n Fig. 2, t o p r o t e c t t h e c o n c r e t e biol o g i c a l s h i e l d from t h e gamma c u r r e n t w i t h i n t h e room were made f o r two conditions: t h e s t e a d y - s t a t e c o n d i t i o n and t h e t r a n s i e n t c o n d i t i o n . Parametric s t u d i e s o f t h e material laminations f o r t h e s t e a d y - s t a t e cond i t i o n were made t o determine whether o r n o t

1.

t h e bulk temperature o f t h e c o n c r e t e p o r t i o n o f t h e w a l l could be maintained a t l e v e l s below 212'F,

2.

t h e temperature d i f f e r e n t i a l i n t h e c o n c r e t e could be maintained a t

less than 40째F, and 3.

t h e conduction loss f o r a r e a c t o r room could be maintained a t 1 Mw o r less.

A t r a n s i e n t c o n d i t i o n was i n v e s t i g a t e d t o determine t h e l e n g t h o f time

over which t h e loss o f c o o l a n t a i r flow could be t o l e r a t e d b e f o r e t h e temperature of t h e c o n c r e t e would exceed t h e maximum allowable temperat u r e o f 212'F.

Cases Studied f o r Steady-State Condition

For t h e parametric a n a l y s i s of t h e composite p l a n e w a l l w i t h i n t e r n a l 3:

h e a t g e n e r a t i o n f o r s t e a d y - s t a t e c o n d i t i o n s , t h e a i r channel was not cons i d e r e d as a m a t e r i a l lamination b u t r a t h e r a s having a f i x e d width o f

3 i n . between t h e f i r s t and second m i l d - s t e e l gamma s h i e l d s .

The tempera-

t u r e of t h e incoming c o o l i n g a i r a t t h e bottom o f t h e a i r channel was assumed t o be 100째F, and t h e v e l o c i t y of t h e a i r w a s set a t 50 f t l s e c . The t h i c k n e s s o f t h e s t a i n l e s s steel s k i n on t h e r e a c t o r s i d e o r i n t e r i o r s u r f a c e of t h e w a l l was f i x e d a t 1/16 in.,

and t h e temperature o f t h e

i n t e r i o r s u r f a c e o f t h e r e a c t o r room w a l l was considered t o be uniform over t h e s u r f a c e and constant a t 110O0F.

Equations 8 through 31 d e r i v e d

i n Chapter 3 were used w i t h t h e TSS computer program d e s c r i b e d i n

c; ?

Appendix D t o examine t h e s t e a d y - s t a t e e f f e c t s o f changing t h e , i


21

1.

thickness

2.

total

amount

of mild

steel

3.

ratio

of

amount

of~steel

to

of

the

the

the

amount

firebrick

of

steel

4.

thickness

and outside

5.

magnitude

of

the

Sixty-four dition

to

Data

selected

from

through

the

gamma currents

of

tables,

and

the

channel

air For

the

the

maximum

the

bottom

with

of

the of

reactor

the

room, 80°F

from and

little

0.04

The largest the

top

of

the

of

1 x 101s

is

approximately

maximum those

temperature cases

with

and an insulation

both

the

of

parameters

varying

the

and are

compiled

(entrance)

the

thickness

.in Tables

all

top

of

these

(exit)

of

1 x 1012

photons/cu?*sec,

increases

the

top.

For

top

the

of

the

the

bottom

maximum

concrete air

with

other at

gamma’current 5 in.

top

of

of

the

the

top of

or more

the

of

the

2 x 10la is

greater

air

very

channel, at

gamma current 5 in.

value air

a given

concrete

of

smallest

the

changes

an incident

the

from

approxi-

For

loss

thickness

hand,

to

increases

conduction

temperature

cases

back

channel.

and the

50°F

an incident

and no conduction of

the

approximately cases‘with

1

for.incident

of

concrete

of

and

were

gamma current

and an insulation

an incident

parameters

gamma current.

those

On the

interest.

incident

the

in

the

of

of

to

to

con-

magnitudes

concrete

Mw)between

ZOOoF,

steady-state

in

thickness,

photons/cn?*sec

the

*set

bottom

the

gamma current.

bhotons/cn?

insulation

channel

and

and 2 x 10la

temperature

for

wall,

given

the

channel

channel,

those

analyses

air

air

are

bottom

value air

of

2 x 101s photons/ca?*sec maximum

the

parameters

channel

the

gamma current (about

air

for

the

the

for

of

of

(1 Mev)

effects

an incident

temperature

of

concrete

changing

these

at

given

the

analyzed

changing

conditions

gamma current

mately

of

1 x 10’s

are

cases

typical

side

side

of

of

of

The effects

7.

reactor

concrete

were

effects

results

gamma shields,

monoenergetic

cases

the

the

on the

incident

of

for

temperature

the

illustrative

used

on the

separate

determine

insulation,

or more for

channel

photons/& than

250’~.

the in *set


22

- .?

w

.

Table 1. Results of Investigation of First Steady-State Case Case Conditions Studied Tg = 50째F Lc = 8 ft To = llOO째F

$=

Ls = 1/16 in. 0,

Ss= 4 in.

5 in.

P 1 x Ida photons/& -see Bottom of Top of Channel Channel 16.57 16.57 75.47 75.47 370.6 370.6 11.69 11.69 33.65 33.65 22.04 25.84 131.2 110.6 0.5382 0.5812

4,

Lss = 2 in.

le8photons/d *bee

o 2 X Bottom of Channel 33.14 151.0 741.2 23.38 67.30 55.31 198.9 0.3520

Top of Channel 33.14 151.0 741.2 23.38 67.30 48.99 253.9 0.2838

1099.9 247.9 240.5 100.o 129.6 129.8

1099.9 297.1 289.9 153.0 186 60 186.2

1099.9 324.6 314.1 100.o 155.5 156 .O

1099.9 402.7 392 5 184.0 249.3 249.7

0.1018 852.0

7.412 140.5 29.63 0.216

0.0946 802.8 7.185 136.9 32.98 0.1916

0.0679 775.3 10.55 214.1 55.52 0.4554

0.0565 697.3 10.19 208.5 65.25 0.4148

140.5 0.5422 1.104

193.6 0.&83 1.103

181.3 0.6343 1.751

268.5 0.4887 1.777

c; i


23

Table 2.

Results of Investigation of Second Steady-State Case Case Conditions Studied Lc = 3 ft T6 = 70째F

To = llOO째F La = 1/16 in.

LFS = 4 in.

LI = 5 in. 0, = 1 X

leaphotoncl/cn? rsec

Bottom of Channel 16.57 75.47 370.6 11.69 33.65 18.33 111.6 0.5812

Top of channel 16.57 75.47 370.6 11.69 33.65 8.446 133.3 0.5385

0 ,

Lss = 2 in.

leaphotons/d -8ec

a 2 X Bottom of Channe1 33.14 151.0 741.2 23.38 67.30 42.64 200.8 0.3520

Top of Channel 33.14 151.0 741.2 23.38 67.30 26.19 258.2 0.2845

1099.9 247.9 240.5 100.0 128.3 128.5

1099.9 296.7 289.5 152.6 183.3 183.4

1099.9 324.6 314.1 100.o 153.4 153.7

1099.9 402.1 391.9 183.4 244.9 245.2

0.1018 852.0 7.412 140.5 28.32 0.1678

0.0947 803.2

0.0566

30.68 0.1043

0.0679 775.3 10.55 214.1 53.36 0.3740

697.9 10.19 208.5 60.55 0.2683

133.4

184.4

0.3124

0.1276

167.4 0.3878

250.o 0.2061


24

Table 3. Results .of Investigation of Third Steady-State Case Case Conditions Studied

L~

To = 1lOOOF

TU = 50째F

8 ft I

5 = 5 in.

L, = 1/16 in. 0,

$s

E 1 X Id2 photonr/cl$ - r e c Bottom of Top of Chainel Channel 16.57 16.57 75.47 75147 299.6 299.6 82.69 82.69 33.65 33.65 25.15 21.50 87.31 1002.6 0.5960 0.5538

Lss

= 2 in. 0,

= 4 in.

le2photons/crdaarec

= 2x Bottom of Channe 1 33.14 151.0 599.2 165.4 67.30 54.08 141.5 0.3799

Top of Channel 33.14 151.o 599.2 165.4 67.30 48.21 177.6 0.3139

1099.9 230.9 227.5 100.o 139.O 140.1

1099.9 279.2 275.9 151.9 193.3 194.2

1099.9 292.7 288.0 100.o 172.2 174.3

0.1043 869 .O 3.452 127.5 39.03 1.028

0.0972 820.7 3.341 124.0 41.35 0.9814

0.0276 807.2 4.754 188 .O 72.19 2.105

0.0616 731.7 4.580 182.5 78.24 2 .om

1m.1 0.5139

201.2 0.3927 1.074

198.2 0.6004 1.689

279.5 0.4745 1.694

1.081

*

1099.9 368.2 363.6 181.1 259.3 261.4


25

Table 4. Results of Investigation of Fourth Steady-State Case Care Conditions Studied Lc 3 ft Te = 70째F

To = llOO째F

Ls = 1/16 in.

Btu/hr'fe qIO Btu/hr*fI? qFsO Btu/hr*fl? qss, Btu/hr-f@ qcO Btu/hr*fP qc ' 9 Btu/hr*ft? qRO Btu/hr*fP HWL, Mu 0

LFS =

LI = 5 in. 4,

q,

P

= 1 X lea photone/ca? osec Bottom of Top of Channel Channel 16.57 16.57 75.47 75.47 299.6 299.6 82.69 82.69 33.65 33.65 7.048 16.53 88.49 104.9 0.5543 0.5960

Lss

2 in.

e,, = 2

X lOla

Bottom of Channel 33.14 151.0 599.2 165.4 67.30 39.42 143.8 0.3799

=

4 in.

photone/ca? -set Top of Channel 33.14 151.0 599.2 165.4 67.30 24.17 182.4 0.3146

1099.9 230.9 227.5 100.o 137.5 138.5

1099.9 278.8 275.5 151.4 190.4 191.2

1099.9 292.7 288.O 100.o 169.7 171.6

1099.9 367.5 362.9 180.3 254.7 256.4

~ 3 0 ~ aOF0 %-Tar OF 0 6-%,F

0.1043 869.O 3.452 127.5 37.54 0.9178

0.0973 821.1 3.342 124.0 38.93 0.7963

0.0726 807.2 4.754 188.O 69.71 1.917

0.0617 732.4 4.581 182.6 74.40 1.722

T-0

142.4

192.8

260.5

0,2724 1.072

0.1052 1,058

183.1 0.3454 1.673

T10 F h8 OF 6 ,OF 0

Tar F 0 t r F 0 b r F %-T10 T1-Tar

OF

%-Tar

OF

9

OF

xTmlax8

ft

D/H0 OF/ft

0.1881 1.669


26

Table 5.

To

6

Results of Investigation of Fifth Steady-State Case

(b

qI, Btu/hr*f3 q*s,

Bm/hr*f?

qss, Btu/hr*f@ qc, Btu/hr*fe qc

@

8

Btu/hr*ft?

qR, Btu/hr'fP W JMW

le3 photons/cu? -see

P 1 x Bottom of Channel

0

F

OF

T1-%8

%-6,OF TS-T,,

OF

t o T ~ 8 OF

OF

Tg't,

T-8

OF

xr alax, AT/&

ft

OF/ft

Top of Channel

3

50째F

2 in.

Lss = 2 in.

= 2 x lo1* photons/& OBec Bottom of Top of

@o

Channel

Channel

16.57 75.47 299.6 71.15 45.19 35.90 87.42 0.5960

16.57 75.47 299.6 71.15 45.19 32.24 102.7 0.5538

33.14 151.0 599.2 142.3 90.38 75.58 141.7 0.3799

33.14 151.0 599.2 142.3 90.38 69.71 177.9 0.3141

1099.9 230.9 227.5 138.9 139.4

1099.9 279.2 275.9 151.9 193.1 193.6

1099.9 292.7 288.O 100.o 171.9 173.0

1099.9 368.1 363.6 181.0 259.0

0.1043 869.O 3.452 127.5 38.89 0.5353

0.0972 820.7 3.341 124.0 41.22 Q.5118

0.0726 807.2 4.754 188.O 71.92 1.095

0.0616 731.8 4.580 182.6 77.39 1.057

155.O 0.5851 1.080

205.6

208.6 0.6638 1.688

289.1 0.5484 1.692

NO .o

%-T1,

LFS =

5 = 5 in.

La = 1/16 in.

qs, Btu/hr'ft?

Case Conditions Studied Lc = 8 ft T6

llOO째F

0.4716 1.073

260.1


27

Table 6. Results of Investigation of Sixth Steady-State Case Case Conditions Studied To = l1OOOF

L~ = 1/16 in.

'& = 50째F

Lc = 8 ft

LFS = 4 in.

LI = 7.5 in.

e,, = 1 X lOla photons/cu? esec

Tl-%D

OF

OF

b-T,,

qCT,D %-%I

0

F

OF

OF

= 2 X lOla photons/d ~ s e c Top of Bottom of Channe1 Channel 33.14 223.8 676.2 21.38 61.40 50.39 164.5 0.0245

Bottom of Channel 16.57 111.9 338.1 10.69 30.70 23.47 86.60 0.2891

Top of Channel 16.57 111.9 338.1 10.69 30.70 20.35 101.1 0.2649

1099.9 223.2 217.2 100.0 124.1 193.6

1099.95 265.1 259.2 144.0 170.5 170.6

1099.99 297.9 288.7 100.0 147.2 147.7

0.0529

0.0488

0.0131

876.7 6.060 117.2 24.10 0.1965

834.8

802.1

115.2 26.42 0.1764

7 47.24 0.4150

134.o

177.6

170.7

1

%-%9

4o

Lss = 2 in.

5.9

5


28

_ _ e

W Table 7.

Results of Investigation of Seventh Steady-State Case Care Conditions Studied

To = llOO째F

La = 1/16 in.

leaphotons/ca? =see

Bottom of

Btu/hr*fi? qI, Btu/hr*ft? qFs, Btu/hr-ft? qsss B-u/hr*f@ qc, Btu/hr*f@

Tan OF t r

0

F

LFS = 4 in.

5 = 10 fn. 0, = 1 x

q,

& = 5O0F

Lc = 8 ft

Channel 16.57 146.7 307.1 9.689 27.89 21.08 73.58 0.1118

Top of Channel 16.57 146.7 307.1 9.689 27.89 18.35 84.92 0.0955

1099.98 208.6 203.3 100.o 120.9 121.0

1099.98 245.9 240.7 138.7 161.3 161.5

0.0232 891.4 5.304 103.3 20.87 0.1769

0.0205 854.1 5.218 102.0 22.59 0.1594

129.6 0.5256 0.8064

167.6 0.4117 0.8088

0,

Lss = 2 in.

E 2 X 10la photons/& =rec Bottom of Top of Channel Channel 33.14 33.14 293.4 293.4 614.2 614.2 l9.38 19,38 . 55.78 55.78


29

6, i Tables

1, 6,

thickness

of

the

The addition

firebrick

of

about

a factor

ature

of

dent

2.5 of

the

total

thickness

of

total

thickness

from

photons/ca?*sec of

Tables

air

air

channel.

ratio

channel

concrete

side

increases

the

temperature Tables

in

the

2 in,

on the

conduction

loss

surface

of

from

8 to 3 ft the

of

the and

respect iid i

to

were

written-to

wall

for

time,

one

analyze

for

with

by temper-

an inci-

changing

the

increase

concrete

the

is

cases

the

in

the

increased

gamma current

steel

with

of

1 x 10la

an incident

side

for

on the

on the

reactor

and

side

effects

reactor

side side

and 2 in. on the

increases

of of

of

on the

concrete the

Changing on the

side

maximum

the

for

temperature

the

effects

over

the

the

thickness

of

outside

surface

from

concrete

about

the

of out-

concrete

50 to 700F

1OoF but

the

appreciably,

Transient

equations,

case,

Condition

with

32 through

proposed

the

lOoF.

and the

of

the

concrete

and 4 in.

slightly

for

: to Eqsi

transient-condition

the

steel

on the

temperature

the

the

wall;

difference similar

loss

Decreasing

a slight

the

concrete

affected

finite

of

3 and 4 may be compared

is

10 in.

maximum

cases

effects

of

of

only

the

the

*sec.

of

Case Studied

Eighteen

those

an incident

reactor

temperature

not

the

2 and 4 may be compared

maximum

loss

the

approximately

concrete the

in

20°F

4 in.

the. concrete

15’F

only

with

thickness

to

and

conduction

two gamma shields.

thickness

from

the

decreases

temperature

cases

Changing

thickness

side

conductian

the

photons/en?

the

in.

also

for

causes

1 and 2 and Tables

the

decreases

of to

of

changing

steel

2 x 1012

to

7.5

changing

photons/ca?*sec.

1 and 3 and Tables

the

the

addition

and by approximately

gamma current

changing

this

the

5 in.

decreases

4 to 2 in.

for

of

insulation

The maximum lOoF

effects

from

1 x 10la

the

the

insulation

5 may be’compared

loss.

for

by approximately of

1 and

approximately

of

2, and

gamma current

conduction

:

in.

concrete

Tables

;

and 7 may be compared

the

differencing

35 discussed

configuration The analysis

of

in the

with Chapter

reactor

was performed

3 room to

-


30

hd

determine the length of time over which a loss of coolant air flow could be tolerated before the temperature of the concrete would exceed the Such a loss of coolant air flow maximum allowable temperature of 212'F. could arise as a result o f a malfunction in the blower system supplying the Although natural convection currents would cause some circulation of the coolant air during 8 blower failure, it was assumed that coolant air.

the coolant air was stagnant during the failure so that the worst case could be analyzed. Under this assumption, the air channel serves only as an insulating material and removes no heat from the wall. The conditions established for the analysis of this particular case were a S-in.-thick layer of firebrick insulation, a 4-in.Othick layer of mild steel for the first gamma shield, the 3-in.-wide air channel, a 2in.-thick layer of mild steel for the second gamma shield, and a 6-ftthick concrete wall for the biological shield. A simple computer program

t

was written to perform the calculations, but the zero-time temperatures and heat depositions for each segment in the composite wall were calculated by hand and used as fixed numbers in the program.

This computer

program was used only to obtain a first approximation to the transient situation for one particular case, and the details of the program are not presented here. The program was run for elapsed times of t = 1.0 hr, t = 2.0 hr, t = 3.0 hr, t = 4.0 hr, and t = 5.0 hr for the condition of internal heat

generation (reactor at power during blower failure) during the transient period.

The program was then run again for the same elapsed times but

for the condition of no internal heat generation (reactor shutdown simultaneous with blower failure) during the transient period.

The

computer program used to analyze the condition for internal heat generation is given in Table 8. To analyze the condition of no internal heat generation, Q2C through Ql9SS in Table 8 are set equal to zero.

The

resulting temperature distribution in the proposed reactor room wall

-

analyzed for the condition of internal heat generation during the transient period is shown in Fig. 4, and the temperature distribution in the wall with no internal heat generation during the transient period is illustrated in Fig. 5.

--

P

cbt


31 i

.

,

Table 8. Cdmputer Program Used to Analyze the Proposed Reactor Room Wall for the Condition of Internal Heat Generatfon


32 Table 8 (continued)

4


33

ORNL Dug. 67-12003

soa

roa

LEQENO

L

@ @ @ @

TEMPERATURE DISTRIBUTION AT 1. 0.0 HRS.

@ @

TEMPERATURE DISTRIBUTION AT T TEMPERATURE DlStRlaUTlON AT T

TEMPERATURE DISTRIBUTION AT 1. 1.0 HRS. TEMPERATURE DISTRIBUTION AT 1. 2.0 HRS. TEMPERATURE DISTRIBUTION AT T 8 3.0 HRS. 4.0 HRS. 5.0 HRS.

200

IO0

30

g.

I-)

.

4. Temperatu rnal Heat Gene ient Period.

35

40

bution i n Proposed Reactor Room Wall te Maintained During Loss-of-Wall-Cool-


34

II ORNL 0-

80f

400

I

6 @

LEGEND

8T-ILDM

TEMPERATURE OlSTRlBUTlON AT T

0.0 HRS.

T

-

@

TEMPERATURE OlSTRlBUTlON AT t

@

TEMPERATURE DISTRIBUTION AT t

1.0 HRS. 0.0 HAS. S.0 HRS.

0

@

TYPERATORE OISTRIBUTION AT t

4.0 WRS.

L

0 TEMPI

u

.

TEMPERATURE OISTR18UTION AT

soa

L

U

s

U

t

200

1

IO0

1 1 1

WALL THICKNESSES t INCHES 1

F i g . 5. Temperature Distribution i n Proposed’Reactor Room Wall With No Internal Heat Generation During the Loss-of-Wall-Coolant Transient Period.

!

i


35 5.

CONCLUSIONS

Two b a s i c conclusions may be drawn from t h e r e s u l t s o f t h e parametric s.tudies made i n t h i s i n v e s t i g a t i o n of t h e proposed c o n f i g u r a t i o n of a laminated wall t o p r o t e c t t h e c o n c r e t e b i o l o g i c a l s h i e l d from t h e gamma c u r r e n t w i t h i n t h e room housing a 250-Mw(e) molten-salt breeder r e a c t o r , a h e a t exchanger, and a b l a n k e t - s a l t - t o - c o o l a n t -

fuel-salt-to-coolant-salt s a l t h e a t exchanger.

The f i r s t b a s i c conclusion i s t h a t w i t h a i r used

as t h e w a l l coolant, t h e proposed c o n f i g u r a t i o n i s a c c e p t a b l e f o r an i n c i d e n t monoenergetic (1 MeV) gamma c u r r e n t of 1 x lola photons/cn?*sec f o r a l l c a s e s considered i n which t h e t h i c k n e s s o f t h e f i r e b r i c k i n s u l a t i o n was 5 i n . o r more.

A second b a s i c conclusion i s t h a t t h e

proposed

c o n f i g u r a t i o n i s n o t a c c e p t a b l e f o r those c a s e s considered w i t h an i n c i d e n t monoenergetic (1 MeV) gamma c u r r e n t o f 2 x 1Ol2 photons/ca? . s e c because t h e maximum allowable temperature o f t h e c o n c r e t e (212OF) i s a

exceeded by 50 to 100째F.

The v a l u e s o f s e v e r a l of t h e parameters o f

i n t e r e s t i n t h i s study t h a t were obtained from t h e cases analyzed f o r a gamma current o f 1 x ' ' 0 1

photons/cnP*sec a r e given i n Table 9 .

Based on t h e assumption t h a t t h e f l o o r and c e i l i n g o f t h e reactor room have t h e same laminated c o n f i g u r a t i o n as t h e walls, g i v i n g a t o t a l llwallll s u r f a c e a r e a of 8276 f ?

, the

proposed w a l l c o n f i g u r a t i o n w i l l allow t h e

conduction l o s s from t h e r e a c t o r room t o be maintained a t a l e v e l below

1 Mw if t h e t h i c k n e s s o f t h e i n s u l a t i o n i s 5 i n . or more.

Further,

based on an a i r v e l o

c and an a i r c o o l a n t channel width

o f 3 in.,

m f o r cooling the wall.

a i r i s an a c c e p t a b l e

A g e n e r a l conclusion t h a t may be drawn from t h e l i m i t e d a n a l y s i s

made o f one t r a n s i e n t - c o n d i t i o n case i s t h a t i f t h e ambient temperature of t h e r e a c t o r room rema

a t approximately llOO째F, t h e proposed con-

f i g u r a t i o n of t h e r e a c t o

om w a l l s t u d i e d i n t h i s c a s e can s u s t a i n a

loss o f c o o l a n t a i r flow under t h e c o n d i t i o n s described i n Chapter 4 f o r approximately 1 hour bef exceed 212'F.

t i

I f a zero

re. of t h e concrete begins t o

a current is assumed, t h e

llpermissiblell l o s s - o f - c o o l a n t - a i r time i s g r e a t e r than one hour b u t less than two hours.


. . .

. Table 9. Range o f Parameters of I n t e r e s t i n S t u d i e s Made of Proposed Wall With An I n c i d e n t Gamma Current of 1 x lora photons/ct#*sec Parametric Conditions LI 5s Lss Lc li3 Variable o f Minimum Maximum I n teres t Value Value (in.) (in.) (in.) (ft) (OF) Skin AT,'F

F i r s t steel s h i e l d AT,

4.

2.5 10

4

906

2

2 a

10.9

10 2.5

2 4

2

2.5 2.5

4 2

2

1.1 1.57

10 2.5

a a

a a

8

50

a a a

a

4

3 8

70 50

2 4

2 2

3 8

70

10

4

2

3

70

5

2

2

8

50

5

2

4

70

0.58

7.5

2

2

3 8

1.32

10 2.5

4 2

2 a

8 a

50 a

2.38 F

Second steel s h i e l d AT, OF

0.08

A i r v e r t i c a l temperat u r e g r a d i e n t , OF/ft

0.77

Tc max' (Q12'F)

2

2

726

Insulation AT, OF

0

10 2.5

4

0.22

0.021

F

124 205.6

T max, f t (Tmax < 212'F)

0.11

m, Mw

0.096

X

a

a

a

50

w

OI

50

~-

a

This parameter h a s l i t t l e e f f e c t i n combination with t h e o t h e r parameters given, and t h e v a l u e s o f t h e v a r i a b l e s of i n t e r e s t are e s s e n t i a l l y t h e same f o r v a r i o u s v a l u e s o f t h i s parameter

.

e:.


37

If a wall of the type proposed is used, the temperature of the conCrete,

TCâ&#x20AC;&#x2122;

or the conduction loss, or both, can be controlled to some

extent by varying the physical characteristics of the wall.

The thickness

of the insulation can be increased, but the desirable effect approaches a limit rather rapidly.

As the results of our parametric studies have

indicated, an insulation thickness can be reached that will cause conduction back into the reactor room.

The total thickness of the mild-

steel gamma shields can be increased with good results up to the point where the gamma current is reduced by several orders of magnitude. After this point is reached, adding more steel for gamma shielding does not produce sizable changes in the maximum temperature of the concrete. A total of approximately 6 in. of steel is sufficient for an incident

monoenergetic (1 MeV) gamma current of 1 x 10â&#x20AC;?

photons/cu?*sec.

The

thickness of the mild-steel gamma shields should be arranged so that the major portion of the steel is on the reactor side of the air channel. Placing the major portion of the steel on the concrete side of the air channel results in the undesirable effect of raising the maximum tempera-

j

.

ture of the concrete.

Shadow shielding of the particular components

within the reactor room that may be causing a large gamma current appears to be a better solution than increasing the thickness of the wall laminations for gamma currents greater than 1 x 10la photons/ca?*sec. When sufficient information becomes available, an overall energy balance should be written, starting with the fissioning process in the reactor and extending out through the wall of the reactor room to an outside surface.

This balance i s necessary to determine whether or not a conduction loss of 1 Mw will permit maintenance of the desired ambient temperature within the reactor room without the addition of auxiliary cooling ar heating systems.


39

APPENDICES


41 Appendix A EQUATIONS NECESSARY 'ID CONSIDER A MULTIENERGETIC GAMMA CURRENT

The equations derived in Chapter 3 of this report were based on the assumption that the incident gamma current is monoenergetic. If the energy distribution of the incident gamma current is known, this curr,ent can be represented as a multigroup current.

The equations in which an

incident multigroup gamma cur nt appears, either directly or indirectly, must be written to account fo this segmentation in gamma energy. This multigroup modification has been made in the following equations, and they are to be used in place of the correspondingly numbered equations in Chapter 3 when the energy distribution of the gamma current is known. The subscript i denotes the energy group, and the terms are defined in Appendix E.

(A.9a)


42 dT = -(T 1 - To) dx L L

J

(A. 13)

(A.

',pie

PiX(cri

'T

=

- 1) + (1 - Ai)e

14)

(A. 16) e

,

(A. 17)

Q j += l

=i

Q j+ li =

i

(QO(j),

-

Sji)

(A. 18)

(A. 18a)


(A. 18b)

(CJ Q( 44 +

i

where

1 +

-Lss +-

k Lc

kSS

c

)


44 Appendix B . EVALUATION OF THE CONVECTIVE HEAT TRANSFER COEFFICIENT

The average convective heat transfer coefficient, h, for the walls of the air channel was evaluated by using the expression published by ~~

Kre ith

. h = 0.036

Ek :eR

* 8 p S/3

,

where 0

k = thermal conductivity of air, Btu/hr*ft* F,

H = vertical length of the air channel, ft, ReH = Reynolds number evaluated at the top of the air channel, and Pr = Prandtl number evaluated for air. The Reynolds number evaluated at the top of the air channel,

where .

- -

U = the bulk air velocity, ft/sec, p = density of the a i r , lb/ft?, and = viscosity of air, lb/ft*sec. The Prandtl number evaluated for air,

where C = the specific heat of air at a constant pressure, Btu/lb*OF. P In the range of temperatures considered, Pr is-approximately constant and equal to 0.72.

Kreith'2

expression for h

was evaluated for various

air-wall mean temperatures in the air channel, and the results are on the following page. lFrank Kreith, p. 286 in Principles of Heat Transfer, International Textbook Company, Scranton, Pennsylvania, 4th printing, 1961.


45

I

-T

.h

0

(Btu/hr*ft? 'OF)

100 130 150

5.15

5.04 5.04

The mean temperature of the walls of the air channel is expected to be approximately 130 to 150째F, and a value of 5 was used for the convective heat transfer coefficient at the walls of the air channel.

i

i


46 Appendix C

VALUES OF PHYSICAL CONSTANTS USED IN THIS STUDY

Values f o r the gamma energy attenuation coefficient, %, the t o t a l gamma rttenuatiou coefficient, p, and the dimensionless constants a, @, and A used i n the Taylor buildup formula f o r a gamma energy of 1 Hev are tabulated belov.

%? Material Type 347 atainleas steel Kaolin insulatingbrick Mild steel Concrete

P

L(ft-11

(ft-1)

a

p

6.28.

14.0ab

0.0895'

0.04C

0.088'

O.02gd

aC lod

0.0895' 0.0886

0.04C 0.029'

lod

0.367' 6.30. 1.99d

0.83Sd 14.02. 4.55d

BC

Values f o r the density, p # Specific heat, c thermal COndUCtiVitp, k, ant equivalent P' thermal conductivity a t interfaces of adjacent materials, f o r materiala in the proposed laminated wall i n t h e i r order of occurrence from the reactor outward a r e tabulated below.

E,

1

0

Material Type 347 rtainless s t e e l Kaolin insulatlag brick Mild steel

l & a lbm/ft3) ( 7.Bb

b86.gb 0.159

0.433' 7.83b

27.03e uq.ab

0.29 0.11e

0.15"

0.298

26.0e 0.0232

Air

0.060e

0.241e

0.0174e 0.0232

Mild steel

7.83b

488Ab

0.lP

Concrere

2.3Sd

146.7d

0.20e

26.0' 0.584 0.W

*E. P. Blizard and L. S. Abbott, editors, p. 107 i n Reactor Handbook, Vol. S, Part B, Johh Uiley and Sons, New York, 1962. bM. M. El-Uakil, p. 223 i n Nuclear Power Engineering, McGraw-Hill Book C~IU~UII~, be., F i r s t Edition, Nev York, N w York, 1962.

%. P. Blizard m d L. S. Abbott, editors, p. 116 i n Reactor Randbook, Vol. S, Part B, John Wiley md Sons, New York, 1962. dnReactor Physics Constants," USAEC Report ANL-5800, Argonne National Laboratory, pp. 653-6578 July 1963. 'Frank Kreith, pp. 533-535 in Principles of Heat Transfer, International Textbook Company, 4th printing, Scranton, Pennsylvmia, 1961.

c


47

Appendix

D

TSS COMPUTER PROGRAM

A program-was

developed 8 through

equations-(Eqs. figuration writ

of

material for

in

order

groups

incident

sixteen

Shield

to

for

Study) the

in Chapter

air

to

the

handle

For

a problem of

and 45 seconds

conAs

up to

and up to eight

The calculations

3.

the

conditions.

will

channel,

solve

proposed

steady-state

program

combinations

one minute

computer

evaluate

the

gamma current.

different

is

CDC 1604-A

necessary

excluding

described

time

the

room wall

TSS (Thermal

the

and

machine

31)

reactor

laminati.ons,

groups the

the

the

ten,

for

five energy

are

performed

five

energy

with

laminations

(cases),

and the

compilation

used

evaluate

the

time

is

56 seconds. A Newton-Raphson The convergence Eq.

29 must

iteration

criterion

agree

for

to within

right

and left

sides

of

gence

criteria

could

machine cause

time, the

but

program

Eq.

with

very

little

more

uses

the

gamma current a vertical

reactor

lations

at

and bottom manner the

,interface

room and several as it

in which

following

the

a given

temperature

for

to within

0.10.

accuracy method

to

If

material

up the

were

necessary

known

program air

present.

increase

in

the

this

the

conver-

calculate

be-

incident

accuracy

the

that

These

be obtained

real

of

is

attenuated

information

gamma the

interfaces.

profile

points

xT max is

would

more

from

and xT max, sides

a corresponding

and to calculate the

&

and left

to calculate

skin,~the

at

right

be modified

the

does

to

criterion

interface.

temperature

could

channel Both

input

data

for

the

be modified

rather

the are

interface

than

setup

of

to do calcu-

just

the

at

program

prepared-are

of

the

top

and

the

explained

in

discussion.

The TSS computer with

at

real

approximate

c0ul.d

the

and the

smaller

program

If

the

be made

required,

incident

that

agree

material

each

is

is

14 must

at each

current.at

Q 0.05,

gamma current the

scheme

photon of

the

program current inside

is

set

incident surface

up for upon

of

the

a given the

wall

..

physical

reactor is

fixed

situation

room wall. at

a given

The value.


48 The composite w a l l i s composed o f f i v e m a t e r i a l regions, and progressing

.

from t h e i n s i d e s u r f a c e outward, these regions are (1) a t h i n s t e e l skin, (2) an i n s u l a t i n g m a t e r i a l , (3) t h e f i r s t steel gamma s h i e l d , (4) t h e second steel gamma s h i e l d , and (5) t h e concrete b i o l o g i c a l s h i e l d with a f i x e d temperature on t h e o u t s i d e surface.

The 3-in.-wide

a i r channel

placed between t h e f i r s t and second gamma s h i e l d s i s n o t considered a

material region.

By c a l c u l a t i n g a v e r t i c a l temperature g r a d i e n t i n t h e

a i r channel, t h e program w i l l c a l c u l a t e a t both t h e bottom and top of t h e r e a c t o r room w a l l t h e

1, gamma h e a t generation r a t e i n each m a t e r i a l , 2. temperature a t each m a t e r i a l i n t e r f a c e and temperature changes a c r o s s each m a t e r i a l ,

3. 4.

conduction h e a t l o s s from t h e r e a c t o r room t o t h e a i r channel,

5.

h e a t i n t h e concrete conducted both toward and away from t h e a i r

r a d i a t i o n heat t r a n s f e r rate between t h e w a l l s of t h e a i r channel, channel, and t h e

6.

maximum temperature i n t h e concrete and i t s corresponding l o c a t i o n . The program i n p u t deck allows t h e use of any material i n any region

of t h e composite wall.

*

For a f i x e d i n c i d e n t photon c u r r e n t , a f i x e d

i n s i d e w a l l temperature, a f i x e d i n l e t a i r v e l o c i t y and temperature, and fixed w a l l m a t e r i a l s , t h e c a l c u l a t i o n o f a p a r t i c u l a r case i s done by s e l e c t i n g a l l material t h i c k n e s s e s and t h e temperature o f t h e o u t s i d e s u r f a c e of the concrete w a l l .

A t p r e s e n t , t h e program w i l l allow a maxi-

mum of 32 cases t o be run, b u t i t can e a s i l y be expanded t o handle more.

P r e p a r a t i o n o f Input Data

The f i r s t set of input d a t a c o n s i s t s o f energy-dependent information p e r t a i n i n g t o t h e i n c i d e n t photon c u r r e n t and t o t h e n u c l e a r p r o p e r t i e s of t h e m a t e r i a l s chosen f o r each region i n t h e wall.

The o r d e r i n which

t h e information i s supplied i s given on t h e following page. - e

Ld *


49

m &i 0

Card 1.

The incident photon current Qslil), Q=(2), . ..> QSl(8). (Btu/hr*ft?) for each of eight possible energy groups. Card 2. EMUl(l), EMLl1(2), . . . . EMIJl(8). The energy absorption coefficient (l/ft) in the first region of the wall (the inner skin) for each of eight possible energy groups. Card 3. AMUl(l), AMU1(2), . . . . AMul(8). The mass attenuation coefficient (l/ft) 'in the first region of the wall (the inner skin) for each of eight possible energy groups. Card 4. ALPHA(l), ALPHA1(2), . . . . ALPHAl(8). The dimensionless constant Q used in the Taylor buildup formula in the first region of the wall (the inner skin) for each of eight possible energy groups. Card 5. BETAl( BETA1(2), . . . . BETAl(8). The dimensionless constant 8.used in the Taylor buildup formula in the first region of the wall

s

(the inner skin) for each of eight possible energy groups. Card 6. Al(l), A1(2), . . . . Al(8). The dimensionless constant A used in the Taylor buildup formula in the first region of the wall (the inner skin) for each of eight possible energy groups. Card 7. EMlJ2(1), EMU2(2), . . . . EMU2(8). The same as Card 2 except for the second region of the wall (insulation). Card 8. AMUP( AMU2(2), . . . . AMJP(8). The same as Card 3 except for the second region of the wall (insulation). Card 9. ALPHA;!(l), ALPHA2(2), . . . . ALPHA2(8). The same as Card 4 except for the second region of the wall (insulation). Card 10. BETA2(1), BETA2(2), . . . . BETA2(8): The same as Card.5 except for the second region of the wall (insulation). Card 11. A2(1), A2(2), . . . . A2(8). The same as Card 6 except for the second region of the,wall (insulation). Card 12. EMU3(1), EMU3(2), . . . . EMID( The same as Card 2 except for the third region of the wall-(the first gamma shield). Card 13. AMU3(1), AMU3(2), ..,, AMU3(8). The same as Card 3 except for the third region of the wall (the first gamma shield)., Card 14. ALPBA3(1), -ALPIiA3(2), .*., ALPHA3(8). The same as Card 4 except for the third region of the wall (the first gamma shield).


50 Card 15.

BETA3(1), BETA3(2),

..., BETM(8).

The same as Card 5 except

f o r t h e t h i r d region of t h e w a l l ( t h e f i r s t gamma s h i e l d ) . Card 16.

A3(1),

A3(2),

.,., A3(8).

The same a s Card 6 f o r t h e t h i r d

region of t h e w a l l ( t h e f i r s t gamma s h i e l d ) . Card 17.

EMU4(1), EMU4(2),

..., EMU4(8).

The same as Card 2 except

f o r t h e f o u r t h region of t h e w a l l ( t h e second. gamma s h i e l d ) . Card 18.

AMU4(1), M 4 ( 2 ) ,

..., AMU4(8).

The same as Card 3 except

f o r t h e f o u r t h region of t h e w a l l ( t h e second gamma s h i e l d ) . Card 19.

..., ALPW4(8).

ALPHA4(1), ALPHA4(2),

The same as Card 4

except f o r t h e f o u r t h region of t h e w a l l ( t h e second gamma s h i e l d ) . Card 20.

BETA4(1),

BETA4(2),

...,

BETA4(8).

The same as Card 5

except f o r t h e f o u r t h region of t h e w a l l ( t h e second gamma s h i e l d ) .

..., A4(8). The same as Card 6 except f o r t h e f o u r t h region o f t h e w a l l ( t h e second gamma s h i e l d ) . Card 22. EMU5(1), EMU5(2), ..., EMU5(8). The same as Card 2 except f o r t h e f i f t h region o f t h e w a l l ( t h e b i o l o g i c a l s h i e l d ) . Card 23. AMU5(1), AMU5(2), ..., AMU5(8). The same as Card 3 except t

Card 21.

A4(1), A4(2),

f o r t h e f i f t h region of t h e w a l l ( t h e b i o l o g i c a l s h i e l d ) . Card 24.

ALPHAs(1); ALPHA5(2),

..., ALPHAs(8).

The same as Card 4

except f o r t h e f i f t h region o f t h e w a l l ( t h e b i o l o g i c a l s h i e l d ) . Card 25.

BETAS(l),

BETAS@),

..., BETAS(8).

The same as Card 5

except f o r t h e f i f t h region o f t h e w a l l ( t h e b i o l o g i c a l s h i e l d ) . Card 26.

A5(1), A5(2),

..., A5(8).

The same as Card 6 except f o r

t h e f i f t h region o f t h e w a l l ( t h e b i o l o g i c a l s h i e l d ) . The format statement f o r a l l o f t h e above c a r d s i s 8F9.0.

Since

only t h e f i r s t 72 spaces on each d a t a card are used, t h e l a s t e i g h t may be used f o r i d e n t i f i c a t i o n purposes.

I f fewer than e i g h t energy groups

are used, t h e unused d a t a f i e l d s may e i t h e r be punched w i t h a z e r o or l e f t blank.

I n e i t h e r case, t h e energy-summing DO loops s u b s c r i p t e d

J, K, L, and N must be changed t o correspond t o t h e number of energy

groups used; t h a t is, i f t h e r e are s i x energy groups, DO 100 I = 1,6; and K, L, and N a r e a l s o 1,6.

I f t h e DO loops are not changed t o c o r r e s -

pond t o t h e number of energy groups used, d i v i s i o n by zero w i l l occur.


51

*

The next s e t of d a t a entered i s energy'independent and i s assumed t o be c o n s t a n t over t h e range of temperatures covered i n t h e program. This information should be given on t h e two following c a r d s . Card 27.

CON1, CON2, CON3, CON4, CONS, TO, HT, and HF.

The thermal

c o n d u c t i v i t i e s (Btu/hr*ft*OF) of t h e m a t e r i a l s i n each of t h e f i v e r e g i o n s The temperature on t h e

should be e n t e r e d i n the f i r s t f i v e d a t a f i e l d s . i n s i d e s u r f a c e o f t h e r e a c t o r room wall, TO i n

OR,

the height of the

r e a c t o r room, HT i n f t , and t h e f i l m c o e f f i c i e n t on t h e s i d e s of t h e a i r channel, HF i n B t u / h t * f e o o F , should be e n t e r e d i n d a t a f i e l d s s i x through eight.

The format f o r t h i s card i s t h e same as t h a t f o r t h e previous

26 c a r d s (8F9.0). Card 28,

TA, EPSIL, VEL, ACHAN, CP, RHO, and SIGMA a r e r e s p e c t i v e l y

t h e i n l e t a i r temperature,

0

R, t h e e m i s s i v i t y o f t h e s u r f a c e o f t h e a i r

channel (dimensionless and assumed t o be equal f o r both s i d e s o f t h e a i r channel), t h e v e l o c i t y of t h e a i r , f t / s e c , ft?, t h e s p e c i f i c h e a t of a i r , Btu/lb-OF,

t h e width o f t h e a i r channel, t h e d e n s i t y of air, lb/ft?,

t h e Stefan-Boltzmann c o n s t a n t (Btu/hr-ft? *OP), e n t e r e d according t o format 6F9.0,

F18.0.

and

These v a l u e s must be

Again, t h e l a s t e i g h t spaces

can be used f o r i d e n t i f i c a t i o n .

P r e p a r a t i o n o f Case Data

Once t h e i n p u t d a t a have been supplied, one card must be prepared f o r each c a s e t o be run. and T6.

EL1 through EL5

be used f o r each of t h e f

t o t h e material t h i c k n e s s e s ( f t ) t o

s i n t h e w a l l , and T6 i s t h e tempera-

t u r e of the external surf

concrete biological shield i n

The format 8F9.0 allows n

f o r each d a t a f i e l d and t h e last e i g h t

spaces f o r i d e n t i f i c a t i o n quired.

OR.

cases, the c a r d s could be numbered

Numbering

t h e u s e r ' s convenience and i s n o t re-

The firstSDO loo

rogram must always be changed t o DO

29 through 44.

w

This c a r d c o n t a i n s EL1, EL2, EL3, EL4, EL5,

5000 I = l , N where N is t h e number o f c a s e s t o be run.

A l l c a s e s must

have t h e same a i r temperature, TA, and t h e statement immediately

1

-


52

following DO 5000 I = 1 , N must be w r i t t e n to correspond t o t h e a i r temperature used.

ELS(I),

The DIMENSION statement c o n t a i n i n g ELl(1) through

T6(I), BOP(I), and BAM(1) must be checked t o see t h a t a s u f f i c i e n t

dimension size i s given t o allow a l l o f t h e c a s e s t o be run.

BOP(1) and

BAM(1) are dummy v a r i a b l e s and may be l e f t blank.

Typical Computer Sheets

The assembly o f t h e c o n t r o l cards, deck, i n p u t d a t a , and case d a t a c a r d s f o r t h e TSS computer program i s i l l u s t r a t e d i n Fig. D.l.

Typical

d a t a f o r 32 cases t o be run w i t h one energy group a r e given i n Table D.1.

The o u t p u t d a t a a t t h e bottom o f t h e a i r channel f o r one case are given i n Table D.2,

and t h e o u t p u t d a t a a t t h e top o f t h e a i r channel f o r t h e

case are given i n Table D.3.


53 t

ks L

c

I

Fig. D . l .

Assembly of Data Cards for TSS Computer Program.


54


55

1


56

3 0 0 2 UP1

3003 V i ? !


n

h d I

57


I

J'


I N A T l d Y THICUNFSSES (FEET)

.

.

- ...

.

.

-.

.-.-

-.

_.

..

..

.

..

..

.. .-


60

Appendix E NOMENCLATURE

A = dimensionless c o n s t a n t used i n t h e Taylor buildup equation

4

= u n i t a r e a o f reactor room wall, f t a

= s p e c i f i c h e a t a t c o n s t a n t pressure, Btu/lb*'F P E = energy o f i n c i d e n t gamma c u r r e n t , MeV H = v e r t i c a l l e n g t h o f a i r channel, f t

C

h = convective h e a t t r a n s f e r c o e f f i c i e n t , Btu/hr*ft? *OF '

-

k = thermal conductivity, Btu/hr*ft*'F

= e q u i v a l e n t c o n d u c t i v i t y where t h e s u b s c r i p t s a and b r e f e r t o

ka-b

any two a d j a c e n t materials

L

5:

t h i c k n e s s o f a material lamination

Lch = width of a i r channel ( d i s t a n c e between a d j a c e n t surfaces of

f i r s t and second s t e e l gamma s h i e l d s ) , f t

MWL = h e a t conduction rate o u t of t h e reactor room t o t h e a i r channel, Mw Q = volumetric gamma h e a t i n g rate, Btu/hr-f$ q* = h e a t conduction rate o u t o f t h e reactor room t

t h e a i r channel,

Btu/hr= ft? q i = rate a t which t h e gamma h e a t generated i n t h e c o n c r e t e i s con-

ducted back toward t h e a i r channel, B t u / h r * f t ?

QR = rate o f r a d i a n t h e a t t r a n s f e r between t h e w a l l s o f t h e a i r channel, Btu/hr* f t?

T = temperature, OF Ua = bulk v e l o c i t y o f c o o l a n t air, f t / s e c x = d i s t a n c e perpendicular t o t h e s u r f a c e o f t h e r e a c t o r room w a l l ,

ft

a

and ~3= dimensionless c o n s t a n t s used i n t h e Taylor builkup equation E = s u r f a c e e m i s s i v i t y of walls o f a i r channel

0 = t i m e , hours p = t o t a l gamma a t t e n u a t i o n c o e f f i c i e n t , ft-1

%

= gamma energy a t t e n u a t i o n c o e f f i c i e n t , f t - l

-<

w


61

p = density, lb/ft? (J

= Stefan-Boltzmann constant

go = incident gamma current, photons/c# â&#x20AC;&#x2DC;sec

Subscripts Used With Terms

0 through 6 = numbers denoting a lamination interface as illustrated in Fig. 2 and usually associated with temperature, T a = air

c = concrete I = insulation i = energy group j = lamination

s = skin lamination on reactor side of wall

FS = first steel gamma shield SS = second steel gamma field T = total


-C

U


63 ORNL TM-2029 Internal 1.

2. 3. 4. 5. 6-7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. , 21. 22. 23. 24. 25.

M. C, E. E. R. W. F. S.

Bender E. Bettis S. Bettis G. Bohlmann B. Briggs K. Crowley L. Culler J. Ditto

H. D. D. W. F. C.

G. A. E. F. C. l-l.

Duggan Dyslin Ferguson Ferguson Fitzpatrick Gabbard

W. W. A. 'P. H. P. R. G. R. H.

R. R. G. N. W. R. J. H. E. E.

Gall Grimes Grindell Haubenreich Hoffman Kasten Kedl Llewellyn MacPherson McCoy

Distribution 26. 27.

R. L. Moore H. A. Nelms

28. 29. 30.

E. L. Nicholson L. C. Oakes A. M. Perry T. W. Pickel J. R. Rose M. W. Rosenthal Dunlap Scott W. C. Stoddart

31. 32-33. 34-35. 36. 37.

External

38. 39. 40. 41. 42. 43. 44. 45-46.

D. R. H. J. M.

A. E. K. R. E.

Sunberg Thoma Walker Weir Whatley

47. 48. 49-58. 59. 60.

Document Reference Section GE Division Library Laboratory Records Department Laboratory Records, ORNL R. C. ORNL Patent Office

J. C. White W. R. Winsbro Central Research Library

Distribution

61.

P. F. Pasqua, Nuclear Engineering Tennessee, Knoxville, Tennessee

62.

L. R. Shobe, Engineering Mechanics Department, Tennessee, Knoxville, Tennessee '

63-77. 78. .

Department,

University

Division of Technical Information Extension Laboratory and University Division, USAEC, OR0

University

of of

&ii

ORNL-TM-2029  

http://www.energyfromthorium.com/pdf/ORNL-TM-2029.pdf

Read more
Read more
Similar to
Popular now
Just for you